{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":58449,"title":"Compute rational expectations in a static, linear NKM model","description":"Consider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equation of the form\r\n    ,\r\na PC equation of the form\r\n    ,\r\na (nominal) interest rate rule of Taylor type of the form\r\n    ,\r\nand a Fisher equation of the form\r\n    .\r\nIn these equations, , , ,  and  denote Okun's output gap, the inflation rate, the nominal interest rate, the real interest rate and the natural real interest rate respectively; a superscript  indicates expectations formed by agents, so  is the expected output gap and  the expected inflation rate. The terms ,  and  are white-noise shock terms; , , ,  and  are positive parameters (with ), and additionally, the Taylor principle holds so that .  is the central bank's (exogenously chosen) target inflation rate, and  is the implied target nominal interest rate.\r\nWe want to compute the rationally expected (model-consistent) inflation rate and output gap  and  that are implied by given values of the model's parameters and a given value of . To do this, we set  for any variable  for which agents form expectations (e.g.  and ), where  denotes the mathematical expectations operator and where the agents' information set  contains both the structure of the model equations and the values of all parameters (as well as  and ).\r\nSince  for any such  by the law of iterated expectations, and since  for the white-noise shocks (where  is ,  or ), this allows us to write down the IS equation as\r\n    ,\r\nthe PC equation as\r\n    ,\r\nand so on. Please solve the model in expectations (you may find it helpful to write the nominal Taylor rule in terms of the real interest rate gap  for this) and write a function that, for given parameter values and a given inflation rate target, computes the model-consistent expectations  and  for  and .\r\n\r\nBonus question 1: what can you say about the relationship of  and ? What happens if ?\r\nBonus question 2: why is there, in fact, always a unique solution for  and ?\r\nBonus question 3: what role does the parameter  play?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 818px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 409px; transform-origin: 407.5px 409px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equation of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.9167px; text-align: left; transform-origin: 384.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"140.5\" height=\"21\" style=\"width: 140.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ea PC equation of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.9167px; text-align: left; transform-origin: 384.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOEAAAAqCAYAAABFnDwNAAAAAXNSR0IArs4c6QAACrBJREFUeF7tnAmsHlUVx393tJaKhShVeRCtJmAFV8SgoRpLTG2VRUQJuIAbWuOOC4IVRUgLUWxFWrR1jU8UUTR1TzUGTDVIYmLFHeMaxeACruA21/xnzrzeN51vnfneezPv3oQ8+t43M+eee/5n+Z8znyOuQgN3B14PrAPOAn5rf1iBY9p51nt4OvC5qLKogSY14Jq8WcvvdSZwBfBSYFewl2XAVmAD8FbgkpbvM4q/wDQQQZgfyOEW7e7w8GLg9uCc7pmD050D/mXAjgV2hlXiHJDARg/HeXgz8J0WyFxXxGNxbMZzE7AJuKvuDefq+ghCkA5eDbzb0lFFPR8cwGHgrnb4VR5ObolBL4NkK/gN4J8AfHOuDGoen7Maxx585iTPBe6cR1lGenQEIUw5+CjwOA9PrTDYtQ52+4RtpJw3ocM9BDgFmCLhKFK2AzeOdJKzPxym0IsHhLDHMpUIwhrGMx+XrgW32+Gv9/Bc4HeBEAeRcCWeVXheCPyoYQET4DSrN8/P759ckZAuTeEVwN/GfF4OQscGPIsKhAnsSDsWCR8InO3gRA+PzwzCgfOWrymOFomb41Z8a9K1wrbvlhMt7oIEvzUFAUG/O8BqirMcnOzhdcAtFYDI9IPjRKQf6cJ0MqOaffq6ldnprD7ybHCbwQtwXwIegeMafBYJ3wf8rxYIczKpCRAK1A8HjiRhNSmPAS4NmGLt5ZgEzvew3sG1KbwJSIHjSTidlDU47sJnjq6oUQ9N4GIPZ3qSD0Kq+nXcNHI1sGdCIJSzPJqEM0izfX4/hSUOjvbwftPDf8c8q8xkqpZ+/wxgC7AyM6gQcGVLy//2FaP2/zikMErBrsaxLgDy7GoskK4A/mzcZzZfx/MdlskAa4DnATc4mPaONdqww3/Lw0bgG2ZQxdZm9ONgZe6HCmF96f9mysuyflYBn0zgJvPcDwDeBXwN2An8Y0g9Vn1sWQJb0+Yi4T0sVb6IlBfg2IvnDOAnwFIxyg42eVhu56MI/hTgT8AdwMHgdoI/IYFLU7gQWJHk+70zhbUJ3JjmzPRfx9z3agd7fMIO0kZrwkON6DkVeAPwceBfwHIStruUU33mTPnimHL3BOGTgHMsv77dwU7vuA2fbU4KPhaYNupenkBLnkAKDEmNfnLlIMz7cr1dQRBdZtm6zF4RuZ7S5T2/DPweeBbwPeBeFg0VEbeBOwn8Rda+KCLTfvoBbvN5GpTrxzGNz1obVfqRrW50cIl50n8DvzKP+tMRdNhLc5OoCSXz2+y/T5t9pCRsIkUORYzkP8nZ5e8CHzFjlYx5xuG4IDNWz8uB11or6IZxjbd0nREzyQ5Im6oJ72sYUEBSlH5HkJ08zMGnPBxVt3VVFQmnLCpcZd74NAfXWUomo8oMCDKSoorIaEinc3Kbcx1s8QnTpJU1mDz2xQ72emY8/1D6cXBeD6JHGzsY+ACg6KcI/LOGd5uB0MEG30w6KvGWQ7IdUg0ySC/qqV5GwhLSLI3/84A9nAJuF/ibIdkLqbIL6WBYpz1IRZNIR0WW7XJwi9/npAs5BNAtOKbwme0oKxhrDWJHD7RosA58Qc9P4TI2Ueo7G1Ct08ZVAEERUDWfHEy4Ms/vcu8vS6mqrQ4kY03dLP2IbTXL6qWfQ1yeBSwtkUGqPR4E/Noyi356vdCpnppVJox8DHvZ51wGXZylz8CjgGcCTzaHrNpvGALpkYAi6JHkbPSrRkw9w+cPkrXf30cZuMicMDCKnkaWbRAIlXZ+3ujyoom9FththbmEHJc8GFnYhi8ojEI5f1VEXw4ZQSLPL1KmSFdDMcbVj2osTd4om3g+8DFA6bkM89uWIovU6AtCM5A6ahnFuLKoAPwcuBlQPa0pI/17mHVvK2FEYlU5vUH3mA8QytF8Ns8CeDvwTuA/9m85HpURtVc/EOpvyq1VPAtsyvllPMqL1dxu+xylWDoZ//Xs35qQYsND10GUJ2nq6kfpjHQqQ9bBXmfR+McNpGhN14TGImc1XbhU171nSHlF4FwOvHJCvbwsHW343pL5RYA4gfuV9q5aX/tXHVxr9QOhap+siR1EigcDnzAKv2DHxhVgMDEz3J3HmZAIjVRpqGqaslcT6FSzaKluU/oYrknrZ7jdV3+qaRCusCi2HhBXIDLihBHTNDltkXmKKr0cX509Nw3Ch1rkO8lwIAeiPvESQKOMAt+47ZRZ++wHwiJShNR6YZhSZtFMlkeXJxcVPcqaTxCuNKr5+B4AO9wMRobWq36ZtH5G0WX5s02DsGCR9Ryl7iKU1EYRoDYbY9qvTybQqq+ojEI/xUA3Teo1CcLw/OV0VDbUaRn1PcteIFRjVlFAUVCv9yhaKDQrNRW9LEUqRT3IfipXbhNBU9S1VbWeXmlSZFTNpvqsalJmoeunaRCqLFHPuIhgfweuzAYV8nNXSi22s2qJ3LvMSJkfBBG1GIaXvuXspOtxe4R6bpMgLOpf3VftqF57q+MoZ64tg1DRSQaoPPg+NkepVOyXQFhYS2HyEArVX22Yam5kY31uEtY3Rb/rL/Z5m2LJplV+aNE+fAOhLfppEoQhQRWm7jJ6pejKKsJsQQyvmGe9xaAMSU5cJJNArCXnptpSZYT+pjRVet02ZG3Z62gnBUIxwZ8pPVR28ljgdKvrC/sZy3bLIBQbpIkNLbE/8laqAcW42ys9WRO/WB8y8qaOBxtL8BoXhfWNSCb1PJVKZZMfplSlTW8BflN6Tlv00yQIQ4IqJOOKl6AV5bTEIguUTzObEQB/YREuTOc0KysSSvalUkeDEgJl3XSvSRDe35yE9qs3UN4YjNppVFFBSjajDHCY9kxfcy2DUA9XmiFjkxGKAQpz/ScabS+WVAB8bxNC1ADUOJcWbQXVJV+3SRWNIWlvehftGjOcqhZBW/TTJAiL1KyqnSHHJVC9JputzOtEvf0h532M2UrZUMUh6Hcaa/uwlTiDGv3DnHOTINTzJKc4EDmVR5sAmgTShI9G15pgsbPbDuoTDrP5tn2mXN+Eb020bS+95NUAuiL8cTZuNRcv9Qr4eq4iw9jDzDUOQM5VJFF8qbeGEufi0l71zVw8Oz5j8WhANfFDAJFS5aUugoYdZoZcFlskDOubqt7f4jGTuNNJaEDZgMgm1cBy+FWrPAi+6NLRorc3yrjWJA4r3rN7GhBR9RJr6IuUUnNfBI5YYtW+mlmtbHUspkgYkhV6zUbjU3UZue6ZUtxRXQ2oBaahf425iX94jr2bq66CmOD91mICoab3VbhrwEDzjmO/hFn3lOL1ndZAMdqpvqe+o1Y/1eoSMCsJq8UEwk6ffNzcgtGA2hp6G0Zv26suvNb6z3rzqHJFEC6Ys4uCdEADR9g3CmjaSqmo3jbS2KNeg1MGpmmi/erCCMIOnHzcwrxrQDjSCJsmsLT0jqj6lcU3t+s9TH33kiaD/lCWNoJw3s8vCtABDYiM0dSQvghKQNP4nuo/AVNzyF8wPqLyKzAiCDtgAXEL7dZABGG7zy9K3wENRBB24BDjFtqtgQjCdp9flL4DGogg7MAhxi20WwMRhO0+vyh9BzQQQdiBQ4xbaLcGIgjbfX5R+g5oIIKwA4cYt9BuDUQQtvv8ovQd0EAEYQcOMW6h3RqIIGz3+UXpO6CBCMIOHGLcQrs18H+HNPRJUrPPtQAAAABJRU5ErkJggg==\" width=\"112.5\" height=\"21\" style=\"width: 112.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ea (nominal) interest rate rule of Taylor type of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.9167px; text-align: left; transform-origin: 384.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"179\" height=\"21\" style=\"width: 179px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand a Fisher equation of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"19\" style=\"width: 63px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106.667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 53.3333px; text-align: left; transform-origin: 384.5px 53.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn these equations, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"19\" style=\"width: 14.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e denote Okun's output gap, the inflation rate, the nominal interest rate, the real interest rate and the natural real interest rate respectively; a superscript \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAmCAYAAAAbdcG0AAAAAXNSR0IArs4c6QAAAPJJREFUSEvt0y1IBEEchvHfbBUvyGK0CGIVy4HYzVZRi+HAZFKDyQPBZrhwNj9AEJvJYtFmNlgEMYrZ5K4sq3Au3K5yZcNOnXmG//vMO8EIK4zAqiecTTWLJZFYYhz7ePuJOmzs7OAOUUyyi0lcood+GTyGQ8I0aQcv2AhspazjoQxewTlWcYFlbKKLWyTD4BhnhBnSK6IWyR1u8F581mLmecJ1DtrGR1kPivAC7nGAPXx+w5mHCbwOXlaEp3CKFtbwiDm5qCM8l8HZXju3bRFPOMbJXzL/q+r17HZlhGbsSkW/DzTCGmGVBpqSVCqqy6/6AmpmKCcgmFZrAAAAAElFTkSuQmCC\" width=\"7.5\" height=\"19\" style=\"width: 7.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e indicates expectations formed by agents, so \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAmCAYAAADTGStiAAAAAXNSR0IArs4c6QAAAhJJREFUWEft1curTWEYBvDfWhk46RiQXBJ/gJRyV6cklxFSJnIJA9eUCGfiWjq5k4FjjBgYkJJSLgMDAylGmMgtciuR3NbSt8+3a9vlnLX3OdsZ2N9orfrW+7zP5X1Xop9O0k+4msB9pXyKqZieMibjPY7iSxmgEVKPwH48w0FMlrgtNxfXGwU8HKelPspsxSfsTWjLWYGnRYAHlbqVLkpk8/LEMLmVuBI/bsU2bIxMNmNVwqacZbiDNZgdwHEfeRHg0fHSj5RDOcvz1BlZCShDh1SLrOTlB+zBcXyXuiFLW8mu4lalt0WAK4O2Fp0J90IDmI8XOF/BYgEuYwtO4md3SS0arolR4pElD3kXGVYWX4qzWBfvlHGHIqT8bWUjRYFH4Rxm4qYu1i+rGE3AJTzEerzCLMzB4XqBB+IINuAY2kte/nkCiYXYh/G4i1O42BuPQ9GQ4AO4FhkHues+RaWeFDsfiydYjAd1o1LoJxGWwok4q6sxQ9ecBs/rPj0xHoDtceOEUQk+h9HqwM44z214hDe1dFENHN4H41cMxBJMww58jaCdFT6Po7SDQ6C+9Qa4PBJD8Dgu+jAaZTZT4siEeQ4KfKa0k2tiGxqsZhz8DHKGLXQBu/C6gkkLduta+CHd4fl5LUxrXZn11O72m57C1eeATcYNk/RvhZse/zPJm1I3pW6YAs1wNUza6sL/n9S/AdSlcycCQo7AAAAAAElFTkSuQmCC\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the expected output gap and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the expected inflation rate. The terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12.5\" height=\"20\" style=\"width: 12.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e are white-noise shock terms; \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eβ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eκ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e are positive parameters (with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), and additionally, the Taylor principle holds so that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"20\" style=\"width: 42px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the central bank's (exogenously chosen) target inflation rate, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"19\" style=\"width: 74px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the implied target nominal interest rate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 52.5px; text-align: left; transform-origin: 384.5px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe want to compute the rationally expected (model-consistent) inflation rate and output gap \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e that are implied by given values of the model's parameters and a given value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. To do this, we set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"77.5\" height=\"19.5\" style=\"width: 77.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for any variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for which agents form expectations (e.g. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAAlCAYAAAD4DEFlAAAAAXNSR0IArs4c6QAAAzxJREFUaEPt2U+oVFUcB/DPTEm2CMoSCYkikrcQEmunkYtwGyJUGkQtojAV0rAS7Y+UWBk+IiKC2hhGDyKI2gWlokJmUFCQoGCLFqEtJFokNRM/PTfsvbl3zry5786j3lkMw51zzv19f9/f/2mZuq7GOH7GSxhrMdFlI4722D/rH7VyQGLCHMjZTWZvJtvGdf7z5toepzPnkzUY6AIsx5foZN53ExbjK3Qzz8gLPC0TurVG1yXaNuvYjV9yhUUbD2Ie3sefOWezfPJidG1Z9m/dXTra0tWNr5c+7spIM2Patup4fkCABZ540TrMzwWaxWTKk8/i6z6a+w0XKvYsxBt4B4dK9sWetTiNgyVsRS4PK/gMX/RjMwukesz1CmzFVXilRPjrkgLuQyjsIXxSAmIMr+JJnKkCmgeynmJgKd7EBpwsEepmfIAV6fdQSlRfvVbIvgXXYhf+KgPaFMhg8QVciecqBAp51mAPTuCpPn57O97GY/hh1CALhl7E5/18aIDfr8Fb+DYx3jOtNMXkvVyMphEVTw0AImfrdtyBR3G+zK4nP5/ShQxZoIepRjezpEqQHDQle0KBL+N+/DgqkIVJnUOkoaoUMx2sd+JTPFzmClXm+iv24Va8h6cz8mSUZxH6L69EIu9FxDycGJ0OkKozkUqiFQxZ9w/K5OPTkOY7PDApRRRCRBSMIqDudRs+TPk03GLK6sVk3UIUIPfiQN2X4/p0b0wt5kDOgIL/uXKmzbW4P/wyioiRmGtTgafUHZrwyZlOIStxBKtSBB8Jk6HIHVg2Q8VARPNtVdVUE0yGZlcjzGlyehk2FhTV1I3YhN9H5ZPx3hAiEnXkyo+HRXbZ+RvSdOCjVLD0vLopJoveL7qRqJz+qAnoPal1e6SqcW4KZGC6JVU84Z/RKw67YsLwGr7Hu1XTuyZBxrvWpzHkzhrYvBtPYDPOVmmsSZAhR7RxMZc5lurN6bK5KA3EXs+xiqZBBqgYKj+TAkaY2qArFBXDqxgwx2C675B5FCALoDG/iUj7zQAoA2CY5/E00uwLMO4eFch4dwSOSC0/5bCRFBEpI87F/zTZa5Qgs4UcduMcyGE1OFvO/y+Y/Buw0twm3AcPZwAAAABJRU5ErkJggg==\" width=\"28.5\" height=\"18.5\" style=\"width: 28.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e denotes the mathematical expectations operator and where the agents' information set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eI\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e contains both the structure of the model equations and the values of all parameters (as well as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"19\" style=\"width: 14.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.4167px; text-align: left; transform-origin: 384.5px 21.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"226\" height=\"19.5\" style=\"width: 226px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for any such \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e by the law of iterated expectations, and since \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHkAAAAoCAYAAADaKFUbAAAAAXNSR0IArs4c6QAABvNJREFUeF7tm3eIHHUUxz8z1rMgMUqwoRGPUwQPEWwRC2KC/9iJsSBBxUQ0aGKJLUYj9nJ2c2BUPNvBqSiCxK5osGIPCoK9YUODFZ2R785v9mZnZ2Znd2dm927nB/nn9lfevO/vvfd97/1iUT/6sBnC4WvgMmAArFFwTwNeiZhf/il/DfQB1wCnA6cAdwJu4NiZWIxhMYLDucDvQZGsSJBhCIIgMwqUIOcPZtwJhwIjFqx24Rjg09DEKRascOFw4Hjg/hLkzoHVyskbArcCc7EZxmEh8GdoIxnrhcbzPgqcBPziz0llyRaMuqUltwJQFmt2AcYs6HdhEZ6XjRqHAI9hsQaXg4OhNRJkG4ac0l1nAVAWe3jgeWMOVEJn1JgBvGx+mA8MJ1pyHcgWo7iZx+RNgV2B5wEnQuq1gT2wmY3DNtisxmFzYDPgZuClEPmI+nAbOAB4G/g5C413YI/zgSuQObrsk0B+Byoe12IQt2Lt5wH/SN4Yd20PgVNl1zm4634bFjhwOfB9hOJ2BK4F+oGzgCfNRdjS8kjFdBcOA95JofStzB43AZ+nmJ80Zao5f1aV2gY16FpYuDW011ey5ldw8sCSlUXF1vDZmr0Ui6WVHxqAbKx8EOxhcKr7p4rJ44vHb0WQv3uSVaRPumn+BwxgswiHi2MAFrAjFSuuZ4oHAs+YjepYZAI607BZjEO7QE81zHVW9SwPNGNoMfqxwHK9nMdMTwtyn/Gq89JYciXVtVxZ8krgOOCnBEsOpVCeu5b5v9HAEtb4LiJmntytFK2PfDFmzkILbgBecD1BvwnM2wFYbsN3jmfhUV4gTsQZYM8BR99Rk0e2ad15Ll8XuMryrF6XJNFdB4xxDDgZ+LVZkNvNk9fCY4frSXDg3wjteDfXYh6wEnf8NmagSZ2vQsEfJqbXO6MMDslhiyVYLDMxIBlkzxgHjRG15K7bBXln4BbgVODjBGUox1NFR15Bgt4HiECtb/4WdTnS6nY6cIeJ0R+mXdThebrwy40MaS35dvONf6W3ZI+2twOyrEjkQYx5CfBfguI2NhZ3UcQcrb2ywfokTCSHSrW6KJe2sU+RuKdNofYEngKkv5p8uhni1Q7I2wIPAJcAT8doSLLsBdwIiF0rbsvqPgM2MG6+UcxPo/yDDNBR5cFG6+uJV6MV0b+nJV5aPRCItY2LIZ4HVHnzWf/ookDWbRSbVjL/SYxeVNl5CNjJ5HjXx8Tt1tQ6vkrkTecsAx5vcrNOgDxe1vSqXdX8NyS7l0972ccJwLdFguy7SKVGVcYXoVzFX7Hq94HZwEdNApB2+iYm5ismy2VPBAI2U6VN4C2TGgUzDn23/01HAWeGiWURlqwYcRvwY8ItlKA+yLqBKnS8HkJN5Es1WVm8LsPfaVENzaukJaZyphAk99btI9hqjKoP+JdAViyi9kPwg5JAViItZW4PrDBkqFGerPKklBZkwMqNFY9VhhTpiRty03ebIog6KRcY176OqXypl6ry5F1tAOyfLQK3L3BsWCFdjLb0qMupLEUe8QMjq/iOjEglTBlKXVUvCWTdiGbHu8DRoRTJJw4iUdWieczG2wELgL0BsUXVm3WxnjNx9ItmBYqZr/glOcOyZrR9btuoxqBavIpEyvfVctzCuPInIlqQFUGiQM5aQh9k1aJrmtkZHaS0TCFB7jw45E1+i4m5UtI5ExDkllQ2GUBWSqT8MDjkshRv/cZGWDklyC1dl/hFzbjrZo/WJT0DeM38E1MWadsIeDAhBVNM1pOapJSuWVm6dn4RlpyWeLWqJBVKVL4T6dvPxHMVVMJPZIL7C2Q12audmlYPnwjrigA5bQrVrr7EzucCVzd4IKB0REUF5e/yAiIwk3oUAbL/yEzdkaRiSDuKngacaIocNTlixKZTTL9az4tVB5/0owiQpUSRI7HrPFIWlf2UdikGp3n54ZdPtaZa353MSBcFsnK5e03D4ZEMFSqAzwZeNQw7TYlScVhuvaa+m6FMXbdVUSDrHFVjVJ1R477VkmRQgcqP9TpEVSAN9VC1t4a6MHp58mVI436xX2/D9BgwzaXoOtCaFagokCWXqlmqeOkR+JvNChoxXwRqa+Ar4EhA/eeHTWn0HvPfSsJdpt1NU0LcQA8Ve2IUCbLOUg9Xz3AFSBbWHARJVrq/uUzvmQZH8AxdCtXiZeFqNfbMKBJkKVWKVoqzqmBF533BuvrCFA2ylKFH9YtNGuN3UvJW0m7AESZ+T4TWYqb66ATIPtAiTWLaaoTnOQSwXqZcN0F6x5nrolMg60PUNlNqpdw2L5arqpb64WpRZs0BMgcjrw07CXJe31TuG9JACXIPXIkS5BLkHtBAD3xiacklyD2ggR74xNKSewDk/wEHkL44RXATIwAAAABJRU5ErkJggg==\" width=\"60.5\" height=\"20\" style=\"width: 60.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for the white-noise shocks (where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), this allows us to write down the IS\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAmCAYAAAAbdcG0AAAAAXNSR0IArs4c6QAAAPJJREFUSEvt0y1IBEEchvHfbBUvyGK0CGIVy4HYzVZRi+HAZFKDyQPBZrhwNj9AEJvJYtFmNlgEMYrZ5K4sq3Au3K5yZcNOnXmG//vMO8EIK4zAqiecTTWLJZFYYhz7ePuJOmzs7OAOUUyyi0lcood+GTyGQ8I0aQcv2AhspazjoQxewTlWcYFlbKKLWyTD4BhnhBnSK6IWyR1u8F581mLmecJ1DtrGR1kPivAC7nGAPXx+w5mHCbwOXlaEp3CKFtbwiDm5qCM8l8HZXju3bRFPOMbJXzL/q+r17HZlhGbsSkW/DzTCGmGVBpqSVCqqy6/6AmpmKCcgmFZrAAAAAElFTkSuQmCC\" width=\"7.5\" height=\"19\" style=\"width: 7.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equation as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"121\" height=\"19.5\" style=\"width: 121px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ethe PC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAmCAYAAAAbdcG0AAAAAXNSR0IArs4c6QAAAPJJREFUSEvt0y1IBEEchvHfbBUvyGK0CGIVy4HYzVZRi+HAZFKDyQPBZrhwNj9AEJvJYtFmNlgEMYrZ5K4sq3Au3K5yZcNOnXmG//vMO8EIK4zAqiecTTWLJZFYYhz7ePuJOmzs7OAOUUyyi0lcood+GTyGQ8I0aQcv2AhspazjoQxewTlWcYFlbKKLWyTD4BhnhBnSK6IWyR1u8F581mLmecJ1DtrGR1kPivAC7nGAPXx+w5mHCbwOXlaEp3CKFtbwiDm5qCM8l8HZXju3bRFPOMbJXzL/q+r17HZlhGbsSkW/DzTCGmGVBpqSVCqqy6/6AmpmKCcgmFZrAAAAAElFTkSuQmCC\" width=\"7.5\" height=\"19\" style=\"width: 7.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equation as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"93\" height=\"19\" style=\"width: 93px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand so on. Please solve the model in expectations (you may find it helpful to write the nominal Taylor rule in terms of the real interest rate gap \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"19.5\" style=\"width: 50px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for this) and write a function that, for given parameter values and a given inflation rate target, computes the model-consistent expectations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAmCAYAAADTGStiAAAAAXNSR0IArs4c6QAAAhJJREFUWEft1curTWEYBvDfWhk46RiQXBJ/gJRyV6cklxFSJnIJA9eUCGfiWjq5k4FjjBgYkJJSLgMDAylGmMgtciuR3NbSt8+3a9vlnLX3OdsZ2N9orfrW+7zP5X1Xop9O0k+4msB9pXyKqZieMibjPY7iSxmgEVKPwH48w0FMlrgtNxfXGwU8HKelPspsxSfsTWjLWYGnRYAHlbqVLkpk8/LEMLmVuBI/bsU2bIxMNmNVwqacZbiDNZgdwHEfeRHg0fHSj5RDOcvz1BlZCShDh1SLrOTlB+zBcXyXuiFLW8mu4lalt0WAK4O2Fp0J90IDmI8XOF/BYgEuYwtO4md3SS0arolR4pElD3kXGVYWX4qzWBfvlHGHIqT8bWUjRYFH4Rxm4qYu1i+rGE3AJTzEerzCLMzB4XqBB+IINuAY2kte/nkCiYXYh/G4i1O42BuPQ9GQ4AO4FhkHues+RaWeFDsfiydYjAd1o1LoJxGWwok4q6sxQ9ecBs/rPj0xHoDtceOEUQk+h9HqwM44z214hDe1dFENHN4H41cMxBJMww58jaCdFT6Po7SDQ6C+9Qa4PBJD8Dgu+jAaZTZT4siEeQ4KfKa0k2tiGxqsZhz8DHKGLXQBu/C6gkkLduta+CHd4fl5LUxrXZn11O72m57C1eeATcYNk/RvhZse/zPJm1I3pW6YAs1wNUza6sL/n9S/AdSlcycCQo7AAAAAAElFTkSuQmCC\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBonus question 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e what can you say about the relationship of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e? What happens if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBonus question 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhy is there, in fact, always a unique solution for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBonus question 3: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhat role does the parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e play?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xe_and_pie = ratexp(b, beta, kappa, k_pi, k_x, pistar)\r\n\r\n    xe  = 0;\r\n    pie = pistar;\r\n    \r\n    xe_and_pie = [xe; pie];\r\n    \r\nend","test_suite":"%%\r\nassert(max(abs(ratexp(1, 0.99, 0.3433, 1.5, 0.5, 2) - [0.056609114067365; 1.943390885932635])) \u003c 1e10)\r\n\r\n%%\r\nassert(max(abs(ratexp(2, 0.97, 0.2, 2, 0.8, 3) - [0.401785714285715; 2.678571428571428])) \u003c 1e10)\r\n\r\n%%\r\nassert(max(abs(ratexp(0.5, 0.98, 0.5, 1.3, 1, 2.5) - [0.088235294117647; 2.205882352941177])) \u003c 1e10)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":332395,"edited_by":332395,"edited_at":"2023-06-28T08:06:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-22T11:37:22.000Z","updated_at":"2023-06-28T08:06:52.000Z","published_at":"2023-06-22T11:40:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equation of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = x^e - b (r - r^n) + \\\\varepsilon_x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea PC equation of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi = \\\\beta \\\\pi^e + \\\\kappa x + \\\\varepsilon_\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea (nominal) interest rate rule of Taylor type of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = i^* + k_\\\\pi (\\\\pi - \\\\pi^*) + k_x x + \\\\varepsilon_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand a Fisher equation of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = r + \\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn these equations, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e denote Okun's output gap, the inflation rate, the nominal interest rate, the real interest rate and the natural real interest rate respectively; a superscript \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{}^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e indicates expectations formed by agents, so \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the expected output gap and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the expected inflation rate. The terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varepsilon_x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varepsilon_\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varepsilon_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are white-noise shock terms; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\beta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\kappa\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek_\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek_x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive parameters (with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\beta \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and additionally, the Taylor principle holds so that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek_\\\\pi \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the central bank's (exogenously chosen) target inflation rate, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei^* = r^n + \\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the implied target nominal interest rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe want to compute the rationally expected (model-consistent) inflation rate and output gap \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that are implied by given values of the model's parameters and a given value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To do this, we set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez^e = \\\\mathbb{E}(z \\\\mid I)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for any variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for which agents form expectations (e.g. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbb{E}(\\\\cdot)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e denotes the mathematical expectations operator and where the agents' information set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e contains both the structure of the model equations and the values of all parameters (as well as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(z^e)^e = \\\\mathbb E(\\\\mathbb E(z \\\\mid I) \\\\mid I) = \\\\mathbb E(z \\\\mid I) = z^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for any such \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by the law of iterated expectations, and since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbb E(\\\\varepsilon_z) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for the white-noise shocks (where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), this allows us to write down the IS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{}^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e = x^e - b (r^e - r^n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe PC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{}^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e = \\\\beta \\\\pi^e + \\\\kappa x^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on. Please solve the model in expectations (you may find it helpful to write the nominal Taylor rule in terms of the real interest rate gap \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(r - r^n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for this) and write a function that, for given parameter values and a given inflation rate target, computes the model-consistent expectations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBonus question 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e what can you say about the relationship of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e? What happens if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\beta = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBonus question 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewhy is there, in fact, always a unique solution for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBonus question 3: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewhat role does the parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e play?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":58449,"title":"Compute rational expectations in a static, linear NKM model","description":"Consider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equation of the form\r\n    ,\r\na PC equation of the form\r\n    ,\r\na (nominal) interest rate rule of Taylor type of the form\r\n    ,\r\nand a Fisher equation of the form\r\n    .\r\nIn these equations, , , ,  and  denote Okun's output gap, the inflation rate, the nominal interest rate, the real interest rate and the natural real interest rate respectively; a superscript  indicates expectations formed by agents, so  is the expected output gap and  the expected inflation rate. The terms ,  and  are white-noise shock terms; , , ,  and  are positive parameters (with ), and additionally, the Taylor principle holds so that .  is the central bank's (exogenously chosen) target inflation rate, and  is the implied target nominal interest rate.\r\nWe want to compute the rationally expected (model-consistent) inflation rate and output gap  and  that are implied by given values of the model's parameters and a given value of . To do this, we set  for any variable  for which agents form expectations (e.g.  and ), where  denotes the mathematical expectations operator and where the agents' information set  contains both the structure of the model equations and the values of all parameters (as well as  and ).\r\nSince  for any such  by the law of iterated expectations, and since  for the white-noise shocks (where  is ,  or ), this allows us to write down the IS equation as\r\n    ,\r\nthe PC equation as\r\n    ,\r\nand so on. Please solve the model in expectations (you may find it helpful to write the nominal Taylor rule in terms of the real interest rate gap  for this) and write a function that, for given parameter values and a given inflation rate target, computes the model-consistent expectations  and  for  and .\r\n\r\nBonus question 1: what can you say about the relationship of  and ? What happens if ?\r\nBonus question 2: why is there, in fact, always a unique solution for  and ?\r\nBonus question 3: what role does the parameter  play?","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 818px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 409px; transform-origin: 407.5px 409px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equation of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.9167px; text-align: left; transform-origin: 384.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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width=\"140.5\" height=\"21\" style=\"width: 140.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ea PC equation of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.9167px; text-align: left; transform-origin: 384.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"112.5\" height=\"21\" style=\"width: 112.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ea (nominal) interest rate rule of Taylor type of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.9167px; text-align: left; transform-origin: 384.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"179\" height=\"21\" style=\"width: 179px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand a Fisher equation of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"19\" style=\"width: 63px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106.667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 53.3333px; text-align: left; transform-origin: 384.5px 53.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn these equations, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"19\" style=\"width: 14.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e denote Okun's output gap, the inflation rate, the nominal interest rate, the real interest rate and the natural real interest rate respectively; a superscript \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAmCAYAAAAbdcG0AAAAAXNSR0IArs4c6QAAAPJJREFUSEvt0y1IBEEchvHfbBUvyGK0CGIVy4HYzVZRi+HAZFKDyQPBZrhwNj9AEJvJYtFmNlgEMYrZ5K4sq3Au3K5yZcNOnXmG//vMO8EIK4zAqiecTTWLJZFYYhz7ePuJOmzs7OAOUUyyi0lcood+GTyGQ8I0aQcv2AhspazjoQxewTlWcYFlbKKLWyTD4BhnhBnSK6IWyR1u8F581mLmecJ1DtrGR1kPivAC7nGAPXx+w5mHCbwOXlaEp3CKFtbwiDm5qCM8l8HZXju3bRFPOMbJXzL/q+r17HZlhGbsSkW/DzTCGmGVBpqSVCqqy6/6AmpmKCcgmFZrAAAAAElFTkSuQmCC\" width=\"7.5\" height=\"19\" style=\"width: 7.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e indicates expectations formed by agents, so \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the expected output gap and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAmCAYAAABK4fLXAAAAAXNSR0IArs4c6QAAAlxJREFUWEft1UuIjWEYB/DfdxZGFCHJwm0lxcqCjSwkaVwyG4RRTBFRKKlhNaEIyd3IwiUsbCiErUJZu2SBBSVFZOMyn54575nOHHNmjplGszjf7py+933+3//2ZIbAkw0BDOogSir8LybGYRkmYgZO4fH/AlFAU8amnD14juMKGnTYim8BZDCZiLtX4wCdA+9gVsb1vMjEWfyuBcRkNMs0ys0t0lfCnXf9zHJyPmApniWap2fcyHmKHZiEI3iI8/jelxwxaQWOykwpDslI07rFOt4s4rmHdfiUkLbKtMm1F/jRwVvcwquuE+mianLMp9BCxzl8LiLPPpLHF4WOs3EZx9Ce7vqFr2nAaFxIX78Wr3vro55AhIPj4OlEWRNuYmcaGmdasRuL8aiHAZGGq2jAGrxP74RRp+IdAnQ3gasBHYmTWFSmd4C8lA40K3qh8hmGtgR0Pa4ggG3DE9xFR60ggvbbKdMbkzQLcR8Hsa/k8B6AjMd+rMLPxGbI96JWT5RiEB4IR8ewuDC+8BC2Y3ky2oDXT289UaJ9Tpn203ANw7ESLweMoI+yCkOFluXRC0nC9ZGMUuMF7UH3l/4CqsbEzDQsWNiVUhFOD2m2lPlhVJLqcBWD1oSrEkQ4ODp+A8am+EVc32BMYqAxOTwivAQPEuBUoTXN/avvyv9YkGo1/otS2pw8EANGdC4fWsoOXEyVHCXV76eSiQk4gQCzN7VhV6lgXlrDkZIAcKa0CfuNYJC3aM24BnOV10HUzECtu+OfL+zPgbon6nJU+qbuibon6p6o1qb1dAypdPwB4XWCJzsSaV8AAAAASUVORK5CYII=\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the expected inflation rate. The terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12.5\" height=\"20\" style=\"width: 12.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e are white-noise shock terms; \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eβ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eκ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e are positive parameters (with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), and additionally, the Taylor principle holds so that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42\" height=\"20\" style=\"width: 42px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAmCAYAAABOFCLqAAAAAXNSR0IArs4c6QAAAnBJREFUWEft1UmozWEYx/HP/y4QkTHZmLK0UBaGEpEQMi0sDAssRBRKClESkSlThixcYYEMG2EjKRZs2CgLO0OGi6xw/3qu91zHzTn+5xpSzlunc86/9/883/d5fr/nzfxDK/uHWPyXMA0Yiufp88OG/K3KDCE7S34JWypJ40/CdMcM3MQbHMc5XMQkvMLtcrA/CTMMZzOaclYkgBsYi+3YhK34XAL6GUx/LCSbmslH5q3HiNe+/iv9yniaMx33yk7bAQE1E6NpeELzhVSR161B0guVYOL5LJnd8mxAlhLn3xhaKVoefX1+FQvwsi1MA3OaGdXAw2Yt+26l1n0nn0owUcolONLyUuaoPHtBvgrvMVymUW4PjqWIn/Cu7LQDcQq9sQzjcB3jsRlrsBfN1drUD/NxCB8wG+exmpbkcYD1WIspbUVYdtSumIb7eJYEHOKNNk3GYzyoRcBdcCCJr6SHgD2ZgizE0wJTfDBOI6y9rb3WHo4ruIPFqc8TcS0F3VjuhipQUc1BeJssXfPQiwChkV2IpGHDcMcOrEwz5HKBqhTeUs3apXaMKNNGnO4MOmEuHhXOVGBjNZh5yQ3llo1WxSRtxPLkrD74iKYC+apuqQQTl1okjaqEBcNFHVPLwqYhwmhdt/S9s6CQa4LphXVYhJ7JtmHzJ+iRKjIVd5P1w7oxOwL824BuZ4naVmYC4v6IFcNtadJIJOqMfWkYltKdSCKPYffLqy1MX+xHQG1I0zUma2mNwcHkqgA5nKB/GSQC/Oyi/C1Jigapw7T3Oiha4d+yr96meptqFVJdM3XN1DVTawXqmqm1YvU5U6liXwA/XocnAWgeeAAAAABJRU5ErkJggg==\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the central bank's (exogenously chosen) target inflation rate, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"19\" style=\"width: 74px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the implied target nominal interest rate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 52.5px; text-align: left; transform-origin: 384.5px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe want to compute the rationally expected (model-consistent) inflation rate and output gap \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e that are implied by given values of the model's parameters and a given value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. To do this, we set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"77.5\" height=\"19.5\" style=\"width: 77.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for any variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for which agents form expectations (e.g. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"28.5\" height=\"18.5\" style=\"width: 28.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e denotes the mathematical expectations operator and where the agents' information set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eI\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e contains both the structure of the model equations and the values of all parameters (as well as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"19\" style=\"width: 14.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.4167px; text-align: left; transform-origin: 384.5px 21.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSince \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"226\" height=\"19.5\" style=\"width: 226px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for any such \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e by the law of iterated expectations, and since \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHkAAAAoCAYAAADaKFUbAAAAAXNSR0IArs4c6QAABvNJREFUeF7tm3eIHHUUxz8z1rMgMUqwoRGPUwQPEWwRC2KC/9iJsSBBxUQ0aGKJLUYj9nJ2c2BUPNvBqSiCxK5osGIPCoK9YUODFZ2R785v9mZnZ2Znd2dm927nB/nn9lfevO/vvfd97/1iUT/6sBnC4WvgMmAArFFwTwNeiZhf/il/DfQB1wCnA6cAdwJu4NiZWIxhMYLDucDvQZGsSJBhCIIgMwqUIOcPZtwJhwIjFqx24Rjg09DEKRascOFw4Hjg/hLkzoHVyskbArcCc7EZxmEh8GdoIxnrhcbzPgqcBPziz0llyRaMuqUltwJQFmt2AcYs6HdhEZ6XjRqHAI9hsQaXg4OhNRJkG4ac0l1nAVAWe3jgeWMOVEJn1JgBvGx+mA8MJ1pyHcgWo7iZx+RNgV2B5wEnQuq1gT2wmY3DNtisxmFzYDPgZuClEPmI+nAbOAB4G/g5C413YI/zgSuQObrsk0B+Byoe12IQt2Lt5wH/SN4Yd20PgVNl1zm4634bFjhwOfB9hOJ2BK4F+oGzgCfNRdjS8kjFdBcOA95JofStzB43AZ+nmJ80Zao5f1aV2gY16FpYuDW011ey5ldw8sCSlUXF1vDZmr0Ui6WVHxqAbKx8EOxhcKr7p4rJ44vHb0WQv3uSVaRPumn+BwxgswiHi2MAFrAjFSuuZ4oHAs+YjepYZAI607BZjEO7QE81zHVW9SwPNGNoMfqxwHK9nMdMTwtyn/Gq89JYciXVtVxZ8krgOOCnBEsOpVCeu5b5v9HAEtb4LiJmntytFK2PfDFmzkILbgBecD1BvwnM2wFYbsN3jmfhUV4gTsQZYM8BR99Rk0e2ad15Ll8XuMryrF6XJNFdB4xxDDgZ+LVZkNvNk9fCY4frSXDg3wjteDfXYh6wEnf8NmagSZ2vQsEfJqbXO6MMDslhiyVYLDMxIBlkzxgHjRG15K7bBXln4BbgVODjBGUox1NFR15Bgt4HiECtb/4WdTnS6nY6cIeJ0R+mXdThebrwy40MaS35dvONf6W3ZI+2twOyrEjkQYx5CfBfguI2NhZ3UcQcrb2ywfokTCSHSrW6KJe2sU+RuKdNofYEngKkv5p8uhni1Q7I2wIPAJcAT8doSLLsBdwIiF0rbsvqPgM2MG6+UcxPo/yDDNBR5cFG6+uJV6MV0b+nJV5aPRCItY2LIZ4HVHnzWf/ookDWbRSbVjL/SYxeVNl5CNjJ5HjXx8Tt1tQ6vkrkTecsAx5vcrNOgDxe1vSqXdX8NyS7l0972ccJwLdFguy7SKVGVcYXoVzFX7Hq94HZwEdNApB2+iYm5ismy2VPBAI2U6VN4C2TGgUzDn23/01HAWeGiWURlqwYcRvwY8ItlKA+yLqBKnS8HkJN5Es1WVm8LsPfaVENzaukJaZyphAk99btI9hqjKoP+JdAViyi9kPwg5JAViItZW4PrDBkqFGerPKklBZkwMqNFY9VhhTpiRty03ebIog6KRcY176OqXypl6ry5F1tAOyfLQK3L3BsWCFdjLb0qMupLEUe8QMjq/iOjEglTBlKXVUvCWTdiGbHu8DRoRTJJw4iUdWieczG2wELgL0BsUXVm3WxnjNx9ItmBYqZr/glOcOyZrR9btuoxqBavIpEyvfVctzCuPInIlqQFUGiQM5aQh9k1aJrmtkZHaS0TCFB7jw45E1+i4m5UtI5ExDkllQ2GUBWSqT8MDjkshRv/cZGWDklyC1dl/hFzbjrZo/WJT0DeM38E1MWadsIeDAhBVNM1pOapJSuWVm6dn4RlpyWeLWqJBVKVL4T6dvPxHMVVMJPZIL7C2Q12audmlYPnwjrigA5bQrVrr7EzucCVzd4IKB0REUF5e/yAiIwk3oUAbL/yEzdkaRiSDuKngacaIocNTlixKZTTL9az4tVB5/0owiQpUSRI7HrPFIWlf2UdikGp3n54ZdPtaZa353MSBcFsnK5e03D4ZEMFSqAzwZeNQw7TYlScVhuvaa+m6FMXbdVUSDrHFVjVJ1R477VkmRQgcqP9TpEVSAN9VC1t4a6MHp58mVI436xX2/D9BgwzaXoOtCaFagokCWXqlmqeOkR+JvNChoxXwRqa+Ar4EhA/eeHTWn0HvPfSsJdpt1NU0LcQA8Ve2IUCbLOUg9Xz3AFSBbWHARJVrq/uUzvmQZH8AxdCtXiZeFqNfbMKBJkKVWKVoqzqmBF533BuvrCFA2ylKFH9YtNGuN3UvJW0m7AESZ+T4TWYqb66ATIPtAiTWLaaoTnOQSwXqZcN0F6x5nrolMg60PUNlNqpdw2L5arqpb64WpRZs0BMgcjrw07CXJe31TuG9JACXIPXIkS5BLkHtBAD3xiacklyD2ggR74xNKSewDk/wEHkL44RXATIwAAAABJRU5ErkJggg==\" width=\"60.5\" height=\"20\" style=\"width: 60.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for the white-noise shocks (where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ez\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), this allows us to write down the IS\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAmCAYAAAAbdcG0AAAAAXNSR0IArs4c6QAAAPJJREFUSEvt0y1IBEEchvHfbBUvyGK0CGIVy4HYzVZRi+HAZFKDyQPBZrhwNj9AEJvJYtFmNlgEMYrZ5K4sq3Au3K5yZcNOnXmG//vMO8EIK4zAqiecTTWLJZFYYhz7ePuJOmzs7OAOUUyyi0lcood+GTyGQ8I0aQcv2AhspazjoQxewTlWcYFlbKKLWyTD4BhnhBnSK6IWyR1u8F581mLmecJ1DtrGR1kPivAC7nGAPXx+w5mHCbwOXlaEp3CKFtbwiDm5qCM8l8HZXju3bRFPOMbJXzL/q+r17HZlhGbsSkW/DzTCGmGVBpqSVCqqy6/6AmpmKCcgmFZrAAAAAElFTkSuQmCC\" width=\"7.5\" height=\"19\" style=\"width: 7.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equation as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"121\" height=\"19.5\" style=\"width: 121px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ethe PC\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAmCAYAAAAbdcG0AAAAAXNSR0IArs4c6QAAAPJJREFUSEvt0y1IBEEchvHfbBUvyGK0CGIVy4HYzVZRi+HAZFKDyQPBZrhwNj9AEJvJYtFmNlgEMYrZ5K4sq3Au3K5yZcNOnXmG//vMO8EIK4zAqiecTTWLJZFYYhz7ePuJOmzs7OAOUUyyi0lcood+GTyGQ8I0aQcv2AhspazjoQxewTlWcYFlbKKLWyTD4BhnhBnSK6IWyR1u8F581mLmecJ1DtrGR1kPivAC7nGAPXx+w5mHCbwOXlaEp3CKFtbwiDm5qCM8l8HZXju3bRFPOMbJXzL/q+r17HZlhGbsSkW/DzTCGmGVBpqSVCqqy6/6AmpmKCcgmFZrAAAAAElFTkSuQmCC\" width=\"7.5\" height=\"19\" style=\"width: 7.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equation as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"93\" height=\"19\" style=\"width: 93px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eand so on. Please solve the model in expectations (you may find it helpful to write the nominal Taylor rule in terms of the real interest rate gap \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"19.5\" style=\"width: 50px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for this) and write a function that, for given parameter values and a given inflation rate target, computes the model-consistent expectations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBonus question 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e what can you say about the relationship of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17.5\" height=\"19\" style=\"width: 17.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e? What happens if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBonus question 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhy is there, in fact, always a unique solution for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"19\" style=\"width: 15px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"19\" style=\"width: 16.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBonus question 3: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhat role does the parameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e play?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xe_and_pie = ratexp(b, beta, kappa, k_pi, k_x, pistar)\r\n\r\n    xe  = 0;\r\n    pie = pistar;\r\n    \r\n    xe_and_pie = [xe; pie];\r\n    \r\nend","test_suite":"%%\r\nassert(max(abs(ratexp(1, 0.99, 0.3433, 1.5, 0.5, 2) - [0.056609114067365; 1.943390885932635])) \u003c 1e10)\r\n\r\n%%\r\nassert(max(abs(ratexp(2, 0.97, 0.2, 2, 0.8, 3) - [0.401785714285715; 2.678571428571428])) \u003c 1e10)\r\n\r\n%%\r\nassert(max(abs(ratexp(0.5, 0.98, 0.5, 1.3, 1, 2.5) - [0.088235294117647; 2.205882352941177])) \u003c 1e10)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":332395,"edited_by":332395,"edited_at":"2023-06-28T08:06:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-22T11:37:22.000Z","updated_at":"2023-06-28T08:06:52.000Z","published_at":"2023-06-22T11:40:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a static, linear approximation of the baseline New Keynesian macroeconomic model. This can be described by an IS equation of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = x^e - b (r - r^n) + \\\\varepsilon_x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea PC equation of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi = \\\\beta \\\\pi^e + \\\\kappa x + \\\\varepsilon_\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea (nominal) interest rate rule of Taylor type of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = i^* + k_\\\\pi (\\\\pi - \\\\pi^*) + k_x x + \\\\varepsilon_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand a Fisher equation of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = r + \\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn these equations, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e denote Okun's output gap, the inflation rate, the nominal interest rate, the real interest rate and the natural real interest rate respectively; a superscript \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{}^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e indicates expectations formed by agents, so \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the expected output gap and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the expected inflation rate. The terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varepsilon_x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varepsilon_\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varepsilon_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are white-noise shock terms; \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\beta\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\kappa\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek_\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek_x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive parameters (with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\beta \\\\le 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), and additionally, the Taylor principle holds so that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek_\\\\pi \u0026gt; 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the central bank's (exogenously chosen) target inflation rate, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei^* = r^n + \\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the implied target nominal interest rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe want to compute the rationally expected (model-consistent) inflation rate and output gap \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that are implied by given values of the model's parameters and a given value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To do this, we set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez^e = \\\\mathbb{E}(z \\\\mid I)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for any variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for which agents form expectations (e.g. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbb{E}(\\\\cdot)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e denotes the mathematical expectations operator and where the agents' information set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e contains both the structure of the model equations and the values of all parameters (as well as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(z^e)^e = \\\\mathbb E(\\\\mathbb E(z \\\\mid I) \\\\mid I) = \\\\mathbb E(z \\\\mid I) = z^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for any such \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by the law of iterated expectations, and since \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbb E(\\\\varepsilon_z) = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for the white-noise shocks (where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), this allows us to write down the IS\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{}^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e = x^e - b (r^e - r^n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethe PC\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{}^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e = \\\\beta \\\\pi^e + \\\\kappa x^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on. Please solve the model in expectations (you may find it helpful to write the nominal Taylor rule in terms of the real interest rate gap \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(r - r^n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for this) and write a function that, for given parameter values and a given inflation rate target, computes the model-consistent expectations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBonus question 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e what can you say about the relationship of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e? What happens if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\beta = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBonus question 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewhy is there, in fact, always a unique solution for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi^e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBonus question 3: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewhat role does the parameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr 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