band of inaction balances the two costs, and turns out to be equivalent to a confidence interval. This makes the band of inaction describable as a two-sided hypothesis test-in other words IE is an “as if theory of optimal decision making. In view of what we consider to be reasonable implications and foundations, our modelling strategy is an extension of the IE work on central banking by Henckel et al. (2011). We treat beliefs about the central bank inflation target as a null belief in a hypothesis test, where Ho corresponds to the official target value. In the case of the ECB we will treat this value as 2 percent. We posit an IE Phillips curve of the following form: T = BH, + (1 – B)E[n] + £ xXi + ŋ. i (1) Aggregate inflation a depends on the inferential expectations of price setters, a fraction ß of whom fail to reject Họ and a fraction 1- B of whom reject Ho and work out the rational expectation of inflation, based on (1). The variable Ho is the value inflation takes under the null, which in our analysis is 2 percent for the ECB. The X; are other explanators, variables like the output gap, which are zero in the steady-state. The estimation error n is assumed to be i.i.d. We can simplify the above equation by noting that, when agents adopt rational expectations, they can use (1) to solve for E[T]: Σ E[7] = BHo + (1 – B)E[n] + £„X; E [7] = H, + i which can be substituted into (1) to obtain the IE Phillips curve: Σ T = Ho + Xị + ŋ. (2) Eq. (2) is noteworthy because the marginal impacts of the X{'s depend upon the proportion of agents that are anchored onto Họ. The more they abandon the inflation target (the lower ß) the more they must rely on other variables for their expectations, which magnifies their marginal impacts. Thus, a testable implication of the IE Phillips curve is that all the coefficients on the X¡'s will rise by the same proportion when agents abandon the null. It is a noteworthy feature of many crises that previously unimportant variables can become more important, and (2) is a new (and testable) model of why this might be so.º 3.2. Steady-State B

band of inaction balances the two costs, and turns out to be equivalent to a confidence interval. This makes the band of inaction describable as a two-sided hypothesis test-in other words IE is an “as if theory of optimal decision making. In view of what we consider to be reasonable implications and foundations, our modelling strategy is an extension of the IE work on central banking by Henckel et al. (2011). We treat beliefs about the central bank inflation target as a null belief in a hypothesis test, where Ho corresponds to the official target value. In the case of the ECB we will treat this value as 2 percent. We posit an IE Phillips curve of the following form: T = BH, + (1 – B)E[n] + £ xXi + ŋ. i (1) Aggregate inflation a depends on the inferential expectations of price setters, a fraction ß of whom fail to reject Họ and a fraction 1- B of whom reject Ho and work out the rational expectation of inflation, based on (1). The variable Ho is the value inflation takes under the null, which in our analysis is 2 percent for the ECB. The X; are other explanators, variables like the output gap, which are zero in the steady-state. The estimation error n is assumed to be i.i.d. We can simplify the above equation by noting that, when agents adopt rational expectations, they can use (1) to solve for E[T]: Σ E[7] = BHo + (1 – B)E[n] + £„X; E [7] = H, + i which can be substituted into (1) to obtain the IE Phillips curve: Σ T = Ho + Xị + ŋ. (2) Eq. (2) is noteworthy because the marginal impacts of the X{'s depend upon the proportion of agents that are anchored onto Họ. The more they abandon the inflation target (the lower ß) the more they must rely on other variables for their expectations, which magnifies their marginal impacts. Thus, a testable implication of the IE Phillips curve is that all the coefficients on the X¡'s will rise by the same proportion when agents abandon the null. It is a noteworthy feature of many crises that previously unimportant variables can become more important, and (2) is a new (and testable) model of why this might be so.º 3.2. Steady-State B

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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