1. In the 1970s in the United States, the inflation rate and the natural rate of unemployment both rose. Let’s use this model of time inconsistency to examine this phenomenon. Assume that policy is discretionary.
In the model as developed so far, what happens to the inflation rate when the natural rate of unemployment rises?
Let’s now change the model slightly by supposing that the Fed’s loss function is quadratic in both inflation and unemployment. That is,
L(u, π) = u2 + γπ2.
Follow steps similar to those in the text to solve for the inflation rate under discretionary policy.
Now what happens to the inflation rate when the natural rate of unemployment rises?
In 1979, President Jimmy Carter appointed the central banker Paul Volcker to head the Federal Reserve. Volcker had a strong distaste for inflation. According to this model, what should have happened to inflation and unemployment? Compare the model’s prediction to what actually happened.
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1 Kathryn M. Dominguez, Ray C. Fair, and Matthew D. Shapiro, “Forecasting the Depression: Harvard Versus Yale,” American Economic Review 78 (September 1988): 595–612. This article shows how badly economic forecasters did during the Great Depression, and it argues that they could not have done any better with the modern forecasting techniques available today.
2 Robert E. Lucas, Jr., “Econometric Policy Evaluation: A Critique,” Carnegie Rochester Conference on Public Policy 1 (Amsterdam: North-Holland, 1976): 19–46. Lucas won the Nobel Prize for this and other work in 1995.
3 To read more about this topic, see Christina D. Romer, “Spurious Volatility in Historical Unemployment Data,” Journal of Political Economy 94 (February 1986): 1–37; and Christina D. Romer, “Is the Stabilization of the Postwar Economy a Figment of the Data?” American Economic Review 76 (June 1986): 314–334.
4 Scott R. Baker, Nicholas Bloom, and Steven J. Davis, “Measuring Economic Policy Uncertainty,” Working Paper, 2013. Available at http://www.policyuncertainty.com.
5 William Nordhaus, “The Political Business Cycle,” Review of Economic Studies 42 (1975): 169–190; Edward Tufte, Political Control of the Economy (Princeton, NJ: Princeton University Press, 1978).
6 See Ben S. Bernanke and Frederic S. Mishkin, “Inflation Targeting: A New Framework for Monetary Policy?” Journal of Economic Perspectives 11 (Spring 1997): 97–116.
7 For a more complete presentation of these findings and references to the large literature on central-bank independence, see Alberto Alesina and Lawrence H. Summers, “Central Bank Independence and Macroeconomic Performance: Some Comparative Evidence,” Journal of Money, Credit, and Banking 25 (May 1993): 151–162. For a study that questions the link between inflation and central-bank independence, see Marta Campillo and Jeffrey A. Miron, “Why Does Inflation Differ Across Countries?” in Christina D. Romer and David H. Romer, eds., Reducing Inflation: Motivation and Strategy (Chicago: University of Chicago Press, 1997), 335–362.
8 The material in this appendix is derived from Finn E. Kydland and Edward C. Prescott, “Rules Rather Than Discretion: The Inconsistency of Optimal Plans,” Journal of Political Economy 85 (June 1977): 473–492; and Robert J. Barro and David Gordon, “A Positive Theory of Monetary Policy in a Natural Rate Model,” Journal of Political Economy 91 (August 1983): 589–610. Kydland and Prescott won the Nobel Prize for this and other work in 2004.
9 Mathematical note: The second derivative, d2L/dπ2 = 2γ, is positive, ensuring that we are solving for a minimum of the loss function rather than a maximum!
10 This corollary is based on Kenneth Rogoff, “The Optimal Degree of Commitment to an Intermediate Target,” Quarterly Journal of Economics 100 (1985): 1169–1190.