DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback - PowerPoint PPT Presentation

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 , 5 2 A Taylor Rule for Fiscal Policy? e David Kendrick and Hans Amman n University of Texas and Utrecht University u 15-17 July 2010 J

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 1 , 5 Feedback Rules 2 2 Fiscal Policy 3 Institutional Considerations 4 e Lags 5 n Uncertainty 6 u Measurement 7 J Conclusions 8 Questions 9

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 1 , 5 Stimulus Package 2008 In February of 2008 Congress passed a tax rebate of about 150 billion 2 that had been proposed by the Bush Administration to slow the downturn in the economy. e n u J

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 1 , 5 Stimulus Package 2008 In February of 2008 Congress passed a tax rebate of about 150 billion 2 that had been proposed by the Bush Administration to slow the downturn in the economy. e Stimulus Package 2009 n One year later, in February of 2009 Congress passed the Obama Administration’s stimulus package of about $800 billion dollars. u J

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 1 , 5 Stimulus Package 2008 In February of 2008 Congress passed a tax rebate of about 150 billion 2 that had been proposed by the Bush Administration to slow the downturn in the economy. e Stimulus Package 2009 n One year later, in February of 2009 Congress passed the Obama Administration’s stimulus package of about $800 billion dollars. u J Unemployment Between these two dates the unemployment rate rose from about 5 percent to about 8 percent across a twelve month span in which no additional fiscal policy measures were enacted.

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 2 , Monetary Policy 5 In contrast, across this same period monetary policy was reviewed 2 monthly - or even more frequently - and corrective actions were taken repeatedly in attempts to mitigate the downturn. e n u J

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 2 , Monetary Policy 5 In contrast, across this same period monetary policy was reviewed 2 monthly - or even more frequently - and corrective actions were taken repeatedly in attempts to mitigate the downturn. e Fiscal Policy n Would smaller and more frequently changes in fiscal policy in the period from the fall of 2007 thru the fall of 2009 have decreased the downward u inertia of the economy and thus mitigated substantially the rise in unemployment. And would this have decreased the decline in government J revenues and thus the amount of the rise in the federal deficit?

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Introduction 2 , Monetary Policy 5 In contrast, across this same period monetary policy was reviewed 2 monthly - or even more frequently - and corrective actions were taken repeatedly in attempts to mitigate the downturn. e Fiscal Policy n Would smaller and more frequently changes in fiscal policy in the period from the fall of 2007 thru the fall of 2009 have decreased the downward u inertia of the economy and thus mitigated substantially the rise in unemployment. And would this have decreased the decline in government J revenues and thus the amount of the rise in the federal deficit? Feedback rules This paper addresses these questions through the framework of feedback rules.

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 1 , 5 2 Phillips’ idea The idea of using control theory methods and feedback rules in macroeconomic stabilization was given it first prominence in the works of e A.W. H. Phillips in the 1950’s. a It was then that he developed the n famous water models of the economy while he was living in Great Britain. The idea was simple, namely that the condition of the economy should u be feedback to the policy controller so that policies could be adjusted to bring the economy back onto desired paths. J a See Phillips (1954).

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 2 , 5 2 The SEDC Phillips’ idea did not gain traction with economists at that time. However, the idea was revived twenty years later by a group of economists e and engineers brought together under the leadership of Michael Athens, Gregory Chow, Ed Kuh and M. Ishaq Nadiri for an NBER conference at n Princeton University in 1972. This time the idea found strong support and resulted in the formation of the Society of Economic Dynamics and u Control which sponsored a series of annual conferences. The group even J created their own journal, the Journal of Economic Dynamics and Control , which quickly rose in the rankings among economics journals.

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 3 , 5 2 The Abel model Early in this period Gregory Chow and his undergraduate assistant, Andrew Abel, developed at Princeton a quarterly macroeconomic model e and applied stochastic control theory methods to it. a That model is small n and simple enough to serve as a good starting point for the discussion in this paper. It had two state variables, consumption ( C ) and investment u ( I ) and two control variables, government expenditures ( G ) and the money supply ( M ). J a See Chow (1967) and Abel (1975).

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 4 , These variables were embedded in the system equations for the 5 econometric model which were written as Systems equation 2 x k +1 = A k x k + B k u k + ξ k (1) e where n k = 0 , ...., N − 1 , being the time subscript u x k = the state vector in period k of dimension n × 1 J u k = the control vector in period k of dimension m × 1 = state vector coefficient matrix in period k of dimension n × n A k = control vector coefficient matrix in period k of dimension n × m B k = vector of additive noise terms in period k of dimension n × 1 ξ k

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 5 , 5 2 and where the state and control vectors were e Two states – two controls model n � � � � I k G k x k = u k = (2) C k M k u There were desired paths for both the state and control variables which J were specified with a quadratic tracking criterion function. Minimization of the criterion function with respect to the systems equation (1) yielded the feedback

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 6 , 5 Minimization of the criterion function with respect to the systems 2 equation (1) yielded the feedback Feedback rule e u k = ˆ G k x k + ˆ g k (3) n u J

DRAFT 9 5 : 9 0 - - 0 1 0 Outline Introduction Feedback Rules Fiscal Policy Institutional Considerations Lags Uncertainty Measurement Conclusions Questions References 2 Feedback Rules in Macroeconomics 6 , 5 Minimization of the criterion function with respect to the systems 2 equation (1) yielded the feedback Feedback rule e u k = ˆ G k x k + ˆ g k (3) n where u ˆ G k = the feedback gain matrix in period k J g k ˆ = the vector of feedback parameters in period k Thus deviations of the consumption or investment state variables from their desired paths worked through the feedback rule to increase or decrease the government expenditure and/or money supply variables as necessary to bring the economy back onto track.