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Working Paper 2009-29 October 2009 Abstract: This paper studies an optimal fiscal policy problem of Lucas and Stokey (1983) but in a situation in which the representative agent's distrust of the probability model for government expenditures puts model uncertainty premia into history-contingent prices. This situation gives rise to a motive for expectation management that is absent within rational expectations and a novel incentive for the planner to smooth the shadow value of the agent's subjective beliefs to manipulate the equilibrium price of government debt. Unlike the Lucas and Stokey (1983) model, the optimal allocation, tax rate, and debt become history dependent despite complete markets and Markov government expenditures. JEL classification: D80, E62, H21, H63 Key words: Ramsey plan, misspecification, robustness, taxes, debt, martingale, expansion 1 Introduction Optimal policy design problems heavily exploit the rational expectations assumption that attributes a unique and fully trusted probability model to all agents. That useful assumption precludes carrying out a coherent analysis that attributes fears of model misspecification to some or all agents. It seems natural to ask the question: How should we approach policy design problems in macroeconomics when at least some agents distrust the model? This question is not just of academic interest but of particular practical relevance. Lack of confidence in models seems to have become pronounced in the recent financial crisis and has entered policy discussions. Caballero and Krishnamurthy (2008), for example, impute sets of probability models and a max-min criterion to private agents as a way to model Knightian uncertainty when a lender of last resort copes with flights to quality, whereas Uhlig (2009) appeals to uncertainty aversion to justify pessimism during bank runs. Our approach can be viewed as putting a particular structure on a decision maker's set of models and thereby on his pessimism. This additional structure opens up channels of influence for policy makers not present in the analyses of Caballero and Krishnamurthy (2008) and Uhlig (2009). (1) This paper features a notion of expectation management that is absent from the standard rational expectations paradigm. We formulate an optimal policy problem in which private agents' fears of model misspecification cause them to adjust their expectations in ways that a Ramsey planner recognizes and exploits, bringing the household's endogenous beliefs into the forefront of an optimal policy design problem because they affect equilibrium prices. We study a Ramsey fiscal policy problem in which a planner knows that a representative household distrusts a probability model for exogenous sequences of government expenditures, while the planner still trusts it. We start with the complete-markets economy without capital analyzed by Lucas and Stokey (1983), but modify the representative household's preferences to express his concerns about misspecification of the stochastic process for government expenditures. The planner can use a distortionary tax on labor income and issue state-contingent debt in order to finance the exogenous government expenditures. Our household expresses distrust of his model by ranking consumption plans according to the multiplier preferences of Hansen and Sargent (2001); when a multiplier parameter assumes a special value, the expected utility preferences of Lucas and Stokey (1983) emerge as a special case in which the decision maker completely trusts his probability model. (2) The Lucas and Stokey (1983) environment isolates essential dimensions of an optimal macroeconomic policy design problem in which a representative household's ambiguity about its statistical model creates an avenue that motivates the planner to manipulate the household's beliefs, because they affect equilibrium Arrow-Debreu prices. … |
