Managing expectations and ¯scal policy Anastasios G. Karantounias with Lars Peter Hansen and Thomas J. Sargent¤ October 6, 2009 Abstract This paper studies an optimal ¯scal 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 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 in order to manipulate the equilibrium price of government debt. Unlike the Lucas and Stokey (1983) model, the optimal allocation, tax rate, and debt all become history dependent despite complete markets and Markov government expenditures. JEL classification: D80; E62; H21; H63. Key words: Ramsey plan, misspeci¯cation, robustness, taxes, debt, martingale, expansion. ¤First draft: November 2007. Karantounias (corresponding author): Federal Reserve Bank of Atlanta (e- mail: [email protected]); Hansen: University of Chicago (e-mail: [email protected]); Sargent: New York University and Hoover Institution (e-mail: [email protected]). This paper circu- lated previously under the title \Ramsey taxation and fear of misspeci¯cation." We are thankful to David Backus, Marco Bassetto, Pierpaolo Benigno, Marco Cagetti, Steve Coate, Kris Gerardi, Ricardo Lagos, An- dreas Lehnert, Guido Lorenzoni, Monika Piazzesi, Will Roberds, John Rust, Martin Schneider, John Shea, Karl Shell, Ennio Stacchetti, Tom Tallarini, Viktor Tsyrennikov, Tao Zha and to seminar participants at Birkbeck College, Cornell, EIEF, FRB, FRB Atlanta, FRB Chicago, Iowa, Maryland, NYU, Oxford, Penn State, Warwick and Wharton. Karantounias would like to thank, without implicating, the Research and Statistics Division of the FRB and the Monetary Policy Strategy Division of the ECB for their hospitality and support. Sargent's research was supported by a grant to the National Bureau of Economic Research from the National Science Foundation. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. 1 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 misspeci¯cation 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 con¯dence in models seems to have become pronounced in the recent ¯nancial 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 misspeci¯cation 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 a®ect equilibrium prices. We study a Ramsey ¯scal 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 misspeci¯cation of the stochastic process for government expen- ditures. The planner can use a distortionary tax on labor income and issue state-contingent debt in order to ¯nance 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 1For further policy recommendations based on the insights of Caballero and Krishnamurthy (2008) see Caballero and Kurlat (2009). 2Multiplier preferences lead to tractable functional forms. See Maccheroni et al. (2006a,b) and Strzalecki 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 house- hold's beliefs, because they a®ect equilibrium Arrow-Debreu prices. More speci¯cally, the Ramsey planner and the household share a common sequence of t t transition densities ¼t+1(gt+1jg ) for government spending gt+1 conditional on histories g of gs for s from 0 to t. The household's concern about misspeci¯cation leads it to twist t ¼t+1(gt+1jg ) pessimistically by multiplying it by a conditional likelihood ratio ³ ´ t+1 Vt+1(g ) exp ¡ θ m¤ (gt+1) = ³ ´; (1) t+1 P t+1 ¼ (g jgt) exp ¡ Vt+1(g ) gt+1 t+1 t+1 θ t+1 where Vt+1(g ) is a continuation value and θ 2 [θ; +1] is a positive multiplier parameter t expressing the household's distrust of ¼t+1(gt+1jg ). Multiplication by (1) raises probabilities of events that give rise to lower continuation values and lowers those giving rise to higher continuation values. The continuation values are themselves constructed recursively in a ¤ way that makes them depend on future distortions mt+j. In a competitive equilibrium, t ¤ t the household's distorted probabilities¼ ~t+1(gt+1jg ) = mt+1¼t+1(gt+1jg ) help determine the prices of date- and history-contingent securities. The Ramsey planner cares about these prices because he wants to manipulate the value of government debt passed from one period ¤ to the next. The fact that the distortions mt+1 depend on continuation values, which in turn depend on continuation allocations, means that the planner influences the household's beliefs and equilibrium prices by its choices of state contingent tax and borrowing strategies. The endogeneity of the household's pessimistic beliefs contributes additional restrictions on allocations that supplement implementability conditions already present in Lucas and Stokey's model. The planner's response to these additional implementability conditions injects a source of history dependence into taxes, government debt, and allocations that is not present in Lucas and Stokey (1983). A salient feature of the Ramsey plan of Lucas and Stokey (1983) is the absence of history dependence in allocations, tax rates, and government debt. For example, with Markov government expenditures, the value of government debt at date t depends only on the date t value of the Markov state that drives government expenditures. Lucas and Stokey failed to rationalize the permanent-income like predictions of Barro (1979) that put extensive history (2008) for axioms that rationalize multiplier preferences as expressions of model ambiguity. 3 dependence into tax rates and government debt. The impression that observed time series of government debt and taxes have apparently exhibited history dependence { observed series on government debt are much smoother series than the ones predicted by the Lucas-Stokey model and more like those in Barro's model { prompted Aiyagari et al. (2002) and Battaglini and Coate (2008) to put history dependence into a Ramsey plan, in the model of Aiyagari et al. (2002), or a political-economic bargaining equilibrium, in the model of Battaglini and Coate (2008), by dropping Lucas and Stokey's assumption of complete markets. In our setup, we retain the assumption of complete markets, but ¯nd that history dependence emerges as a consequence of optimal policy, reflecting the planner's management of the household's endogenous beliefs. For example, with quasi-linear preferences, dependence on the past can be quite striking: for small doubts about the model, we show that the tax rate becomes a random walk, whereas it would stay constant with full con¯dence in the model. We use tools from the recursive contracts literature and utilize the Marcet and Marimon (1998) method to ¯nd state variables with which to cast a recursive representation of the Ramsey problem. Two martingales capture the history dependence of the optimal allocation. What are the economic insights that emerge in our environment? Our state variables let us identify a novel intertemporal smoothing motive for the planner in the form of a desire to smooth the shadow value of the household's continuation value by making it a martingale. There is a simple intuition behind this ¯nding that underscores the price manipulation that partly motivates the planner: the planner strives to make consumption claims cheaper when he buys them and more expensive when he sells them, by manipulating the household's endogenous beliefs. To see that clearly, assume that the government expenditures take two values and that there is a sequence of high shocks. Complete markets allow the planner to hedge shocks by buying ex ante assets for the case of high shocks and selling ex ante assets (issuing government debt) for the case of low shocks.