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Tax Policy and Aggregate Demand Management Under Catching up with the Joneses

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Tax Policy and Aggregate Demand Management Under Catching up with the Joneses Tax Policy and Aggregate Demand Management Under Catching Up with the Joneses By LARS LJUNGQVIST AND HARALD UHLIG* This paper examines the role for tax policies in productivity-shock driven economies with catching-up-with-the-Joneses utility functions. The optimal tax policy is shown to affect the economy countercyclically via procyclical taxes, i.e., “cooling down” the economy with higher taxes when it is “overheating” in booms and “stimulating” the economy with lower taxes in recessions to keep consumption up. Thus, models with catching-up-with-the-Joneses utility functions call for traditional Keynesian demand-management policies but for rather unorthodox reasons. (JEL E21, E62, E63) Envy is one important motive of human be- the aggregate desire by other agents to “catch havior. In macroeconomics, theories built on up.” While this may not make much of a dif- envy have been used in trying to explain the ference for asset-pricing implications aside equity premium puzzle as described by Rajnish from convenience, it is interesting to take the Mehra and Edward C. Prescott (1985). Andrew externality implied by the “catching-up” formu- B. Abel (1990, 1999) and John Y. Campbell and lation seriously, and investigate its policy im- John H. Cochrane (1999) postulate utility func- plications. The externality allows room for tions exhibiting a desire to catch up with the beneficial government intervention: the optimal Joneses, i.e., if others consume more today, you, tax policy would induce agents in the competi- yourself, will experience a higher marginal util- tive equilibrium to behave in a first-best man- ity from an additional unit of consumption in ner, which is given by the solution to a social the future.1 In some ways, the idea of catching planner’s problem with habit formation. up with the Joneses is a variation of the theme While catching up with the Joneses has been of habit formation (see George M. Constantin- the focus of quite some research in the asset- ides, 1990). The key difference is that catching pricing literature, its implications with respect up with the Joneses postulates a consumption to policy-making have rarely been explored. externality since agents who increase their con- The purpose of this paper is to do exactly that. sumption do not take into account their effect on In particular, we examine economies driven by productivity shocks where agents care about consumption as well as leisure, and there is a * Ljungqvist: Stockholm School of Economics, Box 6501, “catching-up” term in the consumption part of SE-113 83 Stockholm, Sweden (e-mail: lars.ljungqvist@ the utility function. For simplicity, the model hhs.se); Uhlig: CentER, Tilburg University, Postbus 90153, 5000 LE Tilburg, The Netherlands (e-mail: [email protected]). abstracts from capital formation. In this frame- Both authors are affiliated with the Center for Economic Re- work, we examine the role for taxing labor search (CEPR). We are thankful to seminar participants at the income. The optimal tax policy turns out to Federal Reserve Bank of Chicago, IIES at Stockholm Univer- affect the economy countercyclically via procy- sity, Stanford University, and London School of Economics, as clical taxes, i.e., “cooling down” the economy well as to three anonymous referees for suggestions that im- proved the paper. The paper was originally circulated under the with higher taxes when it is “overheating” due title “Catching Up with the Keynesians.” Ljungqvist’s research to a positive productivity shock. The explana- was supported by a grant from the Bank of Sweden Tercente- tion is that agents would otherwise end up nary Foundation. consuming too much in boom times since they 1 Jordi Galı´ (1994) explores an alternative assumption where agents’ preferences depend on current, instead of are not taking into account the “addiction ef- lagged, per capita consumption (keeping up with the Jone- fect” of a higher consumption level. In reces- ses as compared to catching up with the Joneses). sions, the effect goes the other way around and 356 VOL. 90 NO. 3 LJUNGQVIST AND UHLIG: CATCHING UP WITH THE JONESES 357 taxes should be lowered to “stimulate” the econ- the leisure part of the utility function. In other omy by bolstering consumption. Thus, models words, we assume that agents are competing in, with catching-up-with-the-Joneses utility func- say, having the biggest car or the biggest house tions call for traditional Keynesian demand- rather than having the most amount of leisure. management policies but for rather unorthodox The utility in leisure is also assumed to be reasons. linear. This assumption is partly done for con- The paper is organized as follows. In Section I, venience, but can also be motivated by indivis- we examine a simple one-shot model as well as an ibilities in the labor market and is an often-used infinite-horizon version, where agents care about assumption in the real-business-cycle literature keeping up with the Joneses. The assumption is (see, e.g., Gary D. Hansen [1985] and the ex- that contemporaneous average consumption planations therein). across all agents enters the utility function. In that We imagine that the production function case, it turns out that there is a constant tax rate on takes the form labor, which delivers the first-best outcome inde- pendent of the productivity shock. In Section II, (1) y ϭ ␪n, we allow the agents’ benchmark level to be a geometric average of past per capita consumption, i.e., specifying a utility function which exhibits where y is output per worker and ␪ is a produc- catching up with the Joneses. The optimal tax rate tivity parameter. Thus, there is no capital, and is now found to vary positively with the produc- output is simply linear in labor. tivity shock, and we explore the determinants, The government levies a flat tax ␶ on all labor dynamics, and welfare implications of such a income and the tax revenues are then handed countercyclical demand policy. Section III back to the agents in a lump-sum fashion. Let ␷ concludes. be the lump-sum transfer to each agent. Since all agents are identical, the government’s bud- get constraint can be written as I. Keeping Up with the Joneses ␷ ϭ ␶y. We imagine an economy with many consum- ers, each with the same utility function A competitive equilibrium is calculated by having an agent maximize the utility function above with respect to c and n subject to his ͑c Ϫ ␣C͒1 Ϫ ␥ Ϫ 1 Ϫ An, budget constraint, 1 Ϫ ␥ c ϭ ͑1 Ϫ ␶͒y ϩ ␷ ϭ ͑1 Ϫ ␶͒␪n ϩ ␷. where c Ն 0 is the individual’s consumption, C Ն 0 is average consumption across all agents, A consumer’s optimal consumption is then and n Ն 0 is labor supplied by the individual. found to be The parameters ␣ ʦ [0, 1), ␥ Ն 0, and A Ͼ 0 determine the relative importance of average ␪ 1/␥ (2) c ϭ ␣C ϩ ͑1 Ϫ ␶͒ , consumption, the curvature of the consumption ͩ A ͪ term, and the relative importance of leisure. This utility function captures the notion of keep- where average consumption C is taken as given ing up with the Joneses, i.e., average consump- by the individual agent. However, in an equi- tion decreases an individual’s level of utility librium it must be true that c ϭ C, so the and increases his marginal utility of an addi- equilibrium consumption level is tional unit of consumption. This specification is different from the formulations in Abel (1990, 1 ␪ 1/␥ 1999), who uses ratios, rather than differences, (3) c ϭ C ϭ ͑1 Ϫ ␶͒ . to aggregate consumption, but is in line with the 1 Ϫ ␣ ͩ A ͪ “catching-up” formulation in Campbell and Co- chrane (1999). No “keeping up” is imposed on The government’s optimal choice of ␶ can be 358 THE AMERICAN ECONOMIC REVIEW JUNE 2000 deduced from the solution to the social plan- yt ϭ ␪t nt , ner’s problem. The social planner would take the externality into account by setting c ϭ C in the utility function above, and then maximize and so are the budget constraints of the govern- with respect to consumption and labor subject to ment and the agents. There is no capital forma- the technology constraint. The first-best out- tion. There is now also some stochastic process come is then given by driving productivity ␪t. Computing the compet- itive equilibrium and the social planner’s solu- tion amounts to the same calculations as above, 1 ␪ 1/␥ since this dynamic model simply breaks into a C* ϭ ͑1 Ϫ ␣͒ . 1 Ϫ ␣ ͩ A ͪ sequence of one-shot models. The first-best so- lution is again achieved at ␶ ϭ ␣, i.e., there are no cyclical consequences for the tax rate. Comparing the social planner’s solution to the The parameter ␣ governing the optimal tax competitive equilibrium, we find the following rate also ties in with the value for the relative proposition. risk aversion ␩ for gambles with respect to consumption, given by ␩ ϭ ␥/(1 Ϫ ␣) from PROPOSITION 1 (Keeping Up with the the perspective of the individual agent, but Joneses): The first-best consumption allocation given by ␩SP ϭ ␥ from the perspective of the can be achieved with a tax rate social planner, taking into account ct ϭ Ct. The social planner would thus be willing to ␶ ϭ ␣. forgo a premium as a fraction of mean con- sumption approximately equal to ␥␴2/2 to avoid mean-zero random fluctuations in ag- This result is quite intuitive. A fraction ␣ of any gregate consumption with a standard devia- ␴ percent. This is also the ء increase in the representative agent’s consump- tion of 100 tion does not contribute to his utility since it is premium an individual agent would pay if that offset through the consumption externality.
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