We re-examine the optimality of tax smoothing from the point of view of frictional labor markets. Since Barro’s (1979) partial-equilibrium intuition, Lucas and Stokey’s (1983) general-equilibrium analysis, and continuing through to today’s quantitative DSGE models used to study optimal fiscal policy, the prescription that governments ought to hold labor tax rates virtually constant in the face of aggregate shocks is well-known to macroeconomists. We show that this cornerstone optimal-policy prescription and the intuition underlying it depend crucially on a Walrasian view of labor markets. If one instead takes what has emerged as the standard search and bargaining view of labor markets, tax-smoothing ceases to be important for empirically-relevant labor market parameters. If wages are determined in bilateral bargaining after workers and firms meet, not only is tax-smoothing unimportant, but purposeful tax-rate volatility is actually welfare-enhancing by partially offsetting cyclical bargaining-induced wedges.
Our baseline search and bargaining environment is identical to the one that has come into widespread use in recent DSGE modeling efforts. We quantitatively demonstrate the optimality of labor tax-rate volatility in this environment. In an effort to recover tax smoothing, we then incrementally alter the environment in a number of ways, each of which in principle reduces the severity of search and bargaining frictions. In particular, we change the timing of labor market flows, introduce a labor-force participation margin, and allow for wages to be determined in a competitive fashion, rather than through ex-post bilateral bargaining. Changing the timing of labor market flows and allowing a labor-force participation choice each, as well as together, only modestly reduces the degree of optimal tax-rate volatility.
However, allowing for competitive determination of wages — using Moen’s (1997) concept of competitive search equilibrium, in which ex-ante posted wages direct search activity — is a critical change in market structure that reinstates the optimality of tax smoothing. For the competitive search economy, we show analytically that it is only labor taxes that create relatively-standard static wedges between marginal rates of substitution between consumption and leisure and corresponding marginal rates of transformation. The usual reasons for tax smoothing — that wedges between this MRS and MRT should be kept (nearly) constant over time — then apply. As a methodological by-product of our analysis, we are, to the best of our knowledge, the first to provide a simple MRT interpretation for a labor-search model, one that differs from the notion of MRT in standard neoclassical model of the labor market.
If wages are determined by ex-post bilateral bargaining, proportional labor taxes affect the labor market in a dramatically different way. We identify two distinct roles played by the labor tax in our bargaining environments: the usual static role, in which a positive labor tax wedge is needed period by-period in order to raise revenue for the government, and a novel dynamic role, in which changes in tax rates affect private-sector search activity. Thus, for any given level of the labor tax rate in period t, the change in the tax rate is a distinct lever that the Ramsey government can use as a way of directing labor-market outcomes over the business cycle. This dynamic role of labor taxes — which we refer to as a dynamic bargaining power effect — only arises in the environment with bilateral bargaining and can only be revealed in an explicitly dynamic analysis.
The key difference between the two market structures, which drives the stark difference in optimal-policy prescriptions, is the fundamental forces underlying wage determination. In the competitive search economy, posted wages allow unemployed individuals to optimally direct their search activity in the labor market, which in turn generates competition amongst wage-setting firms. This competition ensures private-sector labor-market activity is efficient up to the static tax wedge — over the business cycle, much like in standard Walrasian-based Ramsey models; hence the prescription to smooth tax rates over time.
Contents
1 Introduction
2 Baseline Model
2.1 Production
2.2 Households
2.3 Wage Bargaining
2.4 Government
2.5 Matching Technology
2.6 Private-Sector Equilibrium
3 Ramsey Problem in Baseline Model
4 Optimal Taxation in Baseline Model
4.1 Parameterization and Solution Strategy
4.2 Main Result: The Optimality of Tax Volatility
4.3 Recovering Tax Smoothing in the Baseline Model
5 Alternative Views of the Labor Market
5.1 Instantaneous Hiring (Model 2)
- 5.1.1 Modifications of the Model
5.1.2 Optimal Taxation
5.2 Endogenous Labor Force Participation
- 5.2.1 Baseline Timing Assumption (Model 3)
5.2.2 Instantaneous Hiring (Model 4)
5.2.3 Optimal Taxation
5.3 Competitive Search Equilibrium (Model 5)
- 5.3.1 Modifications of the Model
5.3.2 Static Tax Wedge
5.3.3 Optimal Taxation
6 Summary and Discussion
7 Conclusion
A Nash Bargaining in Model with Standard Timing
B Nash Bargaining in Model with Instantaneous Hiring
C Elasticity of Market Tightness to Labor Tax Rate
D Derivation of Implementability Constraint
E Dynamic Bargaining Power Effect
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