Time-Consistent Policy

The goal of this paper is to study optimal government policy when there is no way of committing to future policy and this restriction is binding. The paper has a methodological part and an applied part. The applied part analyzes the optimal choice of government expenditures when the financing of these expenditures involves distortionary taxation and has dynamic consequences—we are studying a simple but canonical dynamic public economics problem here. The analysis is quantitative: we ask how big the expenditures ought to be, and how they ought to be financed, given that only proportional taxation (on labor or capital income) is feasible. The methodological part develops methods that follow up on Kydland and Prescott’s (1977) analysis: we show how to characterize, theoretically and numerically, time-consistent policy. By time-consistent policy we mean that made by a government rationally foreseeing how any of its future counterparts will respond to the initial conditions given to it by the past. Moreover, our focus is on policy outcomes where reputation has no role to play at all. That is, even though our environment may admit trigger mechanisms à la Chari and Kehoe (1990), allowing both better and worse equilibria than the one we look at, our goal is to establish precisely how to find the reputation-free, or “fundamental”, equilibrium. Formally, the central object we search for is a smooth function mapping the directly payoff-relevant state variables into policy. We show that this function has to satisfy a key first-order condition for the government: a generalized Euler equation, which is a functional equation. This equation can be interpreted in several intuitive ways, reflecting both traditional public finance and macroeconomic analysis, and it shows how state variables such as the stock of capital actually does allow the current government to achieve dynamic goals also when reputation cannot be used. Finally, we show how to solve this equation numerically.