Alexander L. Wolman

State-Dependent Pricing and the General Equilibrium Dynamics of Money and Output

Economists have long suggested that nominal product prices are changed infrequently because of fixed costs. In such a setting, optimal price adjustment should depend on the state of the economy. Yet, while widely discussed, statedependent pricing has proved difficult to incorporate into macroeconomic models. This paper develops a new, tractable theoretical state-dependent pricing framework. We use it to study how optimal pricing depends on the persistence of monetary shocks, the elasticities of labor supply and goods demand, and the interest sensitivity of money demand.

Real Implications of the Zero Bound on Nominal Interest Rates

If monetary policy succeeds in keeping average inflation very low, nominal interest rates may occasionally be constrained by the zero lower bound. The degree to which this constraint has real implications depends on the monetary policy feedback rule and the structure of price-setting. Policy rules that make the price level stationary lead to small real distortions from the zero bound. If policy imparts persistence into the inflation rate, the real implications of the zero bound are large in the presence of backward looking price-setting, and small if prices are set to maximize profits.

Fiscal Policy and Regional Inflation in a Currency Union

This paper investigates the ability of a region participating in a currency union to affect its inflation differential with respect to the union through fiscal policy. We study the interaction between regional fiscal policy and inflation differentials in a flexible-price, two-region model with both traded and nontraded goods. For symmetric regions, changes in one region’s tax rule that decrease the volatility of its inflation differential also decrease the volatility of its output. The decrease in the volatility of the inflation differential is brought about by an increase in the volatility of tax rates. The effect of the tax rule on output volatility – but not inflation volatility – depends on country size. For a small country lower volatility of inflation differentials is associated with higher volatility of output. This relationship results from the fact that small countries are more open, and hence there is a greater role for traded goods productivity shocks.

State Dependent Pricing and Dynamics of Business Cycles

The nature of price dynamics has long been thought important for the origin and duration of business cycles. To investigate this topic, we construct a dynamic stochastic general equilibrium macroeconomic model in which monopolistically competitive firms face fixed costs of changing the nominal prices of final goods. These prices are thus changed infrequently and discretely. The framework captures major features of the price dynamics stressed by the New Keynesian research program, particularly work on (s, S) pricing rules. However, by treating firms as heterogenous with respect to the size of fixed costs of price adjustment, we are able to study a wider range of issues than in the prior literature. For example, we explore how the nature of optimal price-setting depends on (i) the extent of persistence of variations in the money stock and (ii) the interest elasticity of money demand. Further, our model can be used to study a wide range of aspects of the positive and normative economics of monetary policy. We illustrate these topics by considering the consequences of changing the rate of inflation and by evaluating alternative policy rules.

The Optimal Rate of Inflation with Trending Relative Prices

The relative prices of different categories of consumption goods have been trending over time. Assuming they are exogenous with respect to monetary policy, these trends imply that monetary policy cannot stabilize the prices of all consumption categories. If prices are sticky, monetary policy then must trade off relative price distortions within different categories of consumption. Optimally, more weight should be placed on stabilizing goods and services prices that are less flexible. Calibrating a simple sticky price model to U.S. data, we find that slight deflation is optimal, even absent transactions frictions leading to a demand for money. Optimality of deflation derives from the fact that relative prices have been trending up for services, whose nominal prices seem to be less flexible.

Discretionary Monetary Policy in the Calvo Model

We study discretionary equilibrium in the Calvo pricing model for a monetary authority that chooses the money supply. The steady-state inflation rate is above 8 percent for a baseline calibration, but it varies substantially with alternative structural parameter values. If the initial condition involves inflation higher than steady state, discretionary policy generates an immediate drop in inflation followed by a gradual increase to the steady state. Unlike the two-period Taylor model, discretionary policy in the Calvo model does not accommodate predetermined prices in a way that inevitably leads to multiple private-sector equilibria.

Payment Choice and the Future of Currency: Insights from Two Billion Retail Transactions

This paper uses transaction-level data from a large discount chain together with zip-code-level explanatory variables to learn about consumer payment choices across size of transaction, location, and time. With three years of data from thousands of stores across the country, we identify important economic and demographic effects; weekly, monthly, and seasonal cycles in payments, as well as time trends and significant state-level variation that is not accounted for by the explanatory variables. We use the estimated model to forecast how the mix of consumer payments will evolve and to forecast future demand for currency. Our estimates based on this large retailer, together with forecasts for the explanatory variables, lead to a benchmark prediction that the cash share of retail sales will decline by 2.54 percentage points per year over the next several years.

Does State-Dependent Pricing Imply Coordination Failure?

The analysis in Ball and Romer [1991] suggests that models with fixed costs of changing price may be rife with multiple equilibria; in their static model price adjustment is always characterized by strategic complementarity, a necessary condition for multiplicity. We extend Ball and Romers analysis to a dynamic setting. In steady states of the dynamic model, we find only weak complementarity and no evidence of multiplicity, although nonexistence of symmetric steady state with pure strategies does arise in a small number of cases.

An inquiry into the existence and uniqueness of equilibrium with state-dependent pricing

State-dependent pricing models are now an operational framework for quantitative business cycle analysis. The analysis in Ball and Romer [1991], however, suggests that such models may be rife with multiple equilibria: in their static model price adjustment is always characterized by complementarity, a necessary condition for multiplicity. We study existence and uniqueness of equilibrium in a discrete-time state-dependent pricing model. In steady states of our model, we find only weak complementarity and no evidence of multiplicity. We likewise find no evidence of multiplicity in the presence of monetary shocks. However, nonexistence of symmetric steady-state equilibrium with pure strategies arises in a small region of the parameter space.

The Pitfalls of Monetary Discretion

In a canonical staggered pricing model, monetary discretion leads to multiple private sector equilibria. The basis for multiplicity is a form of policy complementarity. Specifically, prices set in the current period embed expectations about future policy, and actual future policy responds to these same prices. For a range of values of the fundamental state variable — a ratio of predetermined prices — there is complementarity between actual and expected policy, and multiple equilibria occur. Moreover, this multiplicity is not associated with reputational considerations: it occurs in a two-period model.