Steady-state 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. Sticky prices as coordination failure. American Economic Review 81 (3), 539-552], however, suggests that such models may be rife with multiple equilibria, for in their static model, price adjustment is always characterized by complementarity, a necessary condition for multiplicity. We study existence and uniqueness of steady-state equilibrium in a discrete-time state-dependent pricing model. We find only weak complementarity and no evidence of multiplicity. However, nonexistence of symmetric steady-state equilibrium with pure strategies arises in the region of the parameter space between flexible and sticky prices.     

The Phillips curve under state-dependent pricing

We derive a Phillips curve equation from the dynamic stochastic general equilibrium (DSGE) model with state-dependent pricing developed by Dotsey et al. [1999. State-dependent pricing and the general equilibrium dynamics of money and output. Quarterly Journal of Economics 114, 655-690]. This state-dependent Phillips curve encompasses the new Keynesian Phillips curve (NKPC) based on Calvo-type price setting as a special case. We analyze the effect of the state-dependent terms (that is, the variations in the distributions of price vintages) on inflation persistence, and we examine whether the hybrid NKPC (that is, the NKPC extended by a lagged inflation term) can adequately describe inflation dynamics generated in a calibrated state-dependent pricing economy.     

Inflation dynamics: A cross-country investigation

We document that “persistent and lagged” inflation (with respect to output) is a world-wide phenomenon in that these short-run inflation dynamics are highly synchronized across countries. In particular, the average cross-country correlation of inflation is significantly and systematically stronger than that of output, while the cross-country correlation of money growth is essentially zero. We investigate whether standard monetary models driven by monetary shocks are consistent with the empirical facts. We find that neither the new Keynesian sticky-price model nor the sticky-information model can fully explain the data. An independent contribution of the paper is to provide a simple solution technique for solving general equilibrium models with sticky information.     

New measures of the output gap based on the forward-looking new Keynesian Phillips curve

Forward-looking versions of the New Keynesian Phillips curve imply that the output gap, the deviation of the actual output from its natural level due to nominal rigidities, drives the dynamics of inflation relative to expected inflation. We exploit this to set up a bivariate unobserved component model for extracting new estimates of the output gap in the US. The gap estimates are large and persistent even after allowing for correlated trend and cycle shock. We then augment our model to use the information in the unemployment rate. The estimates confirm the presence of a large and persistent cyclical component.     

The Macroeconomic Effects of Nonzero Trend Inflation

We study the macroeconomic effects of nonzero trend inflation in a simple dynamic stochastic general equilibrium model under three common time-dependent pricing schemes: Calvo, truncated-Calvo, and Taylor. We show that, regardless of the pricing mechanism, trend inflation leads to a reduction in the stochastic means of output, consumption and employment, and an increase in the stochastic mean of inflation beyond its deterministic steady-state level. The variability of most aggregates also increases. These effects are quantitatively much stronger with Calvo pricing.     

Changes in the Federal Reserve's Inflation Target: Causes and Consequences

This paper estimates a New Keynesian model to draw inferences about the behavior of the Federal Reserve's unobserved inflation target. The results indicate that the target rose from 1 1/4% in 1959 to over 8% in the mid to late 1970s before falling back below 2 1/2% in 2004. The results also provide some support for the hypothesis that over the entire post-war period, Federal Reserve policy has systematically translated short-run price pressures set off by supply-side shocks into more persistent movements in inflation itself, although considerable uncertainty remains about the true source of shifts in the inflation target.     

Inflation targeting and nominal-income-growth targeting: When and why are they suboptimal?

We compare optimal and simple interest-rate rules. Our model features optimizing agents, monopolistic competition in both product and labor markets, and one-period nominal contracts (for wages alone or for both wages and prices) signed before shocks are known. Exact solutions ensure that we obtain correct welfare rankings. Optimal rules maximize the unconditional expected utility of the representative agent with commitment subject to the information set of the policymaker. Even with monopolistic distortions, the optimal full-information rule makes the economy mimic the hypothetical full-flexibility equilibrium. Strict versions of inflation targeting, nominal-income-growth targeting, and other such simple rules are suboptimal under both full and partial information but flexible versions are optimal under certain partial-information assumptions. Nominal-income-growth targeting dominates inflation targeting for plausible parameter values.     

Inflation targeting: What inflation rate to target?

In an economy with nominal rigidities in both an intermediate good sector and a finished good sector, and thus with a natural distinction between CPI and PPI inflation rates, a benevolent central bank faces a tradeoff between stabilizing the two measures of inflation, a final output gap and, unique to our model, a real marginal cost gap in the intermediate sector, so that optimal monetary policy is second-best. We discuss how to implement the optimal policy with minimal information requirement and evaluate the robustness of these simple rules when the central bank may not know the exact sources of shocks or nominal rigidities. A main finding is that a simple hybrid rule under which the short-term interest rate responds to CPI inflation and PPI inflation results in a welfare level close to the optimum, whereas policy rules that ignore PPI inflation or PPI sector shocks can result in significant welfare losses.     

Quantifying the uncertainty about the fit of a new Keynesian pricing model

Recent studies by Gali and Gertler [1999. Inflation dynamics: a structural econometric analysis, Journal of Monetary Economics 44, 195-222] and Sbordone [2002. Prices and unit labor costs: testing models of pricing, Journal of Monetary Economics 49, 265-292] conclude that a theoretical inflation series implied by a forward-looking New Keynesian pricing equation fits post-1960 U.S. inflation closely. Their theoretical inflation series is conditional on (i) a reduced-form forecasting process for real marginal cost; and (ii) the calibration of the pricing equation. The present paper shows that both of these determinants are surrounded by considerable uncertainty. When quantifying the impact of this uncertainty on theoretical inflation, we can no longer say whether the forward-looking pricing equation explains observed inflation dynamics very well or very poorly.     

When do firms adjust prices? Evidence from micro panel data

The price-setting behavior of manufacturing firms is examined using a large panel of quarterly firm survey data from 1984 to 2007, which allows changes in firms’ prices to be linked to several firm-specific variables. The results show that state-dependent pricing is clearly present in a low-inflation environment and that variables measuring the current situation of the firm, especially costs for intermediate products, are important determinants of price adjustments. Compared to purely time-dependent features, the state-dependent variables significantly add to the explanatory power of a price adjustment probability model. Macroeconomic factors are significant but contribute little in terms of the goodness of fit. Furthermore, when taking into account sticky plan models by excluding possibly predetermined price changes, the importance of state-dependent factors becomes even greater.     

Do expected future marginal costs drive inflation dynamics?

This article discusses a more general interpretation of the two-step minimum distance estimation procedure proposed in Sbordone (2002). The estimator is again applied to a version of the New Keynesian Phillips curve, where inflation dynamics are driven by the expected evolution of marginal costs. The article clarifies econometric issues, addresses concerns about uncertainty and model misspecification raised in recent studies, and assesses the robustness of previous results. While confirming the importance of forward-looking terms in accounting for inflation dynamics, it suggests how the methodology can be applied to extend the analysis of inflation to a multivariate setting.     

Technology shocks and labor market dynamics: Some evidence and theory

A positive technology shock may lead to a rise or a fall in per capita hours, depending on how hours enter the empirical VAR model. We provide evidence that, independent of how hours enter the VAR, a positive technology shock leads to a weak response in nominal wage inflation, a modest decline in price inflation, and a modest rise in the real wage in the short-run and a permanent rise in the long-run. We then examine the ability of several competing theories to account for this VAR evidence. Our preferred model features sticky prices, sticky nominal wages, and habit formation. The same model also does well in accounting for the labor market evidence in the post-Volcker period.     

Price Stickiness and Sectoral Inflation Persistence: Additional Evidence

In this paper, using U.S. as well as French sectoral data and indicators of price rigidity, we reexamine the (lack of) relation between price stickiness and inflation persistence. This has recently been put forward by Bils and Klenow (2004) as evidence against time‐dependent price setting models. We obtain that, when filtering out sector‐specific shocks along the lines of Boivin, Giannoni, and Mihov (2009), and allowing for an alternative assumption on the marginal cost process, the case against the time‐dependent Calvo model is substantially weakened.     

What Makes the Output–Inflation Trade‐Off Change? The Absence of Accelerating Deflation in Japan

It is standard to model the output–inflation trade-off as a linear relationship with a time-invariant slope. We assess empirical evidence for two sets of theories that allow for endogenous variation in the slope of the short-run Phillips curve. At an empirical level, we examine why large negative output gaps in Japan in the late 1990s did not lead to accelerating deflation but instead coincided with stable, albeit moderately negative inflation. Our results suggest that this episode is most convincingly interpreted as reflecting a gradual flattening of the Phillips curve. We find that this flattening is best explained by models with endogenous price durations. These models imply that in any economy where trend inflation is substantially lower (or substantially higher) today than in past decades, time variation in the slope of the Phillips curve has become too important to ignore.     

Relative Prices as Aggregate Supply Shocks with Trend Inflation

Ball and Mankiw (1995) use a static menu-cost model to explain the historical behavior of the first and higher moments of commodity price changes in U.S. producer prices. We show that when appropriately modified for a world of positive trend inflation and forward-looking behavior by firms, the menu-cost model predicts a much weaker (possibly zero) correlation between the mean and the skewness of price changes than that found in the data.     

Financing constraints, irreversibility, and investment dynamics

We develop a model of an industry with many heterogeneous firms that face both financing constraints and irreversibility constraints. We use this model to examine the cyclical behavior of aggregate fixed investment, variable capital investment, and output in the presence of persistent idiosyncratic and aggregate shocks. Our model yields three main results. First, the effect of the irreversibility constraint on fixed capital investment is reinforced by the financing constraint. Second, the effect of the financing constraint on variable capital investment is reinforced by the irreversibility constraint. Finally, the interaction between the two constraints is key for explaining why input inventories and material deliveries of US manufacturing firms are so volatile and procyclical, and also why they are highly asymmetrical over the business cycle.     

Distributional dynamics under smoothly state-dependent pricing

Starting from the assumption that firms are more likely to adjust their prices when doing so is more valuable, this paper analyzes monetary policy shocks in a DSGE model with firm-level heterogeneity. The model is calibrated to retail price microdata, and inflation responses are decomposed into “intensive”, “extensive”, and “selection” margins. Money growth and Taylor rule shocks both have nontrivial real effects, because the low state dependence implied by the data rules out the strong selection effect associated with fixed menu costs. The response to sector-specific shocks is gradual, but inappropriate econometrics might make it appear immediate.     

Implications of state-dependent pricing for dynamic macroeconomic models

State-dependent pricing (SDP) models treat the timing of price changes as a profit-maximizing choice, symmetrically with other decisions of firms. Using quantitative general equilibrium models which incorporate a “generalized (S,s) approach,” we investigate the implications of SDP for topics in two major areas of macroeconomic research, the early 1990s SDP literature and more recent work on persistence mechanisms. First, we show that state-dependent pricing leads to unusual macroeconomic dynamics, which occur because of the timing of price adjustments chosen by firms as in the earlier literature. In particular, we display an example in which output responses peak at about a year, while inflation responses peak at about 2 years after the shock. Second, we examine whether the persistence-enhancing effects of two New Keynesian model features, namely specific factor markets and variable elasticity demand curves, depend importantly on whether pricing is state dependent. In an SDP setting, we provide examples in which specific factor markets perversely work to lower persistence, while variable elasticity demand raises it.     

Investment dynamics with fixed capital adjustment cost and capital market imperfections

This paper examines the implications of financing frictions on capital stocks and on capital accumulation in the presence of non-convex costs of adjusting the capital stock. In this setup finance has an influence on both, the level of capital and the timing of investment. Finance and productivity are complements and finance influences investment the strongest when firms wish to significantly adjust capital for fundamental reasons. These theoretical considerations are confronted with UK data. While finance is mostly irrelevant for long-term capital decision, the short-run investment function shows a significant impact of finance, which is also strongest for strong fundamental investment incentives.     

Survey Measures of Expected Inflation and the Inflation Process

The accuracy of inflation forecasts obtained from household and professional surveys has deteriorated noticeably of late, to the extent that a simple autoregressive specification outperforms survey forecasts. The decline in (absolute and relative) accuracy has taken place at about the same time as an apparent change in the inflation process. Projections of household forecasts on realized inflation suggests that households have not recognized this change. For the professionals, projections of expected inflation on headline inflation have changed, but on core inflation have not. By contrast, projections of realized headline inflation on core have changed sharply.