How Robust Are Popular Models of Nominal Frictions?

We consider alternative combinations of nominal price and wage frictions in dynamic stochastic general equilibrium models fit to U.S. data. Since inflation was unanchored in the 1970s, we divide the data into early, middle, and late samples (1955–68, 1969–79, and 1983–2007, respectively). We find that prices are reoptimized more frequently and exhibit greater indexation to past inflation in the middle sample than in the other two samples, while wages are reoptimized with increasing frequency and display less evidence of indexation over time. Differences in price and wage setting across samples have important implications for the economy's response to key shocks.     

Price stickiness in Ss models: New interpretations of old results

What is the relation between infrequent price adjustment and the dynamic response of the aggregate price level to monetary shocks? The answer to this question ranges from a one-to-one link [Calvo, G., 1983. Prices in a utility maximizing framework. Journal of Monetary Economics 12, 383–398] to no connection whatsoever [Caplin, A., Spulber, D., 1987. Menu costs and the neutrality of money. Quarterly Journal of Economics 102, 703–726]. The purpose of this paper is to provide a unified framework to understand the mechanisms behind this wide range of results. In doing so, we propose new interpretations of key results in this area, which in turn suggest the kind of Ss model that is likely to generate substantial price rigidity. Among these new interpretations, we revisit Caplin and Spulber's monetary neutrality result. We show that when price stickiness is measured in terms of the impulse response function, this result is not a consequence of aggregation, as is often assumed, but is due instead to the absence of price stickiness at the microeconomic level. We also show that the “selection effect,” according to which units that adjust their prices are those that benefit the most, is neither necessary nor sufficient to account for the higher aggregate flexibility of Ss-type models compared to Calvo models. Instead, the key concept is the contribution of the extensive margin of adjustment to the aggregate price response. The aggregate price level is more flexible than suggested by the microeconomic frequency of adjustment if and only if this term is positive.     

An open-economy new Keynesian Phillips curve for the U.K.

We estimate a pricing equation or “new Keynesian Phillips curve” (NKPC) obtained from a structural dynamic model of price setting based on Rotemberg [1982. Sticky prices in the United States. Journal of Political Economy 90(6), 1187-1211] and extended to capture employment adjustment costs and the openness of the United Kingdom. This model nests the baseline Galí and Gertler [1999. Inflation dynamics: a structural econometric analysis. Quarterly Journal of Economics 110, 127-159) and Sbordone [2002. Prices and unit labor costs: a new test of price stickiness. Journal of Monetary Economics 49, 265-292] relationship between inflation and marginal cost in the limiting case of no employment adjustment costs, no impact of relative prices of imported inputs on real marginal cost and a constant equilibrium markup. Our findings indicate that each of our modifications to the baseline NKPC model is important for U.K. data, so that inflation in the U.K. is explained both by changes in employment and by changes in real import prices, in general, and real oil prices, in particular. External competitive pressures also seem to affect U.K. inflation via their impact on the equilibrium price markup of domestic firms.     

How Do Nominal and Real Rigidities Interact? A Tale of the Second Best

This paper analyzes the importance of real wage rigidities, in particular through their interaction with price stickiness, in a New Keynesian model. Real wage rigidities result from a combination of staggered wage setting and partial indexation of nonreset wages to past inflation. Blanchard and Galí (2007) show real rigidities to introduce a trade‐off between stabilizing inflation and the welfare‐relevant output gap. The present paper complements their findings by showing that the welfare costs of real rigidities can be substantial compared to nominal frictions. In a typical “tale of the second best,” we also show that in the presence of real wage rigidities, higher price stickiness can be welfare enhancing.     

Expectations, learning and macroeconomic persistence

Monetary DGSE models under rational expectations typically require large degrees of features as habit formation in consumption and inflation indexation to match the inertia of macroeconomic variables.This paper presents an estimated model that departs from rational expectations and nests learning by economic agents, habits, and indexation. Bayesian methods facilitate the joint estimation of the learning gain coefficient together with the ‘deep’ parameters of the economy.The empirical results show that when learning replaces rational expectations, the estimated degrees of habits and indexation drop closer to zero, suggesting that persistence arises in the model economy mainly from expectations and learning.     

Nonuniform Staggered Prices and Output Persistence

Staggered prices are a fundamental building block of New Keynesian dynamic stochastic general equilibrium models. In the standard model, prices are uniformly staggered, but recent empirical evidence suggests that deviations from uniform staggering are common. This paper analyzes how synchronization of price changes affects the response to monetary policy shocks. I find that even large deviations from uniform staggering have small effects on the response of output. Aggregate dynamics in a model of uniform staggering may serve well as an approximation to a more complicated model with some degree of synchronization in price setting.     

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.     

Optimal monetary policy in a small open economy with staggered wage and price contracts

We study optimal monetary policy for a small open economy in a model where both domestic prices and wages are sticky due to staggered contracts. The simultaneous presence of the two forms of nominal rigidities introduces an additional trade-off between domestic inflation and the output gap. We derive a second-order approximation to the average welfare losses that can be expressed in terms of the unconditional variances of the output gap, domestic price inflation, and wage inflation. As a consequence, the optimal policy seeks to minimize a weighted average of these variances. We analyze welfare implications of several alternative simple policy rules, and find that domestic price inflation targeting generates relatively large welfare losses, whereas CPI inflation targeting performs nearly as well as the optimal rule.     

Discretionary monetary policy and inflation persistence

Rational expectations models of staggered price/wage contracts have failed to replicate the observed persistence in inflation and unemployment during disinflationary periods. The current literature on this persistency puzzle has focused on augmenting the nominal contract model with imperfect credibility and learning. In this paper, I re-examine the persistency puzzle by focusing on the discretionary nature of monetary policy. I show that when the central bank is allowed to re-optimize a quadratic loss function each period, imperfect credibility and learning, even in the absence of staggered contracts, can generate a significant amount of inflation persistence and employment losses during a disinflationary period.     

How Sticky Is Sticky Enough? A Distributional and Impulse Response Analysis of New Keynesian DSGE Models

In this paper, we add to the literature on the assessment of how well data simulated from new-Keynesian dynamic stochastic general equilibrium (DSGE) models reproduce the dynamic features of historical data. In particular, we evaluate sticky price, sticky price with dynamic indexation, and sticky information models using impulse response and correlation measures and via implementation of a distribution based approach for comparing (possibly) misspecified DSGE models using simulated and historical inflation and output gap data. One of our main findings is that for a standard level of stickiness (i.e., annual price or information adjustment), the sticky price model with indexation dominates other models. We also find that when a lower level of information and price stickiness is used (i.e., bi-annual adjustment), there is much less to choose between the models (see Bils and Klenow 2004 , for evidence in favor of lower levels of stickiness). This finding is due to the fact that simulated and historical densities are "much" closer under bi-annual adjustment.     

Sticky information and sticky prices

In the U.S. and Europe, prices change at least once a year. Yet nominal macro shocks seem to have real effects lasting well beyond a year. “Sticky information” models, as posited by Mankiw and Reis [2002. Sticky information versus sticky prices: a proposal to replace the new Keynesian Phillips curve. Quarterly Journal of Economics 117, 1295–1328], Sims [2003. Implications of rational inattention. Journal of Monetary Economics 50(3), 665–690], and Woodford [2003. Princeton University Press: Princeton, NJ], can reconcile micro flexibility with macro rigidity. We simulate a sticky information model in which price setters update information on macro shocks less frequently than information on micro shocks. We then examine price changes in the micro data underlying the U.S. CPI. Empirical price changes react to old information, just as sticky information models predict.     

New tests of the new-Keynesian Phillips curve

Lagged dependent variables typically play an important role in empirical models of inflation. Do these lags reflect backward-looking inflation expectations, or do they proxy for rational forward-looking expectations, as in the new-Keynesian Phillips curve? Galí and Gertler [1999. Inflation dynamics: a structural econometric analysis. Journal of Monetary Economics 44, 195-222] attempt to answer this question using GMM to estimate specifications incorporating both lagged and future inflation. They report small coefficients on lagged inflation and conclude that the new-Keynesian model provides a good first approximation to inflation dynamics. We show that these tests have low power against alternative backward-looking specifications, and demonstrate that their results are also consistent with a backward-looking Phillips curve. Using an alternative approach, we find that the new-Keynesian pricing model cannot explain the importance of lagged inflation in standard inflation regressions, and find that forward-looking terms play a very limited role in explaining inflation dynamics.     

Trend inflation, wage and price rigidities, and productivity growth

What are the steady-state implications of inflation in a general-equilibrium model with real per capita output growth and staggered nominal price and wage contracts? Surprisingly, a benchmark calibration implies an optimal inflation rate of -1.9 percent. The analysis also shows that trend inflation has important effects on the economy when combined with nominal contracts and real output growth. Steady-state output and welfare losses are quantitatively important even for low values of trend inflation. Further, nominal wage contracting is found to be quantitatively more important than nominal price contracting in generating the results. This conclusion does not arise from price dispersion per se, but from an effect of nominal output growth on the optimal markup of monopolistically competitive labour suppliers. Finally, accounting for productivity growth is found to be important for calculating the welfare costs of inflation. Indeed, the presence of 2 percent productivity growth increases the welfare costs of inflation in the benchmark specification by a factor of four relative to the no-growth case.     

Comment on: “Inflation dynamics with search frictions: A structural econometric analysis” by Krause, Lopez-Salido and Lubik

The implications of search frictions on the inflation dynamics are shown here for the case with wage adjustments typically belonging to the New Keynesian model, not to the Mortensen–Pissarides framework. In that model variant, I identify the role of search frictions by an additional term entering the slope coefficient of the inflation equation. After a numerical exercise, I find results that are in line with those obtained by Krause et al. [2008. Inflation dynamics with search frictions: a structural econometric analysis. Journal of Monetary Economics 55, doi:10.1016/j.jmoneco.2008.05.003.].     

A Theory of Intrinsic Inflation Persistence

We propose a novel theory of intrinsic inflation persistence by introducing trend inflation and Kimball (1995)-type aggregators of individual differentiated goods and labor in a model with staggered price- and wage-setting. Under nonzero trend inflation, the non-CES (constant elasticity of substitution) aggregator of goods and staggered price-setting give rise to a variable real marginal cost of goods aggregation, which becomes a driver of inflation. This marginal cost consists of an aggregate of the goods' relative prices, which depends on past inflation, thereby generating intrinsic inertia in inflation. Likewise, the non-CES aggregator of labor and staggered wage-setting lead to intrinsic inertia in wage inflation, which enhances the persistence of price inflation. With the theory we show that inflation exhibits a persistent, hump-shaped response to monetary policy shocks. We also demonstrate that lower trend inflation reduces inflation persistence and that a credible disinflation leads to a gradual decline in inflation and a fall in output.     

Indexing and inflation

Much of the opposition to indexation as a means of adapting to ongoing inflation arises from the view that indexation is itself inflationary. This paper examines the basic for that view in a simple macroeconomic model in which budget deficits are in part financed through the printing of money. It is shown that all aspects of indexing — wage indexation, bond indexation, and tax indexation — tend to increase the impact on the price level of any inflationary shock. However, this association between indexation and inflation is in large part a consequence of the monetary and fiscal policies being followed by the government. Evidence from a cross-section of forty countries on the effects of indexation on the inflationary impact of the oil price shock of 1973–1974 suggests that indexation did not in general increase the inflationary impact of the oil shock. The evidence is, further, consistent with the view that the absence of an excess inflationary effect of indexation is a result of the countries with substantial indexation not having accommodated the oil price shock as much as other countries.     

The economics of options-implied inflation probability density functions

Recently a market in options based on consumer price index inflation (inflation caps and floors) has emerged in the US. This paper uses quotes on these derivatives to construct probability densities for inflation. We study how these probability density functions respond to news announcements and find that the implied odds of deflation are sensitive to certain macroeconomic news releases. We also estimate empirical pricing kernels using these option prices along with time series models fitted to inflation. The options-implied densities assign considerably more mass to extreme inflation outcomes (either deflation or high inflation) than do their time series counterparts. This yields a U-shaped empirical pricing kernel, with investors having high marginal utility in states of the world characterized by either deflation or high inflation.     

The “price puzzle” reconsidered

A large literature has employed structural vector autoregressive (SVAR) models to investigate the empirical effects of U.S. monetary policy. Many of these models regularly produce a “price puzzle”—a rise in the aggregate price level in response to a contractionary innovation to monetary policy—unless commodity prices are included. Conventional wisdom maintains that commodity prices resolve the price puzzle because they contain information that helps the Federal Reserve forecast inflation. I examine a number of plausible alternative indicator variables and find little correlation between an ability to forecast inflation and an ability to resolve the price puzzle. Additionally, a sub-sample investigation reveals that evidence of a price puzzle is associated primarily with the 1959-1979 sample period, and that most indicators—including commodity prices—cannot resolve the puzzle over this period.     

Identifying the influences of nominal and real rigidities in aggregate price-setting behavior

We formulate a generalized price-setting framework that incorporates staggered contracts of multiple durations and that enables us to directly identify the influences of nominal vs. real rigidities. We estimate this framework using macroeconomic data for Germany (1975-1998) and for the U.S. (1983-2003). In each case, we find that the data are well-characterized by nominal contracts with an average duration of about two to three quarters. We also find that new contracts exhibit very low sensitivity to marginal cost, corresponding to a relatively high degree of real rigidity. Finally, our results indicate that backward-looking price-setting behavior (such as indexation to lagged inflation) is not needed in explaining the aggregate data, at least in an environment with a stable monetary policy regime and a transparent and credible inflation objective.