Maximum Likelihood Estimation of Dynamic Stochastic Theories with an Application to New Keynesian Pricing

This paper proposes a novel Maximum Likelihood (ML) strategy to estimate Euler equations implied by dynamic stochastic theories. The strategy exploits rational expectations cross-equation restrictions, but circumvents the problem of multiple solutions that arises in Sargent's (1979) original work by imposing the restrictions on the forcing variable rather than the endogenous variable of the Euler equation. The paper then contrasts the proposed strategy to an alternative, widely employed method that avoids the multiplicity problem by constraining the ML estimates to yield a unique stable solution. I argue that imposing such a uniqueness condition makes little economic sense and can lead to severe misspecification. To illustrate this point, I estimate Gali and Gertler's (1999) hybrid New Keynesian Phillips Curve using labor income share as the measure of real marginal cost. My ML estimates indicate that forward-looking behavior is predominant and that the model provides a good approximation of U.S. inflation dynamics. By contrast, if the same estimates are constrained to yield a unique stable solution, forward-looking behavior becomes much less important and the model as a whole is rejected.Maximum Likelihood, Rational Expectations, New Keynesian Phillips Curve, Inflation, Real marginal cost.

Maximum Likelihood Estimation of Dynamic Stochastic Theories with an Application to New Keynesian Pricing

This paper proposes a novel Maximum Likelihood (ML) strategy to estimate Euler equations implied by dynamic stochastic theories. The strategy exploits rational expectations cross-equation restrictions, but circumvents the problem of multiple solutions that arises in Sargent's (1979) original work by imposing the restrictions on the forcing variable rather than the endogenous variable of the Euler equation. The paper then contrasts the proposed strategy to an alternative, widely employed method that avoids the multiplicity problem by constraining the ML estimates to yield a unique stable solution. I argue that imposing such a uniqueness condition makes little economic sense and can lead to severe misspecification. To illustrate this point, I estimate Gali and Gertler's (1999) hybrid New Keynesian Phillips Curve using labor income share as the measure of real marginal cost. My ML estimates indicate that forward-looking behavior is predominant and that the model provides a good approximation of U.S. inflation dynamics. By contrast, if the same estimates are constrained to yield a unique stable solution, forward-looking behavior becomes much less important and the model as a whole is rejected.Maximum Likelihood, Rational Expectations, New Keynesian Phillips Curve, Inflation, Real Marginal Cost

Quantifying the Uncertainty about the Fit of a New Keynesian Pricing Model: Extended Version

Recent studies by Gali and Gertler (1999) and Sbordone (2002) conclude that a theoretical inflation series implied by the forward-looking New Keynesian pricing model of Calvo (1983) 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 structural pricing equation implied by the Calvo model. The present paper shows that both of these determinants are surrounded by considerable uncertainty. When quantifying the impact of this uncertainty on theoretical inflation, I find that we can no longer say whether the Calvo model explains observed inflation dynamics very well or very poorly.Inflation, New Keynesian pricing, real marginal cost

News Shocks and the Slope of the Term Structure of Interest Rates

We provide a new structural interpretation of the relationship between the slope of the term structure of interest rates and macroeconomic fundamentals. We first adopt an agnostic identification approach that allows us to identify the shocks that explain most of the movements in the slope. We find that two shocks are sufficient to explain virtually all movements in the slope. Impulse response functions for the first shock, which explains the majority of the movements in the slope, lead us to interpret this main shock as a news shock about future productivity. We confirm this interpretation by formally identifying such a news shock as in Barsky and Sims (2009) and Sims (2009). We then assess to what extent a New Keynesian DSGE model is capable of generating the observed slope responses to a news shock. We find that augmenting DSGE models with a term structure provides valuable information to discipline the description of monetary policy and the model’s response to news shocks in general.Term structure of interest rates, news, productivity shocks, business cycles, monetary policy

The Great Increase in Relative Volatility of Real Wages in the United States

This paper documents that over the past 25 years, aggregate hourly real wages in the United States have become substantially more volatile relative to output. We use micro-data from the Current Population Survey (CPS) to show that this increase in relative volatility is predominantly due to increases in the relative volatility of hourly wages across different groups of workers. Compositional changes, by contrast, account for at most 12% of the increase in relative wage volatility. Using a Dynamic Stochastic General Equilibrium (DSGE) model, we show that the observed increase in relative wage volatility is unlikely to come from changes outside of the labor market (e.g. smaller exogenous shocks or more aggressive monetary policy). By contrast, increased flexibility in wage setting is capable of accounting for a large fraction of the observed increase in relative wage volatility. At the same time, increased wage flexibility generates a substantial decrease in the magnitude of business cycle fluctuations, which suggests a promising new explanation for the Great Moderation.Wage volatility, business cycles, great moderation, current population survey, dynamic stochastic general equilibrium models

Fair Wages in a New Keynesian Model of the Business Cycle

We build a New Keynesian model of the business cycle with sticky prices and real wage rigidities motivated by efficiency wages of the gift exchange variety. Compared to a standard sticky price model, our Fair Wage model provides an explanation for structural unemployment and generates more plausible labor market dynamics - notably accounting for the low correlation between wages and employment. The fair wage induced real wage rigidity also significantly reduces the elasticity of marginal cost with respect to output. The smoother dynamics of real marginal cost increase both amplification and persistence of output responses to monetary shocks, thus remedying the well-known lack of internal propagation of standard sticky price models. We take these improvements as a strong endorsement of the addition of real wage rigidities to nominal price rigidities and conclude that the fair wage extension of this paper constitutes a promising platform for an enriched New Keynesian synthesis.Efficiency wages, business cycles, sticky prices, persistence

The Business Cycle Implications of Reciprocity in Labor Relations

We develop a reciprocity-based model of wage determination and incorporate it into a modern dynamic general equilibrium framework. We estimate the model and find that, among potential determinants of wage policy, rent-sharing (between workers and firms) and a measure of wage entitlement are critical to fit the dynamic responses of hours, wages and inflation to various exogenous shocks. Aggregate employment conditions (measuring workers' outside option), on the other hand, are found to play only a negligible role in wage setting. These results are broadly consistent with micro-studies on reciprocity in labor relations but contrast with traditional efficiency wage models which emphasize aggregate labor market variables as the main determinant of wage setting. Overall, the empirical fit of the estimated model is at least as good as the fit of models postulating nominal wage contracts. In particular, the reciprocity model is more successful in generating the sharp and significant fall of inflation and nominal wage growth in response to a neutral technology shock.efficiency wages; reciprocity; estimated DSGE models

The Business Cycle Implications of Reciprocity in Labor Relations

We develop a reciprocity-based model of wage determination and incorporate it into a modern dynamic general equilibrium framework. We estimate the model and find that, among potential determinants of wages, rent-sharing (between workers and firms) and wage entitlement (based on wages earned in the past) are important to fit the dynamic responses of output, wages and inflation to various exogenous shocks. Aggregate employment conditions (measuring workers' outside option), on the other hand, are found to play only a negligible role for wage setting. These results are broadly consistent with micro-studies on reciprocity in labor relations but contrast with traditional efficiency wage models which emphasize aggregate labor market variables as the main determinant of wage setting.Efficiency Wages, Reciprocity, Estimated DSGE Models

The Business Cycle Implications of Reciprocity in Labor Relations

We develop a reciprocity-based model of wage determination and incorporate it into a moder dynamic general equilibrium framework. We estimate the model and find that, among potential determinants of wage policy, rent-sharing (between workers and firms) and a measure of wage entitlement are critical to fit the dynamic responses of hours, wages and inflation to various exogenous shocks. Aggregate employment conditions (measuring workers' outside option), on the other hand, are found to play only a negligible role in wage setting. These results are broadly consistent with micro-studies on reciprocity in labor relations but contrast with traditional efficiency wage models which emphasize aggregate labor market variables as the main determinant of wage setting. Overall, the empirical fit of the estimated model is at least as good as the fit of models postulating nominal wage contracts. In particular, the reciprocity model is more successful in generating the sharp and significant fall of inflation and nominal wage growth in response to a neutral technology shock.Efficiency wages, Reciprocity, Estimated DSGE models

Expectations and the term structure of interest rates : evidence and implications

Monetary policy ; Interest rates