Creator: Christiano, Lawrence J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 101 Abstract:
This paper describes and implements a procedure for estimating the timing interval in any linear econometric model. The procedure is applied to Taylor’s model of staggered contracts using annual averaged price and output data. The fit of the version of Taylor’s model with serially uncorrelated disturbances improves as the timing interval of the model is reduced.
Creator: Christiano, Lawrence J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 106 Abstract:
Deaton (1986) has noted that if income is a first-order autoregressive process in first differences, then a simple version of Friedman’s permanent income hypothesis (SPIH) implies that measured U.S. consumption is insufficiently sensitive to innovations in income. This paper argues that this implication of the SPIH is a consequence of the fact that it ignores the role of the substitution effect in the consumption decision. Using a parametric version of the standard model of economic growth, the paper shows that very small movements in interest rates are sufficient to induce an empirically plausible amount of consumption smoothing. Since an overall evaluation of the model’s explanation for the observed smoothness of consumption requires examining its implications for other aspects of the data, the paper also explores some of these.
Creator: Christiano, Lawrence J. and Ljungqvist, Lars Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 108 Abstract:
A bivariate Granger-causality test on money and output finds statistically significant causality when data are measured in log levels, but not when they are measured in first differences of the logs. Which of these results is right? The answer to that question matters because a finding of no Granger-causality from money to output would substantially embarrass existing business cycle models in which money plays an important role [Eichenbaum and Singleton (1986)]. Monte Carlo simulation experiments indicate that, most probably, the first difference results reflect lack of power, whereas the level results reflect Granger-causality that is actually in the data.
Creator: Christiano, Lawrence J., Eichenbaum, Martin S., and Marshall, David A. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 129 Abstract:
Measured aggregate U.S. consumption does not behave like a martingale. This paper develops and tests two variants of the permanent income model that are consistent with this fact. In both variants, we assume agents make decisions on a continuous time basis. According to the first variant, the martingale hypothesis holds in continuous time and serial persistence in measured consumption reflects only the effects of time aggregation. We investigate this variant using both structural and atheoretical econometric models. The evidence against these models is far from overwhelming. This suggests that the martingale hypothesis may yet be a useful way to conceptualize the relationship between aggregate quarterly U.S. consumption and income. According to the second variant of the permanent income model, serial persistence in measured consumption reflects the effects of exogenous technology shocks and time aggression. In this model, continuous time consumption does not behave like a martingale. We find little evidence against this variance of the permanent income model. It is difficult, on the basis of aggregate quarterly U.S. data, to convincingly distinguish between the different continuous time models considered in the paper.
Keyword: Time aggregation, Consumption, and Permanent income
Creator: Chari, V. V., Christiano, Lawrence J., and Kehoe, Patrick J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 147 Abstract:
This paper studies the quantitative properties of fiscal and monetary policy in business cycle models. In terms of fiscal policy, optimal labor tax rates are virtually constant and optimal capital income tax rates are close to zero on average. In terms of monetary policy, the Friedman rule is optimal—nominal interest rates are zero—and optimal monetary policy is activist in the sense that it responds to shocks to the economy.
Creator: Christiano, Lawrence J. and Eichenbaum, Martin S. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 150 Abstract:
Several recent papers provide strong empirical support for the view that an expansionary monetary policy disturbance generates a persistent decrease in interest rates and a persistent increase in output and employment. Existing quantitative general equilibrium models, which allow for capital accumulation, are inconsistent with this view. There does exist a recently developed class of general equilibrium models which can rationalize the contemporaneous response of interest rates, output, and employment to a money supply shock. However, a key shortcoming of these models is that they cannot rationalize persistent liquidity effects. This paper discusses the basic frictions and mechanisms underlying this new class of models and investigates one avenue for generating persistence. We argue that once a simplified version of the model in Christiano and Eichenbaum (1991) is modified to allow for extremely small costs of adjusting sectoral flow of funds, positive money shocks generate long-lasting, quantitatively significant liquidity effects, as well as persistent increases in aggregate economic activity.
Creator: Chari, V. V., Christiano, Lawrence J., and Kehoe, Patrick J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 158 Abstract:
We find conditions for the Friedman rule to be optimal in three standard models of money. These conditions are homotheticity and separability assumptions on preferences similar to those in the public finance literature on optimal uniform commodity taxation. We show that there is no connection between our results and the result in the standard public finance literature that intermediate goods should not be taxed.
Keyword: Optimal monetary policy, Ramsey policy, and Inflation tax Subject (JEL): E52 - Monetary Policy, E63 - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy, and E61 - Policy Objectives; Policy Designs and Consistency; Policy Coordination
Creator: Chari, V. V., Christiano, Lawrence J., and Kehoe, Patrick J. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 160 Abstract:
This paper develops the quantitative implications of optimal fiscal policy in a business cycle model. In a stationary equilibrium the ex ante tax rate on capital income is approximately zero. There is an equivalence class of ex post capital income tax rates and bond policies that support a given allocation. Within this class the optimal ex post capital tax rates can range from being close to i.i.d. to being close to a random walk. The tax rate on labor income fluctuates very little and inherits the persistence properties of the exogenous shocks and thus there is no presumption that optimal labor tax rates follow a random walk. The welfare gains from smoothing labor tax rates and making ex ante capital income tax rates zero are small and most of the welfare gains come from an initial period of high taxation on capital income.
Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 163 Abstract:
This paper shows how to derive the family of models in which Cagan’s model of hyperinflation is a rational expectations model. The slope parameter in Cagan’s portfolio balance equation is identified in some of these models and in others it is not—a fact which clarifies results obtained in several recent papers.
Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 165 Abstract:
Theory typically does not give us reason to believe that economic models ought to be formulated at the same level of time aggregation at which data happen to be available. Nevertheless, this is frequently done when formulating econometric models, with potentially important specification-error implications. This suggests examining the alternatives, one of which is to model in continuous time. The primary difficulty in inferring the parameters of a continuous time model given sampled observations is the “aliasing identification problem.” This paper shows how the restrictions implied by rational expectations sometimes do, and sometimes do not, resolve the problem. This is accomplished very simply in the context of a hypothesis about the term structure of interest rates. The paper confirms and extends results obtained for another example by Hansen and Sargent.
Creator: Christiano, Lawrence J. and Fisher, Jonas D. M. (Jonas Daniel Maurice), 1965- Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 171 Abstract:
We describe several methods for approximating the solution to a model in which inequality constraints occasionally bind, and we compare their performance. We apply the methods to a particular model economy which satisfies two criteria: It is similar to the type of model used in actual research applications, and it is sufficiently simple that we can compute what we presume is virtually the exact solution. We have two results. First, all the algorithms are reasonably accurate. Second, on the basis of speed, accuracy and convenience of implementation, one algorithm dominates the rest. We show how to implement this algorithm in a general multidimensional setting, and discuss the likelihood that the results based on our example economy generalize.
Keyword: Occasionally binding constraints, Chebyshev interpolation, Parameterized expectations, and Collocation Subject (JEL): C63 - Computational Techniques; Simulation Modeling, C60 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General, and C68 - Computable General Equilibrium Models
Creator: Christiano, Lawrence J. and Den Haan, Wouter J., 1962- Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 199 Abstract:
We investigate, by Monte Carlo methods, the finite sample properties of GMM procedures for conducting inference about statistics that are of interest in the business cycle literature. These statistics include the second moments of data filtered using the first difference and Hodrick-Prescott filters, and they include statistics for evaluating model fit. Our results indicate that, for the procedures considered, the existing asymptotic theory is not a good guide in a sample the size of quarterly postwar U.S. data.
Keyword: Monte Carlo simulation, Covariance matrix estimation, Hypothesis testing, Spectral density, Prewhitening, and Finite-sample analysis
Creator: Christiano, Lawrence J. and Fisher, Jonas D. M. (Jonas Daniel Maurice), 1965- Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 200 Abstract:
The marginal cost of plant capacity, measured by the price of equity, is significantly procyclical. Yet, the price of a major intermediate input into expanding plant capacity, investment goods, is countercyclical. The ratio of these prices is Tobin's q. Following convention, we interpret the fact that Tobin's q differs from unity at all, as reflecting that there are diminishing returns to expanding plant capacity by installing investment goods ("adjustment costs"). However, the phenomenon that interests us is not just that Tobin's q differs from unity, but also that its numerator and denominator have such different cyclical properties. We interpret the sign switch in their covariation with output as reflecting the interaction of our adjustment cost specification with the operation of two shocks: one which affects the demand for equity and another which shifts the technology for producing investment goods. The adjustment costs cause the two prices to respond differently to these two shocks, and this is why it is possible to choose the shock variances to reproduce the sign switch. These model features are incorporated into a modified version of a model analyzed in Boldrin, Christiano and Fisher (1995). That model incorporates assumptions designed to help account for the observed mean return on risk free and risky assets. We find that the various modifications not only account for the sign switch, but they also continue to account for the salient features of mean asset returns. We turn to the business cycle implications of our model. The model does as well as standard models with respect to conventional business cycle measures of volatility and comovement with output, and on one dimension the model significantly dominates standard models. The factors that help it account for prices and rates of return on assets also help it account for the fact that employment across a broad range of sectors moves together over the cycle.
Creator: Christiano, Lawrence J. and Harrison, Sharon G. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 214 Abstract:
We study a one-sector growth model which is standard except for the presence of an externality in the production function. The set of competitive equilibria is large. It includes constant equilibria, sunspot equilibria, cyclical and chaotic equilibria, and equilibria with deterministic or stochastic regime switching. The efficient allocation is characterized by constant employment and a constant growth rate. We identify an income tax-subsidy schedule that supports the efficient allocation as the unique equilibrium outcome. That schedule has two properties: (i) it specifies the tax rate to be an increasing function of aggregate employment, and (ii) earnings are subsidized when aggregate employment is at its efficient level. The first feature eliminates inefficient, fluctuating equilibria, while the second induces agents to internalize the externality.
Keyword: Stabilization, Fiscal policy, Business cycle, Multiple equilibria, and Regime switching Subject (JEL): E13 - General Aggregative Models: Neoclassical, E62 - Fiscal Policy, and E32 - Business Fluctuations; Cycles
Creator: Christiano, Lawrence J., Eichenbaum, Martin S., and Evans, Charles, 1958- Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 227 Abstract:
We provide new evidence that models of the monetary transmission mechanism should be consistent with at least the following facts. After a contractionary monetary policy shock, the aggregate price level responds very little, aggregate output falls, interest rates initially rise, real wages decline by a modest amount, and profits fall. We compare the ability of sticky price and limited participation models with frictionless labor markets to account for these facts. The key failing of the sticky price model lies in its counterfactual implications for profits. The limited participation model can account for all the above facts, but only if one is willing to assume a high labor supply elasticity (2 percent) and a high markup (40 percent). The shortcomings of both models reflect the absence of labor market frictions, such as wage contracts or factor hoarding, which dampen movements in the marginal cost of production after a monetary policy shock.
Keyword: Mechanism, Prices, Credit, and Monetary transmission Subject (JEL): E30 - Prices, Business Fluctuations, and Cycles: General (includes Measurement and Data)
Creator: Boldrin, Michele, Christiano, Lawrence J., and Fisher, Jonas D. M. (Jonas Daniel Maurice), 1965- Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 280 Abstract:
We introduce two modifications into the standard real business cycle model: habit persistence preferences and limitations on intersectoral factor mobility. The resulting model is consistent with the observed mean equity premium, mean risk free rate and Sharpe ratio on equity. The model does roughly as well as the standard real business cycle model with respect to standard measures. On four other dimensions its business cycle implications represent a substantial improvement. It accounts for (i) persistence in output, (ii) the observation that employment across different sectors moves together over the business cycle, (iii) the evidence of ‘excess sensitivity’ of consumption growth to output growth, and (iv) the ‘inverted leading indicator property of interest rates,’ that high interest rates are negatively correlated with future output.
Keyword: Asset pricing , Capital gains, Habit persistence , and Risk aversion Subject (JEL): E44 - Financial Markets and the Macroeconomy, E32 - Business Fluctuations; Cycles, and O41 - One, Two, and Multisector Growth Models
Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 301 Abstract:
This paper presents a completely worked example applying the frequency domain estimation strategy proposed by Hansen and Sargent [1980, 1981a]. A bivariate, high order continuous time autoregressive moving average model is estimated subject to the restrictions implied by the rational expectations model of the term structure of interest rates. The estimation strategy takes into account the fact that one of the data series are point-in-time observations, while the other are time averaged. Alternative strategies are considered for taking into account nonstationarity in the data. Computing times reported in the paper demonstrate that estimation using the techniques of Hansen and Sargent is inexpensive.
Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 303 Abstract:
This paper investigates—in the context of a simple example—the accuracy of an econometric technique recently proposed by Kydland and Prescott. We consider a hypothetical econometrician who has a large sample of data, which is known to be generated as a solution to an infinite horizon, stochastic optimization problem. The form of the optimization problem is known to the econometrician. However, the values of some of the parameters need to be estimated. The optimization problem—presented in a recent paper by Long and Plosser—is not linear quadratic. Nevertheless, its closed form solution is known, although not to the hypothetical econometrician of this paper. The econometrician uses Kydland and Prescott’s method to estimate the unknown structural parameters. Kydland and Prescott’s approach involves replacing the given stochastic optimization problem by another which approximates it. The approximate problem is a element of the class of linear quadratic problems, whose solution is well-known—even to the hypothetical econometrician of this paper. After examining the probability limits of the econometrician’s estimators under “reasonable” specifications of model parameters, we conclude that the Kydland and Prescott method works well in the example considered. It is left to future research to determine the extent to which the results obtained for the example in this paper applies to a broader class of models.