Papers

September 1988 | Article

Efficiency Bounds Implied by Multiperiod Conditional Moment Restrictions

Lars Peter Hansen, John C. Heaton, Masao Ogaki

In this article we study a class of econometric models that imply a set of multiperiod conditional moment restrictions. These restrictions depend on an unknown parameter vector. We construct an extensive class of consistent, asymptotically normal estimators of this parameter vector and calculate the greatest lower bound for the asymptotic covariance matrices of estimators in this class. In so doing, we extend results reported by Hansen (1985) and Stoica, Soderstrom, and Friedlander (1985), by allowing for more general forms of nonlinearities and temporal dependence. Many dynamic econometric models imply that the expectation of a function of a currently observed data vector and an unknown parameter vector conditioned on information available at some point in the past is 0. We focus on models in which the conditioning information is lagged more than one time period, as in the models considered by Barro (1981), Dunn and Singleton (1986), Eichenbaum and Hansen (1987), Eichenbaum, Hansen, and Singleton (1988), Hansen and Hodrick (1983), Hansen and Singleton (1988), and Hall (1988). Hence we consider econometric models that imply multiperiod conditional moment restrictions that depend on an unknown parameter vector. Within the context of these models, it is possible to estimate the parameter vector without simultaneously estimating the law of motion for the entire set of observable variables. The basic idea is to use the conditional moment restrictions to deduce a set of unconditional moment restrictions. Then estimators of the parameter vector can be obtained by using sample counterparts to the unconditional moment restrictions as described by Sargan (1958) and Hansen (1982). Such estimators are referred to as generalized method of moments (GMM) estimators. For most applications the conditional moment restrictions imply an extensive set of unconditional moment restrictions. As a consequence, there is a vast array of GMM estimators that can be used to estimate consistently the parameter vector of interest. Each member of this set of estimators is constructed using a distinct collection of the unconditional moment restrictions. Hence it is of interest to compare the performances of the alternative GMM estimators. For tractability we investigate only the asymptotic distributions of the estimators in question. More precisely, we use a method suggested by Hansen (1985) for calculating a greatest lower bound for the asymptotic covariance matrices of the alternative GMM estimators, that is, an efficiency bound. We compute the efficiency bound for a rich collection of time series models that imply multiperiod conditional moment restrictions. Hansen (1985) illustrated this method for a time series model with conditionally homoscedastic moving-average disturbance terms for which the moving-average polynomial is invertible. Stoica et al. (1985) calculated efficiency bounds for GMM estimators for autoregressive parameters in autoregressive moving-average models without unit roots. They established that the efficiency bound for GMM estimators of the autoregressive parameters coincides with the asymptotic covariance matrix of the Gaussian maximum likelihood estimators. The models considered by Hansen (1985) in his illustrative example and by Stoica et al. (1885) can be viewed as special cases of the models considered in this article. Although we do not make any direct comparisons to maximum likelihood, we do allow for moving-average disturbances that are conditionally heteroscedastic and moving-average lag polynomials that cannot be inverted.

Journal: Journal of the American Statistical Association|Volume: 83|Issue Number: 403|Pages: 863-871|Tags: Econometrics|Export BibTeX >
@article{hansen1988efficiency,
  title={Efficiency Bounds Implied by Multiperiod Conditional Moment Restrictions},
  author={Hansen, Lars Peter and Heaton, John C and Ogaki, Masao},
  journal={Journal of the American Statistical Association},
  volume={83},
  number={403},
  pages={863--871},
  year={1988},
  publisher={Taylor & Francis Group}
}
February 1988 | Article

A Time-Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty

Martin S. Eichenbaum, Lars Peter Hansen, Kenneth J. Singleton

This paper investigates empirically a model of aggregate consumption and leisure decisions in which utility from goods and leisure is nontime-separable. The nonseparability of preferences accommodates intertemporal substitution or complementarity of leisure and thereby affects the comovements in aggregate compensation and hours worked. These cross-relations are examined empirically using postwar monthly U. S. data on quantities, real wages, and the real return on the one-month Treasury bill. The estimated values of the parameters governing preferences differ significantly from the values assumed in several studies of real business models. Several possible explanations of these discrepancies are discussed.

Journal: Quarterly Journal of Economics|Volume: 103|Issue Number: 1|Pages: 51-78|Tags: Econometrics, Uncertainty and Valuation|Export BibTeX >
@article{ehs:1988,
  title={A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty},
  author={Eichenbaum, Martin S and Hansen, Lars Peter and Singleton, Kenneth J},
  journal={The Quarterly Journal of Economics},
  volume={103},
  number={1},
  pages={51--78},
  year={1988},
  publisher={Oxford University Press}
}
May 1987 | Article

The Role of Conditioning Information in Deducing Testable Restrictions Implied by Dynamic Asset Pricing-Models

Lars Peter Hansen, Scott F. Richard
The purpose of this paper is to investigate testable implications of equilibrium asset pricing models. We derive a general representation for asset prices that displays the role of conditioning information. This representation is then used to examine restrictions implied by asset pricing models on the unconditional moments of asset payoffs and prices. In particular, we analyze the effect of information omission on the mean-variance frontier of one-period returns on portfolios of securities. Also, we deduce an information extension of equilibrium pricing functions that is useful in deriving restrictions on the unconditional moments of payoffs and prices.
Journal: Econometrica|Volume: 55|Issue Number: 3|Pages: 587-613|Tags: Econometrics|Export BibTeX >
@article{hansen1987role,
  title={The Role of Conditioning Information in Deducing Testable Restrictions Implied by Dynamic Asset Pricing Models},
  author={Hansen, Lars Peter and Richard, Scott F},
  journal={Econometrica: Journal of the Econometric Society},
  pages={587--613},
  year={1987},
  publisher={JSTOR}
}
January 1987 | Chapter

Calculating Asset Prices in Three Example Economies

Lars Peter Hansen
Title of book: Advances in Econometrics: Fifth World Congress, Volume 1|Editor(s): T.F. Bewley|Place of Publication: Cambridge|Publisher: Cambridge University Press|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >

@inproceedings{hansen1987calculating,

title={Calculating Asset Prices in Three Example Economies},

author={Hansen, Lars Peter},

booktitle={Advances in Econometrics: Volume 1: Fifth World Congress},

year={1987},

organization={Press Cambridge University}

}

October 1985 | Article

A Method for Calculating Bounds on the Asymptotic Covariance Matrices of Generalized Method of Moments Estimators

Lars Peter Hansen

For many time series estimation problems, there is an infinite-dimensional class of generalized method of moments estimators that are consistent and asymptotically normal. This paper suggests a procedure for calculating the greatest lower bound for the asymptotic covariance matrices of such estimators. The analysis focuses on estimation problems in which the data are generated by a stochastic process that is stationary and ergodic. The calculation of the bound uses martingale difference approximations as suggested by Gordon (1969) and a matrix version of Hilbert space methods.

 

Tag: GMM

Journal: Journal of Econometrics|Volume: 30|Issue Number: 1-2|Pages: 203-238|Tags: Econometrics|Export BibTeX >
@article{hansen1985method,
  title={A Method for Calculating Bounds on the Asymptotic Covariance Matrices of Generalized Method of Moments Estimators},
  author={Hansen, Lars Peter},
  journal={Journal of Econometrics},
  volume={30},
  number={1-2},
  pages={203--238},
  year={1985},
  publisher={Elsevier}
}
January 1985 | Chapter

Linear-Quadratic Duopoly Models of Resource Depletion

Lars Peter Hansen, Dennis Apple, William Roberds

This chapter contains some methods for quantitatively analyzing multiple-agent models of dynamic games in which at least one agent takes into account its influence on the aggregate environment. We confine our attention to models in which the agents solve stochastic, quadratic optimization problems subject to linear constraints. A convenient feature of such models is that the equilibrium laws of motion are linear in the relevant state variables and can be deduced easily. Consequently, we can obtain tractable characterizations of the empirical implications of the models under alternative rules for how the agents interact.

Pages: 101-142|Title of book: Energy Foresight, and Strategy|Editor(s): Thomas J. Sargent|Place of Publication: Washington, DC|Publisher: Rutledge|Tags: Econometrics|Export BibTeX >
@article{hansen:1985,
  title={Linear-Quadratic Duopoly Models of Resource Depletion},
  author={Hansen, Lars P and Epple, Dennis and Roberds, William},
  journal={Energy, Foresight and Strategy},
  year={1985}
}
April 1983 | Article

Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns

Lars Peter Hansen, Kenneth J. Singleton

This paper studies the time-series behavior of asset returns and aggregate consumption. Using a representative consumer model and imposing restrictions on preferences and the joint distribution of consumption and returns, we deduce a restricted log-linear time-series representation. Preference parameters for the representative  agent are estimated and the implied restrictions are tested using postwar data.

Journal: Journal of Political Economy|Volume: 91|Issue Number: 2|Pages: 249-265|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >

@article{hansensingleton:1983,
title={Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns},
author={Hansen, Lars Peter and Singleton, Kenneth J},
journal={Journal of political economy},
volume={91},
number={2},
pages={249–265},
year={1983},
publisher={The University of Chicago Press}
}

March 1983 | Article

The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities

Lars Peter Hansen and Thomas J. Sargent

This paper reconsiders the aliasing problem of identifying the parameters of a continuous time stochastic process from discrete time data. It analyzes the extent to which restricting attention to processes with rational spectral density matrices reduces the number of observationally equivalent models. It focuses on rational specifications of spectral density matrices since rational parameterizations are commonly employed in the analysis of time series data.

Journal: Econometrics|Volume: 51|Issue Number: 2|Pages: 377-387|Tags: Econometrics|Export BibTeX >

@article{hansen1983b,

title={The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities},

author={Hansen, Lars Peter and Sargent, Thomas J},

journal={Econometrica: Journal of the Econometric Society},

pages={377–387},

year={1983},

publisher={JSTOR}

}

February 1983 | Article

Multiperiod Probit Models and Orthogonality Condition Estimation

Robert B. Avery, Lars Peter Hansen, V. Joseph Hotz
Journal: International Economic Review|Volume: 24|Issue Number: 1|Pages: 21-35|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >
@article{ahh:1983multiperiod,
  title={Multiperiod probit models and orthogonality condition estimation},
  author={Avery, Robert B and Hansen, Lars Peter and Hotz, V Joseph},
  journal={International Economic Review},
  pages={21--35},
  year={1983},
  publisher={JSTOR}
}
February 1983 | Article

Aggregation Over Time and the Inverse Optimal Predictor Problem for Adaptive Expectations in Continuous Time

Lars Peter Hansen and Thomas J. Sargent

This paper describes the continuous time stochastic process for money and inflation under which Cagan’s adaptive expectations model is optimal. It then analyzes how data formed by sampling money and prices at discrete points in time would behave.

Journal: International Economic Review|Volume: 24|Issue Number: 1|Pages: 1-20|Tags: Econometrics|Export BibTeX >

@article{hansen1983aggregation,

title={Aggregation over time and the inverse optimal predictor problem for adaptive expectations in continuous time},

author={Hansen, Lars Peter and Sargent, Thomas J},

journal={International Economic Review},

pages={1–20},

year={1983},

publisher={JSTOR}

}