Papers

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}

}

January 1983 | Chapter

Risk Averse Speculation in the Forward Foreign Exchange Market: An Econometric Analysis of Linear Models

Lars Peter Hansen and Robert J. Hedrick

In this paper we study the determination of forward foreign exchange rates. An exchange rate is the price of one currency in terms of another currency, and a forward rate is a contractual exchange rate established at a point in time for a transaction that will take place at the maturity date on the contract in the future. Well-organized forward markets exist for all major currencies of the world for various maturities, with the most active contract lengths being one, three, six, and twelve months.

Pages: 113-142|Title of book: Exchange Rates and International Macroeconomics|Editor(s): J.A. Frenkel|Place of Publication: Chicago|Publisher: University of Chicago Press|Tags: Econometrics|Export BibTeX >
@incollection{hansen:1983,
  title={Risk Averse Speculation in the Forward Foreign Exchange Market: An Econometric Analysis of Linear Models},
  author={Hansen, Lars Peter and Hodrick, Robert J},
  booktitle={Exchange Rates and International Macroeconomics},
  pages={113--152},
  year={1983},
  publisher={University of Chicago Press}
}
September 1982 | Article

Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models

Lars Peter Hansen, Kenneth J. Singleton

This paper describes a method for estimating and testing nonlinear rational expectations models directly from stochastic Euler equations. The estimation procedure makes sample counterparts to the population orthogonality conditions implied by the economic model close to zero. An attractive feature of this method is that the parameters of the dynamic objective functions of economic agents can be estimated without explicitly solving for the stochastic equilibrium.

(See also “Correction,” Econometrica 52(1): 267-268, January 1984.)

Journal: Econometrica|Volume: 50|Issue Number: 5|Pages: 1269-1286|Export BibTeX >

@article{hansensingleton:1982,
title={Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models},
author={Hansen, Lars Peter and Singleton, Kenneth J.},
journal={Econometrica: Journal of the Econometric Society},
pages={1269–1286},
year={1982},
publisher={JSTOR}
}

July 1982 | Article

Large Sample Properties of Generalized Method of Moments Estimators

Lars Peter Hansen

This paper studies estimators that make sample analogues of population orthogonality conditions close to zero. Strong consistency and asymptotic normality of such estimators is established under the assumption that the observable variables are stationary and ergodic. Since many linear and nonlinear econometric estimators reside within the class of estimators studied in this paper, a convenient summary of the large sample properties of these estimators, including some whose large sample properties have not heretofore been discussed, is provided.

Journal: Econometrica|Volume: 50|Issue Number: 4|Pages: 1029-1054|Tags: Econometrics|Export BibTeX >
@article{hansen:1982,
  title={Large Sample Properties of Generalized Method of Moments Estimators},
  author={Hansen, Lars Peter},
  journal={Econometrica: Journal of the Econometric Society},
  pages={1029--1054},
  year={1982},
  publisher={JSTOR}
}
January 1982 | Article

Instrumental Variables Procedures for Estimating Linear Rational Expectations Models

Lars Peter Hansen and Thomas J. Sargent

This paper illustrates how to use instrumental variables procedures to estimate the parameters of a linear rational expectations model. These procedures are appropriate when disturbances are serially correlated and the instrumental variables are not exogenous. We compare our procedures to some alternative estimators that estimate free parameters from restrictions implied by the Euler equations. The procedures are applicable to a variety of linear rational expectations models, several examples of which we cite.

Journal: Journal of Monetary Economics|Volume: 9|Issue Number: 3|Pages: 263-296|Tags: Econometrics|Export BibTeX >
@article{hansen:1982,
  title={Instrumental Variables Procedures for Estimating Linear Rational Expectations Models},
  author={Hansen, Lars Peter and Sargent, Thomas J},
  journal={Journal of Monetary Economics},
  volume={9},
  number={3},
  pages={263--296},
  year={1982},
  publisher={Elsevier}
}