September 1998 | Article

Spectral Methods for Identifying Scalar Diffusions

Lars Peter Hansen, José A. Scheinkman, Nizar Touzi

This paper shows how to identify nonparametrically scalar stationary diffusions from discrete-time data. The local evolution of the diffusion is characterized by a drift and diffusion coefficient along with the specification of boundary behavior. We recover this local evolution from two objects that can be inferred directly from discrete-time data: the stationary density and a conveniently chosen eigenvalue–eigenfunction pair of the conditional expectation operator over a unit interval of time. This construction also lends itself to a spectral characterization of the over-identifying restrictions implied by a scalar diffusion model of a discrete-time Markov process.

Journal: Journal of Econometrics|Volume: 86|Issue Number: 1|Pages: 1-32|Tags: Econometrics|Export BibTeX >
  title={Spectral Methods for Identifying Scalar Diffusions},
  author={Hansen, Lars Peter and Scheinkman, Jos{'e} Alexandre and Touzi, Nizar},
  journal={Journal of Econometrics},
March 1998 | Working Paper

Risk and Robustness in Equilibrium

Evan W. Anderson, Lars Peter Hansen, Thomas J. Sargent
Tags: Risk, Robustness and Ambiguity|Export BibTeX >
  title={Risk and Robustness in General Equilibrium},
  author={Anderson, Evan W and Hansen, Lars Peter and Sargent, Thomas J},
  journal={Preprint University of Chicago},
July 1997 | Article

Short-term Interest Rates As Subordinated Diffusions

Timothy Conley, Lars Peter Hansen, Erzo G. J. Luttmer, José A. Scheinkman

In this article we characterize and estimate the process for short-term interest rates using federal funds interest rate data. We presume that we are observing a discrete-time sample of a stationary scalar diffusion. We concentrate on a class of models in which the local volatility elasticity is constant and the drift has a flexible specification. To accommodate missing observations and to break the link between “economic time” and calendar time, we model the sampling scheme as an increasing process that is not directly observed. We propose and implement two new methods for estimation. We find evidence for a volatility elasticity between one and one-half and two. When interest rates are high, local mean reversion is small and the mechanism for inducing stationarity is the increased volatility of the diffusion process.

Journal: Review of Financial Studies|Volume: 10|Issue Number: 3|Pages: 525-577|Tags: Econometrics|Export BibTeX >
  title={Short-Term Interest Rates as Subordinated Diffusions},
  author={Conley, Timothy G and Hansen, Lars Peter and Luttmer, Erzo GJ and Scheinkman, Jos{'e} A},
  journal={Review of Financial Studies},
  publisher={Soc Financial Studies}
June 1997 | Article

Bootstrapping the Long Run

Timothy Conley, Lars Peter Hansen, Wen-Fang Liu

We develop and apply bootstrap methods for diffusion models whenfitted to the long run as characterized by the stationarydistribution of the data. To obtain bootstrap refinements tostatistical inference, we simulate candidate diffusion processes. Weuse these bootstrap methods to assess measurements of local meanreversion or pull to the center of the distribution for short-terminterest rates. We also use them to evaluate the fit of the model to the empirical density.

Journal: Macroeconomic Dynamics|Volume: 1|Issue Number: 2|Pages: 279-311|Tags: Econometrics|Export BibTeX >
  title={Bootstrapping the Long Run},
  author={Conley, Timothy G and Hansen, Lars Peter and Liu, Wen-Fang},
  journal={Macroeconomic Dynamics},
  publisher={Cambridge University Press}
June 1997 | Article

Assessing Specification Errors in Stochastic Discount Factor Models

Lars Peter Hansen and Ravi Jagannathan

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on χ 2 statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.

Journal: The Journal of Finance|Volume: 52|Issue Number: 2|Pages: 557-590|Tags: Econometrics|Export BibTeX >
  title={Assessing Specification Errors in Stochastic Discount Factor Models},
  author={Hansen, Lars Peter and Jagannathan, Ravi},
  journal={The Journal of Finance},
  publisher={Wiley Online Library}
November 1996 | Article

The Empirical Foundations of Calibration

Lars Peter Hansen and James J. Heckman

Interest in simulating recently developed dynamic stochastic general equilibrium models of the economy stimulated a demand for parameters. This has given rise to calibration as advocated by Finn E. Kydland and Edward C. Prescott (1982). This paper explores the implicit assumptions underlying their calibration method. The authors question that there is a ready supply of micro estimates available to calibrate macroeconomic models. Measures of parameter uncertainty and specification sensitivity should be routinely reported. They propose a more symbiotic role for calibration as providing signals to microeconomists about important gaps in knowledge, which when filled will solidify the empirical underpinning, improving the credibility of the quantitative output.

Journal: Journal of Economic Perspectives|Volume: 10|Issue Number: 1|Pages: 87-104|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={The Empirical Foundations of Calibration},
  author={Hansen, Lars Peter and Heckman, James J},
  journal={The Journal of Economic Perspectives},
July 1996 | Article

Finite-Sample Properties of Some Alternative GMM Estimators

Lars Peter Hansen, John Heaton, Amir Yaron

We investigate the small-sample properties of three alternative generalized method of moments (GMM) estimators of asset-pricing models. The estimators that we consider include ones in which the weighting matrix is iterated to convergence and ones in which the weighting matrix is changed with each choice of the parameters. Particular attention is devoted to assessing the performance of the asymptotic theory for making inferences based directly on the deterioration of GMM criterion functions.

Journal: Journal of Business and Economic Statistics|Volume: 14|Issue Number: 3|Pages: 262-280|Tags: Econometrics|Export BibTeX >
  title={Finite-Sample Properties of Some Alternative GMM Estimators},
  author={Hansen, Lars Peter and Heaton, John and Yaron, Amir},
  journal={Journal of Business & Economic Statistics},
  publisher={Taylor & Francis Group}
April 1996 | Chapter

Mechanics of Forming and Estimating Dynamic Linear Economies

Evan W. Anderson, Ellen R. McGrattan, Lars Peter Hansen, Thomas J. Sargent

This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We display an application to Rosen, Murphy, and Scheinkman’s (1994) model of cattle cycles.

Volume: 1|Pages: 171-252|Title of book: Handbook of Computational Economics|Publisher: Elsevier|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={Mechanics of forming and estimating dynamic linear economies},
  author={Anderson, Evan W and McGrattan, Ellen R and Hansen, Lars Peter and Sargent, Thomas J},
  journal={Handbook of Computational Economics},
January 1996 | Article

Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors

Lars Peter Hansen and Kenneth J. Singleton

This article studies alternative methods for estimating parameters from multiperiod conditional moment restrictions. Our discussion is couched in the context of a multivariate linear time series model, and we use the log-linear intertemporal asset-pricing model as a prototype when comparing alternative econometric methods. We propose a generalized method of moments estimator that is scale invariant and is asymptotically equivalent to one used previously in empirical work on asset pricing. We then show how to improve the efficiency of this estimator. Finally, we apply these methods in an empirical investigation of the log-linear intertemporal asset-pricing model.

Journal: Journal of Business & Economic Studies|Volume: 14|Issue Number: 1|Pages: 53-68|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={Efficient Estimation of Linear Asset-Pricing Models With Moving Average Errors},
  author={Hansen, Lars Peter and Singleton, Kenneth J},
  journal={Journal of Business & Economic Statistics},
  publisher={Taylor & Francis}
November 1995 | Article

Econometric Evaluation of Asset Pricing Models

Lars Peter Hansen, John Heaton, Erzo G.J. Luther

In this article we provide econometric tools for the evaluation of intertemporal asset pricing models using specification-error and volatility bounds. We formulate analog estimators of these bounds, give conditions for consistency, and derive the limiting distribution of these estimators. The analysis incorporates market frictions such as short-sale constraints and proportional transactions costs. Among several applications we show how to use the methods to assess specific asset pricing models and to provide non-parametric characterizations of asset pricing anomalies.

Journal: Review of Financial Studies|Volume: 8|Issue Number: 2|Pages: 237-274|Tags: Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >
  title={Econometric evaluation of asset pricing models},
  author={Hansen, Lars Peter and Heaton, John and Luttmer, Erzo GJ},
  journal={Review of Financial Studies},
  publisher={Soc Financial Studies}