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

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 >

@article{hansensingleton:1996, 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}, volume={14}, number={1}, pages={53--68}, year={1996}, publisher={Taylor & Francis} }✕

## Econometric Evaluation of Asset Pricing Models

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 >

@article{hhl:1995, title={Econometric evaluation of asset pricing models}, author={Hansen, Lars Peter and Heaton, John and Luttmer, Erzo GJ}, journal={Review of Financial Studies}, volume={8}, number={2}, pages={237--274}, year={1995}, publisher={Soc Financial Studies} }✕

## Back To the Future: Generating Moment Implications for Continuous Time Markov-Processes

Continuous-time Markov processes can be characterized conveniently by their infinitesimal generators. For such processes there exist forward and reverse-time generators. We show how to use these generators to construct moment conditions implied by stationary Markov processes. Generalized method of moments estimators and tests can be constructed using these moment conditions. The resulting econometric methods are designed to be applied to discrete-time data obtained by sampling continuous-time Markov processes

**Journal:**Econometrica|

**Volume:**63|

**Issue Number:**4|

**Pages:**767-804|

**Tags:**Econometrics|Export BibTeX >

@misc{hansen1993back, title={Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes}, author={Hansen, Lars P and Scheinkman, Jose A}, year={1993}, publisher={National Bureau of Economic Research Cambridge, Mass., USA} }✕

## Discounted Linear Exponential Quadratic Gaussian Control

In this note, we describe a recursive formulation of discounted costs for a linear quadratic exponential Gaussian linear regulator problem which implies time-invariant linear decision rules in the infinite horizon case. Time invariance in the discounted case is attained by surrendering state-separability of the risk-adjusted costs.

**Journal:**IEEE Transactions on Automatic Control|

**Volume:**40|

**Issue Number:**5|

**Pages:**968-971|

**Tags:**Econometrics|Export BibTeX >

@article{hansensargent:1995},

Author = {Lars P. Hansen and Thomas J. Sargent},

Journal = {IEEE Transactions on Automatic Control},

Month = {May},

Number = {5},

Pages = {968-971},

Title = {Discounted Linear Exponential Quadratic Gaussian Control},

Volume = {40},

Year = {1995}}

## Seasonality and Approximation Errors in Rational-Expectations Models

A frequency domain representation of the approximation criterion that is implicit in Gaussian maximum likelihood estimation is applied to study the effects of using seasonally adjusted versus seasonally unadjusted data to estimate rational expectations models. Three classes of economic mechanisms for generating seasonality are described. Approximating parameter estimates are computed numerically for several examples.

**Journal:**Journal of Econometrics|

**Volume:**55|

**Pages:**21-55|

**Tags:**Econometrics|Export BibTeX >

@article{hansensargent:1993, title={Seasonality and Approximation Errors in Rational Expectations Models}, author={Hansen, Lars P. and Sargent, Thomas J.}, journal={Journal of Econometrics}, volume={55}, number={1-2}, pages={21--55}, year={1993}, publisher={Elsevier} }✕

## Asset Pricing Explorations for Macroeconomics

Asset market data are often ignored in evaluating macroeconomic models, and aggregate quantity data are often avoided in empirical investigations of asset market returns. While there may be short-term benefits to proceeding along separate lines, we argue that security market data are among the most sensitive and, hence, attractive proving grounds for models of the aggregate economy.

**Journal:**NBER Macroeconomics Annual 1992|

**Volume:**7|

**Pages:**115-182|

**Tags:**Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >

@book{hansencochrane:1993,

title={Asset Pricing Explorations for Macroeconomics},

author={Hansen, Lars P. and Cochrane, John H.},

year={1993},

publisher={National Bureau of Economic Research}

}

✕## Implications of Security Market Data for Models of Dynamic Economies

We show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRSs) of consumers. Our approach (i) is nonparametric and applies to a rich class of models of dynamic economies, (ii) characterizes the duality between the mean–standard deviation frontier for IMRSs and the familiear mean- standard deviation frontier for asset returns, and (iii) exploits the restriction that IMRSs are positive random variables. The region provides a convenient summary of the sense in which asset market data are anaomalous from the vantage point of intertemporal asset pricing theory.

**Journal:**Journal of Political Economy|

**Volume:**99|

**Issue Number:**2|

**Pages:**225-262|

**Tags:**Econometrics, Financial Market Linkages to the Macroeconomy|Export BibTeX >

@article{hansen:1991implications,

title={Implications of Security Market Data for Models of Dynamic Economies},

author={Hansen, Lars Peter and Jagannathan, Ravi},

journal={Journal of Political Economy},

volume={99}, number={2},

pages={225–262}, year={1991},

publisher={The University of Chicago Press}

}

## Computing Semiparametric Efficiency Bounds for Linear Time Series Models

**Title of book:**Nonparametric and Semiparametric Methods in Econometrics and Statistics|

**Editor(s):**W.A. Barnett, J. Powell, G.E. Tauchen|

**Place of Publication:**Cambridge|

**Publisher:**Cambridge University Press|

**Tags:**Econometrics|Export BibTeX >

@article{hansen:1991computing, title={Computing Semi-Parametric Efficiency Bounds for Linear Time Series Models}, author={Hansen, Lars Peter and Singleton, Kenneth J}, journal={Nonparametric and Semiparametric Methods in Econometrics and Statistics}, pages={387--412}, year={1991}, publisher={Cambridge University Press} }✕

## Lecture Notes on Least Squares Prediction Theory

In these notes we establish some basic results for least squares prediction theory. These results are useful in a variety of contexts. For instance, they are valuable for solving linear rational expectations models, representing covariance stationary time series processes, and obtaining martingale difference decompositions of strictly stationary processes.

The basic mathematical construct used in these notes is an inner product defined between two random variables. This inner product is calculated by taking the expectation of the product of the two random variables. Many of the results obtained using this particular inner prod- uct are analogous to results obtained using the standard inner product on multi-dimensional Euclidean spaces. Hence intuition obtained for Euclidean spaces can be quite valuable in this context as well.

The formal mathematical machinery that is exploited in these notes is the Hilbert space theory. There is a variety of references on Hilbert spaces that should provide good complementary reading, e.g. Hal- mos (1957) and Luenberger (1969).

**Pages:**13-44|

**Title of book:**Rational Expectations Econometrics|

**Editor(s):**Lars Peter Hansen and Thomas J. Sargent|

**Place of Publication:**Boulder and Oxford|

**Publisher:**Westview Press|

**Tags:**Econometrics|Export BibTeX >

@article{hansen:1991lecture, title={Lecture Notes on Least Squares Prediction Theory}, author={Hansen, LP and Sargent, TJ}, journal={Rational Expectations Econometrics}, year={1991} }✕

## Exact Linear Rational Expectations Models: Specification and Estimation

A distinguishing characteristic of econometric models that incorporate rational expectations is the presence of restrictions across the parameters of different equations. These restrictions emerge because people’s decisions are supposed to depend on the stochastic environment which they confront. Consequently, equations describing variables af- fected by people’s decisions inherit parameters from the equations that describe the environment. As it turns out, even for models that are linear in the variables, these cross-equation restrictions on the parameters can be complicated and often highly nonlinear.

**Pages:**45-76|

**Title of book:**Rational Expectations Econometrics|

**Editor(s):**Lars Peter Hansen and Thomas J. Sargent|

**Place of Publication:**Boulder and Oxford|

**Publisher:**Westview Press|

**Tags:**Econometrics|Export BibTeX >

@techreport{hansen1981exact, title={Exact Linear Rational Expectations Models: Specification and Estimation}, author={Hansen, Lars Peter and Sargent, Thomas J and others}, year={1981}, institution={Federal Reserve Bank of Minneapolis} }✕