Papers

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.

@article{hansen1998spectral,
  title={Spectral Methods for Identifying Scalar Diffusions},
  author={Hansen, Lars Peter and Scheinkman, Jos{'e} Alexandre and Touzi, Nizar},
  journal={Journal of Econometrics},
  volume={86},
  number={1},
  pages={1--32},
  year={1998},
  publisher={Elsevier}
}

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.

@article{conley1997short,
  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},
  volume={10},
  number={3},
  pages={525--577},
  year={1997},
  publisher={Soc Financial Studies}
}

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.

@article{conley1997bootstrapping,
  title={Bootstrapping the Long Run},
  author={Conley, Timothy G and Hansen, Lars Peter and Liu, Wen-Fang},
  journal={Macroeconomic Dynamics},
  volume={1},
  number={02},
  pages={279--311},
  year={1997},
  publisher={Cambridge University Press}
}

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.

@article{hansen:1997assessing,
  title={Assessing Specification Errors in Stochastic Discount Factor Models},
  author={Hansen, Lars Peter and Jagannathan, Ravi},
  journal={The Journal of Finance},
  volume={52},
  number={2},
  pages={557--590},
  year={1997},
  publisher={Wiley Online Library}
}

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.

@article{hansen:1996finite,
  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},
  volume={14},
  number={3},
  pages={262--280},
  year={1996},
  publisher={Taylor & Francis Group}
}