Work in Progress

"Semiparametric Estimation of A Nonlinear Error-Correction Model" (with A. Rahbek)

ABSTRACT: We consider a nonlinear cointegration model where the transfer function (or loadings) of the stationary relationships is unknown and potentially nonlinear. We propose estimators of the parameters for the linear stationary relationships and the nonparametric transfer function, and derive their asymptotic properties.

"Estimation of Stochastic Volatility Models By Nonparametric Filtering" (with S. Kanaya)

ABSTRACT: A new estimation method of stochastic volatility models is proposed based on the nonparametric filter of the instantaneous volatility process of Kristensen (2006). We propose to use standard estimation methods for fully observed diffusion processes but with the filtered volatility process replacing the latent process. The estimator will carry a bias due to the use of the filtered volatility instead of the actual volatility, but under regularity conditons this vanishes asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. The estimation strategy is applicable both for parametric and nonparametric stochastic volatility models, and we give theoretical results for both. A simulation study examines the estimators finite-sample properties.

"Testing Conditional Factor Models" (with Andrew Ang)

ABSTRACT: In conditional factor models with time-varying factor loadings, testing whether an alpha is significantly different from zero, either unconditionally or at a point in time, depends crucially on the time-series variation of betas. We estimate time-varying alphas and betas using nonparametric techniques that allow us to estimate the alpha's and beta's as functions at any given point of time. Using these estimators, we derive a methodology that can test whether conditional alphas averaged over the sample are different from zero and for constancy of the factor loadings.

"Higher Order Improvements for Approximate Estimators" (with Bernard Salanié)

ABSTRACT: We propose two methods to improve on the precision of approximate estimators. Both of these methods only carry a small additional computation burden. The first method is targeted at estimators based on stochastic approximators, such as simulation-based estimators. It consists of a general formula that corrects the objective function and eliminates the leading order of the additional bias of the approximate estimator. Our second proposed improvement is a two-step method which applies quite generally. In the first step, we compute the approximate estimator, using an approximator that may be coarser than what is usually done; and in the second step we run one or several Newton-Raphson iterations based on the same objective function, but with a much finer degree of approximation. The second step removes some or all of the additional bias and variance of the initial approximate estimator.

"Estimation of Non-additive Engle Curves under Revealed Preference Restrictions" (with R. Blundell and R. Matzkin)

ABSTRACT: In the econometric analysis of Engel curves it is standard to assume an additive relationship between the expenditure share, the total expenditure and the error term. In this paper, we relax this assumption and instead consider non-separable relations between the three variables. Furthermore, we impose revealed preferences restrictions in the estimation. A nonparametric sieve estimator is developed, and its asymptotic properties derived. We apply our estimator the UK Family Expenditure Survey data.

"Estimation of Hidden Markov Models with Nonparametric Simulated Maximum Likelihood" (with Y. Shin)

ABSTRACT: We extend the nonparametric simulated maximum-likelihood estimator (NPSMLE) of Kristensen and Shin (2006) to include built-in nonlinear filtering. By recursively approximating the unknown conditional densities, our method enables calculation of simulated version of the MLE of general dynamic models with latent variables---including time-inhomogeneous and non-stationary processes. We establish the asymptotic properties of the NPSMLE’s for hidden Markov models, and then demonstrate the usefulness of our proposed method with Monte Carlo studies.