Uniform Inference for Characteristic Effects of Large Continuous-Time Linear Models

52 Pages Posted: 15 Nov 2017 Last revised: 3 Dec 2018

See all articles by Yuan Liao

Yuan Liao

Rutgers, The State University of New Jersey - Department of Economics

Xiye Yang

Rutgers, The State University of New Jersey - Department of Economics

Date Written: November 26, 2018

Abstract

We consider continuous-time models with a large panel of moment conditions, where the structural parameter depends on a set of characteristics, whose effects are of interest. The leading example is the linear factor model in financial economics where factor betas depend on observed characteristics such as firm specific instruments and macroeconomic variables, and their effects pick up long-run time-varying beta fluctuations. We specify the factor betas as the sum of characteristic effects and an orthogonal idiosyncratic parameter that captures high-frequency movements. It is often the case that researchers do not know whether or not the latter exists, or its strengths, and thus the inference about the characteristic effects should be valid uniformly over a broad class of data generating processes for idiosyncratic parameters. We construct our estimation and inference in a two-step continuous-time GMM framework. It is found that the limiting distribution of the estimated characteristic effects has a discontinuity when the variance of the idiosyncratic parameter is near the boundary (zero), which makes the usual ``plug-in" method using the estimated asymptotic variance only valid pointwise and may produce either over- or under- coveraging probabilities. We show that the uniformity can be achieved by cross-sectional bootstrap. Our procedure allows both known and estimated factors, and also features a bias correction for the effect of estimating unknown factors.

Keywords: Large dimensions, high-frequency data, cross-sectional bootstrap

JEL Classification: C55, C38, G12

Suggested Citation

Liao, Yuan and Yang, Xiye, Uniform Inference for Characteristic Effects of Large Continuous-Time Linear Models (November 26, 2018). Available at SSRN: https://ssrn.com/abstract=3069985 or http://dx.doi.org/10.2139/ssrn.3069985

Yuan Liao (Contact Author)

Rutgers, The State University of New Jersey - Department of Economics ( email )

Xiye Yang

Rutgers, The State University of New Jersey - Department of Economics ( email )

75 Hamilton Street
New Brunswick, NJ 08901
United States

HOME PAGE: http://economics.rutgers.edu/people/474-xiye-yang

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