It has been well known in financial economics that factor betas depend on observed instruments such as firm specific characteristics and macroeconomic variables, and a key object of interest is the effect of instruments on the factor betas. One of the key features of our model is that we specify the factor betas as functions of time-varying observed instruments that pick up long-run beta fluctuations, plus an orthogonal idiosyncratic component that captures high-frequency movements in beta . It is often the case that researchers do not know whether or not the idiosyncratic beta exists, or its strengths, and thus uniformity is essential for inferences. It is found that the limiting distribution of the estimated instrument effect has a discontinuity when the strength of the idiosyncratic beta is near zero , which makes usual inferences fail to be valid and produce misleading results. In addition, the usual "plug-in" method using the estimated asymptotic variance is only valid pointwise . The central goal is to make inference about the effect on the betas of firms' instruments, and to conduct out-of-sample forecast of integrated volatilities using estimated factors. Both procedures should be valid uniformly over a broad class of data generating processes for idiosyncratic betas with various signal strengths and degrees of time-variant. We show that a cross-sectional bootstrap procedure is essential for the uniform inference, and our procedure also features a bias correction for the effect of estimating unknown factors.
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.
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instruments
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characteristics
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a key object of interest is the effect of instruments on the factor betas. One of the key features of our model is that we
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the sum of characteristic effects and
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component
parameter
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in beta
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idiosyncratic beta
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uniformity is essential for inferences.
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.
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instrument effect
characteristic effects
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strength
variance
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beta is near zero
parameter is near the boundary (zero)
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usual inferences fail to be valid and produce misleading results. In addition,
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. The central goal is to make inference about the effect on the betas of firms' instruments, and to conduct out-of-sample forecast of integrated volatilities using estimated factors. Both procedures should be valid uniformly over a broad class of data generating processes for idiosyncratic betas with various signal strengths and degrees of time-variant.
and may produce either over- or under- coveraging probabilities.
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the uniformity can be achieved by
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procedure is essential for the uniform inference, and our procedure
. Our procedure allows both known and estimated factors, and