Analyzing firm growth with parametric quantile regression
用参数分位数回归方法研究英国制造业企业的成长过程，发现厚尾分布（如非对称逻辑分布）比正态分布拟合更好，并检测到企业规模对成长的正向位置效应。
Abstract We apply quantile regression coefficient modeling (QRCM) to investigate the firm growth process. QRCM imposes a parametric structure to the conditional quantile function and allows to estimate all quantiles at once by minimizing an integrated loss. To handle the presence of repeated measures, we fit a two-level model in which both the level-1 and level-2 parts of the distribution depend on predictors according to a quantile regression (QR) structure. Compared with standard QR, in which different quantiles are estimated one at a time, QRCM improves statistical efficiency, mitigates quantile crossing, simplifies estimation of extremes, and allows to incorporate identifying assumptions. We investigate growth in a panel of UK manufacturing firms. Our analysis accounts for variance-size scaling and allows to disentangle the location effect of firm size on growth from the scale effect. We propose alternative parametrizations of the QR coefficients: a flexible model based on Legendre polynomials, and a variety of more structured models that rely on known quantile functions, such as the Gaussian, logistic, and asymmetric logistic distributions, that differ in their tail behavior. Our results indicate that fat-tailed models, such as the asymmetric logistic distribution, provide a better fit than the normal distribution. We are able to detect a positive location effect and to obtain efficient estimates of the extreme quantiles.