Modeling Firm-Size Distribution Using Box-Cox Heteroscedastic Regression

Using the Box-Cox regression model with heteroscedasticity, we examine the size distribution of firms. Analyzing the data set of Portuguese manufacturing firms as in Machado and Mata (2000), we show that our approach compares favorably against the Box-Cox quantile regression method. In particular, we are able to answer the key questions addressed by Machado and Mata, with the additional advantage that our empirical quantile functions are monotonic. Furthermore, confidence intervals of the regression quantiles are easy to compute, and the estimation of the Box-Cox heteroscedastic regression model is straightforward.Box-Cox transformation, Firm-size distribution, Quantile regression.

A Note on Implementing Box-Cox Quantile Regression

The Box-Cox quantile regression model using the two stage method suggested by Chamberlain (1994) and Buchinsky (1995) provides a flexible and numerically attractive extension of linear quantile regression techniques. However, the objective function in stage two of the method may not exists. We suggest a simple modification of the estimator which is easy to implement. The modified estimator is still pn{consistent and we derive its asymptotic distribution. A simulation study confirms that the modified estimator works well in situations, where the original estimator is not well defined. --Box-Cox quantile regression,iterative estimator

New insights on unemployment duration and post unemployment earnings in Germany: censored Box-Cox quantile regression at work

In light of nonstationary search theory (van den Berg, 1990), this paper estimates the effects of benefit entitlement periods and the size of unemployment benefits on unemployment durations and post{unemployment earnings in West Germany. For the unemployment duration, we estimate censored Box{Cox quantile regression, which is robust with respect to the specification of the unobserved error distribution and avoids the common proportional hazard assumption. Our results suggest that the length of benefit entitlement is only of minor importance for the duration of search unemployment and for post unemployment wages. A high wage replacement rate in the low wage sector seem to considerably elongate the duration of unemployment and it is associated with higher post unemployment wages. --Box Cox quantile regression,hazard rate,unemployment,wage

A Note on Implementing Box-Cox Quantile Regression

The Box-Cox quantile regression model using the two stage method introduced by Chamberlain (1994) and Buchinsky (1995) provides an attractive extension of linear quantile regression techniques. However, a major numerical problem exists when implementing this method which has not been addressed so far in the literature. We suggest a simple solution modifying the estimator slightly. This modification is easy to implement. The modified estimator is still n–consistent and its asymptotic distribution can easily be derived. A simulation study confirms that the modified estimator works well

Quantiles for Fractions and Other Mixed Data

This paper studies the estimation of quantile regression for fractional data, focusing on the case where there are mass-points at zero or/and one. More generally, we propose a simple strategy for the estimation of the conditional quantiles of data from mixed distributions, which combines standard results on the estimation of censored and Box-Cox quantile regressions. The implementation of the proposed method is illustrated using a well-known dataset.

Quantiles for Fractions and Other Mixed Data

This paper studies the estimation of quantile regression for fractional data, focusing on the case where there are mass-points at zero or/and one. More generally, we propose a simple strategy for the estimation of the conditional quantiles of data from mixed distributions, which combines standard results on the estimation of censored and Box-Cox quantile regressions. The implementation of the proposed method is illustrated using a well-known dataset

Using Quantile Regression for Duration Analysis

Quantile regression methods are emerging as a popular technique in econometrics and biometrics for exploring the distribution of duration data. This paper discusses quantile regression for duration analysis allowing for a flexible specification of the functional relationship and of the error distribution. Censored quantile regression address the issue of right censoring of the response variable which is common in duration analysis. We compare quantile regression to standard duration models. Quantile regression do not impose a proportional effect of the covariates on the hazard over the duration time. However, the method can not take account of time{varying covariates and it has not been extended so far to allow for unobserved heterogeneity and competing risks. We also discuss how hazard rates can be estimated using quantile regression methods. A small application with German register data on unemployment duration for younger workers demonstrates the applicability and the usefulness of quantile regression for empirical duration analysis. --censored quantile regression,unemployment duration,unobserved heterogeneity,hazard rate

Reference charts for fetal cerebellar vermis height: A prospective cross-sectional study of 10605 fetuses

A prospective cross-sectional study between September 2009 and December 2014 was carried out at ALTAMEDICA Fetal–Maternal Medical Centre, Rome, Italy. Of 25203 fetal biometric measurements, 12167 (48%) measurements of the cerebellar vermis were available. After excluding 1562 (12.8%) measurements, a total of 10605 (87.2%) fetuses were considered and analyzed once only. Parametric and nonparametric quantile regression models were used for the statistical analysis. In order to evaluate the robustness of the proposed reference charts regarding various distributional assumptions on the ultrasound measurements at hand, we compared the gestational age-specific reference curves we produced through the statistical methods used. Normal mean height based on parametric and nonparametric methods were defined for each week of gestation and the regression equation expressing the height of the cerebellar vermis as a function of gestational age was calculated. Finally the correlation between dimension/gestation was measured

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.Comment: 21 pages, 3 figures, 5 tables. Computational Statistics and Data Analysis, 17 October 2011, ISSN 0167-9473 (http://www.sciencedirect.com/science/article/pii/S0167947311003628

A quantile approach to the box-cox transformation in random samples.

This paper presents an alternative approach to the likelihood methods for estimating the parameter A in the Box-Cox family of transformations when the data arise from a random sample. The method is based on a representation of the quantile function of the variable under consideration. Theoretical properties of the method, its practical applications and comparison with the likelihood approach are studied.Asymptotic relative efficiency (ARE); Box-Cox transformation; Influential observations; Quantile function; Kernel density estimation;