Economic Applications of Quantile Regression

In the classical methodology of least-squares regression the conditional mean function, the function that describes how the mean of y changes with the vector of covariates x, is (almost) all we need to know about the relationship between y and x. This is often perceived as the ‘systematic component’ around which y fluctuates due to an “erratic component”. The crucial, and convenient, thing about this view is that the error is assumed to have precisely the same distribution whatever values may be taken by the components of the vector x. If this is the case, we can be fully satisfied with an estimated model of the conditional mean function, supplemented perhaps by an estimate of the conditional dispersion of y around its mean.

Considerable effort has been exercised in estimating mean returns to education while carefully considering biases arising from unmeasured ability and measurement error. Recent work has investigated whether there are variations from the “mean” return to education across the population with mixed results. We use an instrumental variables estimator for quantile regression on a sample of twins to estimate an entire family of returns to education at different quantiles of the conditional distribution of wages while addressing simultaneity and measurement error biases. We test whether there is individual heterogeneity in returns to education and find that: more able individuals obtain more schooling perhaps due to lower marginal costs and/or higher marginal benefits of schooling and that higher ability individuals (those further to the right in the conditional distribution of wages) have higher returns to schooling consistent with a non-trivial interaction between schooling and unobserved abilities in the generation of earnings. The estimated returns are never lower than 9 percent and can be as high as 13 percent at the top of the conditional distribution of wages but they vary significantly only along the lower to middle quantiles. Our findings may have meaningful implications for the design of educational policies.

The rise of unemployment in West Germany is often attributed to an inflexibility of the wage structure in the face of a skill bias in labor demand trends. In addition, there is concern in Germany that during the 70s and 80s unions were pursuing a too egalitarian wage policy. In a cohort analysis, we estimate quantile regressions of wages taking account of the censoring in the data. We present a new framework to describe trends in the entire wage distribution across education and age groups in a parsimonious way. We explore whether wage trends are uniform across cohorts, thus defining a macroeconomic wage trend. Our findings are that wages of workers with intermediate education levels, among them especially those of young workers, deteriorated slightly relative to both high and low education levels. Wage inequality within age-education groups stayed fairly constant. Nevertheless, the German wage structure was fairly stable, especially in international comparison. The results appear consistent with a skill bias in labor demand trends, recognizing that union wages are only likely to be binding floors for low-wage earners.

This study uses quantile regression techniques to analyze changes in the returns to education for women. The data used is the March Current Population Survey for the years 1968, 1973, 1979, 1986 and 1990. The first step in estimating the single (linear) index selection equation uses Ichimura’s (1993) semiparametric procedure. To correct for an unknown form of a sample selection bias in the quantile regression, the second step incorporates a nonparametric method, using an idea similar to one developed by Heckman (1980) and Newey (1991) for mean regression, and Buchinsky (1998) for quantile regression.

The results show that: (a) the returns to education increased enormously for the younger cohorts, but very little for the older cohorts; (b) in general the returns are higher at the lower quantiles in the beginning of the sample period and higher at the higher quantiles by the end of the sample period; (c) there is a significant sample selection bias for all age groups at almost all quantiles; (d) toward the end of the sample period there is a significant convergence of the returns at the various quantiles, especially for the younger cohorts and age groups; and (e) the semiparametric estimates of the selection equation are considerably different from those obtained for a parametric probit model.

This paper uses quantile regressions to describe the conditional wage distribution in Portugal and its evolution over the 1980’s as well as the implications for increased wage inequality. We find that, although returns to schooling are positive at all quantiles, education is relatively more valued for highly paid jobs. Consequently, schooling has a positive impact on wage inequality. Moreover, this tendency has sharpened over the period. We also find that most of the estimated change in wage inequality was due to changes in the distribution of the worker’s attributes, rather than to increased inequality within a particular type of worker.

In this paper we analyze the increase in wage inequality observed in the Uruguayan labour market during the last decade, by studying how the changes in minimum wage and returns to education affected the wage structure. Although in most developed countries a significant proportion of the increase in wage inequality is explained by a fall in the real minimum wage, this is not the case for the Uruguayan labour market. We observe that returns to education increased significantly, which could explain the increase of wage dispersion by its effects on the upper tail of the wage distribution. To derive these conclusions we follow a parametric and nonparametric quantile regression approach.

In this paper we re-examine the link between subjective perceptions and objective measures of wage discrimination by estimating the mean and several quantiles in the conditional wage distribution of men and women in order to decompose the gender wage gap into the part attributed to different characteristics and the part attributable to differential returns to these characteristics at points other than the conditional expectation. In the process we take into account the endogeneity of educational choice and the participation decision of women. The results suggest that the absolute wage gap and the component of the latter that can be attributed to different returns to characteristics increase over the wage scale.

We investigate the determinants of wages in Zambia and based on the quantile regression approach, we analyze how their effects differ at different points in the wage distribution and over time. We use three cross-sections of Zambian household data from the early nineties, which was a period of economic transition, because items as privatization and deregulation were on the political agenda. The focus is placed on the public-private sector wage gap, and the results show that this gap was relatively favorable for the low-skilled and less favorable for the high-skilled. This picture was further strengthened during the periosd 1991–1996.

The estimation of labor supply elasticities has been an important issue in the economic literature. Yet all works have estimated conditional mean labor supply functions only. The objective of this paper is to obtain more information on labor supply, estimating a conditional quantile labor supply function. We use a sample of prime age urban males employees in Brazil. Two stage estimators are used as the net wage and nonlabor income are found to be endogenous to the model. Contrary to previous works using conditional mean estimators, it is found that labor supply elasticities vary significantly and asymmetrically across hours of work. While the income and wage elasticities at the standard work week are zero, for those working longer hours the elasticities are negative.

We argue that quantile regression methods can play a constructive role in the analysis of duration (survival) data offering a more flexible, more complete analysis than is typically available with more conventional methods. We illustrate the approach with a reanalysis of the data from the Pennsylvania Reemployment Bonus Experiments. These experiments, conducted in 1988–89, were designed to test the efficacy of cash bonuses paid for early reemployment in shortening the length of insured unemployment spells

In this paper the controversial educational topic of class size reduction is addressed. Controlling for a large number of observable characteristics and potential endogeneity in the class size variable, an educational production function is estimated using a quantile regression technique. The “conventional wisdom” that class size reduction is a viable means to increase scholastic achievement is discounted. Rather, the results point towards a far stronger peer effect through which class size reduction may play an important role. Due to heterogeneity in the newly identified peer effect, class size reduction is shown to be a potentially regressive policy measure.

This paper utilizes quantile-regression techniques in order to estimate the effects of demographics and maternal behavior during pregnancy at various quantiles of the birthweight distribution. Due to the high costs and longterm effects (both medical and economic) associated with low-birthweight babies, there is a great deal of interest in quantifying these effects, particularly at the lower end of the birthweight distribution. Using large samples of 1992 and 1996 births in the United States, the quantile-regression estimates indicate that several factors (including race, education, and prenatal care) have a significantly higher impact at lower quantiles and lower impact at higher quantiles. These effects at lower quantiles are underestimated by least-squares regression estimates. The inequality in birthweights implied by these results is quite significant, and there is little indication that the inequality has changed much in recent years.

This paper applies the nonparametric quantile regression estimation procedure to the analysis of the innovation-firm size relationship using Korean manufacturing firms data. Due to the high asymmetric distribution of R&D expenditure, the mean regression does not capture properly the stylized facts of R&D behavior; hence it underestimates the sales elasticity. Comparing the parametric estimates and nonparametric estimates allows us to see that there exists a nonlinear relationship in innovative activity and sales. Dividing the data into three groups according to the sales volume, the elasticity in the medium-sized firms is the biggest for scientific firms. This result conforms that the findings of Scherer (1965) coincide with findings from Korean manufacturing firms data in the sense that R&D expenditure tends to increase faster than firm size with size up to a point and then more slowly among larger firms. For the non-scientific firms, it steadily increases showing increasing returns to scale

This paper considers flexible conditional (regression) measures of market risk. Value-at-Risk modeling is cast in terms of the quantile regression function — the inverse of the conditional distribution function. A basic specification analysis relates its functional forms to the benchmark models of returns and asset pricing. We stress important aspects of measuring the extremal and intermediate conditional risk. An empirical application characterizes the key economic determinants of various levels of conditional risk.

In this paper we propose a consistent test of the linearity of quantile regression models, similar to the Integrated Conditional Moment (ICM) test of Bierens (1982) and Bierens and Ploberger (1997). This test requires reestimation of the quantile regression model by minimizing the ICM test statistic with respect to the parameters. We apply this ICM test to examine the correctness of the functional form of three median regression wage equations.