Reconsideration of a simple approach to quantile regression for panel data
This note discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay’s assumption about n/Ts → 0 for some s > 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay’s estimator, we propose a simple correction that may reduce the bias. The second error concerns the incorrect asymptotic standard error of the estimator of the constant term. We show that, contrary to Canay’s assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate nT−−−√nT, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay’s estimator.
The paper documents the changes in the size of the wage distribution in Russia over the period 1994–2003. Developments in wage inequality varied a lot by sub-periods: overall wage inequality stayed stable in 1994–1996, then it jumped following the 1998 crisis and remained at higher levels for three years. In 2002 the trend reversed again and in the course of a single year wage inequality fell back to the level of the mid-1990s. We find that evolution wage inequality was largely driven by changes in the upper end of the wage distribution. Decomposition of wage inequality by population sub-groups shows that inequality has been higher for men, younger and low-educated workers, and rural inhabitants. The structure of inequality did not change much over the period from 1994 to 2003. Demographic variables (mainly gender and region) explain the largest proportion of wage dispersion (over 40% of the explained variation and 15% of total variation). Nearly equivalent is the contribution of firm characteristics with industry affiliation of employer playing the leading role. Our results show that returns to education continued to rise at all percentiles of the wage distribution converging at the level of about 8–9% of wage increase for an additional year of schooling.
Gender differences in mathematical performance have received considerable scrutiny in the fields of sociology, economics and psychology. We analyse a large data-set of high school graduates who took a standardised mathematical test in Russia in 2011 (n=738,456) and find no substantial difference in mean test scores across boys and girls. However, boys have a greater variance of scores and more numerous at top of the distribution. We apply quantile regression tj model the association between school characteristics and gender differences in test scores throughout the distribution of test scores. Male advantage in test scores, particularly at the top of the distribution, is concentrated in cities and in schools with an advanced curriculum. In other high schools, especially in the countryside, gender differences in all parts of the distribution are small. We suggest several mechanisms based on selection and school effects that account for our findings.
This article analyses the determinants of attendees’ tourism spending at professional basketball matches during the 2012/2013 season. For this purpose, it applies a linear quantile regression and considers the effect of specific sports event variables which have rarely been assessed in this type of study. Empirical results confirm that the determinants of expenditure have a different influence depending on the spending level. Individual spending is principally influenced by the origin of the attendees as well as by several other sports factors such as the time the match takes place, the admission price, or the sporting level of the rival team. The study establishes two levels of spending to identify the different behaviors that correspond to each of the factors under study. The findings could provide a useful input into tourism strategies related to the hosting of sport events.
This article addresses the issue of unobserved heterogeneity in film characteristics influence on box-office. We argue that the analysis of pooled samples, most common among researchers, does not shed light on underlying segmentations and leads to significantly different estimates obtained by researchers running similar regressions for movie success modeling. For instance, it may be expected that a restrictive MPAA rating is a box office poison for a family comedy, whereas it insignificantly influences an action movie’s revenues. Using a finite mixture model we extract two latent groups, the differences between that can be explained in part by the movie genre, the source, the creative type and the production method. On the basis of this result, the authors recommend developing separate movie success models for different segments, rather than adopting an approach, that was commonly used in previous research, when one explanatory or predictive model is developed for the whole sample of movies.
Students’ perception of the labor market makes a great deal in students’ decisions concerning effort to study, work during university studies, etc. The aim of the research is to define whether students identify significant returns on effort with respect to wage after graduation. Moreover, it seems reasonable to single out other factors that students expect to influence their wage significantly. With the use of the data of Russian students’ questionnaire conducted in 2012 within the framework of the Monitor of Economics of Education project the regressions with the use of instrumental variables and stochastic frontier approach are estimated. The results suggest effort is considered as an influential factor in determining wage by Russian students if students’ incomplete awareness about labor market is taken into account. Besides, university quality, abilities, wage received by working students, region, specialty, family’s income and gender make the difference in the amount of wage expected by students. For additional analysis the 20% and 80% quantile regressions are built. According to the results, persons having the highest wage forecasts base them on the amount of wage offered to working students on the labor market and do not correct them subject to their effort, university quality and abilities. At the same time another group of students, keeping similar basis for expectation formation as a previously analyzed group, expect significant contribution of effort and abilities.
Using changes in consumption as a proxy for ‘vulnerability’ we identify the characteristics associated with vulnerability around the time of the 1998 Russian financial crisis. In addition, we examine the role of formal and informal safety nets in preserving individual well being. We apply quantile regression techniques in order to identify the characteristics associated with vulnerability across the two periods. Amongst those most vulnerable during the crisis were, less educated individuals living in urban areas, in households containing greater numbers of pensioners. Furthermore, we found that increases in home production and help from relatives acted to decrease vulnerability, especially amongst those suffering the largest changes in consumption. Following the crisis, amongst the least vulnerable were, better educated individuals, resident in urban areas, able to increase home production, and in receipt of improved pension payments and child benefits.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.