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Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.

Quantile and quantile effect (QE) functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This article offers a simple, practical construction of simultaneous confidence bands for quantile and QE functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling methods for observed and counterfactual distributions, and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. We find that universal insurance coverage increases the number of doctor visits across the entire distribution, and that the racial test score gap is small at early ages but grows with age due to socio-economic factors especially at the top of the distribution. Supplementary materials (additional results, R package, replication files) for this article are available online.

In this paper, we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest. Both fixed and infinitesimal changes are considered. We show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed, but are typically only partially identified if its distribution is discrete. For the latter case, we derive informative bounds, making use of the available information. We also discuss estimation and inference.

We contribute to understanding the impact of potential drivers of farm income inequality and the redistributive impact of Common Agricultural Policy (CAP) payments. Our approach provides information at any quantile of the income distribution, in contrast to the widely used Gini coefficient. Income growth and inequality dynamics of French commercial farms between 2000 and 2017 are found to be explained by a change in both income levels and farm characteristics. Further, CAP payments are shown to participate in levelling off income inequalities, with Pillar 1 and 2 payments performing differently along the distribution. Our results may help inform on-going policy debates about fairness in the distribution of farm support and structural change implications for the future of European agriculture.

We consider the identification of counterfactual distributions and treatment effects when the outcome variables and conditioning covariates are observed in separate data sets. Under the standard selection on observables assumption, the counterfactual distributions and treatment effect parameters are no longer point identified. However, applying the classical monotone rearrangement inequality, we derive sharp bounds on the counterfactual distributions and policy parameters of interest.

This paper suggests a generalization of covariate shifts to study distributional impacts on inequality and distributional measures. It builds on the recentered influence function (RIF) regression method, originally designed for location shifts in covariates, and extends it to general policy interventions, such as location–scale or asymmetric interventions. Numerical simulations for the Gini, Theil, and Atkinson indexes demonstrate strong performance across a myriad of cases and distributional measures. An empirical application examining changes in Mincerian equations is presented to illustrate the method.

In this article, we study the structure of the composition effect, which is the part of the observed between-group difference in the distribution of some economic outcome that can be explained by differences in the distribution of covariates. Using results from copula theory, we derive a new representation that contains three types of components: (i) the \"direct contribution\" of each covariate due to between-group differences in the respective marginal distributions, (ii) several \"two-way\" and \"higher-order interaction effects\" due to the interplay between two or more marginal distributions, and (iii) a \"dependence effect\" accounting for between-group differences in dependence patterns among the covariates. We show how these components can be estimated in practice, and use our method to study the evolution of the wage distribution in the United States between 1985 and 2005. We obtain some new and interesting empirical findings. For example, our estimates suggest that the dependence effect alone can explain about one-fifth of the increase in wage inequality over that period (as measured by the difference between the 90% and the 10% quantile).

This study develops a biennial Malmquist–Luenberger productivity index that is used to measure the sources of economic growth by utilizing data envelopment analysis and the directional distance function. Taking restrictions on resources and the environment into account based on the green growth accounting framework; we split economic growth into seven components: technical efficiency change, technological change, labor effect, capital effect, energy effect, output structure effect and environmental regulation effect. Further, we apply the Silverman test and Li-Fan-Ullah nonparametric test in combination with kernel distribution to test for the counterfactual contributions at the provincial level in China from 1998 to 2012. The empirical results show that: (1) technological progress and TFP make positive contributions to economic growth in China, while technical efficiency drags it down; (2) the effect of output structure and CO2 emissions with environmental regulation restrain economic growth in some provinces; and (3) overall, physical capital accumulation is the most important driving force for economic take-off, irrespective of whether the government adopts environmental regulations.

This paper studies the gender wage gap by educational attainment in Italy using the 1994–2001 ECHP data. We estimate wage distributions in the presence of covariates and sample selection separately for highly and low educated men and women. Then, we decompose the gender wage gap across all the wage distribution and isolate the part due to gender differences in the remunerations of the similar characteristics. We find that women are penalized especially if low educated. When we control for sample selection induced by unobservables, the penalties for low educated women become even larger, above all at the bottom of the wage distribution.

This paper uses household survey data from five Southeast Asian countries (Cambodia, Indonesia, the Philippines, Thailand and Vietnam) to examine changes in the distribution of per capita consumption over the period 2006–2014. We perform a decomposition analysis to study the factors that contribute to changes in per capita consumption at the mean and along the entire distribution. Our findings indicate that changes in per capita consumption over time are mainly driven by changes in household income, especially at the top of the distribution. We also find that a sizeable part of the changes in per capita consumption may be attributed to changes in the household size and educational attainment. Urbanization typically contributes to an increase in per capita consumption with exception of the Philippines, where urbanization has declined over time. The contribution of changes in demographic characteristics to changes in per capita consumption is generally positive but relatively small. Our findings highlight the importance of policies that aim to alleviate poverty by enhancing educational attainment and reducing fertility. These policies are particularly relevant in Cambodia, Indonesia and the Philippines, where national fertility rates remain high.