arXiv subjects

Francis Vella

Publications and source records attributed to Francis Vella.

10 recordsLinked to original sources

arXiv2025

Bivariate Distribution Regression; Theory, Estimation and an Application to Intergenerational Mobility

We employ distribution regression (DR) to estimate the joint distribution of two outcome variables conditional on chosen covariates. While Bivariate Distribution Regression (BDR) is useful in a variety of settings, it is particularly valuable when some dependence between the outcomes persists after accounting for the impact of the covariates. Our analysis relies on a result from Chernozhukov et al. (2018) which shows that any conditional joint distribution has a local Gaussian representation. We describe how BDR can be implemented and present some associated functionals of interest. As modeling the unexplained dependence is a key feature of BDR, we focus on functionals related to this dependence. We decompose the difference between the joint distributions for different groups into composition, marginal and sorting effects. We provide a similar decomposition for the transition matrices which describe how location in the distribution in one of the outcomes is associated with location in the other. Our theoretical contributions are the derivation of the properties of these estimated functionals and appropriate procedures for inference. Our empirical illustration focuses on intergenerational mobility. Using the Panel Survey of Income Dynamics data, we model the joint distribution of parents' and children's earnings. By comparing the observed distribution with constructed counterfactuals, we isolate the impact of observable and unobservable factors on the observed joint distribution. We also evaluate the forces responsible for the difference between the transition matrices of sons' and daughters'.

econ.EM↗

arXiv2024

A simple distributional difference-in-differences estimator for univariate and bivariate outcomes

We provide a simple distribution regression estimator for treatment effects in the difference-in-differences (DiD) design. Our procedure is particularly useful when the treatment effect differs across the distribution of the outcome variable. Our proposed estimator easily incorporates covariates and, importantly, can be extended to settings where the treatment potentially affects the joint distribution of multiple outcomes. Our key identifying restriction is that the untreated outcome distribution does not exhibit an interaction effect of group and time. This assumption results in a parallel trend assumption on a transformation of the distribution. We highlight the relationship between our procedure and assumptions with the changes-in-changes approach of Athey and Imbens (2006). We also reexamine the Card and Krueger (1994) study of the impact of minimum wages on employment to illustrate the utility of our approach.

econ.EM↗

arXiv2024

Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem

We address the estimation of endogenous treatment models with social interactions in both the treatment and outcome equations. We model the interactions between individuals in an internally consistent manner via a game theoretic approach based on discrete Bayesian games. This introduces a substantial computational burden in estimation which we address through a sequential version of the nested fixed point algorithm. We also provide some relevant treatment effects, and procedures for their estimation, which capture the impact on both the individual and the total sample. Our empirical application examines the impact of an individual's exercise frequency on her level of self-esteem. We find that an individual's exercise frequency is influenced by her expectation of her friends'. We also find that an individual's level of self-esteem is affected by her level of exercise and, at relatively lower levels of self-esteem, by the expectation of her friends' self-esteem.

econ.EM↗

arXiv2024

Conditional Rank-Rank Regression

Rank-rank regression is commonly employed in economic research as a way of capturing the relationship between two economic variables. The slope of this regression is the Spearman rank correlation, a classical measure of association. However, in many applications it is common practice to include covariates to account for differences in association levels between groups as defined by the values of these covariates. This is either done by including the covariates or by modeling the residuals obtained after partialing out the impact of the covariates. In each of these instances the resulting rank-rank regression coefficients can be difficult to interpret. We propose the conditional rank-rank regression, which uses conditional ranks instead of unconditional ranks, to measure average within-group persistence. The coefficient of this new regression corresponds to the average Spearman rank correlation conditional on the covariates, a natural summary measure of within-group association. We develop a flexible estimation approach using distribution regression and establish a theoretical framework for large sample inference. An empirical study on intergenerational income mobility in Switzerland demonstrates the advantages of this approach. The study reveals stronger intergenerational persistence between fathers and sons compared to fathers and daughters, with the within-group persistence explaining 62% of the overall income persistence for sons and 52% for daughters. Smaller families and those with highly educated fathers exhibit greater persistence in economic status.

econ.EM↗

arXiv2023

Marital Sorting, Household Inequality and Selection

Using CPS data for 1976 to 2022 we explore how wage inequality has evolved for married couples with both spouses working full time full year, and its impact on household income inequality. We also investigate how marriage sorting patterns have changed over this period. To determine the factors driving income inequality we estimate a model explaining the joint distribution of wages which accounts for the spouses' employment decisions. We find that income inequality has increased for these households and increased assortative matching of wages has exacerbated the inequality resulting from individual wage growth. We find that positive sorting partially reflects the correlation across unobservables influencing both members' of the marriage wages. We decompose the changes in sorting patterns over the 47 years comprising our sample into structural, composition and selection effects and find that the increase in positive sorting primarily reflects the increased skill premia for both observed and unobserved characteristics.

econ.EM↗

arXiv2022

Dynamic Heterogeneous Distribution Regression Panel Models, with an Application to Labor Income Processes

We introduce a dynamic distribution regression panel data model with heterogeneous coefficients across units. The objects of primary interest are functionals of these coefficients, including predicted one-step-ahead and stationary cross-sectional distributions of the outcome variable. Coefficients and their functionals are estimated via fixed effect methods. We investigate how these functionals vary in response to counterfactual changes in initial conditions or covariate values. We also identify a uniformity problem related to the robustness of inference to the unknown degree of coefficient heterogeneity, and propose a cross-sectional bootstrap method for uniformly valid inference on function-valued objects. We showcase the utility of our approach through an empirical application to individual income dynamics. Employing the annual Panel Study of Income Dynamics data, we establish the presence of substantial coefficient heterogeneity. We then highlight some important empirical questions that our methodology can address. First, we quantify the impact of a negative labor income shock on the distribution of future labor income. Second, we demonstrate the existence of heterogeneity in income mobility, and its implications for an individuals' incidence to be trapped in poverty. Simulation evidence confirms that our procedures work well in small samples.

econ.EM↗

arXiv2022

Selection and the Distribution of Female Hourly Wages in the U.S

We analyze the role of selection bias in generating the changes in the observed distribution of female hourly wages in the United States using CPS data for the years 1975 to 2020. We account for the selection bias from the employment decision by modeling the distribution of the number of working hours and estimating a nonseparable model of wages. We decompose changes in the wage distribution into composition, structural and selection effects. Composition effects have increased wages at all quantiles while the impact of the structural effects varies by time period and quantile. Changes in the role of selection only appear at the lower quantiles of the wage distribution. The evidence suggests that there is positive selection in the 1970s which diminishes until the later 1990s. This reduces wages at lower quantiles and increases wage inequality. Post 2000 there appears to be an increase in positive sorting which reduces the selection effects on wage inequality.

econ.EM↗

arXiv2021

Hours Worked and the U.S. Distribution of Real Annual Earnings 1976-2019

We examine the impact of annual hours worked on annual earnings by decomposing changes in the real annual earnings distribution into composition, structural and hours effects. We do so via a nonseparable simultaneous model of hours, wages and earnings. Using the Current Population Survey for the survey years 1976--2019, we find that changes in the female distribution of annual hours of work are important in explaining movements in inequality in female annual earnings. This captures the substantial changes in their employment behavior over this period. Movements in the male hours distribution only affect the lower part of their earnings distribution and reflect the sensitivity of these workers' annual hours of work to cyclical factors.

econ.EM↗

arXiv2020

Nonseparable Sample Selection Models with Censored Selection Rules

We consider identification and estimation of nonseparable sample selection models with censored selection rules. We employ a control function approach and discuss different objects of interest based on (1) local effects conditional on the control function, and (2) global effects obtained from integration over ranges of values of the control function. We derive the conditions for the identification of these different objects and suggest strategies for estimation. Moreover, we provide the associated asymptotic theory. These strategies are illustrated in an empirical investigation of the determinants of female wages in the United Kingdom.

econ.EM↗

arXiv2019

Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models

Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these limitations. They are based on distribution and quantile regression modelling of the reduced form conditional distributions of the endogenous variables. We show that average, distribution and quantile structural functions are identified in these systems through a control function approach that does not require a large support condition. We propose a computationally attractive three-stage procedure to estimate the structural functions where the first two stages consist of quantile or distribution regressions. We provide asymptotic theory and uniform inference methods for each stage. In particular, we derive functional central limit theorems and bootstrap functional central limit theorems for the distribution regression estimators of the structural functions. These results establish the validity of the bootstrap for three-stage estimators of structural functions, and lead to simple inference algorithms. We illustrate the implementation and applicability of all our methods with numerical simulations and an empirical application to demand analysis.

econ.EM↗