Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility

This paper considers the effect of a continuous treatment on the entire distribution of outcomes after adjusting for differences in the distribution of covariates across different levels of the treatment. Our methodology encompasses dose-response functions, counterfactual distributions, and ‘distributional policy effects’ depending on the assumptions invoked by the researcher. We propose a three-step estimator that consists of (i) estimating the distribution of the outcome conditional on the treatment and other covariates using quantile regression; (ii) for each value of the treatment, averaging over a counterfactual distribution of the covariates holding the treatment fixed; (iii) converting the resulting counterfactual distribution into parameters of interest that are easy to interpret. We show that our estimators converge uniformly to Gaussian processes and that the empirical bootstrap can be used to conduct uniformly valid inference across a range of values of the treatment. We use our method to study intergenerational income mobility where we consider effects of parents’ income on features of their child's income distribution such as (i) the fraction of children with income below the poverty line; (ii) the variance of child's income; and (iii) the inter-quantile range of child's income–all as a function of parents’ income.     

一种新的收入差距研究的计量方法——基于分布函数的半参数化估计

收入差距扩大的成因分解方法的最新研究强调描述整个收入分布,并且对收入分布的变化进行分解,进而得到各个统计量的分解,这类方法的优点是可以显示收入差距的变化主要集中在哪些收入群体中。本文着重介绍了两类对收入分布函数进行成因分解的半参数化方法:一类是Lemieux及其合作者们发展起来的权重重置法;另一类是Machado和Mata首创的基于分位数回归的分解方法。     

Predicting default risk under asymmetric binary link functions

In this article we propose the use of an asymmetric binary link function to extend the proportional hazard model for predicting loan default. The rationale behind this approach is that the symmetry assumption that has been widely used in the literature could be considered as quite restrictive, especially during periods of financial distress. In our approach we allow for a flexible level of asymmetry in the probability of default by the use of the skewed logit distribution. This enable us to estimate the actual level of asymmetry that is associated with the data at hand. We implement our approach to both simulated data and a rich micro dataset of consumer loan accounts. Our results provide clear evidence that ignoring the actual level of asymmetry leads to seriously biased estimates of the slope coefficients, inaccurate marginal effects of the covariates of the model, and overestimation of the probability of default. Regarding the predictive power of the covariates of the model, we have found that loan-specific covariates contain considerably more information about the loan default than macroeconomic covariates, which are often used in practice to carry out macroprudential stress testing.     

Semiparametric estimation of logistic regression model with missing covariates and outcome

We consider a semiparametric method to estimate logistic regression models with missing both covariates and an outcome variable, and propose two new estimators. The first, which is based solely on the validation set, is an extension of the validation likelihood estimator of Breslow and Cain (Biometrika 75:11–20, 1988). The second is a joint conditional likelihood estimator based on the validation and non-validation data sets. Both estimators are semiparametric as they do not require any model assumptions regarding the missing data mechanism nor the specification of the conditional distribution of the missing covariates given the observed covariates. The asymptotic distribution theory is developed under the assumption that all covariate variables are categorical. The finite-sample properties of the proposed estimators are investigated through simulation studies showing that the joint conditional likelihood estimator is the most efficient. A cable TV survey data set from Taiwan is used to illustrate the practical use of the proposed methodology.     

Stochastic volatility with leverage: Fast and efficient likelihood inference

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).     

Nonparametric estimation and inference about the overlap of two distributions

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.     

On the Practice of Rescaling Covariates

Whether doing parametric or nonparametric regression with shrinkage, thresholding, penalized likelihood, Bayesian posterior estimators (e.g., ridge regression, lasso, principal component regression, waveshrink or Markov random field ), it is common practice to rescale covariates by dividing by their respective standard errors ρ. The stated goal of this operation is to provide unitless covariates to compare like with like, especially when penalized likelihood or prior distributions are used. We contend that this vision is too simplistic. Instead, we propose to take into account a more essential component of the structure of the regression matrix by rescaling the covariates based on the diagonal elements of the covariance matrix Σ of the maximum-likelihood estimator. We illustrate the differences between the standard ρ- and proposed Σ-rescalings with various estimators and data sets.     

Zero-inflated count regression models with applications to some examples

In this paper, we employed SAS PROC NLMIXED (Nonlinear mixed model procedure) to analyze three example data having inflated zeros. Examples used are data having covariates and no covariates. The covariates utilized in this article have binary outcomes to simplify our analysis. Of course the analysis can readily be extended to situations with several covariates having multiple levels. Models fitted include the Poisson (P), the negative binomial (NB), the generalized Poisson (GP), and their zero-inflated variants, namely the ZIP, the ZINB and the ZIGP models respectively. Parameter estimates as well as the appropriate goodness-of-fit statistic (the deviance D) in this case are computed and in some cases, the Pearson’s X ² statistic, that is based on the variance of the relevant model distribution is also computed. Also obtained are the expected frequencies for the models and GOF tests are conducted based on the rule established by Lawal (Appl Stat 29:292–298, 1980). Our results extend previous results on the analysis of the chosen data in this example. Further, results obtained are very consistent with previous analyses on the data sets chosen for this article. We also present an hierarchical figure relating all the models employed in this paper. While we do not pretend that the results obtained are entirely new, however, the analyses give opportunities to researchers in the field the much needed means of implementing these models in SAS without having to resort to S-PLUS, R or Stata.     

Finite sample inference for quantile regression models

Under minimal assumptions, finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the “conditional pivotal property” of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear and nonlinear quantile models with endogenous or exogenous covariates. The confidence regions can be computed using Markov Chain Monte Carlo (MCMC) methods. We illustrate the finite sample procedure through two empirical examples: estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling. We find pronounced differences between asymptotic and finite sample confidence regions in cases where the usual asymptotics are suspect.     

Gender wage gap: A semi-parametric approach with sample selection correction

Sizeable gender differences in employment rates are observed in many countries. Sample selection into the workforce might therefore be a relevant issue when estimating gender wage gaps. We propose a semi-parametric estimator of densities in the presence of covariates which incorporates sample selection. We describe a simulation algorithm to implement counterfactual comparisons of densities. The proposed methodology is used to investigate the gender wage gap in Italy. We find that, when sample selection is taken into account, the gender wage gap widens, especially at the bottom of the wage distribution.     

Parameter-efficient deep probabilistic forecasting

Probabilistic time series forecasting is crucial in many application domains, such as retail, ecommerce, finance, and biology. With the increasing availability of large volumes of data, a number of neural architectures have been proposed for this problem. In particular, Transformer-based methods achieve state-of-the-art performance on real-world benchmarks. However, these methods require a large number of parameters to be learned, which imposes high memory requirements on the computational resources for training such models. To address this problem, we introduce a novel bidirectional temporal convolutional network that requires an order of magnitude fewer parameters than a common Transformer-based approach. Our model combines two temporal convolutional networks: the first network encodes future covariates of the time series, whereas the second network encodes past observations and covariates. We jointly estimate the parameters of an output distribution via these two networks. Experiments on four real-world datasets show that our method performs on par with four state-of-the-art probabilistic forecasting methods, including a Transformer-based approach and WaveNet, on two point metrics (sMAPE and NRMSE) as well as on a set of range metrics (quantile loss percentiles) in the majority of cases. We also demonstrate that our method requires significantly fewer parameters than Transformer-based methods, which means that the model can be trained faster with significantly lower memory requirements, which as a consequence reduces the infrastructure cost for deploying these models.     

The Asymptotics of MM-Estimators for Linear Regression with Fixed Designs

MM-estimators achieve simultaneous high efficiency and high breakdown point over contamination neighborhoods. Inference based on these estimators relies on their asymptotic properties, which have been studied for the case of random covariates. In this paper we show that, under relatively mild regularity conditions, MM-estimators for linear regression models are strongly consistent when the design is fixed. Moreover, their strong consistency allows us to show that these estimators are also asymptotically normal for non-random covariates. These results justify the use of a normal approximation to the finite-sample distribution of MM-estimators for linear regression with fixed explanatory variables. Additionally, these results have been used to extend the robust bootstrap (Salibian-Barrera and Zamar in Ann Stat 30:556–582, 2002) to the case of fixed designs [see Salibian-Barrera 2004, submitted].Research supported by an NSERC Research Grant (Individual)     

Counterfactual decomposition of changes in wage distributions using quantile regression

We propose a method to decompose the changes in the wage distribution over a period of time in several factors contributing to those changes. The method is based on the estimation of marginal wage distributions consistent with a conditional distribution estimated by quantile regression as well as with any hypothesized distribution for the covariates. Comparing the marginal distributions implied by different distributions for the covariates, one is then able to perform counterfactual exercises. The proposed methodology enables the identification of the sources of the increased wage inequality observed in most countries. Specifically, it decomposes the changes in the wage distribution over a period of time into several factors contributing to those changes, namely by discriminating between changes in the characteristics of the working population and changes in the returns to these characteristics. We apply this methodology to Portuguese data for the period 1986–1995, and find that the observed increase in educational levels contributed decisively towards greater wage inequality. Copyright © 2005 John Wiley & Sons, Ltd.     

An optimization approach for making causal inferences

To make causal inferences from observational data, researchers have often turned to matching methods. These methods are variably successful. We address issues with matching methods by redefining the matching problem as a subset selection problem. Given a set of covariates, we seek to find two subsets, a control group and a treatment group, so that we obtain optimal balance, or, in other words, the minimum discrepancy between the distributions of these covariates in the control and treatment groups. Our formulation captures the key elements of the Rubin causal model and translates nicely into a discrete optimization framework.     

Nonparametric estimation of distributional policy effects

This paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest. In contrast to other methods, we do not restrict attention to the effect on the mean. In particular, our method can be used to conduct inference on the change of the distribution function as a whole, its moments and quantiles, inequality measures such as the Lorenz curve or Gini coefficient, and to test for stochastic dominance. The practical applicability of our procedure is illustrated via a simulation study and an empirical example.     

Socio‐economic distance and spatial patterns in unemployment

This paper examines the spatial patterns of unemployment in Chicago between 1980 and 1990. We study unemployment clustering with respect to different social and economic distance metrics that reflect the structure of agents' social networks. Specifically, we use physical distance, travel time, and differences in ethnic and occupational distribution between locations. Our goal is to determine whether our estimates of spatial dependence are consistent with models in which agents' employment status is affected by information exchanged locally within their social networks. We present non‐parametric estimates of correlation across Census tracts as a function of each distance metric as well as pairs of metrics, both for unemployment rate itself and after conditioning on a set of tract characteristics. Our results indicate that there is a strong positive and statistically significant degree of spatial dependence in the distribution of raw unemployment rates, for all our metrics. However, once we condition on a set of covariates, most of the spatial autocorrelation is eliminated, with the exception of physical and occupational distance. Racial and ethnic composition variables are the single most important factor in explaining the observed correlation patterns. Copyright © 2002 John Wiley & Sons, Ltd.     

Effect of factors with time-dependent covariates on the survival status of the elderly in Taiwan

The elderly population has been increasing rapidly in recent years because of improvements in medical care and the progress in economics in Taiwan. Now, the population of old people age above 65 has approached 10%, and problems of the elderly have become a major concern for public health. In this study, we use five waves of Survey of Health and Living Status of the Elderly in Taiwan held from 1989 to 2003 to explore 15 variables related to demographic characteristic, health status, health behavior and home condition etc. affect the survival status of the elderly by employing Cox proportional hazard model. The results show that there are nine variables, e.g. age, gender, ethnic group, ADL, self-rated health, physical function, smoking, chewing betel nuts and marital status, were strongly related to the survival status of the elderly. In addition, Aalen’s nonparametric additive model is not only used as an alternative to a proportional hazards to describe the effects of covariates on survival time but assist in detecting and describing the nature of time-dependent effects of covariates used for Cox proportional model. We find there are some time-dependent covariates (e.g. self-rate health, ADL function, and physical function), and Aalen’s nonparametric additive model provides a flexible and nonparametric method for investigating the time-dependent variables through plots of the estimated cumulative regression coefficients, with confidence intervals.     

Methods for multicountry studies of corporate governance: Evidence from the BRIKT countries

We discuss empirical challenges in multicountry studies of the effects of firm-level corporate governance on firm value, focusing on emerging markets. We assess the severe data, “construct validity”, and endogeneity issues in these studies, propose methods to respond to those issues, and apply those methods to a study of five major emerging markets—Brazil, India, Korea, Russia, and Turkey. We develop unique time-series datasets on governance in each country. We address construct validity by building country-specific indices which reflect local norms and institutions. These similar-but-not-identical indices predict firm market value in each country, and when pooled across countries, in firm fixed-effects (FE) and random-effects (RE) regressions. In contrast, a “common index”, which uses the same elements in each country, has no predictive power in FE regressions. For the country-specific and pooled indices, FE and RE coefficients on governance are generally lower than in pooled OLS regressions, and coefficients with extensive covariates are generally lower than with limited covariates. These results confirm the value of using FE or RE with extensive covariates to reduce omitted variable bias. We develop lower bounds on our estimates which reflect potential remaining omitted variable bias.     

Do European business cycles look like one?

This paper provides a comprehensive framework to analyze business cycle features other than synchronization. We use stationary bootstrap and model-based clustering methods to analyze similarities and differences among the European cycles. We find evidence that the length, deep and shape of cycles differ across European countries and that these differences are not decreasing over time. Finally, even though we find some correlation between business cycle synchronization and characteristics, there is important information in the characteristics that is not captured by the synchronization measures.     

Treatment effect estimation with covariate measurement error

This paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates. The approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects. The approximations can be estimated using data on observed outcomes, the treatment indicator and error contaminated covariates without employing additional information from validation data or instrumental variables. The results can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects.