Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling

We consider the problem of causal effect heterogeneity from a Bayesian point of view. This is accomplished by introducing a three-equation system, similar in spirit to the work of Heckman and Vytlacil (1998), describing the joint determination of a scalar outcome, an endogenous “treatment” variable, and an individual-specific causal return to that treatment. We describe a Bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population, the object which has been the focus of most previous work. Parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed.Combining data sets from High School and Beyond (HSB) and the 1980 Census, we illustrate our methods in practice and investigate heterogeneity in returns to education. Our analysis decomposes the impact of key HSB covariates on log wages into three parts: a “direct” effect and two separate indirect effects through educational attainment and returns to education. Our results strongly suggest that the quantity of schooling attained is determined, at least in part, by the individual’s own return to education. Specifically, a one percentage point increase in the return to schooling parameter is associated with the receipt of (approximately) 0.14 more years of schooling. Furthermore, when we control for variation in returns to education across individuals, we find no difference in predicted schooling levels for men and women. However, women are predicted to attain approximately 1/4 of a year more schooling than men on average as a result of higher rates of return to investments in education.     

(No) Foundations of dominant-strategy mechanisms: a comment on Chung and Ely (2007)

This comment revisits Chung and Ely (Rev Econ Stud 74:447–476, 2007) in which robustly optimal auctions where investigated. Chung and Ely used a maxmin approach to define robust optimality. Chung and Ely provided conditions under which dominant strategy auctions are robustly optimal in their sense. This comment proposes a refinement of Chung and Ely’s criterion and shows that, with this refined criterion, dominant strategy auctions are not optimal if there are at least three bidders. According to the refinement the auctioneer should not choose dominated auctions, that is, auctions for which there exist other mechanisms that never generate lower expected revenue, and sometimes higher expected revenue. We construct such a dominating mechanism for dominant strategy auctions. The construction exploits the possibility of side bets when beliefs are not derived from common priors. Chung and Ely (Rev Econ Stud 74:447–476, 2007) admitted such beliefs.     

Estimating the error variance in regression after a preliminary test of restrictions on the coefficients

Maximum-likelihood estimation of the variance of the disturbances in a linear regression is considered in the context of exact linear restrictions on the coefficient vector. The exact risk function for the associated preliminary-test estimator of this variance is derived and evaluated numerically on the basis of relative quadratic loss. Our results indicate that in practical situations the risk of the pre-test estimator differs only slightly from that of the naive estimator which ignores the restrictions without testing. Applying the coefficient restrictions without testing their validity is not recommended.     

The scale of hospital production in different settings: one size does not fit all

This paper analyses the productive efficiency of 141 public hospitals from 1998 to 2004 in two Canadian provinces; one a small province with a few small cities and a generally more rural population and the other a large province that is more urban in nature, with a population who mainly live in large cities. The relative efficiencies of the hospitals, the changes in productivity during this time period, and the relationship between efficiency and the size or scale of the hospitals are investigated using data envelopment analysis. The models for the production of health care use case mix adjusted hospital discharges as the output, and nursing hours as inputs. We find clear differences between the two provinces. Making use of ‘own’ and ‘meta’ technical efficiency frontiers, we demonstrate that efficient units in the larger and more urban province are larger than non-efficient units in that province. However, efficient hospitals in the smaller and more rural province are smaller than non-efficient hospitals in that province. Overall, efficient hospitals in the larger more urban province are larger than efficient hospitals in the smaller more rural province. This has interesting policy implications—different hospitals may have different optimal sizes, or different efficient modes of operation, depending on location, the population they serve, and the policies their respective provincial governments wish to implement. In addition, there are lessons to be learned by comparing the hospitals across the two provinces, since the inefficient hospitals in the small rural province predominantly use hospitals from the large urban province as benchmarks, such that substantially larger improvement potential can be identified by inter-provincial rather than intra-provincial benchmarking analysis.     

The effect of physician advice on alcohol consumption: count regression with an endogenous treatment effect

Although there are encouraging trends, alcohol abuse continues to be a significant public health problem. Econometric studies of alcohol demand have yielded a great deal of information for alcohol abuse prevention policy. These studies suggest that higher alcohol taxes and stricter drunk‐driving policies can reduce heavy drinking and drunk driving. In this paper we explore the role physician advice plays in the campaign to prevent alcohol‐related problems. Compared to alcohol taxation, physician advice is a more precisely targeted intervention that does not impose extra costs on responsible drinkers. Compared to the resource costs of arresting, processing, and punishing drunk drivers, physician advice may be a lower‐cost intervention. To provide a basis for alcohol policy analysis, we use an alcohol demand framework to test whether physician‐provided information about the adverse consequences of alcohol abuse shifts demand to more moderate levels. There are three aspects of our alcohol demand model that complicate the estimation: (1) the dependent variable is non‐negative (it is a count variable—number of drinks consumed); (2) a non‐trivial number of sample observations have zero values for the dependent variable; and (3) because the data we use is non‐experimental, the treatment variable indicating receipt of advice from a physician may be endogenous. We implement an estimation method that is specifically designed to deal with these three complicating factors. Our results show that advice has a substantial and significant impact on alcohol consumption by males with hypertension, and that failing to account for the endogeneity of advice masks this result. Copyright © 2001 John Wiley & Sons, Ltd.     

The information revolution,innovation diffusion and economic growth: an examination of causal links in European countries

Quality & Quantity - Over the last 5 decades, the economic landscape in Europe has been transformed rapidly due to innovation, digitisation of the economy, and emergence of new sources of...     

The Monty Hall problem is not a probability puzzle* (It's a challenge in mathematical modelling)

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to switch your choice? The answer is ‘yes’ but the literature offers many reasons why this is the correct answer. This article argues that the most common reasoning found in introductory statistics texts, depending on making a number of ‘obvious’ or ‘natural’ assumptions and then computing a conditional probability, is a classical example of solution driven science. The best reason to switch is to be found in von Neumann's minimax theorem from game theory, rather than in Bayes’ theorem.     

Current practice in the modelling of age,period and cohort effects with panel data: a commentary on Tawfik et al. (2012), Clarke et al. (2009), and McCulloch (2012)

This comment assesses how age, period and cohort (APC) effects are modelled with panel data in the social sciences. It considers variations on a 2-level multilevel model which has been used to show apparent evidence for simultaneous APC effects. We show that such an interpretation is often misleading, and that the formulation and interpretation of these models requires a better understanding of APC effects and the exact collinearity present between them. This interpretation must draw on theory to justify the claims that are made. By comparing two papers which over-interpret such a model, and another that in our view interprets it appropriately, we outline best practice for researchers aiming to use panel datasets to find APC effects, with an understanding that it is impossible for any statistical model to find and separate all three effects.     

Omission of an observation from a regression analysis: A dicussion on efficiency loss,with applications

A scalar measure of loss of efficiency is defined for the case of a single observation omitted from a regression analysis. This measure is used to algebraically analyse the structure of loss of efficiency, and shows that it arises from a multiplicative relationship between three distinct components. The theory is applied to (a) assessment of the effect of the next observation when time series data is used, (b) the likely advantage to be gained from the use of mixed estimation, and (c) the efficiency of the Cochrane-Orcutt procedure.     

How to use interaction terms in BMA: Reply to Crespo Cuaresma's comment on Masanjala and Papageorgiou (2008)

Jesus Crespo Cuaresma (How different is Africa? A comment on Masanjala and Papageorgiou. Journal of Applied Econometrics, 2011) shows that the results in Masanjala and Papageorgiou (Rough and lonely road to prosperity: a reexamination of the sources of growth in Africa using Bayesian model averaging. Journal of Applied Econometrics 2008; 23 (5): 671–682) are sensitive to an alternative prior model structure in considering interaction terms. As a side issue, the algorithm for averaging over models is also challenged. In this reply I show that the prior used in Masanjala and Papageorgiou is as sensible as the prior suggested by Crespo Cuaresma. What we learn from Crespo Cuaresma's comment and this reply is that further effort should be dedicated to the study of parameter heterogeneity in the framework of BMA methods. Copyright © 2011 John Wiley & Sons, Ltd.     

The role of human capital philosophy in promoting firm innovativeness and performance: test of a causal model

In the present study, we developed and tested a causal model of the relationships between firm strategy, industry environment, human capital philosophy, innovativeness, and firm performance. Our results indicate that a differentiation-oriented strategy influences the relative use of an empowerment-oriented human capital philosophy of the firm, moderated by a firm's industry environment. Moreover, firms' human capital philosophies moderated the relationship between strategy and firm innovativeness. We also found support for the proposition that innovativeness mediated the relationship between human capital philosophy and firm performance. In addition, results also indicate that industry dynamism influences new product sales directly and industry survival difficulty moderates the relationship between firm strategy and new product sales. Survival difficulty also had a negative effect on firm profit. Overall, we found support for the mediating roles of human capital philosophy and innovativeness in the relationships between firm strategy, industry environment and firm performance. Implications are discussed.     

The effect of a Durbin–Watson pretest on confidence intervals in regression

Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin–Watson pretest of the null hypothesis of zero first‐order autocorrelation of the random errors against the alternative hypothesis of positive first‐order autocorrelation. If this null hypothesis is accepted then the confidence interval centered on the ordinary least squares estimator is used; otherwise the confidence interval centered on the feasible generalized least squares estimator is used. For any given design matrix and parameter of interest, we compare the confidence interval resulting from this two‐stage procedure and the confidence interval that is always centered on the feasible generalized least squares estimator, as follows. First, we compare the coverage probability functions of these confidence intervals. Second, we compute the scaled expected length of the confidence interval resulting from the two‐stage procedure, where the scaling is with respect to the expected length of the confidence interval centered on the feasible generalized least squares estimator, with the same minimum coverage probability. These comparisons are used to choose the better confidence interval, prior to any examination of the observed response vector.     

The presence of a feedback-seeking role model in promoting employee feedback seeking: a moderated mediation model

Abstract

Despite an increasing number of studies that show a positive relationship between the supportiveness of a feedback source and feedback seeking, little is known about the impact of supervisors’ demonstration of feedback-seeking behavior on promoting employees seeking feedback from them. In addition, although previous studies have shown that feedback seeking is an interactive process and is emotionally charged, to our knowledge, no studies have investigated the role that the source’s emotion regulation played in the feedback seeker’s seeking frequency. The present article developed a moderated mediation model to fill this void and tested it with data from a sample of 215 supervisor–subordinate dyads from China. We hypothesized and found that supervisors’ feedback seeking from subordinates were positively related to subordinates’ feedback seeking from supervisors, mediated by the perceived value and cost of the feedback seeking. The results also supported the moderating roles of supervisors’ emotion regulation in the mediation model.     

The dynamics of changes in the female wage distribution in the USA: a quantile regression approach

This paper examines the female wage structure focusing on changes at different points in the wage distribution. Newly developed quantile regression methods are used in analysing data from the March Current Population Survey. The results show that while the most significant changes for the less skilled women took place at the bottom of the wage distribution, for the more skilled groups changes occurred at both ends of the distribution. Consequently, wage inequality decreased for the high-school graduates and increased for the younger college graduates. Furthermore, the more highly skilled women experienced the steepest gain in wages regardless of their position in the distribution. © 1998 John Wiley & Sons, Ltd.     

The use (and abuse) of governance indicators in economics: a review

The relatively recent increase in empirical work on the relationship between governance and economic performance has come about largely as a result of the development of a series of indicators that has allowed this relationship to be quantified. For the researcher, it is important to understand the advantages and disadvantages of these indicators, both to ensure the appropriate indicator is chosen, and to be aware of the limitations each entail. To that end, this paper reviews the common indicators used in empirical analysis, as well as some of the other estimation problems that can arise when using these measures.      

The study between shadow banking and financial fragility in China: an empirical analysis based on the co-integration test and error correction model

The rapid development of shadow banking manifesting systematic risk has attracted increasing attention recently, but there exists a lack of empirical research in this field. This article applies co-integration analysis and error correction model using annual data during the 2001–2010 period to test the short-term fluctuation and long-term equilibrium between expansion velocity of shadow banking and financial fragility, and puts forward corresponding policy recommendations.