Abstract:The role of education in the process of socioeconomic attainment is a topic of long standing interest to sociologists and economists. Recently there has been growing interest not only in estimating the average causal effect of education on outcomes such as earnings, but also in estimating how causal effects might vary over individuals or groups. In this paper we point out one of the under-appreciated hazards of seeking to estimate heterogeneous causal effects: conventional selection bias (that is, selection on baseline differences) can easily be mistaken for heterogeneity of causal effects. This might lead us to find heterogeneous effects when the true effect is homogenous, or to wrongly estimate not only the magnitude but also the sign of heterogeneous effects. We apply a test for the robustness of heterogeneous causal effects in the face of varying degrees and patterns of selection bias, and we illustrate our arguments and our method using National Longitudinal Survey of Youth 1979 (NLSY79) data. data.Keywords: causality; sample selection bias; heterogeneous treatment effects; propensity score; education; NLSY79 T HE role of education in the process of socioeconomic attainment is a topic of longstanding interest to sociologists and economists. Following the causal revolution of the past thirty years in the social sciences, there is a growing interest not only in estimating the causal effect of education on outcomes, such as earnings, but also in understanding and estimating how these effects differ among individuals (Brand and Xie 2010 provide a sociological example, Carneiro, Heckman, and Vytlacil 2011 an economic one). In this paper, drawing on earlier work by Heckman and Navarro-Lozano (2004), we point out one of the under-appreciated hazards of seeking to estimate heterogeneous causal effects: conventional selection bias (that is, selection on baseline differences) can easily be confused with heterogeneity of causal effects. One consequence is that analyses might find heterogeneous effects when the true effect is homogenous; another is that we might wrongly estimate either the direction or magnitude, or both, of a truly heterogeneous effect.We develop this argument initially using the potential outcomes approach to explain what we mean by selection on baseline differences and by heterogeneous causal effects. Our focus here is on heterogeneity of the causal effects according to the probability of receiving treatment. Then we show how, in both an important special case and in general, selection may confound estimates of heterogeneous causal effects, or, more simply, how selection on baseline differences may easily be mistaken for heterogeneous causal effects. Next we describe a test that allows us to calculate the degree to which estimates of heterogeneous causal effects are robust to different types and kinds of baseline selection bias. We apply this method
Increased LV filling pressure, assessed by E/e' ratio, is an independent predictor of 30-day and 1-yr MACE in patients who undergo elective off-pump coronary artery bypass graft surgery. These findings indicate that measurements of E/e' may assist in preoperative risk stratification of these patients.
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