Issues in the Estimation of Causal Effects in Population Research, with an Application to the Effects of Teenage Childbearing

The estimation of causal effects has become an important subject of study in population research. This essay surveys the recent literature in economics on this issue, with a focus on the method of instrumental variables. Conditions for the validity of instrumental variable methods are discussed along with the proper interpretation of the resulting estimates. Several difficult issues with the method are outlined, including the problem of external validity, reconciling the differences in estimates when different instruments are used, and detecting instrument validity. Population research has a distinguished history of empirical work on a wide variety of important topics related to population growth, the components of demographic trends, estimation of vital rates, life table construction, investigation into causes of historical population developments, and many others. However, one branch of population research that has seen increasing interest has been in the area of social demography, where the determinants of individual behavior regarding fertility, marriage, and related areas has been studied. It is in that branch that issues of causal inference have arisen, and with which this essay is concerned. This development in population research coincides with a more general interest in causal inference in statistics and in other social sciences such as economics. In statistics, the development of the Rubin Causal Model (Rubin, 1974) as a framework for studying causal questions has become a dominant paradigm even though, at the same time, there is considerable work by other statisticians using somewhat different frames. The development in statistics, while having many historical antecedents in the field, by and large occurred only in the 1970s and 1980s. Prior to that time, randomized experiments were regarded as the only method for true causal inference. However, randomized experiments are generally not possible in many fields, including population research, and hence methods for the analysis of causation using observational data are needed. In economics, while causality has a much longer history dating to the development of the simultaneous equations model, which saw its fullest development in the Cowles Commission work in the 1950s, renewed interest in the issue has arisen since the 1980s and 1990s as more 2 subtle issues have been addressed. Other social science disciplines such as sociology and political science are following the developments in statistics and in economics, with new developments adapted to their unique sets of questions and issues. This essay will review the issues in causal modeling using primarily the framework adapted in economics, and will apply those modeling issues to the study of population questions. The economics framework is, when boiled down to essentials, observationally equivalent to the Rubin Causal model in statistics, although the interpretation and language used to describe the two are quite different. In addition, their practical empirical implementation is often quite different, with economists leaning toward modeling by the use of regression equations with explicitly represented error terms, an approach different from that in statistics. While the causal modeling developments in economics have taken many directions, the vast majority of applications in the field use the method of instrumental variables (IV) to estimate causal effects. Therefore, this essay will also concentrate on that method, outlining both its rationale and advantages and the pitfalls and weaknesses associated with its use. Brief mention will be made of other methods such as panel data fixed effects methods and matching. The running example in the essay is the question of whether teenage childbearing has a deleterious effect on female economic outcomes such as income and earnings. The increase in rates of teen childbearing in the U.S. has been a source of public concern not only because much of that childbearing is nonmarital but also because of the widespread perception that women who begin their childbearing at a very young age run the risk of harming their educational progress and their later economic and social success. There has been a great deal of research on this issue with, surprisingly, much less support for this conventional view as might be expected. But the See Moffitt (2003,2005) for earlier reviews. 1 3 literature has also generated much discussion of the method of causal effects and of the effects of using different instruments for estimation. Thus, this particular literature can be used to illustrate a number of the issues in causal modeling in population research in general. The first section below lays out the general causal model in economics and discusses a number of the main issues. The method of instrumental variables is then outlined, followed by a categorization of the types of instruments most often used. Additional issues in the use of instrumental variables are then reviewed, followed by a set of conclusions. Some of the points made in the essay are (i) a tradeoff between internal validity and external validity is often faced by analysts using the method; (ii) multiple instruments or instruments with multiple values can be used to learn more about effects in heterogeneous populations than binary instruments; and (iii) use of theory is important to determine mechanisms by which treatments affect outcomes and how differing instruments interact with those mechanisms. The Basic Causal Model The basic causal model in economics dates to the Cowles Commission work on simultaneous equations in economics and, later, its adaptation to individual actions represented in the switching regression model (Heckman, 1978; Lee, 1979). Heckman and Robb (1985) and Bjorklund and Moffitt (1987) made the connection between that model and newer thinking in causal modeling as well as introducing the notion of heterogeneity to be discussed momentarily. Heckman et al. (2006) provide a recent overview of the model. The prototype linear regression model used in this literature is