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Book Econometric Analysis of Cross Section and Panel Data By Wooldridge - Chapter 2

The Role of Conditional Expectations in Econometrics As we suggested in Section 1.1, the conditional expectation plays a crucial role in modern econometric analysis. Although it is not always explicitly stated, the goal of most applied econometric studies is to estimate or test hypotheses about the expectation of one variable—called the explained variable, the dependent variable, the regressand, or the response variable, and usually denoted y—conditional on a set of explanatory variables, independent variables, regressors, control variables, or covariates, usually denoted x ¼ ðx1 ; x2 ; . . . ; xK Þ. A substantial portion of research in econometric methodology. | Conditional Expectations and Related Concepts in Econometrics 2.1 The Role of Conditional Expectations in Econometrics As we suggested in Section 1.1 the conditional expectation plays a crucial role in modern econometric analysis. Although it is not always explicitly stated the goal of most applied econometric studies is to estimate or test hypotheses about the expectation of one variable called the explained variable the dependent variable the regressand or the response variable and usually denoted y conditional on a set of explanatory variables independent variables regressors control variables or covariates usually denoted x x1 x2 xK . A substantial portion of research in econometric methodology can be interpreted as finding ways to estimate conditional expectations in the numerous settings that arise in economic applications. As we briefly discussed in Section 1.1 most of the time we are interested in conditional expectations that allow us to infer causality from one or more explanatory variables to the response variable. In the setup from Section 1.1 we are interested in the effect of a variable w on the expected value of y holding fixed a vector of controls c. The conditional expectation of interest is E y w c which we will call a structural conditional expectation. If we can collect data on y w and c in a random sample from the underlying population of interest then it is fairly straightforward to estimate E y w c especially if we are willing to make an assumption about its functional form in which case the effect of w on E y w c holding c fixed is easily estimated. Unfortunately complications often arise in the collection and analysis of economic data because of the nonexperimental nature of economics. Observations on economic variables can contain measurement error or they are sometimes properly viewed as the outcome of a simultaneous process. Sometimes we cannot obtain a random sample from the population which may not allow us to estimate E y w c . .