National accounts, social indicators, and other data have been accumulating for most less developed countries for more than 40 years. Writers on development frequently apply the technique of multiple regression to these data to estimate what they believe are underlying behavioral relationships among various economic, political, and social variables. They report their results in regression tables.
A number of selections in this book contain regression tables. Fortunately, lack of training in econometrics or statistics need not prevent the reader from understanding the important economic (as opposed to statistical) information contained in a regression table. The purpose of this Appendix is to show the untrained reader how to extract this information, using as an illustration a table adapted from the widely cited paper by Robert J. Barro, “Economic Growth in a Cross Section of Countries,” Quarterly Journal of Economics 106 (May 1991): 407—43. The presentation applies to multiple regressions performed using a method called or- dinary least squares, but the most important aspects of the discussion carry through even if other methods were used.
A regression table is read one column at a time. Each column reports an estimated relationship between the values of a dependent variable, y I, and the values of a set of explanatory variables, x1i, x2i, … ,xKi, where i indexes observations and K is the number of explanatory variables. This estimated relationship takes the form
where the number b0 is the constant or intercept, the numbers b1, b2, …, bK are the estimat- ed coefficients, and ei is the residual. The quantity b0 + b1x1i + b2x2i + … +bKxKi is the pre- dicted value of the dependent variable for observation i, so called because it gives the value of the dependent variable we would predict for observation i given knowledge of the values of the explanatory variables for observation i. It follows that the residual is simply the difference between the actual value of the dependent variable and its predicted value for each observation. By construction, the average or mean of the predicted values taken over all observations equals the mean of the actual values; equivalently, the mean of the residual is zero. As a consequence, if we know the estimated coefficients and the means of the dependent variable and the explanatory variables, we can compute the constant:
where the bar over a variable denotes its mean.
The estimated coefficients are the same for all observations because they are supposed to be estimates of underlying behavioral relationships between the dependent variable and the explanatory variables. The estimated coefficient b1, for example, tells us that a one-unit increase in the value of the explanatory variable x1 should cause the value of the dependent variable to increase by b1 units, holding the values of all other explanatory variables constant. These estimated behavioral relationships are the most important economic information contained in a regression table.
With these preliminaries out of the way, we now turn to Table 1. In all regressions reported, an observation consists of the values of the dependent variable and the explanatory variables for one country for one time period. The number of observations used to estimate the coeffi-