8 - Simultaneous Equations

Summary

Introduction

This chapter explains simultaneous-equation models, and how to estimate them using instrumental variables (or two-stage least squares). These techniques are needed to avoid simultaneity bias (aka endogeneity bias). The lead example will be hypothetical supply and demand equations for butter in the state of Wisconsin. The source of endogeneity bias will be explained, and so will methods for working around this problem.

Then we discuss two real examples—(i) the way education and fertility influence each other, and (ii) the effect of school choice on social capital. These examples indicate how social scientists use two-stage least squares to handle (i) reciprocal causation and (ii) self-selection of subjects into the sample. (In the social sciences, two-stage least squares is often seen as the solution to problems of statistical inference.) At the end of the chapter there is a literature review, which puts modeling issues into a broader perspective.

We turn now to butter. Supply and demand need some preliminary discussion. For an economist, butter supply is not a single quantity but a relationship between quantity and price. The supply curve shows the quantity of butter that farmers would bring to market at different prices. In the left Figure 1. Supply and demand. The vertical axis shows quantity; the horizontal axis, price.

hand panel of figure 1, price is on the horizontal axis and quantity on the vertical. (Economists usually do it the other way around.)

Notice that the supply curve slopes up.