Definitions of variables:

N = observation number

Xi = wifes height (cm)

X2 = wifes age at marriage

Xi = wifes schooling years

X4 = net dowry paid (including marriage expenses)

by the brides household to the grooms household (in constant 1983 rupees) Xs = dryland owned by wifes household when she was 15 X(, = wetland owned by wifes household when she was 15 Xn = husbands age at marriage Zg = husbands school years Z9 = husbands height (cm)

,0 = dryland owned by husbands household when he was 15

Z, = wetland owned by husbands household when he was 15

Z,2 = years of marriage

Xn = low-caste dummy

Z,4 = medium-low-caste dummy

= medium-high-caste dummy (excluded category is high caste) Alb = whether the husbands father was an agricultural cultivator (former) Xxn = whether the husbands father was a (landless) laborer Als = dummy (husbands father had some primary education) ,, = dummy (husbands father completed primary education) Xy = dummy (husbands father completed middle or secondary school education)

Simultaneous Equations Models

9.1 Introduction

9.2 Endogenous and Exogenous Variables

9.3 The Identification Problem: Identification Through Reduced Form

9.4 Necessary and Sufficient Conditions for Identification

9.5 Methods of Estimation: The Instrumental Variable Method

9.6 Methods of Estimation: The Two-Stage Least Squares Method

9.7 The Question of Normalization

*9.8 The Limited-Information Maximum Likelihood Method *9.9 On the Use of OLS in the Estimation of Simultaneous-Equations Models *9.10 Exogeneity and Causality Summary Exercises

Appendix to Chapter 9

9.1 Introduction

In the usual regression model is the dependent or determined variable and jc,, jcj, . . . , are the independent or determining variables. The crucial assumption we make is that the jcs are independent of the error term u. Sometimes, this assumption is violated: for example, in demand and supply models. It is also violated in the case where the jcs are measured with error, but we postpone discussion of this case to Chapter 11. We illustrate here the case of a demand and supply model. Suppose that we write the demand function as

q = a + +

(9.1)

where q is the quantity demanded, p the price, and the disturbance term, which denotes random shifts in the demand function. In Figure 9.1 we see that a shift in the demand function produces a change in both price and quantity if the supply curve has an upward slope. If the supply curve is horizontal (i.e..

Supply curve sloping upward

Supply curve horizontal

Supply curve vertical

Figure 9.1 Effects of shifts in the demand function on price.