System Estimation by Instrumental Variables Introduction and Examples In Chapter 7 we covered system estimation of linear equations when the explanatory variables satisfy certain exogeneity conditions. For many applications, even the weakest of these assumptions, Assumption , is violated, in which case instrumental variables procedures | System Estimation by Instrumental Variables Introduction and Examples In Chapter 7 we covered system estimation of linear equations when the explanatory variables satisfy certain exogeneity conditions. For many applications even the weakest of these assumptions Assumption is violated in which case instrumental variables procedures are indispensable. The modern approach to system instrumental variables SIV estimation is based on the principle of generalized method of moments GMM . Method of moments estimation has a long history in statistics for obtaining simple parameter estimates when maximum likelihood estimation requires nonlinear optimization. Hansen 1982 and White 1982b showed how the method of moments can be generalized to apply to a variety of econometric models and they derived the asymptotic properties of GMM. Hansen 1982 who coined the name generalized method of moments treated time series data and White 1982b assumed independently sampled observations. Though the models considered in this chapter are more general than those treated in Chapter 5 the derivations of asymptotic properties of system IV estimators are mechanically similar to the derivations in Chapters 5 and 7. Therefore the proofs in this chapter will be terse or omitted altogether. In econometrics the most familar application of SIV estimation is to a simultaneous equations model SEM . We will cover SEMs specifically in Chapter 9 but it is useful to begin with a typical SEM example. System estimation procedures have applications beyond the classical simultaneous equations methods. We will also use the results in this chapter for the analysis of panel data models in Chapter 11. Example Labor Supply and Wage Offer Functions Consider the following labor supply function representing the hours of labor supply hs at any wage w faced by an individual. As usual we express this in population form hs w g1w z1d1 u1 where z1 is a vector of observed labor supply shifters including such
