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## 12.5 Where Do Valid Instruments Come From?

Chapter 12.5 of the book presents a comprehensive discussion of approaches to find valid instruments in practice by the example of three research questions:

• Does putting criminals in jail reduce crime?
• Does cutting class sizes increase test scores?
• Does aggressive treatment of heart attacks prolong lives?

This section is not directly related to applications in R which is why we do not discuss the contents here. We encourage you to work through this on your own.

#### Summary

ivreg() from the package AER provides convenient functionalities to estimate IV regression models in R. It is an implementation of the TSLS estimation approach.

Besides treating IV estimation, we have also discussed how to test for weak instruments and how to conduct an overidentifying restrictions test when there are more instruments than endogenous regressors using R.

An empirical application has shown how ivreg() can be used to estimate the long-run elasticity of demand for cigarettes based on CigarettesSW, a panel data set on cigarette consumption and economic indicators for all 48 continental U.S. states for 1985 and 1995. Different sets of instruments were used and it has been argued why using the general sales tax as the only instrument is the preferred choice. The estimate of the demand elasticity deemed the most trustworthy is $-0.94$. This estimate suggests that there is a remarkable negative long-run effect on cigarette consumption of increasing prices.