Two-Stage Least Squares (Statistical Associates Blue Book Series 40)

Two-stage least squares regression (2SLS) is a method of extending regression to cover models which violate ordinary least squares (OLS) regression's assumption that there is no correlated error between one or more predictor variables and the disturbance term of the dependent variable. Correlated error may arise for three major reasons, each of which 2SLS may address:
1. Non-recursive models, which are ones in which there is reciprocal causation (simultaneity bias).
2. Unobserved variables which are correlated with a predictor variable (specification bias).
3. The sample itself is biased on variables affecting the dependent variable (selection bias)
All three situations involve the effect of unmeasured effects not specified in the model. In each situation, 2SLS may be more appropriate than OLS regression if suitable instrumental variables can be identified.

Table of Contents

Two-Stage Least Squares Regression Analysis (2SLS) 5
Overview 5
Key Terms and Concepts 5
The recursivity assumption. 6
Endogenous vs exogenous variables. 6
Disturbance terms 7
Two stages 7
Stage 1 7
Stage 2 9
Example 10
Data 10
The Model 10
2SLS in Stata 11
Stata syntax 11
Default Stata output 12
Comparing types of instrumental variable estimation 14
Comparing 2SLS and OLS with the Hausman test 15
Testing for weak instruments 17
Testing for endogeneity 19
Testing for overidentifying restrictions 20
Additional Stata output 20
Saving estimates in Stata 21
2SLS in SPSS 22
SPSS user interface 22
Default SPSS output 23
Diagnostic tests in SPSS 25
Saving estimates in SPSS 26
2SLS in SAS 27
SAS syntax 27
Estimation methods in SAS 28
Default SAS output 29
Testing for heteroskedasticity 30
Diagnostic plots 31
Testing for overidentifying restrictions 32
Testing for weak instruments 33
Assumptions 34
Data level 34
Uncorrelated exogenous variables 34
Sample size 34
Multivariate normality 35
Normally distributed error 35
Multivariate equivariance 35
Linearity 35
No complete nonrecursivity 35
No under-identification 35
Regression model assumptions 35
Testing assumptions 36
Frequently Asked Questions 36
Will 2SLS parameters be much different from OLS coefficients for the same data? 36
How do I create lagged variables for use in 2SLS? 36
Could I do 2SLS manually? 37
What computer software supports 2SLS? 38
Why is ML estimation generally preferred to 2SLS in estimating path parameters? 38
In SEM, is there any reason to use 2SLS instead of ML? 38
How is 2SLS used to test for selection bias? 39
How is the intercept interpreted in 2SLS? 40
May one apply 2SLS to cointegrated time series? 41
Bibliography 42
Pagecount 45