TWO-STAGE LEAST SQUARES
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.
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Below is the unformatted table of contents.
TWO STAGE LEAST SQUARES Table of Contents 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