INSTRUMENTAL VARIABLES & 2SLS REGRESSION
Instrumental variables regression, for which two-stage least squares estimation is one method, is a way 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 methods in this monograph 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, instrumental variables/2SLS regression 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 6 Data used in examples 8 Key Terms and Concepts 9 Why instrumental variables/2SLS regression? 9 When to use instrumental variables/2SLS regression? 10 What are instrumental variables? 12 Endogenous vs exogenous variables. 12 Error/disturbance terms 12 Instruments and instrumental variables 12 Types of IV estimation 14 The two 2SLS stages 14 Overview 14 Stage 1 15 Stage 2 15 Selecting instrumental variables 16 Is an instrumental variables approach needed? 16 Testing for endogeneity 17 Selecting instruments 17 Using lagged variables as instrumented variables 20 Testing for homoscedasticity 21 Testing for validity (overidentifying restrictions tests) 21 Testing for weak instrumentation 22 Testing for good fit 23 Instrumental variables/2SLS example 24 The Model 24 2SLS in Stata 25 Stata syntax 25 Basic Stata output 27 IV estimation in Stata 30 DWH and WH tests for endogeneity of regressors 31 Hausman chi-square test for endogeneity 34 Overidentifying restrictions tests 38 Testing for weak instruments 41 Stored values in Stata 51 Extended regression model (ERM) in Stata 53 Overview 53 The example model 54 Stata syntax 54 Stata output 55 2SLS in SPSS 62 SPSS overview 62 SPSS input 63 Default SPSS output 65 Diagnostic tests in SPSS 67 Saving estimates in SPSS 69 2SLS in SAS 69 SAS overview 69 SAS syntax 69 Estimation methods in SAS 71 Default SAS output 72 Testing for heteroskedasticity* 73 Diagnostic plots 74 Testing for overidentifying restrictions 76 Testing for weak instruments 76 Assumptions 77 Data level 77 Uncorrelated exogenous variables 78 Instruments are not weak 79 Well selected instruments 80 External validity 80 Sample size 81 Homogeneity of regressions 81 Multivariate normality 82 Multivariate equivariance 82 Normally distributed error 82 Linearity 82 No complete nonrecursivity 83 No under-identification 83 Regression model assumptions 83 Testing assumptions 83 Frequently Asked Questions 83 Are "instrumental variables" and "2SLS" synonyms? 83 Will 2SLS estimates be much different from OLS estimates for the same data? 84 What are natural experiments and how do they relate to 2SLS 84 How do I create lagged variables for use in 2SLS? 85 How do I handle interactions involving problematic regressors? 86 Do I need to report first-stage results? 87 Could I do 2SLS manually? 87 What computer software supports 2SLS? 87 What options exist in Stata for computing standard errors? 87 How do I test whether a robust model is required? 89 Why is ML estimation generally preferred to 2SLS in estimating path parameters? 90 In SEM, is there any reason to use 2SLS instead of ML? 91 What is the SEM approach to correlated error? 92 Should I drop non-significant instruments? 93 How is 2SLS used to test for selection bias? 94 How is the intercept interpreted in 2SLS? 96 May one apply 2SLS to cointegrated time series? 96 Bibliography 97 Pagecount: 104