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INSTRUMENTAL VARIABLES & 2SLS REGRESSION

Overview

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.

New in the 2018 edition:

• Over double the coverage.
• Detailed treatment of tests related to instrumental variables regression (e.g., weak instruments tests, homoscedasticity tests, overidentifying restrictions tests, fit measures, more).
• Worked econometric examples in Stata, SPSS, and SAS.

The full content is now available from Statistical Associates Publishers. Click here.

```TWO STAGE LEAST SQUARES
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
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
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