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Garson, G. D. (2018). Instrumental Variables & 2SLS Regression. Asheboro, NC: Statistical Associates Publishers.

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ISBN: 978-1-62638-049-3
@c 2018 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.



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.

    Below is the unformatted table of contents.

    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