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Garson, G. D. (2013). Two Stage Least Squares. Asheboro, NC: Statistical Associates Publishers.

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ISBN: 978-1-62638-004-2
@c 2013 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.



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.

New in the 2013 edition:

  • Over 250% more coverage.
  • Worked econometric examples in Stata, SPSS, and SAS.
  • Coverage of diagnostics.

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

    Below is the unformatted table of contents.

    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