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    Testing Endogeneity

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    This document discusses how to perform the Durbin-Wu-Hausman test to test for endogeneity. It involves running an augmented regression with the residuals from the endogenous variable's reduced form regression included as an additional independent variable. If the coefficient on the residual term is statistically significant, then endogeneity is present and instrumental variables regression should be used instead of ordinary least squares. The example shows running the reduced form, calculating residuals, including the residual in the main regression, and testing its coefficient to determine if instrumental variables are needed.

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    Testing Endogeneity

    Uploaded by

    sharkbait_fb
    219 views3 pages
    This document discusses how to perform the Durbin-Wu-Hausman test to test for endogeneity. It involves running an augmented regression with the residuals from the endogenous variable's reduced form regression included as an additional independent variable. If the coefficient on the residual term is statistically significant, then endogeneity is present and instrumental variables regression should be used instead of ordinary least squares. The example shows running the reduced form, calculating residuals, including the residual in the main regression, and testing its coefficient to determine if instrumental variables are needed.

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    How do I test endogeneity? How do I perform a Durbin–Wu–Hausman test?

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    This document discusses how to perform the Durbin-Wu-Hausman test to test for endogeneity. It involves running an augmented regression with the residuals from the endogenous variable's reduced form regression included as an additional independent variable. If the coefficient on the residual term is statistically significant, then endogeneity is present and instrumental variables regression should be used instead of ordinary least squares. The example shows running the reduced form, calculating residuals, including the residual in the main regression, and testing its coefficient to determine if instrumental variables are needed.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    219 views3 pages

    Testing Endogeneity

    Uploaded by

    sharkbait_fb
    This document discusses how to perform the Durbin-Wu-Hausman test to test for endogeneity. It involves running an augmented regression with the residuals from the endogenous variable's reduced form regression included as an additional independent variable. If the coefficient on the residual term is statistically significant, then endogeneity is present and instrumental variables regression should be used instead of ordinary least squares. The example shows running the reduced form, calculating residuals, including the residual in the main regression, and testing its coefficient to determine if instrumental variables are needed.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 3

    How do I test endogeneity?

    How do I perform a Durbin–Wu–Hausman


    test?

    Consider a regression

    y = b0 + b1*z + b2*x3 + e

    where z is endogenous. Suppose that x1 and x2 are instrumental variables for z. One
    should decide whether it is necessary to use an instrumental variable, i.e., whether a set of
    estimates obtained by least squares is consistent or not.

    An augmented regression test can easily be formed by including the residuals of each
    endogenous right-hand side variable, as a function of all exogenous variables, in a
    regression of the original model. We would first perform a regression

    z = c0 + c1*x1 + c2*x2 + c3*x3 + u

    to get residuals z_res, then perform an augmented regression:

    y = d0 + d1*z + d2*x3 + d3*z_res + 

    If d3 is significantly different from zero, then OLS is not consistent.

    For example, let us assume that you wish to estimate

    rent = b0 + b1*hsngval + b2*pcturban + e

    where hsngval is endogenous amd pcturban is exogenous. Instrumental variables for


    hsngval are: faminc, reg2, reg3 and reg4. To test the endogeneity of hsngval,

    (i) we first run a reduced form model, using all exogenous variables:

    . regress hsngval faminc reg2-reg4 pcturban

    Source | SS df MS Number of obs = 50


    -------------+------------------------------ F( 5, 44) = 19.66
    Model | 8.4187e+09 5 1.6837e+09 Prob > F = 0.0000
    Residual | 3.7676e+09 44 85626930.6 R-squared = 0.6908
    -------------+------------------------------ Adj R-squared = 0.6557
    Total | 1.2186e+10 49 248700555 Root MSE = 9253.5

    ------------------------------------------------------------------------------
    hsngval | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    faminc | 2.731324 .6818931 4.01 0.000 1.357058 4.105589
    reg2 | -5095.038 4122.112 -1.24 0.223 -13402.61 3212.533
    reg3 | -1778.05 4072.691 -0.44 0.665 -9986.019 6429.919
    reg4 | 13413.79 4048.141 3.31 0.002 5255.296 21572.28
    pcturban | 182.2201 115.0167 1.58 0.120 -49.58092 414.0211
    _cons | -18671.87 11995.48 -1.56 0.127 -42847.17 5503.438
    ------------------------------------------------------------------------------

    (ii) Then, we save the residual from the above regression. Call it “hsng_res”. Then,
    include hsng_res in the main equation, and estimate the main equation by OLS.

    . predict hsng_res, res

    . regress rent hsngval pcturban hsng_res


    Source | SS df MS Number of obs = 50
    -------------+------------------------------ F( 3, 46) = 47.05
    Model | 46189.1513 3 15396.3838 Prob > F = 0.0000
    Residual | 15053.9687 46 327.26019 R-squared = 0.7542
    -------------+------------------------------ Adj R-squared = 0.7382
    Total | 61243.12 49 1249.85959 Root MSE = 18.09

    ------------------------------------------------------------------------------
    rent | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    hsngval | .0022398 .0002681 8.36 0.000 .0017003 .0027794
    pcturban | .081516 .2438355 0.33 0.740 -.4092993 .5723313
    hsng_res | -.0015889 .0003984 -3.99 0.000 -.0023908 -.000787
    _cons | 120.7065 12.42856 9.71 0.000 95.68912 145.7239
    ------------------------------------------------------------------------------

    Then, we test the significance of the coefficient of the added residual.


    . test hsng_res

    ( 1) hsng_res = 0.0

    F( 1, 46) = 15.91
    Prob > F = 0.0002

    The small p-value indicates that OLS is not consistent.

    To perform an IV regression, run ivreg

    . ivreg rent pcturban (hsngval = faminc reg2-reg4)

    Instrumental variables (2SLS) regression

    Source | SS df MS Number of obs = 50


    -------------+------------------------------ F( 2, 47) = 42.66
    Model | 36677.4033 2 18338.7017 Prob > F = 0.0000
    Residual | 24565.7167 47 522.674823 R-squared = 0.5989
    -------------+------------------------------ Adj R-squared = 0.5818
    Total | 61243.12 49 1249.85959 Root MSE = 22.862

    ------------------------------------------------------------------------------
    rent | Coef. Std. Err. t P>|t| [95% Conf. Interval]
    -------------+----------------------------------------------------------------
    hsngval | .0022398 .0003388 6.61 0.000 .0015583 .0029213
    pcturban | .081516 .3081528 0.26 0.793 -.5384074 .7014394
    _cons | 120.7065 15.70688 7.68 0.000 89.10834 152.3047
    ------------------------------------------------------------------------------
    Instrumented: hsngval
    Instruments: pcturban faminc reg2 reg3 reg4
    ------------------------------------------------------------------------------

    Note that the coefficients of the last two estimates are the same, however, the standard

    errors are different.

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