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    T-Statistics: Standard Errors

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    W. Bowen and T. Finegan (1965) published a paper titled "Labor Force Participation and Unemployment." In that paper they estimated the following regression using a data set of 78 cities:

    i = 94.2 - .24Ui + .2Ei -.69Ii - .06Si + .002Ci - .8Di
    (.08) (.06) (.16) (.18) (.03) (.43)

    The standard errors for the OLS coefficient estimates are in parentheses. (Note: You might have already noticed that many research papers choose to report the standard errors for the coefficients instead of the t-statistics.)

    Li = percent labor force participation (males age 25 to 54) in the ith city
    Ui = percent unemployment rate in the ith city
    Ei = average earnings (hundreds of dollar/year) in the ith city
    Ii = average other income(hundreds of dollars/year) in the ith city
    Si = average schooling completed (years) in the ith city
    Ci = percent of the labor force that is nonwhite in the ith city
    Di = a dummy equal to 1 if the city is in the South and 0 otherwise

    A. Calculate the t-statistics for each of the coefficients assuming the null hypotheses are that the independent variables are not correlated with the dependent variable.

    B. For which of the independent variables can you reject the null hypothesis at the 5% level of confidence?

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    Solution Preview

    Test statistics is given as
    t = Estimate of Coefficient/Standard Error of coefficient

    Test statistics for Ui is
    t=-0.24/0.08 = -3

    Test statistics for Ei is
    t=0.2/0.06 = 3.33

    Test statistics for Ii ...