# T-Statistics: Standard Errors

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.)

Where:

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 ...