The following is a panel of data on investment (y) and profit (x) for n = 3 firms over T = 10 periods.

a. Pool the data and compute the least squares regression coefficients of the model yi t = α + βxit + εit.

b. Estimate the fixed effects model of (13-2), and then test the hypothesis that the constant term is the same for all three firms.

c. Estimate the random effects model of (13-18), and then carry out the Lagrange multiplier test of the hypothesis that the classical model without the common effect applies.

d. Carry out Hausman??s specification test for the random versus the fixed effect model.

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1 ·234567890 10 y 13.32 26.30 2.62 14.94 15.80 12.20 14.93 29.82 20.32 4.77 i=1 X 12.85 25.69 5.48 13.79 15.41 12.59 16.64 26.45 19.64 5.43 y 20.30 17.47 9.31 18.01 7.63 19.84 13.76 10.00 19.51 18.32 i=2 X 22.93 17.96 9.16 18.73 11.31 21.15 16.13 11.61 19.55 17.06 y 8.85 19.60 3.87 24.19 3.99 5.73 26.68 11.49 18.49 20.84 i=3 8.65 16.55 1.47 24.91 5.01 8.34 22.70 8.36 15.44 17.87