The file agriculture.csv contains data on M = 3 inputs and N = 2 Quputs for I = 8 representative agricultural firms, one from each Australian state and territory, over the T = 32 years from 1990 to 2021. The file also contains data on J = 2 environmental variables. These are the data that were used in Assignments 1 and 2. Consider the following output-oriented deterministic frontier model: 77.882qzit 3 In = a+ at+ 8; Inzji + 2 Bminxmir - Uit (1 92it - 0.011q1 j=1 m= 1 where t is a time index that takes the value one in YTJ 1990 and uit > 0 is an unobserved outputoriented technical inefficiency effect. Assume that uit is an independent half-normal random variable obtained by lower-truncating the N(0,o 2 u ) distribution at zero. (a) (5 marks) Estimate the unknown parameters of the model using corrected ordinary least squares (COLS). Interpret your estimates. # first ols y = log((77. 882*q2 2)/(q2-0. 011*q1)) t = YTJ - 1989 1z1 = 109(z1) 1z2 = 10g(z2) 1x1 = log (x1) 1x2 = log(x2) 1x3 = 10g(x3) x = cbind(t, 1z1, 122, 1x1, 1x2, 1x3) ols = 1m(y ~ x) out = summary (ols) outCall : 1m (formula = y ~ x) Residuals : Min 1Q Median 3Q Max -3. 5317 -0. 3350 0. 0526 0.4542 2 1. 5914 Coefficients : Estimate Std. Error t value Pr (>|t/) (Intercept) 4. 217486 0. 125953 33.485 allow intercepts to vary by country summary (uls) The answer provided is using an F test to test for fixed effects. You need to part c) use an F-test to test the null hypothesis that production frontiers exhibit constant returns to scale. Constant returns to scale apply when eta = 1 Eta = b1 + b2 + b3