contains data on M = 3 inputs and N = 2 ouputs 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. Assume that there has been no technical change since 1990. Also assume that (a) production possibilities sets can be represented by distance, revenue, cost and/or profit functions, (b) all relevant quantities, prices and environmental variables are observed and measured without error; (c) production frontiers are locally linear; (d) all outputs, inputs and environmental variables are strongly disposable; and (e) production possibilities sets are convex. (a) (4 marks) Use the Benchmarking package in R to estimate the output-oriented technical efficiency (OTE) of each firm in each period. Report the results for the WA firm (rounded to three decimal places).

I = 8 # no. of firms T = 32 # no. of time periods M = 3 # no. of inputs N = 2 # no. of outputs J = 2 # no. of environmental variables

t = YTJ - 1989 a = 6.235 lam = 0.101 d1 = 2.437 d2 = 1.040 b1 = 0.109 b2 = 1.186 b3 = 0.179 g2 = 77.882 g1 = 0.011

answser to a)

in Rstudio

library(Benchmarking)

q = cbind(q1, q2) x = cbind(x1, x2, x3, z1, z2) pfa = dea(x, q, ORIENTATION = "out") OTE = 1/pfa$eff

results = data.frame(YTJ, State, roundup(OTE,3)) colnames(results) = c("Year","State", "OTE") results[YTJ <= 2021 & State =='WA',] summary(results)

(h) (3 marks) Assume that the good output (q1) is strongly disposable the bad output (q2) is merely weakly disposable. Re-estimate the OTE of each firm in each period. In what way, if any, do your answers differ from those obtained in part (a)? please only answer parts (a), (h)

PLEASE ONLY ANSWER H)