The file fuglie.csv contains data on M = 6 agricultural inputs, N = 4 agricultural outputs and one environmental variable for 41 countries for the 36 years from 1985 to 2020.  This is the same data file that was used in Assignment 1.  Recall that some data is missing for some countries in some years (i.e., the dataset is “unbalanced”).  Assume that there has been no technical change since 1985.  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) outputs, inputs and environmental variables are strongly disposable; and (e) production possibilities sets are convex.

(a)  (2 marks) Normalise all the variables (i.e., divide each variable by a constant) in such a way that the normalised variables have unit means. Report the minima and maxima of the normalised inputs.

(b)  (4 marks) Use the Benchmarking package in R to estimate the output-oriented technical

efficiency (OTE) of each country in each period.  Report the results for Japan (rounded to three decimal places).

(c)  (4 marks) Assume the inefficiency effects are exponentially distributed.  Construct a 95% confidence interval for the OTE of each country in each period.

(d)  (4 marks) Assume the inefficiency effects are exponentially distributed. Test the null hypoth- esis that the average level of inefficiency in Japan is less than or equal to the average level of inefficiency in Brazil. Use a 5% level of significance.

(e)  (3 marks) Use the Benchmarking package in R to estimate the output and input shadow prices for each country in each period. Report the average shadow prices of each output and input.

(f)  (6 marks) Consider an additive TFP index that uses the average shadow prices computed in part (e) as weights. Use the lpSolve package in R to estimate associated levels of technical, scale and mix efficiency (TSME) and output-oriented scale and mix efficiency (OSME) for each country in each period. Report the results for Japan (rounded to three decimal places).