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)

Course hero answer

Step 1: Load the Benchmarking package

If you haven't already installed the Benchmarking package, you can install it viainstall.packages("Benchmarking"). Then, you load it into your R session.

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library(Benchmarking)

Step 2: Prepare the data

You should have your input matrixxwhich includes inputs and environmental variables, and your output matrixqwhich includes both types of outputs. Here I assume that the data is already loaded into R and named appropriately (you will need to adjust this according to your actual data).

Step 3: Modify the DEA function to account for disposability

The DEA model must be adjusted to handle weak disposability for the bad output (q2). In the Benchmarking package, this can be done using theDEAfunction with a disposability matrix. The matrix indicates which outputs are weakly disposable (value of 0) and which are strongly disposable (value of 1).

Here's how you can set up your DEA model:

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# Strong disposability for good output (q1), weak disposability for bad output (q2) disposabilityMatrix = matrix(c(1, 0), ncol = 2) # Running DEA with adjusted disposability settings pfa = dea(x, q, ORIENTATION = "out", DISPOSABILITY = disposabilityMatrix) OTE = 1/pfa$eff

Step 4: Extract and report results

You may want to format the results as before, filtering for the Western Australia (WA) firm if required and summarizing as needed.

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results = data.frame(YTJ, State, round(OTE, 3)) colnames(results) = c("Year", "State", "OTE") # Filter for WA firm results up to 2021 wa_results = results[results$YTJ <= 2021 & results$State == 'WA',] # Display WA firm results print(wa_results) # Optional: Overall summary of results summary(results)

Discussion of Differences

In answering how the results differ from part (a) to part (h):

• In part (a), all outputs are assumed to be strongly disposable, which means increasing the production of one output does not necessarily lead to an increase in the production of the other.
• In part (h), with weak disposability for the bad output (q2), when production of q2 is increased, it could constrain the reduction in q2 even if inputs or other outputs are reduced. This typically results in lower technical efficiency scores, reflecting the costs of managing or reducing the bad output.

This approach not only follows the given assumptions but also adjusts the efficiency analysis to better reflect environmental constraints and management.

ERROR IN ANSWER

# Strong disposability for good output (q1), weak disposability for bad output (q2) disposabilityMatrix = matrix(c(1, 0), ncol = 2) # Running DEA with adjusted disposability settings pfa = dea(x, q, ORIENTATION = "out", DISPOSABILITY = disposabilityMatrix) OTE = 1/pfa$eff

> disposabilityMatrix = matrix(c(1,0), ncol = 2) > pfa = dea(xx, qq, ORIENTATION = "out", DISPOSABILITY = disposabilityMatrix) Error in dea(xx, qq, ORIENTATION = "out", DISPOSABILITY = disposabilityMatrix) : unused argument (DISPOSABILITY = disposabilityMatrix)

please fix and use a different method to finding the disposability