README.md

In alessandromagrini/CobbDouglas: Efficiency Analysis using the Cobb-Douglas Production Frontier

CobbDouglas

Efficiency analysis using the Cobb-Douglas production frontier

CobbDouglas is an R package implementing functionalities to estimate a Cobb-Douglas production frontier from sample data through constrained least squares. It is possible to set the desired returns to scale, to predict the maximum producible output or technical efficiency, and to obtain boostrap confidence intervals for parameters.

R (The R Project for Statistical Computing) needs to be installed on your system in order to use the CobbDouglas package. R can be downloaded from https://www.r-project.org/.

To install the CobbDouglas package, open the console of R and type:

install.packages("devtools")  ## do not run if package 'devtools' is already installed
library(devtools)
install_github("alessandromagrini/CobbDouglas")

For any request or feedback, please write to [e-mail] (Alessandro Magrini)

Below, you find some examples of use of the package.

Load the CobbDouglas package

library(CobbDouglas)

Load simulated data

data(production)

Frontier with 1 input variable: 'labour'

m1 <- CobbDouglas("output", "labour", data=production)
summary(m1)

# plot the estimated frontier
plot(m1, cex.axis=1.1, cex.lab=1.2)

# technical efficiencies
m1_eff <- m1$efficiency
## NOT RUN:
# m1_eff

# efficient units
m1_eff[which(m1_eff$y.side==1),]

# setting beta=1 (constant returns to scale) seems to fit worse
m1c <- CobbDouglas("output", "labour", data=production, beta.sum=1)
m1c$parameters
m1c$efficiency[which(m1c$efficiency$y.side==1),]
plot(m1c, cex.axis=1.1, cex.lab=1.2, main="beta = 1", cex.main=1.6)

Frontier with 2 input variables: 'labour' and 'capital'

# no constraints on the sum of beta parameters
m2 <- CobbDouglas("output", c("labour","capital"), data=production)
summary(m2)
m2$efficiency[which(m2$efficiency$y.side==1),]

## plot the estimated frontier from the side of 'labour'
# 'capital' fixed at its empirical mean
plot(m2, x.name="labour", cex.axis=1.1, cex.lab=1.2)
# 'capital' fixed at value 1
plot(m2, x.name="labour", x.fixed=c(capital=1), cex.axis=1.1, cex.lab=1.2)

## plot the estimated frontier from the side of 'capital'
# 'labour' fixed at its empirical mean
plot(m2, x.name="capital", cex.axis=1.1, cex.lab=1.2)
# 'labour' fixed at value 1
plot(m2, x.name="capital", x.fixed=c(labour=1), cex.axis=1.1, cex.lab=1.2)

# beta.sum=1 (constant returns to scale)
m2c <- CobbDouglas("output", c("labour","capital"), data=production, beta.sum=1)
summary(m2c)
m2c$efficiency[which(m2c$efficiency$y.side==1),]

# beta.sum=0.7 (decreasing returns to scale)
m2d <- CobbDouglas("output", c("labour","capital"), data=production, beta.sum=0.7)
summary(m2d)
m2d$efficiency[which(m2d$efficiency$y.side==1),]

Prediction of the maximum producible output

predict(m2, newdata=data.frame(labour=20,capital=5))

Prediction of technical efficiency

predict(m2, newdata=data.frame(output=11.5,labour=20,capital=5), type="eff")

Bootstrap confidence intervals

set.seed(123)
m2_boot <- CobbDouglas_boot(m2, nboot=500)
m2_boot$parameters  ## parameters
m2_boot$y.side      ## output-side efficiencies
m2_boot$x.side      ## input-side efficiencies

alessandromagrini/CobbDouglas documentation built on July 4, 2021, 1:21 a.m.