technical.efficiency.change {snfa}

Technical and efficiency change estimation

Description

Estimates technical and efficiency change using SNFA

Usage

technical.efficiency.change(df, input.var.names, output.var.name,
  firm.var.name, time.var.name, method = "u")

Arguments

df

Data frame with variables used in estimation

input.var.names

Names of input variables; must appear in df

output.var.name

Name of output variable; must appear in df

firm.var.name

Name of firm variable; must appear in df

time.var.name

Name of time variable; must appear in df

method

Constraints to apply; "u" for unconstrained, "m" for monotonically increasing, and "mc" for monotonically increasing and concave

Details

This function decomposes change in productivity into efficiency and technical change, as in Fare et al. (1994), using smooth non-parametric frontier analysis. Denoting D_s(x_t, y_t) as the efficiency of the production plan in year t relative to the production frontier in year s, efficiency change for a given firm in year t is calculated as

\frac{D_{t+1}(x_{t+1}, y_{t+1})}{D_t(x_t, y_t)},

and technical change is given by

\left( \frac{D_t(x_{t+1}, y_{t+1})}{D_{t+1}(x_{t+1}, y_{t+1})}\times \frac{D_t(x_t, y_t)}{D_{t+1}(x_t, y_t)} \right)^{1/2}.

Value

Returns a data.frame with the following columns

firm.var.name

Column of firm name data

time.var.name

Column of time period data

efficiency.change

Average annual efficiency change since the previous period in data

technical.change

Average annual technical change since the previous period in data

productivity.change

Average annual productivity change since the previous period in data

References

Fare R, Grosskopf S, Norris M, Zhang Z (1994). “Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries.” The American Economic Review, 84(1), 66-83.

Examples

data(panel.production)

results.df <- technical.efficiency.change(df = panel.production,
                                          input.var.names = c("X.1", "X.2", "X.3"),
                                          output.var.name = "y",
                                          firm.var.name = "Firm",
                                          time.var.name = "Year")

#Plot changes over time by firm
library(ggplot2)

ggplot(results.df, aes(Year, technical.change)) +
  geom_line(aes(color = Firm))
ggplot(results.df, aes(Year, efficiency.change)) +
  geom_line(aes(color = Firm))
ggplot(results.df, aes(Year, productivity.change)) +
  geom_line(aes(color = Firm))