npsf (version 0.8.0)

nptestind: Nonparametric Test of Independence

Description

In output based efficiency measurement, routine nptestind perform test that radial (Debreu-Farrell) output-based measure of technical efficiency under chosen assumption about the technology and mix of outputs are independent. In input-based efficiency measurement, routine nptestind perform test that radial (Debreu-Farrell) input-based measure of technical efficiency under chosen assumption about the technology and mix of inputs are independent. Testing is performed using bootstrap technique.

Usage

nptestind(formula, data, subset,
 rts = c("C", "NI", "V"), base = c("output", "input"),
 reps = 999, alpha = 0.05,
 print.level = 1, dots = TRUE)

Arguments

formula

an object of class ``formula'' (or one that can be coerced to that class): a symbolic description of the model. The details of model specification are given under `Details'.

data

an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment (formula), typically the environment from which teradial is called.

subset

an optional vector specifying a subset of observations for which technical efficiency is to be computed.

rts

character or numeric. string: first letter of the word ``c'' for constant, ``n'' for non-increasing, or ``v'' for variable returns to scale assumption. numeric: 3 for constant, 2 for non-increasing, or 1 for variable returns to scale assumption.

base

character or numeric. string: first letter of the word ``o'' for computing output-based or ``i'' for computing input-based technical efficiency measure. string: 2 for computing output-based or 1 for computing input-based technical efficiency measure

reps

specifies the number of bootstrap replications to be performed. The default is 999. The minimum is 100. Adequate estimates of confidence intervals using bias-corrected methods typically require 1,000 or more replications.

alpha

sets significance level; default is alpha=0.05.

dots

logical. Relevant if print.level>=1. If TRUE, one dot character is displayed for each successful replication; if FALSE, display of the replication dots is suppressed.

print.level

numeric. 0 - nothing is printed; 1 - print summary of the model and data. 2 - print summary of technical efficiency measures. 3 - print estimation results observation by observation. Default is 1.

Value

nptestrts returns a list of class npsf containing the following elements:

K

numeric: number of data points.

M

numeric: number of outputs.

N

numeric: number of inputs.

rts

string: RTS assumption.

base

string: base for efficiency measurement.

reps

numeric: number of bootstrap replications.

alpha

numeric: significance level.

t4n

numeric: value of the T4n statistic.

pval

numeric: p-value of the test of independence.

Details

In output based efficiency measurement, routine nptestind perform test that radial (Debreu-Farrell) output-based measure of technical efficiency under chosen assumption about the technology and mix of outputs are independent. In input-based efficiency measurement, routine nptestind perform test that radial (Debreu-Farrell) input-based measure of technical efficiency under chosen assumption about the technology and mix of inputs are independent.

Testing is performed using bootstrap technique (see Wilson, 2003).

Results can be summarized using summary.npsf.

References

F<U+00E4>re, R. and Lovell, C. A. K. (1978), Measuring the technical efficiency of production, Journal of Economic Theory, 19, 150--162, 10.1016/0022-0531(78)90060-1

F<U+00E4>re, R., Grosskopf, S. and Lovell, C. A. K. (1994), Production Frontiers, Cambridge U.K.: Cambridge University Press

Wilson P.W. (2003), Testing Independence in Models of Productive Efficiency, Journal of Productivity Analysis, 20, 361--390, 10.1023/A:1027355917855

See Also

teradial, tenonradial, teradialbc, tenonradialbc, nptestrts, sf

Examples

# NOT RUN {
# }
# NOT RUN {
require( npsf )

# Prepare data and matrices

data( ccr81 )
head( ccr81 )

# Create some missing values

ccr81 [64, "x4"] <- NA # just to create missing
ccr81 [68, "y2"] <- NA # just to create missing

Y2 <- as.matrix( ccr81[ , c("y1", "y2", "y3"), drop = FALSE] )
X2 <- as.matrix( ccr81[ , c("x1", "x2", "x3", "x4", "x5"), drop = FALSE] )

# Perform nonparametric test that radial (Debreu-Farrell) 
# output-based measure of technical efficiency under assumption of 
# NIRS technology and mix of outputs are independent. Test is 
# performed based on 999 replications at the 5<!-- % significance level. -->

t1 <- nptestind ( y1 + y2 + y3 ~ x1 + x2 + x3 + x4 + x5, 
	data = ccr81, base = "o", rts = "n", 
	reps = 999, dots = TRUE)


# Really large data-set

data(usmanuf)
head(usmanuf)

nrow(usmanuf)
table(usmanuf$year)

# This will take some time depending on computer power

data(usmanuf)
head(usmanuf)

t2 <- nptestind ( Y ~ K + L + M, data = usmanuf, 
	subset = year >= 1999 & year <= 2000, 
	reps = 999, dots = TRUE, base = "i", rts = "v")

# }
# NOT RUN {
# }