Benchmarking (version 0.10)

sfa: Stochastic frontier estimation

Description

Estimate a stochastic frontier production functin using a maximum likelihood method.

Usage

sfa(x, y, beta0 = NULL, lambda0 = 1, resfun = ebeta, 
    TRANSPOSE = FALSE, DEBUG=FALSE,..., control, hessian=2)

Arguments

x

input as a k x m matrix of observations on m inputs of k firms; (unit x input); MUST be a matrix. No constant for the intercept should be included in x as it is added by default.

y

output; k times 1 matrix (one output)

beta0

optional initial parameter values

lambda0

optional initial ratio of variances

resfun

function to calculate the residuals, default is a linear model with an intercept. Must be called as resfun(x,y,parm) where parm=c(beta,lambda) or parm=c(beta), and return the residuals as an array of length

TRANSPOSE

Data is transposed, ie. input is now m x k matrix

DEBUG

Set to TRUE to get various debuggen informatin written on the console

...

optional parameters for the ucminf method

control

list of control parameters to ucminf

hessian

how the Hessian is delivered, see the ucminf documentation

Value

• The values returned is the same as for ucminf, i.e. a list with components plus some espicifically relevant for sfa:
• par
  The best set of parameters found c(beta,lambda).
• value
  The value of minus loglikelihood function corresponding to 'par'.
• beta
  The parameters for the function
• sigma2
  The estimate of the total variance
• lambda
  The estimate of lambda
• N
  The number of observations
• df
  The degrees of freedom for the model
• residuals
  The residuals as a n times 1 matrix/vector, can also be obtained by residuals(sfa-object)
• fitted.values
  Fitted values
• vcov
  The varians-covarians matrix for all estimaed parameters incl. lambda
• convergence
  An integer code. '0' indicates successful convergence. Some of the error codes taken from ucminf are '1' Stopped by small gradient (grtol). '2' Stopped by small step (xtol). '3' Stopped by function evaluation limit (maxeval). '4' Stopped by zero step from line search More codes are found in ucminf
• message
  A character string giving any additional information returned by the optimizer, or 'NULL'.
• o
  The object returned by ucminf, for further information on this see ucminf

Details

The optimization is done by the R method ucminf. The efficiency terms are asumed to be half--normal distributed.

References

See the method ucminf for the possible optimization methods and further options

See Also

ucminf

Examples

# Example from the book by Coelli et al.
# d <- read.csv("c:/0work/rpack/front41Data.csv", header = TRUE, sep = ",")
# x <- cbind(log(d$capital), log(d$labour))
# y <- matrix(log(d$output))

n <- 50
x1 <- 1:50 + rnorm(50,0,10)
x2 <- 100 + rnorm(50,0,10)
x <- cbind(x1,x2)
y <- 0.5 + 1.5*x1 + 2*x2 + rnorm(n,0,1) - pmax(0,rnorm(n,0,1))
sfa(x,y)
summary(sfa(x,y))


# Estimate efficiency for each unit
o <- sfa(x,y)
te <- te.sfa(o)
te1 <- te1.sfa(o)
te2 <- te2.sfa(o)
cbind(te,te1,te2)[1:10,]

# Detailed calculations with out the method te.sfa
e <- o$residuals    # Residuals
residuals(o)[1:10]        # or

sigma2.sfa(o)       # Estimated varians
lambda.sfa(o)       # Estimated lambda