systemfit (version 0.5-6)

threestage: Three-Stage Least Squares Estimation

Description

Fits a set of structural equations using Three-Stage Least Squares. The resulting object is an array of fitting regression equations that contain information about the fitting process as well as the resulting parameter estimates, standard error estimates and covaraince matrix.

Usage

threestage.systemfit( eqns, instruments, eqnlabels, data )

Arguments

eqns

a list of structural equations to be estimated; a regression constant is implied if not explicitly omitted.

instruments

one-sided model formula specifying instrumental variables.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment from which threestage is called.

eqnlabels

list of character vectors of names for the equation labels.

Value

• threestage returns a list of objects of class threestage, with the following components:
• n
  number of observations.
• p
  number of parameters.
• coefficients
  parameter estimates.
• V
  estimated covariance matrix of coefficients.
• s
  residual standard error.
• residuals
  vector of residuals.
• response
  vector of response values.
• X
  model matrix.
• Z
  instrumental-variables matrix.
• response.name
  name of response variable, or expression evaluating to response.
• formula
  model formula.
• instruments
  one-sided formula for instrumental variables.
• method
  estimation method for the object, in this case, "3SLS".
• eqnlabel
  the equation label from the labels list for the equation.
• formula
  model formula.
• dfe
  error degrees of freedom.
• dfm
  model degrees of freedom.
• model.matrix
  model matrix for the ith equation
• model.frame
  model frame for the ith equation
• instruments
  list of instruments for the set of equations.
• response
  y
• predicted
  predicted values
• residuals
  residuals
• ztzinv
  two-stage instrument regression matrix - ztzinv.
• v
  v
• b
  parameter estimates
• n
  number of observations for the ith equation
• s
  estimation of sigma
• sse
  sum of squares
• mse
  mean squared error
• rmse
  square root of mse or root mean squared error
• se
  estimates standard errors of the parameter estimates.
• t
  t values for b
• p
  p values for b
• r2
  r2
• adjr2
  adjusted r-squared
• covb
  covb
• se.prediction
  standard error of the predicted values
• prediction.limts
  lower and upper 95 percent prediction limits
• confidence.limts
  lower and upper 95 percent confidence limits

References

Greene, W. H. (1993) Econometric Analysis, Second Edition, Macmillan. Kmenta, J. (1997) Elements of Econometrics, Second Edition, University of Michigan Publishing

See Also

ols,twostage,surand threestage

Examples

library( systemfit )

data( kmenta )
attach( kmenta )
demand <- q ~ p + d
supply <- q ~ p + f + a
inst <- ~ d + f + a
labels <- list( "demand", "supply" )
system <- list( demand, supply )

## perform 2SLS on each of the equations in the system
fit2sls <- twostage.systemfit( system, inst, labels, kmenta )
print( fit2sls )
print( varcov.systemfit( fit2sls ) )


fit3sls <- threestage.systemfit( system, inst, labels, kmenta )
print( fit3sls )
print( "covariance of residuals used for estimation (from 2sls)" )
print( varcov.systemfit( fit2sls ) )
print( "covariance of residuals" )
print( varcov.systemfit( fit3sls ) )

## examine the correlation between the predicted values
## of suppy and demand by plotting the correlation over
## the value of q
r12 <- correlation.systemfit( fit3sls, 1, 2 )
plot( q, r12, main="correlation between predictions from supply and demand" )  

## examine the improvement of 3SLS over OLS by computing
## the ratio of the standard errors of the estimates
improve.ratio <- se.ratio.systemfit( fit2sls, fit3sls, 2 )
print( "summary values for the ratio in the std. err. for the predictions" )
print( summary( improve.ratio ) )

## perform the hausman test 
h <- hausman.systemfit( fit2sls, fit3sls )
pval <- pchisq( h, dim( fit3sls[[1]]$systemcovb )[1] )