correlation.systemfit: Correlation between Predictions from Equation i and j

Description

correlation returns a vector of the correlations between the preditions of two equations in a set of equations. The correlation between the predictions is defined as, $$r_{ijk} = \frac{x'_{ik}C_{ij}x_{jk}}{\sqrt{(x'_{ik}C_{ii}x_{ik})(x'_{jk}C_{jj}x_{jk})}}$$ where $r_{ijk}$ is the correlation between the predicted values of equation i and j and $C_{ij}$ is the cross-equation variance-covariance matrix between equations i and j.

Usage

correlation.systemfit( results, eqni, eqnj )

Arguments

results

an object of type systemfit.system.

eqni

index for equation i

eqnj

index for equation j

Value

correlation returns a vector of the correlations between the predicted values in equation i and equation j.

References

Greene, W. H. (1993) Econometric Analysis, Second Edition, Macmillan. Hasenauer, H; Monserud, R and T. Gregoire. (1998) Using Simultansous Regression Techniques with Individual-Tree Growth Models. Forest Science. 44(1):87-95 Kmenta, J. (1997) Elements of Econometrics, Second Edition, University of Michigan Publishing

Examples

Run this code

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 <- systemfit( "2SLS", system, labels, inst)
print( fit2sls )
print( fit2sls$rcov )

## perform the 3SLS
fit3sls <- systemfit( "3SLS", system, labels, inst )
print( fit3sls )
print( "covariance of residuals used for estimation (from 2sls)" )
print( fit3sls$rcovest )
print( "covariance of residuals" )
print( fit3sls$rcov )

## 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" )