Correlation between Predictions from Equation i and j

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Description

correlation returns a vector of the correlations between the predictions 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}}{√{(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

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correlation.systemfit( results, eqni, eqnj )

Arguments

results

an object of type systemfit.

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.

Author(s)

Jeff D. Hamann jeff.hamann@forestinformatics.com

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

See Also

systemfit

Examples

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data( "Kmenta" )
eqDemand <- consump ~ price + income
eqSupply <- consump ~ price + farmPrice + trend
inst <- ~ income + farmPrice + trend
system <- list( demand = eqDemand, supply = eqSupply )

## perform 2SLS on each of the equations in the system
fit2sls <- systemfit( system, "2SLS", inst = inst, data = Kmenta )
print( fit2sls )
print( fit2sls$rcov )

## perform the 3SLS
fit3sls <- systemfit( system, "3SLS", inst = inst, data = Kmenta )
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( Kmenta$consump, r12, main="correlation between predictions from supply and demand" )

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