tsls: Two-Stage Least Squares
In sem1: Structural Equation Models

Description Usage Arguments Value Author(s) References See Also Examples

Fits an equation in a structural-equation model by two-stage least squares. This is equivalent to direct instrumental-variables estimation when the number of instruments is equal to the number of predictors.

tsls(y, ...)
## S3 method for class 'formula'
tsls(formula, instruments, data, subset, na.action, contrasts=NULL, ...)
## Default S3 method:
tsls(y, X, Z, names=NULL, ...)

## S3 method for class 'tsls'
print(x, ...)
## S3 method for class 'tsls'
summary(object, digits=4, ...)
## S3 method for class 'tsls'
anova(object, model.2, s2, dfe, ...)

## S3 method for class 'tsls'
fitted(object, ...)
## S3 method for class 'tsls'
residuals(object, ...)
## S3 method for class 'tsls'
coef(object, ...)
## S3 method for class 'tsls'
vcov(object, ...)

`formula`	model formula for structural equation 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 tsls is called.
`subset`	an optional vector specifying a subset of observations to be used in fitting the model.
`na.action`	a function that indicates what should happen when the data contain `NA`s. The default is set by the `na.action` option.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`y`	Response-variable vector.
`X`	Matrix of predictors, including a constant (if one is in the model).
`Z`	Matrix of instrumental variables, including a constant (if one is in the model).
`names`	optional character vector of names for the columns of the `X` matrix.
`x, object, model.2`	objects of class `tsls` returned by `tsls.formula`, containing nested models to be compared by an incremental F-test. One model should be nested in the other; the order of models is immaterial.
`s2`	an optional estimate of error variance for the denominator of the F-test. If missing, the error-variance estimate is taken from the larger model.
`dfe`	optional error degrees of freedom, to be specified when an estimate of error variance is given.
`digits`	number of digits for summary output.
`...`	arguments to be passed down.

tsls.formula returns an object of class tsls, 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.

John Fox jfox@mcmaster.ca

Fox, J. (1979) Simultaneous equation models and two-stage least-squares. In Schuessler, K. F. (ed.) Sociological Methodology 1979, Jossey-Bass.

Greene, W. H. (1993) Econometric Analysis, Second Edition, Macmillan.

sem

data(Kmenta)
summary(tsls(Q ~ P + D, ~ D + F + A, data=Kmenta))     # demand equation

##  2SLS Estimates
##  
##  Model Formula: Q ~ P + D
##  
##  Instruments: ~D + F + A
##  
##  Residuals:
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##  -3.43e+00 -1.24e+00 -1.89e-01 -2.49e-13  1.58e+00  2.49e+00 
##  
##              Estimate Std. Error t value  Pr(>|t|)
##  (Intercept)  94.6333    7.92084  11.947 1.076e-09
##  P            -0.2436    0.09648  -2.524 2.183e-02
##  D             0.3140    0.04694   6.689 3.811e-06
##  
##  Residual standard error: 1.9663 on 17 degrees of freedom

summary(tsls(Q ~ P + F + A, ~ D + F + A, data=Kmenta)) # supply equation

##  2SLS Estimates
##  
##  Model Formula: Q ~ P + F + A
##  
##  Instruments: ~D + F + A
##  
##  Residuals:
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##  -4.87e+00 -1.26e+00  6.42e-01 -5.64e-12  1.47e+00  3.49e+00 
##  
##              Estimate Std. Error t value  Pr(>|t|)
##  (Intercept)  49.5324   12.01053   4.124 7.954e-04
##  P             0.2401    0.09993   2.402 2.878e-02
##  F             0.2556    0.04725   5.410 5.785e-05
##  A             0.2529    0.09966   2.538 2.193e-02
##  
##  Residual standard error: 2.4576 on 16 degrees of freedom

anova(tsls(Q ~ P + F + A, ~ D + F + A, data=Kmenta),
    tsls(Q ~ 1, ~ D + F + A, data=Kmenta))
##    
##  Analysis of Variance
##    
##  Model 1:  Q ~ P + F + A   Instruments: ~D + F + A
##  Model 2:  Q ~ 1   Instruments: ~D + F + A
##    
##          Res.Df     RSS Df Sum of Sq      F    Pr(>F)    
##  Model 1     16  96.633                                  
##  Model 2     19 268.114  3   171.481 9.4643 0.0007834 ***
##  ---
##  Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1