Two stage least squares estimation

Function to estimate a linear model by the two stage least squares method.

tsls(g,x,data)

Arguments

g

A formula describing the linear regression model (see details below).

x

The matrix of instruments (see details below).

data

A data.frame or a matrix with column names (Optionnal).

Details

The function just calls gmm with the option vcov="iid". It just simplifies the the implementation of 2SLS. The users don't have to worry about all the options offered in gmm. The model is $$ Y_i = X_i\beta + u_i $$ In the first step, lm is used to regress \(X_i\) on the set of instruments \(Z_i\). The second step also uses lm to regress \(Y_i\) on the fitted values of the first step.

Value

'tsls' returns an object of 'class' '"tsls"' which inherits from class '"gmm"'.

The functions 'summary' is used to obtain and print a summary of the results. It also compute the J-test of overidentying restriction

The object of class "gmm" is a list containing at least:

coefficients

\(k\times 1\) vector of coefficients

residuals

the residuals, that is response minus fitted values if "g" is a formula.

fitted.values

the fitted mean values if "g" is a formula.

vcov

the covariance matrix of the coefficients

objective

the value of the objective function \(\| var(\bar{g})^{-1/2}\bar{g}\|^2\)

terms

the terms object used when g is a formula.

call

the matched call.

y

if requested, the response used (if "g" is a formula).

x

if requested, the model matrix used if "g" is a formula or the data if "g" is a function.

model

if requested (the default), the model frame used if "g" is a formula.

algoInfo

Information produced by either optim or nlminb related to the convergence if "g" is a function. It is printed by the summary.gmm method.

References

Hansen, L.P. (1982), Large Sample Properties of Generalized Method of Moments Estimators. Econometrica, 50, 1029-1054,

Examples

n <- 1000
e <- arima.sim(n,model=list(ma=.9))
C <- runif(n,0,5)
Y <- rep(0,n)
Y[1] = 1 + 2*C[1] + e[1]
for (i in 2:n){
Y[i] = 1 + 2*C[i] + 0.9*Y[i-1] + e[i]
}
Yt <- Y[5:n]
X <- cbind(C[5:n],Y[4:(n-1)])
Z <- cbind(C[5:n],Y[3:(n-2)],Y[2:(n-3)],Y[1:(n-4)]) 

res <- tsls(Yt~X,~Z)
#> Error in eval(predvars, data, env): object 'Yt' not found
res
#> Error: object 'res' not found