tsls function

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

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.

Returns

'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)
res