dLagM (version 0.0.8)

koyckDlm: Implement finite autoregressive distributed lag model

Description

A function that applies autoregressive distributed lag models of order (p , q) with one predictor.

Usage

koyckDlm(x , y , show.summary = TRUE)

Arguments

x

A vector including the observations of predictor time series. This is not restricted to ts objects.

y

A vector including the observations of dependent time series. This is not restricted to ts objects.

show.summary

If TRUE, prints standard model summary for the model of interest.

Value

model

An object of class ivreg. See the details of ivreg function.

geometric.coefficients

A vector composed of corresponding geometric distributed lag model coefficients.

Details

To deal with infinite DLMs, we can use the Koyck transformation. When we apply Koyck transformation, we get the following:

$$ Y_{t} - \phi Y_{t-1} = \alpha (1-\phi)+\beta X_{t} + (\epsilon_{t}-\phi \epsilon_{t-1}). $$

When we solve this equation for \(Y_{t}\), we obtain Koyck DLM as follows: $$ Y_{t} = \delta_{1} + \delta_{2} Y_{t-1} + \delta_{3} X_{t} + \nu_{t}, $$ where \(\delta_{1} = \alpha (1-\phi),\delta_{2}=\phi,\delta_{3}=\beta\) and the random error after the transformation is \(\nu_{t}=(\epsilon_{t}-\phi \epsilon_{t-1})\) (Judge and Griffiths, 2000).

Then, instrumental variables estimation is employed to fit the model.

References

B.H. Baltagi. Econometrics, Fifth Ed. Springer, 2011.

R.C. Hill, W.E. Griffiths, G.G. Judge. Undergraduate Econometrics. Wiley, 2000.

Examples

# NOT RUN {
data(warming)
model.koyck = koyckDlm(x = warming$NoMotorVehicles , 
y = warming$Warming , show.summary = TRUE)
# }