lagged variables in a model


i am reading an academic article and i am not sure i understood the model correctly.

1. It is written that the dependent variable is lagged. is it mean that the independent var in period T influences (theoretically) on the dependent var in T+1 ?

2. what is the correct meaning of the following equation\which dependency the model tries to find ?

MODEL: C(t) = constant + b1(E(t-1)) delta Y(t) + b2(E(t-1))delta D(t+l) + error

C - dependent var (consumption)
Y - Independent var (Income)
D - Independent var (credit growth)

the next sentence is written under the equations :

"The column labeled "t-" give the t-statistic for that coefficient. Instruments: lag 1 of income growth, credit
growth, and consumption growth; a constant is included as a regressor and an instrument. "


Fortran must die
They probably mean that an IV is influencing the DV at different points in time. So X may have one impact on Y at t and a second impact at t+1. But it is also possible they mean the DV itself is influencing itself at latter points in time. So Yt predicts Yt+1. You can not use linear regression to model the latter (you need something like autoregressive distributed lag ARDL) and unlike normal AR regression if you have lags of Y in your model and get the AR error wrong it will bias your results not just mess up the statistical test.

I am not certain from the symbols what they are doing here, they are different than what I have seen for time series.

thanks for the quick answer.

when DV is not influencing itself at latter points in time, can i you linear reggression for
IV is influencing the DV at different points in time ?

the original equation from the article is attached.

thank you very much for the help


Fortran must die
It is generally not a good idea to use linear regression with time series because of auto-regression. You can do one of the AR tests to check for this ( Durbin Watson is best known, but not the best test, this discusses other options ). AR ruins the test of significance unless corrected (linear regression does not correct for it as far as I know although it is possible you might use a robust SE with linear regression to address this such as White's, not sure if White's works with linear regression).

I believe that if you have lagged variables (predictors or lags of the DV) and you have auto regression than the slopes are biased as well. There are regressions such as ARDL that have been specifically developed for this issue.

thanks for the help.

i would like to check the lagged predictors variables only on a dependent var -

for instance - dep var is Y and independents are X, Z.

i would like to check what is the lag of X,Z that has the most significance on Y.
Do i need to run separately multiple regression of Y = f(Z,Z-1,Z-2...) AND Y = f(X,X-1,X-2,X-3....) than to select one lag of each regression and place them in the
final regression ?

for example Y = f(X-1,Z-2)