first difference regression

[Hachemi SOLTANI]

hello stata community,

Is it possible to run first difference regression if I have time series data?

reg d.y d.x1 d.x2

[Andrew Musau]

Yeah, but what do you intend to achieve in doing that? In the context of panel data, differencing eliminates the time-invariant individual effect. In a time-series, you only observe a single unit. So you are more concerned about spurious correlation between the outcome and one or more regressors leading to a spurious regression. The way to detect this is to check if the variables are stationary - then if not, difference them to make them stationary just in case they are not cointegrated. So look at the literature on stationary time-series and cointegration.

[Hachemi SOLTANI]

Yeah, but what do you intend to achieve in doing that? In the context of panel data, differencing eliminates the time-invariant individual effect. In a time-series, you only observe a single unit. So you are more concerned about spurious correlation between the outcome and one or more regressors leading to a spurious regression. The way to detect this is to check if the variables are stationary - then if not, difference them to make them stationary just in case they are not cointegrated. So look at the literature on stationary time-series and cointegration.

Thanks for this valuable addition @4687-andrew-musau

Regarding my case, I have some variables are not stationary at level.

I have a query regarding the equation, should the equation be written without the constant variable?

This way: dy= dx1+ dx2 +u

[Andrew Musau]

There is an intercept. All you are doing is first stationarizing the variables by differencing and then running OLS.

\(Y(t) - Y(t-1) = a + b_{1}(X1(t) - X1(t-1)) + b_{2}(X2(t) - X2(t-1))\)

which could also be parametrized as

\(Y(t) = Y(t-1) + a + b_{1}X1(t) - b_{1}X1(t-1)+ b_{2}X2(t) - b_2X2(t-1)\)

to include the lagged outcome on the right-hand side.

[Hachemi SOLTANI]

There is an intercept. All you are doing is first stationarizing the variables by differencing and then running OLS.

\(Y(t) - Y(t-1) = a + b_{1}(X1(t) - X1(t-1)) + b_{2}(X2(t) - X2(t-1))\)

which could also be parametrized as

\(Y(t) = Y(t-1) + a + b_{1}X1(t) - b_{1}X1(t-1)+ b_{2}X2(t) - b_2X2(t-1)\)

to include the lagged outcome on the right-hand side.

Thanks for this explanation Mr. Andrew Musau