Static models are of the form:
\(y_{t}=\alpha+\beta x_{t}+\epsilon_{t}\)
These have no lagged variables or difference operators.
What we use should depend on I(1), I(0) etc from ADF
if we’re missing time invariant data, we can do first differences and this isn’t a problem if we do diff in diff this removes trends?
page on first difference estiamtion? OLS on first differences. No other lags page on first difference ESTIMATOR
Create a dummy for before/after a date.
Consider the grouped linear model:
\(y_{ij}=\mu+\tau_i+X_{j}\theta +\epsilon_{ij}\)
By taking differences with another observation in the same group we remove the average terms.
\(y_{ij}-y_{ik}=(\mu+\tau_i+X_{j}\theta +\epsilon_{ij})- (\mu + \tau_i + X_{k}\theta + \epsilon_{ik})\)
\(y_{ij}-y_{ik}=(X_{j}\theta - X_{k})+(\epsilon_{ij}- \epsilon_{ik})\)
diff in diff: control group and treated group. page on leakiness? are control affected too? Assumption: in absense of treatment, price would have evolved like control
Testing for structural breaks with the Chow test.
Static panel data: No lags of independent variables. Dynamic panel data: Lags of independent variables.
OLS is consistent for static panel data, not for dynamic This results in Nickell’s bias for dynamic panel data
Dynamic panel data: \(y_{t-1}\) is a regressor Panel data estimation: LSDV. Least squares dummy variable estimator arnello bond