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Any suggestions on how to combine time series of labor market variables (such as, for example, labor force participation) when there is a methodological change in the way the variable is calculated by the statistical office? Say the time series is computed using an "old" methodology during 2000-2010 and using a "new" methodology during 2010-present. This change in methodologies create a break in the time series, when combining the data over the whole sample (the series "shifts up")

I would like to use the full sample time series (i.e., from 2000 to present) in the context of estimating a VAR. Should I simply combine the two series and then add a structural break in 2001 when estimating the VAR?

Alternatively, are there standard way to combine the two series, in such a way as to attenuate the break that arises from the change in methodology? For example, could I regress the combined full sample time series on a constant which allow for a dummy variable equal to 1 from 2001 onward, such as

$y_t = a_1 + a_2\times D_t + \epsilon_t$

and then just use the residuals of the regression as my new series that I can then input in my VAR model?

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