Quarterly Output-Gap Interpolation

[obviou191]

Hi,

I am in the process of running a Phillips curve model for a particular country. The problem is that all my data, from 1986-2010, is quarterly - barring the figures for the output gap which are annual. I was just wondering what the best way (if any!) would be to interpolate this data from annual to quarterly without affecting the results.

Any feedback would be great!
Thanks

[startz]

Since business cycle swings, at least on the downside, are typically on the order of a few quarters, the basic answer is DON'T.

You might see if higher frequency unemployment rate data is available.

[trubador]

Since this is not a simple interpolation, do not forget to constrain the sum of quarters to be equal to the observed annual data. You can use frequency conversion options of EViews for that purpose. There are also other interpolation techniques that require some degree of programming or modeling.

I agree with Startz. Therefore, if you desperately need the quarterly figures, try interpolating the potential output data instead. Potential level of the economy is assumed to have a smoother behavior than the output gap. So, I suggest you to do the following:

1) Compute the annual potential output data (i.e. y - y_gap)
2) Copy and paste special the annual potential output data to your quarterly page
3) When asked, choose one of the frequency conversion options from the drop-down list of "Low to high frequency methods" (e.g. Quadratic-match sum)
4) Since you have a quarterly potential output series now, you can easily compute quarterly output gap data (i.e. y - y_pot)

The quality of your results may depend on the interpolation method you choose. So, you should try several other methods and carry out a simple sensitivity analysis.

[startz]

Let me follow up on Trubador's good advice. If you have quarterly GDP and annual potential GDP, you might reasonably interpolate the latter and then create a quarterly gap series. But if you only have GDP annually, then you probably shouldn't try fora quarterly gap measure.