# A Guide to Specifying Observation Equations: A Question

Dear Mr. Pfeifer,

Now I have come to the following general question:
I am using data form germany, which are adjusted for price changes. (Fachserie 18 Reihe 1.3 des Statistischen Bundesamtes)
Now, I see that obviously the sum of price adjusted consumption, investments, governmental consumption, exports minus imports is not the price adjusted GDP, as they are all chained indexes.
Thus, I’m sure that I cannot use them in my estimation as in my model it has to hold that Y = C + I + G + EX - IM.

What should I do? Or isn’t that a problem?
Should I rather use growth rates for all observable variables like log(Y) - log(Y(-1))?

Daniel
DatenGER2013.rar (708 KB)

You are correct in that you cannot do this with chained indices. Note that most models are one-good models, i.e. there is no difference between e.g. consumption or capital goods. The model implies there is only one deflator. That is the reason why e.g. Smets/Wouters (2007) use nominal series and make them real by deflating with the GDP deflator instead of using real NIPA values.

so if I understand you right, in my case it is better to use growth rates?

No. Why do you think using growth rates would help?

I thought that then the problem would vanish, since the sum of the growth rates of consumption, investment, governmental consumption and exports minus imports does not have to equal anymore with the growth rate of the gdp???
Obviously I’m wrong???

So I will try again by using the data measured in Euro than dividing them by the gdp deflator, taking logs and detrending them with the one-sided HP-filter. I hope this will help. (This should be the right way???)

Just one other question:
I have exports in my model defined as: EX = ePxQx, where e is the exchange rate, Px is the export price and Qx is the exported amount.
Now I have data for the exports EX and data for the export price Px. Then it is not allow to use both in the estimation since they are perfectly linear dependent (only if I use measurement errors). Am I right?

I have updated the guide. The issue is that with chain-weighting you would miss the changing relative price of the GDP components. When using growth rates, your model would still neglegt the growth rate of the relative price and would still be wrong. Also note that your resource constraint will imply weighted additivity of the growth rates, which still does not hold.

Regarding stochastic singularity: it depends on whether e and/or Qx then have degenenerate probability distributions (because they are directly or indirectly fully observed). You allude to perfect linear dependence. Consider a resource constraint

Here you only have a problem, if you observe all three (not a subset of two out of three).

Thank you. You are allways a big help. I also have posted a answer to the new topic (A small question to Bay. Est). In fact in summarizes all the stuff I have learnt from you and the paper you have recommended. Perhaps you can have a quick look at this answer, if everything is right.

Thanks again, with your help I finally have managed to estimate a model with ML after nearly two years work. The estimation result is still not perfect but I have never come so far without your dedicated help!