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While looking at the GDP deflator this situation popped up that made me question the quote above from Mankiw Economics 5edition p446.

But if we do the maths, we can see that the GDP deflator for this simplified economy is 66.7. However if we look at JUST the price movements wouldn't we expect the inflation to be 75 (the price of burgers has risen by 100% and buns 50% giving an average of 75%)?

This means it is a weighted average, which means quantities do feed into the deflator. Changing the quantities produced will change the deflator.

Therefore I wonder how we can really say the deflator measures "inflation" and that the deflator reflects what's happening to prices NOT quantities.

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I think this is a matter of how you are interpreting the statement. I'm assuming that we are defining the annual GDP deflator between period $t-1$ and period $t$ as:

$$\frac{\text{nominal GDP}}{\text{real GDP}} = \frac{\sum (P_t\times Q_t)}{\sum (P_{t-1}\times Q_t)} $$

Then we can clearly see that it does depend, in some sense on the quantities of products produced. In particular, it depends on the distribution of products produced across the economy in period $t$.

What it doesn't depend on is the change in quantities produced. We can see that $Q_{t-1}$ doesn't feature in the calculation.

I think this is what the quote refers to. If we interpret the 'what's happening to' in the quote to mean annual change to, then it would read as:

$$\text{the GDP deflator reflects the annual change in prices not the annual change in quantities}$$

This is clearly true. You can change the quantities in period $t-1$ and it won't change the deflator.

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  • $\begingroup$ I think that's a lovely way of looking at it. I think can live with that! I just read the statement and then created the following example and assumed that if Q plays no role then the inflation rate had to be 75%. As Chris Jude says above it depends on the weighting and non weighted aspect. $\endgroup$
    – Studi
    Nov 18, 2022 at 13:52
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Essentially, $$ GDP deflator = \frac {\Sigma P_{t+1}* Q_{t+1}}{\Sigma P_t*Q_{t+1}}*100 $$ ie; nominal GDP divided by real GDP which includes the weighted change in price as you rightly mentioned.

However, the cpi index is based on a fixed basket of goods implying $$ \frac {\Sigma P_{t+1}* Q_b}{\Sigma {P_t*Q_b}}*100 $$ Where b belongs to a set of fixed goods.If the weightage in the basket of goods changes inflation would also change.

In Deflator the set of basket(which is the whole set of goods and services) are dynamically changing over time with the changes in consumer demand reflecting the current trend in the economy.

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  • $\begingroup$ Thanks. So would you agree that the deflator does take into account what is happening to the quantities then? Making Mankiw's statement essentially incorrect. $\endgroup$
    – Studi
    Nov 17, 2022 at 10:06
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    $\begingroup$ I think the confusion is regarding simple averages and weighted averages. A simple average would not be a sufficient summary statistic as it may not reflect the whole information on the change in the overall price level. $\endgroup$
    – chris jude
    Nov 18, 2022 at 12:58
  • $\begingroup$ I think the issue here come from the difference between thinking about the distribution of goods produced within period and the amount of goods produced between periods. The quote in the original question is simply saying that the GDP deflator doesn’t depend on the change in quantity of goods produced between periods. We can see that as only quantities of goods produced in this period are in the sum. $\endgroup$
    – hmmmm
    Nov 18, 2022 at 13:12
  • $\begingroup$ Fully agree about the simple and weighted. $\endgroup$
    – Studi
    Nov 18, 2022 at 13:50

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