# The GDP deflator

This post is a guide to understanding the GDP deflator, which the government uses to arrive at the economic growth numbers we all hear on TV or read about in the newspaper. This post is the product of a lot of background research and some good confirmatory side conversations on the topic with Jake at EconomPic Data.

In essence, the GDP deflator is an inflation statistic. And it has wide-ranging consequences in terms of how ‘real’ the real GDP numbers actually are. However, because it is not a ‘true’ measure of inflation, the GDP deflator can create an inaccurate picture of the economy. Recently, we saw just such an inaccuracy because of the last two quarters’ oil prices.

When we were paying all that money for imported oil in Q2, you would think this would have left less over for consumption and decreased GDP. Nope! That’s not how the statistics work. And, in the past quarter with prices falling dramatically, we had more to spend — that increased GDP. Wrong again.

Actually, the increasing oil prices in the Spring perversely increased real GDP in Q2. And, then yesterday in the Q3 GDP numbers, we saw that falling oil prices in the Summer decreased GDP.

How is this possible?

Well, now, before I rush in here with an explanation, let me warn you up front that this post will be heavy math-oriented — so get ready.

Back to the question: how can spending more on imports possibly increase GDP?

This is so because GDP is not always a true and accurate reflection of domestic economic growth. Gross Domestic Purchases might actually be a better indicator of true domestic economic growth. This is a problem because of how exports and imports are calculated.

Price and Quantity
You see, the price deflators in the GDP numbers are used primarily to disaggregate quantity and price, not to measure true inflation. Thus the deflators can distort the final numbers. This disaggregation allows government’s statisticians to report nominal GDP as a pure ‘quantity’ statistic and real GDP as the final number by simply deflating it according to the price deflator, which is a pure ‘price’ statistic.

The whole exercise actually goes straight back to Econ 101. Remember when they taught you that quantity times price equals revenue? Well, that is basically what the GDP is all about on a grand scale — revenue. And the statisticians are trying to measure quantity times price to arrive at that revenue number. Hence the need to find a pure quantity measure and a pure price measure.

The UK and the U.S. use the same general methodology here and Her Majesty’s Treasury does a pretty good job at explaining this:

What is the GDP deflator?
The GDP deflator can be viewed as a measure of general inflation in the domestic economy. Inflation can be described as a measure of price changes over time. The deflator is usually expressed in terms of an index, i.e. a time series of index numbers. Percentage changes on the previous year are also shown. The GDP deflator reflects movements of hundreds of separate deflators for the individual expenditure components of GDP. These components include expenditure on such items as bread, investment in computers, imports of aircraft, and exports of consultancy services.

Uses of the GDP deflator series
The series allows for the effects of changes in price (inflation) to be removed from a time series, i.e. it allows the change in the volume of goods and services to be measured. The resultant series can be used to express a given time series or data set in real terms, i.e. by removing price changes.

What is going on here is that the statisticians are trying to use the nominal numbers to measure changes in the quantity of things sold in the economy and they use the deflators to measure changes in the price of things sold. For example, if one looked at Q2 nominal durable goods purchases and compared it to Q3 nominal goods purchases, the proportion represents growth in the amount sold, not in the price of the goods sold.

The durable goods price deflator takes care of the price changes in durable goods. So, if washing machines became less expensive in Q3 than in Q2 say, this price decline would be reflected only in the price deflator and not in nominal GDP.

Example:
Here are the real numbers:

\$1.059 trillion of durable goods in Q2 versus \$1.0183 trillion in Q3 represents an absolute decline in the amount sold of 14.6% on an annualized basis. However the price deflator for Q3 was -0.6% (meaning prices declined at an annualized 0.6% rate). Put these two together and it leads to a real decline of 14.1% in durable goods on an annualized basis. This last real number — the 14.1% — is the one most people hear and care about.

Imports and Exports
Where things get tricky are imports and exports. If you remember from Econ 201, Gross Domestic Product is measured as Consumption plus Investment plus Government Spending plus Exports minus Imports. Remember the minus because that is the crux of the problem.

The equation is:

GDP = C + I + G + (EX – IM)

The problem here is that the imports have a negative number on them. All the other numbers are just fine but the negative number on imports has perverse effects. Let me give you a live example. In Q1 of 2008, the United States imported a nominal \$2.1180 trillion of goods. In Q2, we imported more, a nominal \$2.2255 trillion amount. That means imports were rising — we were buying a higher quantity of imported goods in Q2 than in Q1. But if you recall, import prices were rising like crazy in Q2 — oil went to \$147 a barrel. As a result, the Price Deflator for imported goods was 31.2% in Q2.

To get the GDP deflator, one must multiply each of the price deflators times the ratio of the deflator to the whole. For example, in the case of the goods imports we have 31.2%. But, since you have to subtract imports, you are actually decreasing the deflator massively (remember C + I + G + EX – IM). This leads to the perverse effect of high import inflation decreasing the deflator and thus INcreasing GDP.

However, in Q3, when import prices came off the boil, the effect was the opposite — to decrease the GDP inflator by MUCH less than in Q2. So lower import prices meant a higher deflator and thus a lower GDP.

Gross Domestic Purchases
If you think the preceding examples sound crazy, you will have no quarrel here. I think the whole thing is nuts (see my other posts below). This is one reason a lot of economists have been looking askance at the GDP deflator and the GDP numbers themselves recently.

Instead, a lot of economists have turned to Gross Domestic Purchases, which is the C + I + G without the imports and exports. Gross Domestic Purchases equal Consumption plus Investment plus Government Spending — and that’s it.

The chart for Gross Domestic Purchases looks a lot more like the world we are living in — with the numbers at zero or below every quarter since 2007 Q4.

As for GDP, there are lies, damn lies and statistics.

Sources
User’s guide: Overview of GDP deflator series – HM Treasury