# Third Quarter GDP

Updated October 29, 2022.  This has turned into quite the adventure.  This is the first of several articles on what happened to the US economy in the third quarter. I’m going to start with the obvious meaning of the numbers.  Then I’ll take a deep dive into national income accounting issues that really matter in this data. In part 2 I’ll delve into the financial statements of RTX (formerly Raytheon) to see if I can find evidence there.

Third quarter GDP reported the advance estimate Thursday, October 27. But I wanted to post the real GDP workbook. Hot off the BEA computers.

Here are some important numbers.

Some important numbers. These are the contributions of each category to the overall 2.4% growth. Click for larger image.

## Inside the Numbers

The topline number is 2.6%.  That’s the annualized third quarter growth in real GDP.  But that number masks a number of interesting and important components.

### The Parts

I want to focus on contributions to the real GDP growth rate.  There are five major parts:

1. personal consumption spending,
2. business investment spending,
3. government spending (federal, state, and local),
4. exports of goods and services, and
5. imports of goods and services.

A sixth part, the net change in business inventories, is included in business investment.  If you want to make it the sixth big piece, you have my permission.

This is also the time when I give my occasional reminder.  GDP does not measure spending.  It measures production, total output produced during the third calendar quarter.  Real GDP tries to measure actual physical output by using deflators to adjust nominal (current dollar) GDP for inflation.

So if we add up the contributions from each of the four major pieces of GDP, the sum should be 2.6%. Let’s see if that’s true.

(click for larger image)

The calculated sum is 2.57% while the reported growth is 2.6%.  Rounded, the two are equal.

### The Bad

Gross private domestic investment pulled overall growth down by 1.59 percentage points.  That follows a whopping 2.63 point negative contribution in the second quarter.  Standard Keynesian analysis says this is bad for the future of the economy.  Business investment means building factories and office buildings, installing the varied forms of hardware (desks to web servers), and housing.  An important part is the change in business inventories.  Let’s take a closer look.

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There are two dreadful numbers in this table: nonresidential structures and residential structures.  In total, those subtracted 1.78 points from GDP growth.  The change in business inventories contributed an additional -0.70 points after knocking off 1.91 points in the second quarter.  The only bright spots were positive contributions from equipment and intellectual property products.  Those are less durable than structures.

Business inventories can fall for two reasons.  Businesses may be reducing desired inventories because they expect future sales to fall.  Or inventories could fall because demand was greater than output.  This is kind of important.  More on that when we discuss the strangeness of inventories and government spending in the third quarter.

### The Good

Exports rose dramatically, contributing 1.63 percentage points to growth.  Imports fell, contributing an additional 1.14 points. (Remember, imports are subtracted in the calculation.  A decrease in imports means there was a shift in spending toward domestically produced goods and services.) The strong dollar is a likely reason for the decrease in imports.  Exports, according to standard theory, should have fallen since the foreign currency price of U.S. exports rises.  But there are other factors in play here that I’ll discuss in the following section. I’ll also add an example there to show how exchange rate changes affect import and export prices.e

Government spending added 0.42 points to growth.  About 55% came from the Federal government with the other 45% stemming from higher spending in state and local governments. I leave it to you to decide whether this is good or bad.

Finally, consumer spending contributed 0.97 points to growth.  A full 1.24 points came from services spending. Households spent less on durable goods, no doubt partly caused by very high prices for motor vehicles.  Consumer spending on durable goods is similar to business fixed investment.  Both create demand for long-lasting assets.  That tends to be more stimulative than spending on services because there are economies of scale in manufacturing that are far less pronounced in the services sector.

The next section is sort of special topics including

• a possible relationship between higher government spending and exports;
• a simple example of how exchange rate changes affect export and import prices.
• a reminder of the role of inventory change in all this.

## Government Spending, Exports, and Inventories

### The Odd Situation Created by Ukraine

Suppose you work at Raytheon Missiles and Defense (a division of RTX).  You oversee production of Javelin missiles. (The facts about Raytheon and the Javelin missile are real. I chose Raytheon because I’ll delve into their financial statements in part 2 of this series to estimate the impact of our aid to Ukraine.  From this point forward, all facts about Raytheon, RTX, and the Javelin missile are my inventions.)

In August you produced 100 missiles.  Those are stashed in inventory.  GDP increases by 100 missiles.  In September you sold those missiles to Ukraine.  This decreases business inventories by 100 and increases exports by 100.  So far so good.  It should surprise no one that Raytheon Missiles and Defense sales and profits benefit from war.  The net increase in real GDP is 100 missiles because the increase in exports is exactly offset by the decrease in inventories.

The question is, “How did Ukraine pay for those missiles?”  A substantial fraction of the funds came from American taxpayers as represented by the Federal government.  The government sends aid to Ukraine.  That increases government spending.  Ukraine buys the 100 Javelin missiles.  Those count as exports.  The increase in government spending may have spurred the sharp rise in exports. This despite the dollar appreciating during the third quarter. I’ll have more to say about exchange rates and foreign trade later in this section.

### A Digression on Adding Up GDP

Suppose we run a business making buggy whips. (A buggy whip once was used as a motivational device for a horse pulling a carriage.  Today, most of the demand for buggy whips originates on Folsom Street in San Francisco.)  We sell to a small, but devoted group of buyers.  We’re trying to plan production for the holiday shopping season.  Our economic consultant forecasts sales of 17,000 whips in the fourth quarter.  We gear up production to produce 17,000.

January rolls around.  We’ve only sold 15,000 whips.  The 2,000 unsold whips go into inventory.  Our inventory has an unplanned increase.  We will have to reduce production by enough to meet current demand and to sell the excess inventory of 2,000.  That means we will reduce worker hours by more than we would have if our stupid economist had made a correct forecast.  In traditional macroeconomics, if this happens to enough businesses the economy will fall into a recession.  The inventory cycle is one of the earliest models of a business cycle.

A calculation is important because it helps us figure out how spending is converted into production when calculating GDP.

Let production be Qs and sales be Qd. The change in inventories, ∆Inv, is equal to +2,000. Qs = 17,000 and Qd = 15,000. We know that

or

So

Translating this into macroeconomics, Qs is real GDP and Qd is spending. Adding inventory change to spending gives output, real GDP. However, that only applies to a closed economy with no foreign trade.  We must add products produced in the U.S. but sold in other countries.  Those are exports, products that add to domestic production but are not part of domestic spending.  Similarly, we subtract imports because they are part of domestic spending but are not produced in the U.S.  Those are the three factors that convert domestic spending into domestic production.

### Exchange Rates and Foreign Trade

The best way to explain this is with another example.  First, two definitions:

(click for larger image)

Let’s consider the dollar – euro exchange rate between July 1 and September 30, 2022.  That’s exactly the third quarter. Here’s what happened to the exchange rate:

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First, let’s see how to interpret these numbers. Consider the \$/€ exchange rate.  On July 1, one euro would buy 1.04495 dollars.  On September 30, one euro would buy 0.97313 dollars.  On September 30, one euro would buy fewer dollars than it would have on July 1.  The euro has depreciated vis-a-vis the dollar. (See the definitions above to make sure you understand this.)

Another iron rule of exchange rates is that the €/\$ is the reciprocal of the \$/€ exchange rate.  On September 30, the €/\$ rate should equal 1/0.97313. In fact, that value is 1.02612.  Not quite the same.  The reason is transactions costs, the fees charged by foreign exchange traders so they can stay in business.  In the parlance of financial markets, this is called the bid-ask spread.  Luckily, we don’t have to worry about that because we have the actual market-determined rates.

Having said that, we turn to the law of one price. As applied to foreign exchange markets, this law says,

The foreign price of a domestically produced produce should roughly equal the domestic price times the relevant exchange rate.

Consider the market for wine.  A bottle of California wine has a price of \$20.00.  A bottle of French Beaujolais has a price of €20.00.  On July 1, 2022 the price of the bottle of California wine in France will be about \$20.00 x (0.95683€/\$) = €19.14.  On September 30, the domestic price of wine has not changed because dollars are money in the U.S.  But the French price will be \$20.00 x (1.0274€/\$) = €20.55.  The euro has depreciated vis-a-vis the dollar.  That means the French price of U.S. products will rise.  lf nothing else changed, U.S. exports to the euro zone should have decreased because the euro price of euro zone imports from the U.S. increased.  This is nothing more than the first law of demand.

The table below shows the results for both the California and French wines.  A good exercise is to figure out what will happen to U.S. imports from the euro zone after the exchange rate changes.

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But U.S. exports increased.  That means some other factor affecting demand (besides price) must have changed.  One possible source is more purchasing power in Europe caused by U.S. aid to the various countries.

I know, Ukraine is not part of the euro zone. Ukraine’s currency is the hryvnia (₴).  Like nearly every country in the world, Ukraine has a wine industry.  I’m not going to look up the varietals. Let’s just call it HRed.  The price of a bottle of HRed is 20.00₴ (big surprise). The hryvnia depreciated vis-a-vis the dollar in the third quarter.  The results only differ from the euro table by the currency symbol and the degree of the depreciation.

(click for larger image)

### Conclusion

There’s a good chance that a lot of the increase in third quarter GDP was caused by U.S. government spending, specifically foreign aid.  Remember, other European countries are also buying U.S. weapons and receiving financial aid.  I leave it to better econometricians than me to sort all this out.

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## About Tony Lima

Retired after teaching economics at California State Univ., East Bay (Hayward, CA). Ph.D., economics, Stanford. Also taught MBA finance at the California University of Management and Technology. Occasionally take on a consulting project if it's interesting. Other interests include wine and technology.