Noah Smith on why imports do not subtract from GDP

I am not a macroeconomist. Against my protestations, I have taught macroeconomics in the past, but now I exclusively teach microeconomics. There are certain aspects of macroeconomics that I thought I knew well, like how GDP is calculated. There is a simple method of calculating GDP that we teach in first-year economics, which we call the expenditure method: Y=C+I+G+(X-M). Y is GDP, C is consumption spending, I is investment spending, G is government spending, X is exports, and M is imports. It all seems rather straightforward. However, I genuinely learned something new and important this week about that formula.

Noah Smith has a great post explaining why imports do not subtract from GDP. Check the formula above, and then read that sentence again. Imports do not subtract from GDP. But it's right there in the formula! The thing I learned from Noah's post is that imports are included in C, I, and G. And so, the subtraction of M in the expenditure method formula prevents us from counting imports in measured GDP, by zeroing them out. Imports are not subtracted from GDP. Because they are both added to GDP (through C, I, and G), then subtracted (through -M), the net effect of imports on GDP is zero.

As further explanation, it is worth quoting Smith's post at length (the strikethrough and underline in one of the formulas is my correction of it):

Let’s talk about what GDP is. GDP is the total value of everything produced in a country:

GDP = all the stuff we produce

Imports aren’t produced in the country, so they just don’t count in the formula above. And they aren’t alone. There are plenty of other important things in the Universe that have don’t get counted in GDP, simply because they have nothing to do with domestic economic production. The number of asteroid impacts in the Andromeda galaxy is probably important to someone, but it doesn’t count in U.S. GDP. The population of the beluga sturgeon in Kazakhstan is probably important to someone, but it doesn’t count in U.S. GDP. Imports don’t count in U.S. GDP because, like asteroid impacts in the Andromeda Galaxy and the population of beluga sturgeon in Kazakhstan, they don’t involve domestic economic production in the United States.

In fact we can divide GDP up a different way from the Econ 101 breakdown. Let’s divide it up according to all the categories of people who might ultimately use the stuff... we produce in the U.S.:

GDP = Capital goods we produce for companies + Consumer goods we produce for consumers + Stuff we produce for the government + Stuff we produce for foreigners

Again, imports are nowhere to be seen. But exports are in here! Exports are just all the stuff we produce for foreigners. So the formula is:

GDP = Capital goods we produce for companies + CapitalConsumer goods we produce for consumers + Stuff we produce for the government + Exports

This is a perfectly good formula for GDP. But instead, here’s what economists do. They add imports to the first three categories, and then subtract them again at the end:

GDP =

(Capital goods we produce for companies + Capital goods we import for companies)

+ (Consumer goods we produce for consumers + Consumer goods we import for consumers)

+ (Stuff we produce for the government + Stuff we import for the government)

+ Exports - Capital goods we import for companies - Capital goods we import for consumers - Stuff we import for the government

This type of equation adds in three different types of imports, then subtracts them all again at the end. It’s mathematically equivalent to the formula above it, because if you add imports and then subtract them out again, you’ve just added 0. And adding 0 does nothing. Imports still don’t count in GDP in this equation.

OK, now let’s realize what the terms in the equation mean:

(Capital goods we produce for companies + Capital goods we import for companies) is just Investment.

(Consumer goods we produce for consumers + Consumer goods we import for consumers) is just Consumption.

(Stuff we produce for the government + Stuff we import for the government) is just Government purchases.

Exports - Stuff we import for companies - Stuff we import for consumers - Stuff we import for the government is just Exports - Imports.

So the equation is now:

GDP = Consumption + Investment + Government purchases + Exports - Imports

This is just our good old Econ 101 equation. It looks like imports are being subtracted from GDP, but now you (hopefully realize) that this is because imports are also being added to consumption, investment, and government purchases! Consumption, Investment, and Government purchases include imports, so we subtract out imports at the end so that the total effect of imports on GDP is zero.

Smith leverages that explanation to explain why a focus on reducing imports will not increase measured GDP (at least, not directly). That is an important argument in an era of increasing trade protection, aimed at reducing imports to the benefit of the domestic economy. That trade protection is not likely to work - at least, not through the simple mechanism of reducing something that is subtracted from GDP. Because, as Smith tells us, imports are not subtracted from GDP.

[HT: Marginal Revolution]