Contribution to GDP Growth of the Change in Inventories: Econ 101 Again

A.  Introduction

The contribution of changes in inventories to changes in reported GDP is easily misunderstood.  One saw this in reports on the recent release (on July 28) by the Bureau of Economic Analysis (BEA) of its first estimate of GDP for the second quarter of 2022.  It estimated that GDP fell – at an annualized rate of -0.9% in the quarter – and that along with the first quarter decline in GDP (at an estimated rate of -1.6%), the US has now seen two straight quarters of falling GDP.  While there will be revisions in the coming months of the second quarter figures, as additional data become available, a fall in GDP for two straight quarters has often been used as a rule of thumb for an economy being in recession.

News reports on the figures noted also that were it not for the estimated change in inventories, GDP would have gone up rather than down.  The estimate was that GDP fell by -0.9% (at an annual rate) in the second quarter, and that the change in private inventories alone accounted for a 2.0% point reduction in GDP.  That is, if the inventory contribution had been neutral, GDP would have grown by about 1% rather than fallen by almost 1%.

But it would be wrong to attribute this to “decreases in inventories”, as some reports did.  Inventories grew strongly in the fourth quarter of 2021, with this continuing at a similarly strong pace in the first quarter of 2022 and still (although at a slower pace) in the second quarter of 2022.  How, then, could this have contributed to a reduction in GDP in 2022?

It is easy to become confused on this.  While really just a consequence of some basic arithmetic, it does require a good understanding of what GDP is and how changes in inventories are reflected in GDP.  I discussed this in a January 2012 post on this blog, but that was more than a decade ago and a revisit to the issue may be warranted.  This post will examine the problem from a different perspective from that used before.  It will start with a review of what GDP measures, and then use some simple numerical examples to show how changes in inventories affect GDP.  It will then use a series of charts, based on actual numbers from the GDP accounts in recent years, to show how changes in inventories have mattered.

A note of the data:  All the figures used come from the BEA National Income and Product Accounts (NIPA), as updated through the July 28 release.  These are often also called by many (including myself) the GDP accounts, but NIPA is the more proper term.  Also, the figures for inventories in the NIPA accounts are for private inventories only.  Inventories held by government entities are small and are not broken out separately in the accounts.  Instead, changes in such inventories are aggregated into the figures for government consumption.  While I will often refer to “inventories” in this post, the measures of those inventories are technically for private inventories only.

B.  Inventories and GDP, with Some Simple Numerical Illustrations

GDP – Gross Domestic Product – is a measure of production (product).  Yet as anyone who has ever taken an Econ 101 class knows, GDP is typically described as (and measured by) how those goods and services are used:  for Consumption plus Investment plus Government Spending plus Net Foreign Trade (Exports less Imports).  In symbols:

GDP = C + I + G + (X-M)

Where “C” is private consumption; “I” is private investment; “G” is government spending on goods or services for direct consumption or investment; and “X-M” is exports minus imports, or net foreign trade.

(Imports, M, can be thought of either as an addition to the supply of available goods or netted out from exports, X, to yield net exports.  To keep the language simple, I will treat it as being netted out from exports.)

Private investment includes investment both in new fixed assets (such as buildings or machinery and equipment) and in accumulation of inventory.  This accumulation of inventory, or net change in inventory, is key to why this equation adds up.  As noted above, GDP is product – how much is produced.  Whatever is produced can then be sold for consumption, fixed asset investment, government spending on consumption or investment, or net exports.  If whatever is produced exceeds what is sold in the period for these various purposes, then the difference will accrue as inventories.  If the amount produced falls short of what is sold, there will have to have been a drawdown of inventories for the demands to have been met.  Otherwise it would not have been possible – the goods had to come from somewhere.

The balancing item is therefore the change in inventories.  It is what allows us to go from an estimate of what is sold to an estimate (if one knows how much inventories changed by) of what was produced, i.e. to Gross Domestic Product.

How then do changes in inventories affect measured GDP?  This is best seen through a series of simple numerical examples, tracing changes in the stock of inventories over time.

Period

Stock

Change

Change in the Change

0

2000

1

2200

200

2

2400

200

0

Start with a stock of inventories in the economy as a whole in period 0 of say 2000 (in whatever units – perhaps billions of dollars).  This stock then grows to 2200 in period 1 and 2400 in period 2.  The change in inventories in period 1 will then be 200, and that change in inventories will be one of the components making up GDP (along with private consumption, private fixed investment, and so on).  It is an investment – an investment in inventories – and thus one of the uses of whatever product was produced in the period.  It will equal the total of what was produced (GDP) less what was sold for the sum of all final demands (private consumption, private fixed Investment, government, and net foreign trade).

With the stock of inventories growing to 2400 in period 2, the change in inventories in that period will once again be 200.  Hence the contribution to GDP will once again be 200.  This is the same as what its contribution to GDP was in the previous period, and hence the higher inventories would not have been a contributor to some higher level of GDP – its contribution to GDP is the same as before.  The change in the change in the stock of inventories is zero.

But this does not mean that inventories fell in period 2.  They grew by 200.  But that was simply the same as its accumulation in the prior period, so it did not add to GDP growth.

To make a contribution to GDP growth in period 2, the addition to inventories would have had to have grown.  For example:

Period

Stock

Change

Change in the Change

0

2000

1

2200

200

2

2500

300

100

In this example, the stock of inventories grew to 2500 in period 2.  The change in inventories was then 300, which is higher than the change in inventories of 200 in period 2 – it is 100 more.  This would be reflected in a GDP in period 2 which would be 100 higher than it would have been otherwise.

If, on the other hand, the pace of inventory accumulation slows, then inventory accumulation will subtract from GDP:

Period

Stock

Change

Change in the Change

0

2000

1

2200

200

2

2300

100

-100

In this example, inventories are still growing in period 2 – to a level of 2300.  This is 100 higher than what it was in period 2.  But the change in inventories is then only 100 – which is less than the change of 200 in period 1.  Inventories are still growing but they will add less to GDP than they had in period 2.  Hence they will subtract from whatever growth in GDP there might have been otherwise.

This is what happened in the recently released estimates for GDP growth in the second quarter of 2022.  Inventories were still growing, but they were growing at a slower pace than in the prior quarter.  In terms of annual rates (and with seasonally adjusted figures), inventories grew by $81.6 billion in the second quarter (in terms of constant 2012 dollar prices; see line 40 of Table 3 of the BEA release).  But this was less than the $188.5 billion growth in inventories in the first quarter of 2022.  In percentage point terms, that difference (a reduction of $106.8 billion) subtracted 2.0% from what GDP growth would have otherwise been in the second quarter (see line 40 of Table 2 of the BEA release).  With the changes in the other components of GDP, the end result was that estimated GDP fell by 0.9% in the quarter.  Thus one can attribute the fall in GDP in the quarter to what happened to inventories, but not because inventories fell.  It was because they did not grow as fast as they had in the previous quarter.

C.  Changes in Inventories in the Data

Based on this, it is of interest to see how inventories have in fact changed quarter to quarter in recent years.  These changes, and especially the changes in the changes, are volatile.  They can make a big difference in the quarter-to-quarter changes in GDP.  Over time, however, they will even out, as there is some desired level of inventories in relation to their sales and producers will target their purchases to levels to try to reach that desired level.

Start with the chart at the top of this post.  It shows the stock of private inventories by quarter going back to 1998.  The figures are in constant 2012 dollars so that inflation is not a factor (and more precisely using what are called “chained” dollars where the weights used to compute the overall indices are based on prior period shares of each of the goods – so the weights shift over time as these shares shift).

Stocks generally move up over time as the economy grows, although there have been reductions in periods when the economy was in recession or otherwise disrupted.  Thus one sees a fall in 2001, due to the recession in the first year of the Bush II administration, an especially sharp fall in 2008 with the onset of the economic and financial collapse in the last year of the Bush II administration with this then carrying over into 2009, and then a fall again in 2020 due to the Covid lockdowns.  The trough in the most recent downturn was reached in the third quarter of 2021, following which the stock of inventories grew rapidly.  They are still, however, slightly below the level reached in mid-2019 even though GDP is higher now than what it was then.

One starts with the stocks, but as was discussed above, the contribution to GDP comes from the accumulation of inventories – the change in the stocks.  These changes, based on the figures underlying the chart at the top of this post, have been:

There is considerable quarter-to-quarter volatility.  Note that the figures here are expressed in terms of annual rates.  That is, they are each four times what the actual change was (in dollar terms) in the given quarter.  One sees that the change in the fourth quarter of 2021 was quite high – higher than in any other quarter of this 24-year period – and was still almost as high in the first quarter of 2022.  The increase was then less in the second quarter of 2022, but was still a substantial increase (of $81.6 billion at an annual rate) in the quarter.

The changes in inventories are a component of GDP, but the contribution to the growth in GDP comes from the changes in the change in inventories.  These are easily computed as well by simple subtraction, and were:

These are now very highly volatile, and one sees especially sharp fluctuations in the last couple of years.  With all the disruptions of the lockdowns, the subsequent supply chain disruptions, and the very strong recovery of the economy in 2021 (with GDP growing faster than in any year in almost four decades, and private consumption growing faster than in any year since 1946!), it has been difficult to manage production to meet expected demands and allow for some desired target level of inventories.

This had a substantial impact on the quarter-to-quarter changes in GDP, both positive and negative.  Focussing on the recent quarters, the changes in inventories were a $193.2 billion increase in the fourth quarter of 2021, and as noted before, a further $188.5 billion increase in the first quarter of 2022 and a further although smaller increase of $81.6 billion in the second quarter of 2022.  These were the changes in inventories.  But the changes in the changes, which is what will add to or subtract from GDP growth, were a very high $260.0 billion in the fourth quarter of 2021, and then a fall of $4.7 billion in the first quarter of 2022.  This reduction in the first quarter of 2022 came despite inventories increasing in that quarter by close to a record high level.  But they followed a quarter where inventories rose by a bit more, so the change in the change was small and indeed a bit negative.

In the second quarter of 2022 inventories again rose – by $81.6 billion.  But following the close to record high growth in the first quarter of 2022, its contribution to the growth in GDP in the quarter was substantially negative.  The $81.6 billion increase in inventories in the second quarter was $106.9 billion less than the increase of $188.5 billion in the first quarter.  And it is this $106.9 billion which is a contribution to (or in this case a subtraction from) what GDP growth would have been in the quarter.

Finally, one can show this also in the possibly more helpful units of the percentage point contribution to the growth in GDP:

Although in different units, the chart here mirrors closely the preceding one, as one would expect if one has been doing the calculations correctly.  The only difference, in principle, is that with GDP growth over time, the dollar values of the quarter-to-quarter changes will look larger when expressed as a share of GDP in the earlier years of the period.

There are, however, some minor differences deriving from the nature of the data used.  The chart here was drawn directly from the figures presented in the BEA NIPA accounts for the percentage point contributions to GDP growth from changes in inventories.  One can also calculate it by taking the quarterly changes in the change in constant dollar terms (from the preceding chart, in red), dividing it by the previous quarter’s GDP (as one is looking at growth over the preceding quarter), and then annualizing it by taking one plus the ratio to the fourth power.  I did that, and the curve lies very close to on top of the curve shown here (in orange).

But not quite, due in part to rounding errors that compound when one is taking the changes and then the changes in the changes.  In addition, inventories by their nature are highly heterogeneous, with some going up and some down in any given period even though there is some bottom line total on whether the aggregate rose or fell.  This makes working with price indices tricky.  The BEA figures are based on far more disaggregated calculations than the ones they present in the NIPA accounts, and their underlying data also have more significant digits than what they show in the tables they report.

D.  Inventories to Sales, and Near Term Prospects

What will happen to inventories now?  Given how important changes in inventories are to the quarter-to-quarter figures on GDP growth, economists have long tried to develop some system to predict how they will change (as have Wall Street analysts, where success in this could make some of them very rich).  But they have all failed (at least to my knowledge).

One statistic that many focus on, quite logically, is the ratio of inventory to sales:

The figures here were computed from data reported in the BEA NIPA Accounts, Table 5.8.6B, where inventories include all private inventories while sales are of goods (including newly built structures) sold by domestic businesses.  Inventories are by nature of goods only, and hence one should leave out services (as an increasing share of services in GDP would, on its own, lead to a fall in the ratio).  Sales of newly built structures are included as one has inventories of building materials.  The figures on the sale of goods by domestic businesses are provided by the BEA.  Note that “sales” here are expressed on a monthly basis.  Hence the ratio is of inventories in terms of months of sales.

As one sees in the chart, the ratio of inventory to sales has been coming down over time.  This is consistent with all the literature advising on tighter inventory management.  There was then an unusually sharp decline in 2020 – a consequence of the Covid lockdowns – that bottomed out in the second quarter of 2021 (as a share of sales) and has since grown strongly.  But the ratio is still below where it was prior to the pre-Covid trend, although how much below depends on how one would draw the trend line pre-Covid.

Where will it go from here?  While important to what will happen to the quarter-to-quarter figures for GDP growth, as discussed above, I doubt that anyone has a good forecast of what that will be.  While there might well be room for the inventory to sales ratio to rise from where it is now, keep in mind that the ratio can rise not only by adding to inventories but also by sales going down.  And while GDP growth was exceptionally strong in 2021, it has been weak so far this year (indeed negative) and that weakness might well worsen.  Personally, while I do not see that the economy is in recession now (employment growth has been strong, with 2.7 million net new jobs in the first half of 2022, and the unemployment rate has been just 3.6% for several months now), the likelihood of a recession in 2023 is, I would say, quite high.

There also have been recent announcements by major retailers that the inventories they are currently holding are well in excess of what they want, and that they will take exceptional measures to try to bring them down.  Target announced a plan to do so in June (with a warning it will squeeze their near-term profits), Walmart announced in July they had similar issues (and that it would slash prices to move that inventory), and other retailers have announced similar problems.  If this is indeed a general issue, then those efforts to bring down inventories in themselves will act as a strong drag on the economy, making a recession even more likely.  And as was discussed above, the stock of inventories does not need to fall in absolute terms to cut GDP growth – a change that is less than what the change had been in the prior period will subtract from GDP growth, even though the inventories may still be growing in absolute terms.

Firms such as Target and Walmart employ many highly trained professionals to manage their inventories.  Yet even they find it difficult to get their inventories to come out where they want them to be.  If they and others now begin a concerted effort to bring down their inventory levels in the coming months, the impact on GDP in the rest of this year could be severe.

Why Do the Quarterly GDP Figures Bounce Around So Much?: Econ 101

A.  Introduction

The Bureau of Economic Analysis (BEA) released on July 27 its initial estimate of GDP growth in the second quarter of 2018 (what it technically calls its “advance estimate”).  It was a good report:  Its initial estimate is that GDP grew at an annualized rate of 4.1% in real terms in the quarter.  Such growth, if sustained, would be excellent.

But as many analysts noted, there are good reasons to believe that such a growth rate will not be sustained.  There were special, one-time, factors, such as that the second quarter growth (at a 4.1% annual rate) had followed a relatively modest rate of growth in the first quarter of 2.2%.  Taking the two together, the growth was a good, but not outstanding, rate of 3.1%.

More fundamentally, with the economy now at full employment, few (other than Trump) expect growth at a sustained rate of 4% or more.  Federal Reserve Board members, for example, on average expect GDP growth of 2.8% in 2018 as a whole, with this coming down to a rate of 1.8% in the longer run.  And the Congression Budget Office (in forecasts published in April) is forecasting GDP growth of 3.0% in 2018, coming down to an average rate of 1.8% over 2018 to 2028.  The fundamental issue is that the population is aging, so the growth rate of the labor force is slowing.  As discussed in an earlier post on this blog, unless the productivity of those workers started to grow at an unprecedented rate (faster than has ever been achieved in the post-World War II period), we cannot expect GDP to grow for a sustained period going forward at a rate of 3%, much less 4%.

But there will be quarter to quarter fluctuations.  As seen in the chart at the top of this post covering the period just since 2006, there have been a number of quarters in recent years where GDP grew at an annualized rate of 4% or more.  Indeed, growth reached 5.1% in the second quarter of 2012, with this followed by an also high 4.9% rate in the next quarter.  But it then came back down.  And there were also two quarters (setting aside the period of the 2008/09 recession) which had growth of a negative 1.0%.  On average, GDP growth was around 2% (at an annual rate) during Obama’s two terms in office (2.2% annually from the end of the recession in mid-2009).

Seen in this context, the 4.1% rate in the initial estimate for the second quarter of 2018 was not special.  There have been a number of such cases (and with even substantially higher growth rates for a quarter or even two) in the recent past, even though average growth was just half that.  The quarterly rates bounce around.  But it is of interest to examine why they bounce around so much, and that is the purpose of this blog post.

B.  Reasons for this Volatility

There are a number of reasons why one should not be surprised that these quarter to quarter growth rates in GDP vary as they do.  I will present several here.  And note that these reasons are not mutually exclusive.  Several of them could be acting together and be significant factors in any given quarter.

a)  There may have been actual changes in growth:

To start, and to be complete, one should not exclude the possibility that the growth in the quarter (or the lack of it) was genuine.  Perhaps output did speed up (or slow down) as estimated.  Car plants might go on extra shifts (or close for a period) due to consumers wanting to buy more cars (or fewer cars) in the period for some reason.  There might also be some policy change that might temporarily spur production (or the opposite).  For example, Trump’s recent trade measures, and the response to them from our trading partners, may have brought forward production and trade that would have been undertaken later in the year, in order to avoid tariffs threatened to be imposed later.  This could change quarterly GDP even though GDP for the year as a whole will not be affected positively (indeed the overall impact would likely be negative).

[Side note:  But one special factor in this past quarter, cited in numerous news reports (see, for example, here, here, here, here, and here), was that a jump in exports of soybeans was a key reason for the higher-than-recently-achieved rate of GDP growth.  This was not correct.  Soybean exports did indeed rise sharply, with this attributed to the response threatened by China and others to the new tariffs Trump has imposed.  China and others said they would respond with higher tariffs of their own, targeted on products such as soybeans coming from the US.  There was thus a rush to export soybeans in the period between when China first announced they would impose such retaliatory tariffs (in late March) and when they were then imposed (ultimately on July 6).

But while soybean exports did indeed increase sharply in the April to June quarter, soybeans are a crop that takes many months to grow.  Whatever increase in shipments there was had to come out of inventories.  An increase in exports would have to be matched by a similar decrease in inventories, with this true also for corn and other such crops.  There would be a similar issue for any increase in exports of Kentucky bourbon, also a target of retaliatory tariffs.  Any decent bourbon is aged for at least three years.

One must keep in mind that GDP (Gross Domestic Product) is a measure of production, and the only production that might have followed from the increased exports of soybeans or similar products would have been of packing and shipping services.  But packing and shipping costs are only a relatively small share of the total value of the products being exported.

Having said that, one should not then go to the opposite extreme and assume that the threatened trade war had no impact on production and hence GDP in the quarter.  It probably did.  With tariffs and then retaliatory tariffs being threatened (but to be imposed two or three months in the future), there were probably increased factory orders to make and ship various goods before such new tariffs would enter into effect.  Thus there likely was some impact on GDP, but to an extent that cannot be quantified in what we see in the national level accounts.  And with such factory orders simply bringing forward orders that likely would have been made later in the year, one may well see a fallback in the pace of GDP growth in the remainder of the year.  But there are many other factors as well affecting GDP growth, and we will need to wait and see what the net impact will be.]

So one should not exclude the possibility that the fluctuation in the quarterly growth rate is real.  But it could be due to many other factors as well, as we will discuss below.

b)  Change at an Annualized Rate is Not the Change in a Quarter:

While easily confused, keep in mind also that in the accounts as normally published and presented in the US, the rates of growth of GDP (and of the other economic variables) are shown as annual equivalent rates.  The actual change in the quarter is only about one-fourth of this (a bit less due to compounding).  That is, in the second quarter of 2018, the BEA estimated that GDP (on a seasonally adjusted basis, which I will discuss below as a separate factor) grew by 1.00% (and yes, exactly 1.00% within two significant digits).  But at an annualized rate (some say “annual rate”, and either term can be used), this would imply a rate of growth of 4.06% (which rounded becomes 4.1%).  It is equal to slightly more than 4.0% due to compounding.  [Technically, 1% growth in the quarter means 1.00 will grow to 1.01, and taking 1.01 to the fourth power yields 1.0406, or an increase of 4.06%.]

Thus it is not correct to say that “GDP grew by 4.1% in the second quarter”.  It did not – it grew by 1.0%.  What is correct is to say that “GDP grew at an annualized rate of 4.1% in the second quarter”.

Not all national statistical agencies present such figures in annualized terms.  European agencies, for example, generally present the quarterly growth figures as simply the growth in the quarter.  Thus, for example, Eurostat on June 7 announced that GDP in the eurozone rose by an estimated 0.4% in the first quarter of 2018.  This 0.4% was the growth in the quarter.  But that 0.4% growth figure would be equivalent to growth of 1.6% on an annualized basis (actually 1.61%, if the growth had been precisely 0.400%).  Furthermore, the European agencies will generally also focus on the growth in GDP over what it had been a year earlier in that same quarter.  In the first quarter of 2018, this growth over the year-earlier period was an estimated 2.5% according to the Eurostat release.  But the growth since the year-earlier period is not the same as the growth in the current quarter at an annualized rate.  They can easily be confused if one is not aware of the conventions used by the different agencies.

c)  Don’t confuse the level of GDP with the change in GDP:

Also along the lines of how we might misleadingly interpret figures, one needs to keep in mind that while the quarterly growth rates can, and do, bounce around a lot, the underlying levels of GDP are really not changing much.  While a 4% annual growth rate is four times as high as a 1% growth rate, for example, the underlying level of GDP in one calendar quarter is only increasing to a level of about 101 (starting from a base of 100 in this example) with growth at a 4% annual rate, versus to a level of 100.25 when  growth is at an annual rate of 1%.  While such a difference in growth rates matters a great deal (indeed a huge deal) if sustained over time, the difference in any one quarter is not that much.

Indeed, I personally find the estimated quarter to quarter levels of GDP in the US (after seasonal adjustment, which will be discussed below) to be surprisingly stable.  Keep in mind that GDP is a flow, not a stock.  It is like the flow of water in a river, not a stock such as the body of water in a reservoir.  Flows can go sharply up and down, while stocks do not, and some may mistakenly treat the GDP figures in their mind as a stock rather than a flow.  GDP measures the flow of goods and services produced over some period of time (a calendar quarter in the quarterly figures).  A flow of GDP to 101 in some quarter (from a base of 100 in the preceding quarter) is not really that different to an increase to 100.25.  While this would matter (and matter a good deal) if the different quarterly increases are sustained over time, this is not that significant when just for one quarter.

d)  Statistical noise matters:

Moving now to more substantive reasons why one should expect a significant amount of quarter to quarter volatility, one needs to recognize that GDP is estimated based on surveys and other such sources of statistical information.  The Bureau of Economic Analysis (BEA) of the US Department of Commerce, which is responsible for the estimates of the GDP accounts in the US (which are formally called the National Income and Product Accounts, or NIPA), bases its estimates on a wide variety of surveys, samples of tax returns, and other such partial figures.  The estimates are not based on a full and complete census of all production each quarter.  Indeed, such an economic census is only undertaken once every five years, and is carried out by the US Census Bureau.

One should also recognize that an estimate of real GDP depends on two measures, each of which is subject to sampling and other error.  One does not, and cannot, measure “real GDP” directly.  Rather, one estimates what nominal GDP has been (based on estimates in current dollars of the value of all economic transactions that enter into GDP), and then how much prices have changed.  Price indices are estimated based on the prices of surveyed samples, and the components of real GDP are then estimated from the nominal GDP of the component divided by the relevant price index.  Real GDP is only obtained indirectly.

There will then be two sets of errors in the measurements:  One for the nominal GDP flows and one for the price indices.  And surveys, whether of income flows or of prices, are necessarily partial.  Even if totally accurate for the firms and other entities sampled, one cannot say with certainty whether those sampled in that quarter are fully representative of everyone in the economy.  This is in particular a problem (which the BEA recognizes) in capturing what is happening to newly established firms.  Such firms will not be included in the samples used (as they did not exist when the samples were set up) and the experiences of such newly established firms can be quite different from those of established firms.

And what I am calling here statistical “noise” encompasses more than simply sampling error.  Indeed, sampling error (the fact that two samples will come up with different results simply due to the randomness of who is chosen) is probably the least concern.  Rather, systemic issues arise whenever one is trying to infer measures at the national level from the results found in some survey.  The results will depend, for example, on whether all the components were captured well, and even on how the questions are phrased.  We will discuss below (in Section C, where we look at a comparison of estimates of GDP to estimates of Gross Domestic Income, or GDI, which in principle should be the same) that the statistical discrepancy between the estimates of GDP and GDI does not vary randomly from one quarter to the next but rather fairly smoothly (what economists and statisticians call “autocorrelation” – see Section C).  This is an indication that there are systemic issues, and not simply something arising from sample randomness.

Finally, even if that statistical error was small enough to allow one to be confident that we measured real GDP within an accuracy of just, say, +/- 1%, one would not then be able to say whether GDP in that quarter had increased at an annualized rate of about 4%, or decreased by about 4%.  A small quarterly difference looms large when looked at in terms of annualized rates.

I do not know what the actual statistical error might be in the GDP estimates, and it appears they are well less than +/- 1% (based on the volatility actually observed in the quarter to quarter figures).  But a relatively small error in the estimates of real GDP in any quarter could still lead to quite substantial volatility in the estimates of the quarter to quarter growth.

e)  Seasonal adjustment is necessary, but not easy to do:

Economic activity varies over the course of the year, with predictable patterns.  There is a seasonality to holidays, to when crops are grown, to when students graduate from school and enter the job market, and much much more.  Thus the GDP data we normally focus on has been adjusted by various statistical methods to remove the seasonality factor, making use of past data to estimate what the patterns are.

The importance of this can be seen if one compares what the seasonally adjusted levels of GDP look like compared to the levels before seasonal adjustment.  Note the level of GDP here is for one calendar quarter – it will be four times this at an annual rate:

There is a regular pattern to GDP:  It is relatively high in the last quarter of each year, relatively low in the first quarter, and somewhere in between in the second and third quarters.  The seasonally adjusted series takes account of this, and is far smoother.  Calculating quarterly growth rates from a series which has not been adjusted for seasonality would be misleading in the extreme, and not of much use.

But adjusting for seasonality is not easy to do.  While the best statisticians around have tried to come up with good statistical routines to do this, it is inherently difficult.  A fundamental problem is that one can only look for patterns based on what they have been in the past, but the number of observations one has will necessarily be limited.  If one went back to use 20 years of data, say, one would only have 20 observations to ascertain the statistical pattern.  This is not much.  One could go back further, but then one has the problem that the economy as it existed 30 or 40 years ago (and indeed even 20 years ago) was quite different from what it is now, and the seasonal patterns could also now be significantly different.  While there are sophisticated statistical routines that have been developed to try to make best use of the available data (and the changes observed in the economy over time), this can only be imperfect.

Indeed, the GDP estimates released by the BEA on July 27 incorporated a number of methodological changes (which we will discuss below), one of which was a major update to the statistical routines used for the seasonal adjustment calculations.  Many observers (including at the BEA) had noted in recent years that (seasonally adjusted) GDP growth in the first quarter of each year was unusually and consistently low.  It then recovered in the second quarter.  This did not look right.

One aim of the update to the seasonal adjustment statistical routines was to address this issue.  Whether it was fully successful is not fully clear.  As seen in the chart at the top of this post (which reflects estimates that have been seasonally adjusted based on the new statistical routines), there still appear to be significant dips in the seasonally adjusted first quarter figures in many of the years (comparing the first quarter GDP figures to those just before and just after – i.e. in 2007, 2008, 2010, 2011, 2014, and perhaps 2017 and 2018.  This would be more frequent than one would expect if the residual changes were now random over the period).  However, this is an observation based just on a simple look at a limited sample.  The BEA has looked at this far more carefully, and rigorously, and believes that the new seasonal adjustment routines it has developed have removed any residual seasonality in the series as estimated.

f)  The timing of weekends and holidays may also enter, and could be important:

The production of the goods and services that make up the flow of GDP will also differ on Saturdays, Sundays, and holidays.  But the number of Saturdays, Sundays, and certain holidays may differ from one year to the next.  While there are normally 13 Saturdays and 13 Sundays in each calendar quarter, and most holidays will be in the same quarter each year, this will not always be the case.

For example, there were just 12 Sundays in the first quarter of 2018, rather than the normal 13.  And there will be 14 Sundays in the third quarter of 2018, rather than the normal 13.  In 2019, we will see a reversion to the “normal” 13 Sundays in each of the quarters.  This could have an impact.

Assume, just for the sake of illustration, that production of what goes into GDP is only one-half as much on a Saturday, Sunday, or holiday, than it is on a regular Monday through Friday workday.  It will not be zero, as many stores, as well as certain industrial plants, are still open, and I am just using the one-half for illustration.  Using this, and based on a simple check of the calendars for 2018 and 2019, one will find there were 62 regular, Monday through Friday, non-holiday workdays in the first quarter of 2018, while there will be 61 such regular workdays in the first quarter of 2019.  The number of Saturdays, Sundays, and holidays were 28 in the first quarter of 2018 (equivalent to 14 regular workdays in terms of GDP produced, assuming the one-half figure), while the number of Saturdays, Sundays, and holidays will be 29 in the first quarter of 2019 (equivalent to 14.5 regular workdays).  Thus the total regular work-day equivalents will be 76 in 2018 (equal to 62 plus 14), falling to 75.5 in 2019 (equal to 61 plus 14.5).  This will be a reduction of 0.7% between the periods in 2018 and 2019 (75.5/76), or a fall of 2.6% at an annualized rate.  This is not small.

The changes due to the timing of holidays could matter even more, especially for certain countries around the world.  Easter, for example, was celebrated in March (the first quarter) in 2013 and 2016, but came in April (the second quarter) in 2014, 2015, 2017, and 2018.  In Europe and Latin America, it is customary to take up to a week of vacation around the Easter holidays.  The change in economic activity from year to year, with Easter celebrated in one quarter in one year but a different one in the next, will make a significant difference to economic activity as measured in the quarter.

And in Muslim countries, Ramadan (a month of fasting from sunrise to sunset), followed by the three-day celebration of Eid al-Fitr, will rotate through the full year (in terms of the Western calendar) as it is linked to the lunar cycle.

Hence it would make sense to adjust the quarterly figures not only for the normal seasonal adjustment, but also for any changes in the number of weekends and holidays in some particular calendar quarter.  Eurostat and most (but not all) European countries make such an adjustment for the number of working days in a quarter before they apply the seasonal adjustment factors.  But I have not been able to find how the US handles this.  The adjustment might be buried somehow in the seasonal adjustment routines, but I have not seen a document saying this.  If no adjustment is made, then this might explain part of the quarterly fluctuations seen in the figures.

g)  There have been, and always will be, updates to the methodology used:

As noted above, the GDP figures released on July 27 reflected a major update in the methodology followed by the BEA to arrive at its GDP estimates.  Not only was there extensive work on the seasonal adjustment routines, but there were definitional and other changes.  The accounts were also updated to reflect the findings from the 2012 Economic Census, and prices were changed from a previous base of 2009 to now 2012.  The July 27 release summarized the changes, and more detail on what was done is available from a BEA report issued in April.  And with the revisions in definitions and certain other methodological changes, the BEA revised its NIPA figures going all the way back to 1929, the first year with official GDP estimates.

The BEA makes such changes on a regularly scheduled basis.  There is normally an annual change released each year with the July report on GDP in the second quarter of the year.  This annual change incorporates new weights (from recent annual surveys) and normally some limited methodological changes, and the published estimates are normally then revised going back three and a half years.  See, for example, this description of what was done in July 2017.

On top of this, there is then a much larger change once every five years.  The findings from the most recent Economic Census (which is carried out every five years) are incorporated, seasonal adjustment factors are re-estimated, and major definitional or methodological changes may be incorporated.  The July 2018 release reflected one of those five-year changes.  It was the 15th such comprehensive revision to the NIPA accounts undertaken by the BEA.

I stress this to make the point that the GDP figures are estimates, and as estimates are always subject to change.  The professionals at the BEA are widely admired around the world for the quality of their work, and do an excellent job in my opinion.  But no estimates will ever be perfect.  One has to recognize that there will be a degree of uncertainty surrounding any such estimates, and that the quarter to quarter volatility observed will derive at least in part from the inherent uncertainty in any such estimates.

C.  Estimates of GDP versus Estimates of GDI

One way to develop a feel for how much the changes in quarterly GDP may be due to the inherent uncertainty in the estimates is to compare it to the estimated quarterly changes in Gross Domestic Income (GDI).  GDP (Gross Domestic Product) measures the value of everything produced.  GDI measures the value of all incomes (wages, profits, rents, etc.) generated.  In principle, the totals should be the same, as the value of whatever is produced accrues to someone as income.  They should add up to the same thing.

But the BEA arrives at its estimates of GDP and of GDI by different routes.  As a consequence, the estimates of the totals will then differ.  The differences are not huge in absolute amount, nor have they grown over time (as a share of GDP or of GDI).  That is, on average the estimates match each other over time, with the same central tendency.  But they differ by some amount in any individual quarter, and hence the quarter to quarter growth rates will differ.  And for the reasons reviewed above, those slight changes in the levels in any individual quarter can translate into often major differences in the growth rates from one quarter to the next.  And these differences may appear to be particularly large when the growth rates are then presented in annualized terms.

For the period since 2006, the two sets of growth rates were (where the initial estimate for the second quarter of 2018 will not be available until the end-August figures come out):

As is seen, the alternative estimates of growth in any individual quarter can be quite different.  There was an especially large difference in the first quarter of 2012, when the estimated growth in GDP was 3.2% at an annual rate, while the estimated growth in GDI was a giant 8.7%.

Which is correct?  Was the growth rate in the first quarter of 2012 3.2% (as found with the GDP estimate) or 8.7% (as found with the GDI estimate)?  The answer is we do not know, and indeed that probably neither is correct.  What is most likely is that the true figure is probably somewhere in between.

Furthermore, and also moderating what the impact on the differences in the respective estimated growth rates will be, it is not the case that the estimates of GDP and GDI are statistically independent of each other, with the two bouncing around randomly with respect to each other.  Rather, if one looks at what the BEA calls the “statistical discrepancy” (the difference between GDP and GDI), one finds that if, say, the estimate of GDP were above the estimate of GDI in one quarter, then it likely would also be above in the next quarter.  Not by the same amount, and the differences would evolve over time, but moving more like waves than as balls ricocheting around.  Economists and statisticians refer to this as “autocorrelation”, and it indicates that there is some systemic error in the estimates of GDP and of GDI, which carries over from one quarter to the next.  What the source of that is, we do not know.  If we did know, then it would be eliminated.  But the fact such autocorrelation exists tells us that there is some source of systemic error in the measures of GDP and GDI, and we have not been able to discover the source.

Estimates are estimates.  We need to recognize that there will be statistical uncertainty in any such figures.  Even if they even out over time, the estimated growth from one quarter to the next will reflect such statistical volatility.  The differences seen in the estimated rates of growth in any one quarter for total output (estimated by way of GDP versus by way of GDI) provides a useful benchmark for how to judge the reported changes seen in growth for GDP in any individual quarter.  The true volatility (for purely statistical reasons) is likely to be at least as much, if not more.

D.  Conclusion

There are many reasons, then, to expect the quarterly growth figures to bounce around.  One should not place too much weight on the estimates from any individual quarter.  It is the longer term trends that matter.  The estimated figure for growth in GDP of 4.1% in the second quarter was not out of line with what has been seen in a number of quarters in recent years.  But growth since mid-2009 has only been about one half as much on average, despite several quarters when estimated growth was well in excess of 4.1%.

To conclude, some may find of interest three country cases I am personally familiar with which illustrate why one needs to exercise care, and with an understanding of the country context, when considering what is meaningful or not for reported figures on GDP growth.  The countries are Japan, China, and an unidentified, but newly independent, former colony in the 1960s.

a)  Japan:  In the late 1990s / early 2000s, while holding a position within the World Bank Group, I was responsible for assessments of the prospects and risks of the countries of East Asia where the World Bank was active.  This was not long after the East Asia crisis of 1997, and the countries were just beginning to recover.  Japan was important, both as a trading partner to the others and because Japan itself had gone through a somewhat similar crisis following 1990, when the Japanese financial bubble burst.

As part of this, I followed closely the quarterly GDP growth figures for Japan.  But as many analysts at the time noted, the quarter to quarter figures behaved in ways that were difficult to understand.  Components went up when one would have thought they would go down (and vice versa), the quarterly changes were far more extreme than seen elsewhere, and in general the quarter to quarter fluctuations were difficult to make sense of.  The volatility in the figures was far greater than one would have expected for an economy such as Japan’s.

This view among analysts was such a common one that the government agency responsible for the estimates felt it necessary to issue a news release in June 2000 defending its work and addressing a number of the concerns that had been raised.

I have no doubt that the Japanese government officials responsible for the estimates were well-qualified and serious professionals.  But it is not easy to estimate GDP and its components, the underlying data on which the statisticians relied might have had problems (including sample sizes that were possibly too small), and there may have been segments of the economy (in the less formal sectors) which might not have been captured well.

I have not followed closely in recent years, and do not know if the issues continue.  But Japan’s case illustrates that even a sophisticated agency, with good professionals, can have difficulty in arriving at GDP estimates that behave as one would expect.

b)  China:  The case of China illustrates the mirror image problem of what was found in Japan.  While the Japanese GDP estimates bounced around far too sharply from one quarter to the next, the GDP estimates for China showed remarkable, and not believable, stability.

Chinese growth rates have normally been presented as growth of GDP in the current period over what it was in the same period one year ago.  Seasonal adjustment is then not needed, and indeed China only started to present seasonally adjusted figures in 2011.  However, these estimates are still not fully accepted by many analysts.  Comparing GDP in the current quarter to what it was in the same quarter a year before overcomes this, but at the cost that it does not present information on growth just in the quarter, as opposed to total growth over the preceding year.

And the growth rates reported over the same quarter in the preceding year have been shockingly smooth.  Indeed, in recent years (from the first quarter of 2015 through to the recently released figures for the second quarter of 2018), China’s reported growth of its GDP over the year-earlier period has not been more than 7.0% nor less than 6.7% in each and every quarter.  Specifically, the year on year GDP growth rates from the first quarter of 2015 through to the second quarter of 2018 were (in sequence):  7.0%, 7.0%, 6.9%, 6.8%, 6.7%, 6.7%, 6.7%, 6.8%, 6.9%, 6.9%, 6.8%, 6.8%, 6.8%, and 6.7% (one can find the figures in, for example, the OECD database).  Many find this less than credible.

There are other problems as well in the Chinese numbers.  For example, it has often been the case that the reported growth in provincial GDP of the 31 provincial level entities in China was higher in almost all of the 31 provinces, and sometimes even in all of the provinces, than GDP growth was in China as a whole.  This is of course mathematically impossible, but not surprising when political rewards accrue to those with fast reported growth.

With such weak credibility, analysts have resorted to coming up with proxies to serve as indicators of what quarter to quarter might have been.  These might include electricity consumption, or railway tonnage carried, or similar indicators of economic production.  Indeed, there is what has been labeled the “Li index”, named after Li Keqiang (who was vice premier when he formulated it, and later China’s premier).  Li said he did not pay much attention to the official GDP statistics, but rather focused on a combination of electricity production, rail cargo shipments, and loan disbursements.  Researchers at the Federal Reserve Bank of San Francisco who reproduced this and fitted it through some regression analysis found that it worked quite well.

And the index I found most amusing is calculated using nighttime satellite images of China, with an estimation of how much more night-time illumination one finds over time.  This “luminosity” index tracks well what might be going on with China’s GDP.

c)  An unidentified, newly independent, former colony:  Finally, this is a story which I must admit I received third hand, but which sounds fully believable.  In the mid-1970s I was working for a period in Kuala Lumpur, for the Government of Malaysia.  As part of an economic modeling project I worked closely with the group in the national statistical office responsible for estimating GDP.  The group was led by a very capable, and talkative, official (of Tamil origin), who related a story he had heard from a UN consultant who had worked closely with his group in the early 1970s to develop their system of national accounts.

The story is of a newly independent country in the mid-1960s (whose name I was either not told or cannot remember), and its estimation of GDP.  An IMF mission had visited it soon after independence, and as is standard, the IMF made forecasts of what GDP growth might be over the next several years.  Such forecasts are necessary in order to come up with estimates for what the government accounts might be (as tax revenues will depend on GDP), for the trade accounts, for the respective deficits, and hence for what the financing needs might be.

Such forecasts are rarely very good, especially for a newly independent country where much is changing.  But something is needed.

As time passed, the IMF received regular reports from the country on what estimated GDP growth actually was.  What they found was that reported GDP growth was exactly what had been forecast.  And when asked, the national statisticians responded that who were they to question what the IMF officials had said would happen!

The Simple Economics of What Determines the Foreign Trade Balance: Econ 101

“There’s no reason that we should have big trade deficits with virtually every country in the world.”

“We’re like the piggybank that everybody is robbing.”

“the United States has been taken advantage of for decades and decades”

“Last year,… [the US] lost  … $817 billion on trade.  That’s ridiculous and it’s unacceptable.”

“Well, if they retaliate, they’re making a mistake.  Because, you see, we have a tremendous trade imbalance. … we can’t lose”

Statements made by President Trump at the press conference held as he left the G-7 meetings in, Québec, Canada, June 9, 2018.

 

A.  Introduction

President Trump does not understand basic economics.  While that is not a surprise, nor something necessarily required or expected of a president, one should expect that a president would appoint advisors who do understand, and who would tell him when he is wrong.  Unfortunately, this president has been singularly unwilling to do so.  This is dangerous.

Trump is threatening a trade war.  Not only by his words at the G-7 meetings and elsewhere, but also by a number of his actions on trade and tariffs in recent months, Trump has made clear that he believes that a trade deficit is a “loss” to the nation, that countries with trade surpluses are somehow robbing those (such as the US) with a deficit, that raising tariffs can and will lead to reductions in trade deficits, and that if others then also raise their tariffs, the US will in the end necessarily “win” simply because the US has a trade deficit to start.

This is confused on many levels.  But it does raise the questions of what determines a country’s trade balance; whether a country “loses” if it has a trade deficit; and what is the role of tariffs.  This Econ 101 blog post will first look at the simple economics of what determines a nation’s trade deficit (hint:  it is not tariffs); will then discuss what tariffs do and where do they indeed matter; and will then consider the role played by foreign investment (into the US) and whether a trade deficit can be considered a “loss” for the nation (a piggybank being robbed).

B.  What Determines the Overall Trade Deficit?

Let’s start with a very simple case, where government accounts are aggregated together with the rest of the economy.  We will later then separate out government.

The goods and services available in an economy can come either from what is produced domestically (which is GDP, or Gross Domestic Product) or from what is imported.  One can call this the supply of product.  These goods and services can then be used for immediate consumption, or for investment, or for export.  One can call this the demand for product.  And since investment includes any net change in inventories, the goods and services made available will always add up to the goods and services used.  Supply equals demand.

One can put this in a simple equation:

GDP + Imports = Domestic Consumption + Domestic Investment + Exports

Re-arranging:

(GDP – Domestic Consumption) – Domestic Investment = Exports – Imports

The first component on the left is Domestic Savings (what is produced domestically less what is consumed domestically).  And Exports minus Imports is the Trade Balance.  Hence one has:

Domestic Savings – Domestic Investment = Trade Balance

As one can see from the way this was derived, this is simply an identity – it always has to hold.  And what it says is that the Trade Balance will always be equal to the difference between Domestic Savings and Domestic Investment.  If Domestic Savings is less than Domestic Investment, then the Trade Balance (Exports less Imports) will be negative, and there will be a trade deficit.  To reduce the trade deficit, one therefore has to either raise Domestic Savings or reduce Domestic Investment.  It really is as straightforward as that.

Where this becomes more interesting is in determining how the simple identity is brought about.  But here again, this is relatively straightforward in an economy which, like now, is at full employment.  Hence GDP is essentially fixed:  It cannot immediately rise by either employing more labor (as all the workers who want a job have one), nor by each of those laborers suddenly becoming more productive (as productivity changes only gradually through time by means of either better education or by investment in capital).  And GDP is equal to labor employed times the productivity of each of those workers.

In such a situation, with GDP at its full employment level, Domestic Savings can only rise if Domestic Consumption goes down, as Domestic Savings equals GDP minus Domestic Consumption.  But households want to consume, and saving more will mean less for consumption.  There is a tradeoff.

The only other way to reduce the trade deficit would then be to reduce Domestic Investment.  But one generally does not want to reduce investment.  One needs investment in order to become more productive, and it is only through higher productivity that incomes can rise.

Reducing the trade deficit, if desirable (and whether it is desirable will be discussed below), will therefore not be easy.  There will be tradeoffs.  And note that tariffs do not enter directly in anything here.  Raising tariffs can only have an impact on the trade balance if they have a significant impact for some reason on either Domestic Savings or Domestic Investment, and tariffs are not a direct factor in either.  There may be indirect impacts of tariffs, which will be discussed below, but we will see that the indirect effects actually could act in the direction of increasing, not decreasing, the trade deficit.  However, whichever direction they act in, those indirect effects are likely to be small.  Tariffs will not have a significant effect on the trade balance.

But first, it is helpful to expand the simple analysis of the above to include Government as a separate set of accounts.  In the above we simply had the Domestic sector.  We will now divide that into the Domestic Private and the Domestic Public (or Government) sectors.  Note that Government includes government spending and revenues at all levels of government (state and local as well as federal).  But the government deficit is primarily a federal government issue.  State and local government entities are constrained in how much of a deficit they can run over time, and the overall balance they run (whether deficit or surplus) is relatively minor from the perspective of the country as a whole.

It will now also be convenient to write out the equations in symbols rather than words, and we will use:

GDP = Gross Domestic Product

C = Domestic Private Consumption

I = Domestic Private Investment

G = Government Spending (whether for Consumption or for Investment)

X = Exports

M = Imports

T = Taxes net of Transfers

Note that T (Taxes net of Transfers) will be the sum total of all taxes paid by the private sector to government, minus all transfers received by the private sector from government (such as for Social Security or Medicare).  I will refer to this as simply net Taxes (T).

The basic balance of goods or services available (supplied) and goods or services used (demanded) will then be:

GDP + M = C + I + G + X

We will then add and subtract net Taxes (T) on the right-hand side:

GDP + M = (C + T) + I + (G – T) + X

Rearranging:

GDP – (C + T) – (G – T) – I = X – M

(GDP – C – T) – I + (T – G) = X – M

Or in (abbreviated) words:

Dom. Priv. Savings – Dom. Priv. Investment + Govt Budget Balance = Trade Balance

Domestic Private Savings (savings by households and private businesses) is equal to what is produced in the economy (GDP), less what is privately consumed (C), less what is paid in net Taxes (T) by the private sector to the public sector.  Domestic Private Investment is simply I, and includes investment both by private businesses and by households (primarily in homes).  And the Government Budget Balance is equal to what government receives in net Taxes (T), less what Government spends (on either consumption items or on public investment).  Note that government spending on transfers (e.g. Social Security) is already accounted for in net Taxes (T).

This equation is very much like what we had before.  The overall Trade Balance will equal Domestic Private Savings less Domestic Private Investment plus the Government Budget Balance (which will be negative when a deficit, as has normally been the case except for a few years at the end of the Clinton administration).  If desired, one could break down the Government Budget Balance into Public Savings (equal to net Taxes minus government spending on consumption goods and services) less Public Investment (equal to government spending on investment goods and services), to see the parallel with Domestic Private Savings and Domestic Private Investment.  The equation would then read that the Trade Balance will equal Domestic Private Savings less Domestic Private Investment, plus Government Savings less Government Investment.  But there is no need.  The budget deficit, as commonly discussed, includes public spending not only on consumption items but also on investment items.

This is still an identity.  The balance will always hold.  And it says that to reduce the trade deficit (make it less negative) one has to either increase Domestic Private Savings, or reduce Domestic Private Investment, or increase the Government Budget Balance (i.e. reduce the budget deficit).  Raising Domestic Private Savings implies reducing consumption (when the economy is at full employment, as now).  Few want this.  And as discussed above, a reduction in investment is not desirable as investment is needed to increase productivity over time.

This leaves the budget deficit, and most agree that it really does need to be reduced in an economy that is now at full employment.  Unfortunately, Trump and the Republican Congress have moved the budget in the exact opposite direction, primarily due to the huge tax cut passed last December, and to a lesser extent due to increases in certain spending (primarily for the military).  As discussed in an earlier post on this blog, an increase in the budget deficit to a forecast 5% of GDP at a time when the economy is at full employment is unprecedented in peacetime.

What this implies for the trade balance is clear from the basic identity derived above.  An increase in the budget deficit (a reduction in the budget balance) will lead, all else being equal, to an increase in the trade deficit (a reduction in the trade balance).  And it might indeed be worse, as all else is not equal.  The stated objective of slashing corporate taxes is to spur an increase in corporate investment.  But if private investment were indeed to rise (there is in fact little evidence that it has moved beyond previous trends, at least so far), this would further worsen the trade balance (increase the trade deficit).

Would raising tariffs have an impact?  One might argue that this would raise net Taxes paid, as tariffs on imports are a tax, which (if government spending is not then also changed) would reduce the budget deficit.  While true, the extent of the impact would be trivially small.  The federal government collected $35.6 billion in all customs duties and fees (tariffs and more) in FY2017 (see the OMB Historical Tables).  This was less than 0.2% of FY2017 GDP.  Even if all tariffs (and other fees on imports) were doubled, and the level of imports remained unchanged, this would only raise 0.2% of GDP.  But the trade deficit was 2.9% of GDP in FY2017.  It would not make much of a difference, even in such an extreme case.  Furthermore, new tariffs are not being pushed by Trump on all imports, but only a limited share (and a very limited share so far).  Finally, if Trump’s tariffs in fact lead to lower imports of the items being newly taxed, as he hopes, then tariffs collected can fall.  In the extreme, if the imports of such items go to zero, then the tariffs collected will go to zero.

Thus, for several reasons, any impact on government revenues from the new Trump tariffs will be minor.

The notion that raising tariffs would be a way to eliminate the trade deficit is therefore confused.  The trade balance will equal the difference between Domestic Savings and Domestic Investment.  Adding in government, the trade balance will equal the difference between Domestic Private Savings and Domestic Private Investment, plus the equivalent for government (the Government Budget Balance, where a budget deficit will be a negative).  Tariffs have little to no effect on these balances.

C.  What Role Do Tariffs Play, Then?

Do tariffs then matter?  They do, although not in the determination of the overall trade deficit.  Rather, tariffs, which are a tax, will change the price of the particular import relative to the price of other products.  If applied only to imports from some countries and not from others, one can expect to see a shift in imports towards those countries where the tariffs have not been imposed.  And in the case when they are applied globally, on imports of the product from any country, one should expect that prices for similar products made in the US will then also rise.  To the extent there are alternatives, purchases of the now more costly products (whether imported or produced domestically) will be reduced, while purchases of alternatives will increase.  And there will be important distributional changes.  Profits of firms producing the now higher priced products will increase, while the profits of firms using such products as an input will fall.  And the real incomes of households buying any of these products will fall due to the higher prices.

Who wins and who loses can rapidly become turn into something very complicated.  Take, for example, the new 25% tariff being imposed by the Trump administration on steel (and 10% on aluminum).  The tariffs were announced on March 8, to take effect on March 23.  Steel imports from Canada and Mexico were at first exempted, but later the Trump administration said those exemptions were only temporary.  On March 22 they then expanded the list of countries with temporary exemptions to also the EU, Australia, South Korea, Brazil, and Argentina, but only to May 1.  Then, on March 28, they said imports from South Korea would receive a permanent exemption, and Australia, Brazil, and Argentina were granted permanent exemptions on May 2.  After a short extension, tariffs were then imposed on steel imports from Canada, Mexico, and the EU, on May 31.  And while this is how it stands as I write this, no one knows what further changes might be announced tomorrow.

With this uneven application of the tariffs by country, one should expect to see shifts in the imports by country.  What this achieves is not clear.  But there are also further complications.  There are hundreds if not thousands of different types of steel that are imported – both of different categories and of different grades within each category – and a company using steel in their production process in the US will need a specific type and grade of steel.  Many of these are not even available from a US producer of steel.  There is thus a system where US users of steel can apply for a waiver from the tariff.  As of June 19, there have been more than 21,000 petitions for a waiver.  But there were only 30 evaluators in the US Department of Commerce who will be deciding which petitions will be granted, and their training started only in the second week of June.  They will be swamped, and one senior Commerce Department official quoted in the Washington Post noted that “It’s going to be so unbelievably random, and some companies are going to get screwed”.  It would not be surprising to find political considerations (based on the interests of the Trump administration) playing a major role.

So far, we have only looked at the effects of one tariff (with steel as the example).  But multiple tariffs on various goods will interact, with difficult to predict consequences.  Take for example the tariff imposed on the imports of washing machines announced in late January, 2018, at a rate of 20% in the first year and at 50% should imports exceed 1.2 million units in the year.  This afforded US producers of washing machines a certain degree of protection from competition, and they then raised their prices by 17% over the next three months (February to May).

But steel is a major input used to make washing machines, and steel prices have risen with the new 25% tariff.  This will partially offset the gains the washing machine producers received from the tariff imposed on their product.  Will the Trump administration now impose an even higher tariff on washing machines to offset this?

More generally, the degree to which any given producer will gain or lose from such multiple tariffs will depend on multiple factors – the tariff rates applied (both for what they produce and for what they use as inputs), the degree to which they can find substitutes for the inputs they need, and the degree to which those using the product (the output) will be able to substitute some alternative for the product, and more.  Individual firms can end up ahead, or behind.  Economists call the net effect the degree of “net effective protection” afforded the industry, and it can be difficult to figure out.  Indeed, government officials who had thought they were providing positive protection to some industry often found out later that they were in fact doing the opposite.

Finally, imposing such tariffs on imports will lead to responses from the countries that had been providing the goods.  Under the agreed rules of international trade, those countries can then impose commensurate tariffs of their own on products they had been importing from the US.  This will harm industries that may otherwise have been totally innocent in whatever was behind the dispute.

An example of what can then happen has been the impact on Harley-Davidson, the American manufacturer of heavy motorcycles (affectionately referred to as “hogs”).  Harley-Davidson is facing what has been described as a “triple whammy” from Trump’s trade decisions.  First, they are facing higher steel (and aluminum) prices for their production in the US, due to the Trump steel and aluminum tariffs.  Harley estimates this will add $20 million to their costs in their US plants.  For a medium-sized company, this is significant.  As of the end of 2017, Harley-Davidson had 5,200 employees in the US (see page 7 of this SEC filing).  With $20 million, they could pay each of their workers $3,850 more.  This is not a small amount.  Instead, the funds will go to bolster the profits of steel and aluminum firms.

Second, the EU has responded to the Trump tariffs on their steel and aluminum by imposing tariffs of their own on US motorcycle imports.  This would add $45 million in costs (or $2,200 per motorcycle) should Harley-Davidson continue to export motorcycles from the US to the EU.  Quite rationally, Harley-Davidson responded that they will now need to shift what had been US production to one of their plants located abroad, to avoid both the higher costs resulting from the new steel and aluminum tariffs, and from the EU tariffs imposed in response.

And one can add thirdly and from earlier, that Trump pulled the US out of the already negotiated (but still to be signed) Trans-Pacific Partnership agreement.  This agreement would have allowed Harley-Davidson to export their US built motorcycles to much of Asia duty-free.  They will now instead be facing high tariffs to sell to those markets.  As a result, Harley-Davidson has had to set up a new plant in Asia (in Thailand), shifting there what had been US jobs.

Trump reacted angrily to Harley-Davidson’s response to his trade policies.  He threatened that “they will be taxed like never before!”.  Yet what Harley-Davidson is doing should not have been a surprise, had any thought been given to what would happen once Trump started imposing tariffs on essential inputs needed in the manufacture of motorcycles (steel and aluminum), coming from our major trade partners (and often closest allies).  And it is positively scary that a president should even think that he should use the powers of the state to threaten an individual private company in this way.  Today it is Harley-Davidson.  Who will it be tomorrow?

There are many other examples of the problems that have already been created by Trump’s new tariffs.  To cite a few, and just briefly:

a)  The National Association of Home Builders estimated that the 20% tariff imposed in 2017 on imports of softwood lumber from Canada added nearly $3,600 to the cost of building an average single-family home in the US and would, over the course of a year, reduce wages of US workers by $500 million and cost 8,200 full-time US jobs.

b)  The largest nail manufacturer in the US said in late June that it has already had to lay off 12% of its workforce due to the new steel tariffs, and that unless it is granted a waiver, it would either have to relocate to Mexico or shut down by September.

c)  As of early June, Reuters estimated that at least $2.5 billion worth of investments in new utility-scale solar installation projects had been canceled or frozen due to the tariffs Trump imposed on the import of solar panel assemblies.  This is far greater than new investments planned for the assembly of such panels in the US.  Furthermore, the jobs involved in such assembly work are generally low-skill and repetitive, and can be automated should wages rise.

So there are consequences from such tariffs.  They might be unintended, and possibly not foreseen, but they are real.

But would the imposition of tariffs necessarily reduce the trade deficit, as Trump evidently believes?  No.  As noted above, the trade deficit would only fall if the tariffs would, for some reason, increase domestic savings or reduce domestic investment.  But tariffs do not enter directly into those factors.  Indirectly, one could map out some chains of possible causation, but these changes in some set of tariffs (even if broadly applied to a wide range of imports) would not have a major effect on overall domestic savings or investment.  They could indeed even act in the opposite direction.

Households, to start, will face higher prices from the new tariffs.  To try to maintain their previous standard of living (in real terms) they would then need to spend more on what they consume and hence would save less.  This, by itself, would reduce domestic savings and hence would increase the trade deficit to the extent there was any impact.

The impacts on firms are more various, and depend on whether the firm will be a net winner or loser from the government actions and how they might then respond.  If a net winner, they have been able to raise their prices and hence increase their profits.  If they then save the extra profits (retained earnings), domestic savings would rise and the trade deficit would fall.  But if they increase their investments in what has now become a more profitable activity (and that is indeed the stated intention behind imposing the tariffs), that response would lead to an increase in the trade deficit.  The net effect will depend on whether their savings or their investment increases by more, and one does not know what that net change might be.  Different firms will likely respond differently.

One also has to examine the responses of the firms who will be the net losers from the newly imposed tariffs.  They will be paying more on their inputs and will see a reduction in their profits.  They will then save less and will likely invest less.  Again, the net impact on the trade deficit is not clear.

The overall impact on the trade deficit from these indirect effects is therefore uncertain, as one has effects that will act in opposing directions.  In part for this reason, but also because the tariffs will affect only certain industries and with responses that are likely to be limited (as a tariff increase today can be just as easily reversed tomorrow), the overall impact on the trade balance from such indirect effects are likely to be minor.

Increases in individual tariffs, such as those being imposed now by Trump, will not then have a significant impact on the overall trade balance.  But tariffs still do matter.  They change the mix of what is produced, from where items will be imported, and from where items will be produced for export (as the Harley-Davidson case shows).  They will create individual winners and losers, and hence it is not surprising to see the political lobbying as has grown in Washington under Trump.  Far from “draining the swamp”, Trump’s trade policy has made it critical for firms to step up their lobbying activities.

But such tariffs do not determine what the overall trade balance will be.

D.  What Role Does Foreign Investment Play in the Determination of the Trade Balance?

While tariffs will not have a significant effect on the overall trade balance, foreign investment (into the US) will.  To see this, we need to return to the basic macro balance derived in Section B above, but generalize it a bit to include all foreign financial flows.

The trade balance is the balance between exports and imports.  It is useful to generalize this to take into account two other sources of current flows in the national income and product accounts which add to (or reduce) the net demand for foreign exchange.  Specifically, there will be foreign exchange earned by US nationals working abroad plus that earned by US nationals on investments they have made abroad.  Economists call this “factor services income”, or simply factor income, as labor and capital are referred to as factors of production.  This is then netted against such income earned in the US by foreign nationals either working here or on their investments here.  Second, there will be unrequited transfers of funds, such as by households to their relatives abroad, or by charities, or under government aid programs.  Again, this will be netted against the similar transfers to the US.

Adding the net flows from these to the trade balance will yield what economists call the “current account balance”.  It is a measure of the net demand for dollars (if positive) or for foreign exchange (if a deficit) from current flows.  To put some numbers on this, the US had a foreign trade deficit of $571.6 billion in 2017.  This was the balance between the exports and imports of goods and services (what economists call non-factor services to be more precise, now that we are distinguishing factor services from non-factor services).  It was negative – a deficit.  But the US also had a surplus in 2017 from net factor services income flows of $216.8 billion, and a deficit of $130.2 billion on net transfers (mostly from households sending funds abroad).  The balance on current account is the sum of these (with deficits as negatives and surpluses as positives) and came to a deficit of $485.0 billion in 2017, or 2.5% of GDP.  As a share of GDP, this deficit is significant but not huge.  The UK had a current account deficit of 4.1% of GDP in 2017 for example, while Canada had a deficit of 3.0%.

The current account for foreign transactions, basically a generalization of the trade balance, is significant as it will be the mirror image of the capital account for foreign transactions.  That is, when the US had a current account deficit of $485.0 billion (as in 2017), there had to be a capital account surplus of $485.0 billion to match this, as the overall purchases and sales of dollars in foreign exchange transactions will have to balance out, i.e. sum to zero.  The capital account incorporates all transactions for the purchase or sale of capital assets (investments) by foreign entities into the US, net of the similar purchase or sale of capital assets by US entities abroad.  When the capital account is a net positive (as has been the case for the US in recent decades), there is more such investment going into the US than is going out.  The investments can be into any capital assets, including equity shares in companies, or real estate, or US Treasury or other bonds, and so on.

But while the two (the current account and the capital account) have to balance out, there is an open question of what drives what.  Look at this from the perspective of a foreigner, wishing to invest in some US asset.  They need to get the dollars for this from somewhere.  While this would be done by means of the foreign exchange markets, which are extremely active (with trillions of dollars worth of currencies being exchanged daily), a capital account surplus of $485 billion (as in 2017) means that foreign entities had to obtain, over the course of the year, a net of $485 billion in dollars for their investments into the US.  The only way this could be done is by the US importing that much more than it exported over the course of the year.  That is, the US would need to run a current account deficit of that amount for the US to have received such investment.

If there is an imbalance between the two (the current account and the capital account), one should expect that the excess supply or demand for dollars will lead to changes in a number of prices, most directly foreign exchange rates, but also interest rates and other asset prices.  These will be complex and we will not go into here all the interactions one might then have.  Rather, the point to note is that a current account deficit, even if seemingly large, is not a sign of disequilibrium when there is a desire on the part of foreign investors to invest a similar amount in US markets.  And US markets have traditionally been a good place to invest.  The US is a large economy, with markets for assets that are deep and active, and these markets have normally been (with a few exceptions) relatively well regulated.

Foreign nationals and firms thus have good reason to invest a share of their assets in the US markets.  And the US has welcomed this, as all countries do.  But the only way they can obtain the dollars to make these investments is for the US to run a current account deficit.  Thus a current account deficit should not necessarily be taken as a sign of weakness, as Trump evidently does.  Depending on what governments are doing in their market interventions, a current account deficit might rather be a sign of foreign entities being eager to invest in the country.  And that is a good sign, not a bad one.

E.  An “Exorbitant Privilege”

The dollar (and hence the US) has a further, and important, advantage.  It is the world’s dominant currency, with most trade contracts (between all countries, not simply between some country and the US) denominated in dollars, as are contracts for most internationally traded commodities (such as oil).  And as noted above, investments in the US are particularly advantageous due to the depth and liquidity of our asset markets.  For these reasons, foreign countries hold most of their international reserves in dollar assets.  And most of these are held in what have been safe, but low yielding, short-term US Treasury bills.

As noted in Section D above, those seeking to make investments in dollar assets can obtain the dollars required only if the US runs a current account deficit.  This is as true for assets held in dollars as part of a country’s international reserves as for any other investments in US dollar assets.  Valéry Giscard d’Estaing in the 1960s, then the Minister of Finance of France, described this as an “exorbitant privilege” for the US (although this is often mistakenly attributed Charles de Gaulle, then his boss as president of France).

And it certainly is a privilege.  With the role of the dollar as the preferred reserve currency for countries around the world, the US is able to run current account deficits indefinitely, obtaining real goods and services from those countries while providing pieces of paper generating only a low yield in return.  Indeed, in recent years the rate of return on short-term US Treasury bills has generally been negative in real terms (i.e. after inflation).  The foreign governments buying these US Treasury bills are helping to cover part of our budget deficits, and are receiving little to nothing in return.

So is the US a “piggybank that everybody is robbing”, as Trump asserted to necessarily be the case when the US is has a current account deficit?  Not at all.  Indeed, it is the precise opposite.  The current account deficit is the mirror image of the foreign investment inflows coming into the US.  To obtain the dollars needed to do this those countries must export more real goods to the US than they import from the US.  The US gains real resources (the net exports), while the foreign entities then invest in US markets.  And for governments obtaining dollars to hold as their international reserves, those investments are primarily in the highly liquid and safe, short-term US Treasury bills, despite those assets earning low or even negative returns.  This truly is an “exorbitant privilege”, not a piggybank being robbed.

Indeed, the real concern is that with the mismanagement of our budget (tax cuts increasing deficits at a time when deficits should be reduced) plus the return to an ideologically driven belief in deregulating banks and other financial markets (such as what led to the financial and then economic collapse of 2008), the dollar may lose its position as the place to hold international reserves.  The British pound had this position in the 1800s and then lost it to the dollar due to the financial stresses of World War I.  The dollar has had the lead position since.  But others would like it, most openly by China and more quietly Europeans hoping for such a role for the euro.  They would very much like to enjoy this “exorbitant privilege”, along with the current account deficits that privilege conveys.

F.  Summary and Conclusion

Trump’s beliefs on the foreign trade deficit, on the impact of hiking tariffs, and on who will “win” in a trade war, are terribly confused.  While one should not necessarily expect a president to understand basic economics, one should expect that a president would appoint and listen to advisors who do.  But Trump has not.

To sum up some of the key points:

a)  The foreign trade balance will always equal the difference between domestic savings and domestic investment.  Or with government accounts split out, the trade balance will equal the difference between domestic private savings and domestic private investment, plus the government budget balance.  The foreign trade balance will only move up or down when there is a change in the balance between domestic savings and domestic investment.

b)  One way to change that balance would be for the government budget balance to increase (i.e. for the government deficit to be reduced).  Yet Trump and the Republican Congress have done the precise opposite.  The massive tax cuts of last December, plus (to a lesser extent) the increase in government spending now budgeted (primarily for the military), will increase the budget deficit to record levels for an economy in peacetime at full employment.  This will lead to a bigger trade deficit, not a smaller one.

c)  One could also reduce the trade deficit by making the US a terrible place to invest in.  This would reduce foreign investment into the US, and hence the current account deficit.  In terms of the basic savings/investment balance, it would reduce domestic investment (whether driven by foreign investors or domestic ones).  If domestic savings was not then also reduced (a big if, and dependant on what was done to make the US a terrible place to invest in), this would lead to a similar reduction in the trade deficit.  This is of course not to be taken seriously, but rather illustrates that there are tradeoffs.  One should not simplistically assume that a lower trade deficit achieved by any means possible is good.

d)  It is also not at all clear that one should be overly concerned about the size of the trade and current account deficits, at where they are today.  The US had a trade deficit of 2.9% of GDP in 2017 and a current account deficit of 2.5% of GDP.  While significant, these are not huge.  Should they become much larger (due, for example, to the forecast increases in government budget deficits to record levels), they might rise to problematic levels.  But at the current levels for the current account deficit, we have seen the markets for foreign exchange and for interest rates functioning pretty well and without overt signs of concern.  The dollars being made available through the current account deficit have been bought up and used for investments in US markets.

e)  Part of the demand for dollars to be invested and held in the US markets comes from the need for international reserves by governments around the world.  The dollar is the dominant currency in the world, and with the depth and liquidity of the US markets (in particular for short-term US Treasury bills) most of these international reserves are held in dollars.  This has given the US what has been called an “exorbitant privilege”, and permits the US to run substantial current account deficits while providing in return what are in essence paper assets yielding just low (or even negative) returns.

f)  The real concern should not be with the consequences of the dollar playing such a role in the system of international trade, but rather with whether the dollar will lose this privileged status.  Other countries have certainly sought this, most openly by China but also more quietly for the euro, but so far the dollar has remained dominant.  But there are increasing concerns that with the mismanagement of the government budget (the recent tax cuts) plus ideologically driven deregulation of banks and the financial markets (as led to the 2008 financial collapse), countries will decide to shift their international reserves out of the dollar towards some alternative.

g)  What will not reduce the overall trade deficit, however, is selective increases in tariff rates, as Trump has started to do.  Such tariff increases will shift around the mix of countries from where the imports will come, and/or the mix of products being imported, but can only reduce the overall trade deficit to the extent such tariffs would lead somehow to either higher domestic savings and/or lower domestic investment.  Tariffs will not have a direct effect on such balances, and indirect effects are going to be small and indeed possibly in the wrong direction (if the aim is to reduce the deficits).

h)  What such tariff policies will do, however, is create a mess.  And they already have, as the Harley-Davidson case illustrates.  Tariffs increase costs for US producers, and they will respond as best they can.  While the higher costs will possibly benefit certain companies, they will harm those using the products unless some government bureaucrat grants them a special exemption.

But what this does lead to is officials in government picking winners and losers.  That is a concern.  And it is positively scary to have a president lashing out and threatening individual firms, such as Harley-Davidson, when the firms respond to the mess created as one should have expected.