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.




Change in the Change










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:




Change in the Change










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:




Change in the Change










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.

Growth in France and the US: The Bottom 90% Have Done Better in France

France vs US, 1980-2012, GDP per capita overall and of bottom 90%

A.  Introduction

Conservative media and conservative politicians in the US have looked down on France over the last decade (particularly after France refused to join the US in the Iraq war, and then turned out to be right), arguing that France is a stagnant, socialist state, with an economy being left behind by a dynamic US.  They have pointed to faster overall growth in the US over the last several decades, and average incomes that were higher in the US to start and then became proportionately even higher as time went on.

GDP per capita has indeed grown faster in the US than it has in France over the last several decades.  Over the period of 1980 to 2007 (the most recent cyclical peak, before the economic collapse in the last year of the Bush administration from which neither the US nor France has as yet fully recovered), GDP per capita grew at an annual average rate of 2.0% in the US and only 1.5% in France.

But GDP per capita reflects an average covering everyone.  As has been discussed in this blog (see here and here), the distribution of income became markedly worse in the US since around 1980, when Reagan was elected and began to implement the “Reagan Revolution”.  The rich in the US have done extremely well since 1980, while the not-so-rich have not.  Thus while overall GDP per capita has grown by more in the US than in France, one does not know from just this whether that has also been the case for the bulk of the population.

In fact it turns out not to be the case.  The bottom 90%, which includes everyone from the poor up through the middle classes to at least the bottom end of the upper middle classes, have done better in France than in the US.

B.  Growth in GDP per Capita in France vs. the US:  Overall and the Bottom 90%

The graph at the top of this post shows GDP per capita from 1980 to 2012 for both the US and France.  The figures come from the Total Economy Database (TED database) of the Conference Board, and are expressed in terms of 2012 constant prices, in dollars, with the conversion from French currency to US dollars done in terms of Purchasing Power Parity (PPP) of 2005.  PPP exchange rates provide conversions based on the prices in two respective countries of some basket of goods.  They provide a measure of real living standards.  Conversions based on market exchange rates can be misleading as those rates will vary moment to moment based on financial market conditions, and also do not take into account the prices of goods which are not traded internationally.

Real GDP per capita (for the entire population) rose for both the US and France over this period, and by proportionately somewhat more in the US than in France.  These incomes are shown in the top two lines in the graph above, with the US in black and France in blue.  GDP per capita in France was 83% of the US value in 1980, and fell to 72% of the US by 2012.

But the story is quite different if one instead focuses on the bottom 90%.  The GDP per person of those in the bottom 90% of the US and in France are presented in the lower two lines of the graph above.  The figures were calculated using the distribution data provided in the World Top Incomes Database, assembled by Thomas Piketty, Emmanuel Saez, and others, applied to the GDP and population figures from the TED database.  The US distribution data extends to 2012, but the French data only reaches 2009 in what is available currently.

The Piketty – Saez distribution data is drawn from information provided in national income tax returns, and hence is based on incomes as defined for tax purposes in the respective countries.  Thus they are not strictly comparable across countries.  Nor is taxable income the same as GDP, even though GDP (sometimes referred to as National Income) reflects a broad concept of what constitutes income at a national level.  But for the moment (the direction of some adjustments will be discussed below), distributing GDP according to income shares of taxable income is a good starting point.

Based on this, incomes (as measured as a share of GDP, and then per person in the group) of the bottom 90% in France were 88% of the US level in 1980.  But this then grew to 98% of the US level by 2007, before backing off some in the downturn.  That is, the real income of the bottom 90%, expressed purely in GDP per person, rose in France over this period from substantially less than that for the US in 1980, to very close to the average US income of that group by 2007.  And since one is talking about 90% of the population, that is all those other than the well-off and rich, this is not an insignificant group.

C.  Most of the US Income Growth Went to the Top 10%

Figures on the growth of the different groups, and their distributional shares, show what happened:

France US
GDP per Capita, Rate of Growth, 1980-2007
  Overall 1.5% 2.0%
  Bottom 90% 1.4% 1.0%
Share of GDP, 1980
  Top 10% 31% 35%
  Bottom 90% 69% 65%
Share of GDP, 2007
  Top 10% 33% 50%
  Bottom 90% 67% 50%
Share of Increment of GDP Growth, 1980-2007
  Top 10% 36% 62%
  Bottom 90% 64% 38%

As noted before, overall GDP per capita grew at a faster average rate in the US than in France over this period:  2.0% annually in the US vs. 1.5% in France.  But for the bottom 90%, GDP per capita (for the group) grew at a rate of only 1.0% in the US while in France it grew at a rate of 1.4% per year.  The French rate for the bottom 90% was almost the same as the overall average rate for everyone there, while in the US the rate of income growth for the bottom 90% was only half as much as for the overall average.

Following from this, income shares did not vary much over the 1980 to 2007 period in France.  That is, all groups shared similarly in growth in France.  In contrast, the top 10% in the US enjoyed a disproportionate share of the income growth, leaving the bottom 90% behind.

In 1980 in France, the top 10% received 31% of the income generated in the economy and the bottom 90% received 69%.  With perfect equality, the top 10% would have had 10% and the bottom 90% would have had 90%, but there is no perfect equality.  The US distribution in 1980 was somewhat more unequal than in France, but not by much.  In 1980, the top 10% received 35% of national income, while the bottom 90% received 65%.

This then changed markedly after 1980.  Of the increment in GDP from growth over the 1980 to 2007 period, the top 10% received 36% in France (somewhat above their initial 31% share, but not by that much), while the bottom 90% received 64%.  The pattern in the US was almost exactly the reverse:  The top 10% in the US received fully 62% of the increment in GDP, while the bottom 90% received only 38%.  As a result of this disproportionate share of income growth, the top 10% in the US increased their overall share of national income from 35% in 1980 to 50% in 2007.  Distribution became far more unequal in the US over this period, while in France it did not.

The data continue to 2012 for the US, but the results are the same within roundoff.  That is, the top 10% received 62% again of the increment of GDP between 1980 and 2012 while the bottom 90% only received 38%.  For France the data continue to 2009, but again the results are the same as for 1980 to 2007, within roundoff.

With this deterioration in distribution, the bottom 90% in the US saw their income grow at only half the rate for the economy as a whole.  The top 10% received most (62%) of the growth in GDP over this period.  In France, in contrast, the bottom 90% received close to a proportionate share of the income growth.  For those who make up the first 90%, economic performance and improvement in outcomes were better in France than in the US.  Only the top 10% fared better in the US.

D.  Other Factors Affecting Living Standards:  Social Services and Leisure Time

In absolute terms, even with the faster growth of real incomes of the bottom 90% in France relative to the US over this period, the bottom 90% in France came close to but were still a bit below US income levels in 2007.  They reached 98% of US income levels in that year, and then fell back some (in relative terms) with the start of the 2008 downturn.

But the calculations discussed above were based on applying distributional shares from tax return data to GDP figures.  For income earning comparisons, this is reasonable.  But living standards includes more than cash earnings.  In particular, one should take into account the impact on living standards of social services and leisure time.

Social services include services provided by or through the government, which are distributed to the population either equally or with a higher share going to the poorer elements in society.  An example of a service distributed equally would be health care services.  In France government supported health care services (largely provided via private providers such as doctors and hospitals) are made available to the entire population.  Since individual health care needs are largely similar for all, one would expect that the bottom 90% would receive approximately 90% of the benefit from such services, while the top 10% would receive about 10%.  If anything, the poor might receive a higher share, as their health conditions will on average likely be worse (and might account for why they are poor).  For other social services, such as housing allowances or unemployment compensation, more than 90% will likely accrue to the bottom 90%.

Taking such services into account, the bottom 90% in France will be receiving more than the 67% share of income (in 2007) seen in tax return data.  How much more I cannot calculate as I do not have the data.  The direction of change would be the same in the US.  However, one would expect a much lower impact in the US than in France because social services provided by or through the government are much more limited in the US than in France.  While Medicare provides similar health care as one finds in France, Medicare in the US is limited to those over 65, while government supported health care in France goes to the entire population.  And the social safety net, focussed on the poor and middle classes, is much more limited in the US than in France.

In addition, economists recognize that GDP per capita is a only crude measure of living standards as it does not take into account how many hours each individual must work to obtain that income.  Your living standard is higher if you can earn the same income but work fewer hours as someone else to receive that income, as the remaining time can be spent on leisure.  And there is nothing irrational to choose to work 10% fewer hours a year, say, even though your annual income would then be 10% less.  The work / leisure tradeoff is a choice to be made.

GDP per capita may often be the best measure available due to lack of data on working hours, but for the US and France such data are available (and are provided in the TED database referred to previously).  One can then calculate GDP per hour of work instead of GDP per capita, both overall and (using the same distributional data as above) for the bottom 90%.  The resulting graph for 1980 to 2012 is as follows:

France vs US, 1980-2012, GDP per hour overall and of bottom 90% (Autosaved)

By this measure, overall GDP per hour of work in France was similar to that of the US in the 1990s, but somewhat less before and after.  Overall GDP per capita was always higher in the US over this full period (the top graph in this post), and by a substantial 20% (in 1980) to 38% (in 2012).  Yet GDP per hour worked never varied by so much, and indeed in some years was slightly higher in France than in the US.

But for the bottom 90%, income received per hour of work has been far better in France than in the US since 1983.  By 2007, GDP per hour worked was 30% higher in France than in the US for the bottom 90%.  This is not a small difference.  French workers are productive, and take part of their higher productivity per hour in more annual leisure time than their US counterparts do.

E.  Summary and Conclusions

The French economic record has been much criticized by conservative media and politicians in the US, with France seen as a stagnant, socialist, state.  Overall GDP per capita has indeed grown faster in recent decades in the US than in France, averaging 2.0% per annum in the US vs. a rate of 1.5% in France.  While such a difference in rates might appear to be small, it compounds over time.

But the picture is quite different if one focusses on the bottom 90%.  This is not a small segment of the population, but rather everyone from the poor up to all but the quite well off.  Growth in average real income of this group was substantially faster in France than in the US since 1980.  While overall growth was faster in the US than in France, most of this income growth went to the top 10% in the US, while the gains were shared more equally in France.

Furthermore, when one takes into account social services, which are more equally distributed than taxable income and which are much more important in France than in the US, as well as leisure time, the real living standards of the bottom 90% have not only grown faster in France, but have substantially surpassed that of the US.

For those other than those fortunate enough to be in the top 10%, living standards are now higher, and have improved by more in recent decades, in France than in the US.

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

An update to this post, looking at the issue from a different perspective, is available here.

This is the first post in a series that I will label “Econ 101”.  Their purpose will be to explain some economic concept that might generally not be clear to many, yet often appears (and often incorrectly) in news reports or other items that readers of this blog might see.  This first Econ 101 post is on how changes in private inventories enter into the National Income and Product (GDP) accounts, where there is often confusion on the contribution of rising or falling inventories to the growth of GDP.

In the most recent (December 22) release by the government of the GDP accounts in the third quarter of 2011, growth in overall GDP was an estimated (and disappointing) 1.8%. But many news reports stated that private inventories fell, and that had these inventories not changed, GDP growth would have been 1.4% points higher, or a more respectable 3.2%.  Yet when one looks at the underlying GDP figures issued by the BEA (the Bureau of Economic Analysis, US Department of Commerce), one sees that the change in private inventories was essentially zero (and in fact was slightly positive).  If inventories did not fall, why did many commentators state that a fall in inventories reduced GDP growth in the quarter?

The confusion arises because while the GDP (Gross Domestic Product) accounts measure the flow of production (how much was produced during some period of time), and the flow of how much was then sold (e.g. for consumption or investment), inventories are a stock, and it is the change in the stock of inventories that enters into the GDP accounts.  GDP is the flow of goods and services produced in the economy, and these goods and services are then sold for various purposes, including private consumption, private fixed investment, government consumption and investment, and exports, with imports also a supply of goods that can be sold.  But goods produced in some period will not necessarily match goods sold in that same period.  The difference is accounted for by either a rise or a fall in inventories.  Hence the change in the stock of inventories, when added to final sales (with imports entering as a negative), will equal total goods and services produced, which is GDP.

From one period to the next, we are normally interested in how much GDP rose or fell in that period compared to the previous one.  And we are interested in seeing how much of that growth in GDP will match up with and can be accounted for by growth of consumption, investment, and other elements of final sales.  These demand components are important, particularly in the economy as it is now.  With high unemployment and production well less than capacity, production of goods and services is driven by the demand for them.  Hence one is looking at the change in consumption or fixed investment or government expenditures from one period to the next.  And as the balancing item between GDP production and final sales, one would now be looking at the change in the change in inventories.

The term “the change in the change in inventories”  is a mouthful, and not often seen in news reports (indeed, I have never seen it used).  But that is what then leads to the confusion.  In the third quarter of 2011 (in the estimates released by the BEA on December 22), the change in private inventories was essentially zero, as noted above.  But there had been some positive growth in private inventories in the second quarter of 2011. Hence, the change in the change in inventories, going from something positive to essentially zero, was negative.  That is, if inventories had continued to increase in the third quarter of 2011 as much as they had in the second quarter, GDP growth would not have been 1.8% but rather would have been 3.2%.  The change in the change in inventories meant GDP growth was 1.4% points less than what it otherwise would have been.

The point can perhaps best be illustrated by some simple numerical examples.  Suppose for some fictitious economy, that GDP (the production of goods and services) is initially 1000 (in, say, billions of dollars), while the total of final sales (for consumption, fixed investment, and so on) is 950.  With production of 1000 and sales of 950, inventories will increase by 50.  Assume the stock of inventories at the start of the period is 500, so the stock will total 550 (50 more) by the end of the period.  The figures are as in this table:

Period 1 Period 2 Change % Change
GDP 1000 1050 +50 5%
  Change in Inventories  50  80 +30 3.0% points
  Final Sales 950 970 +20 2.0% points
Stock of Inventories:
    Start 500 550
    End 550 630
In the second period, suppose that production (GDP) increases by 50, or 5%, to 1050, while final sales only grow by 20, to 970.  The difference between production and sales must accumulate in inventories, so the change in inventories will now be 80.  Therefore, the change in the change in inventories will be 30 ( =80-50), and the contributions to the 5% growth in GDP will be 2.0% points from the change in final sales, and 3.0% points from the change in the change in inventories.  It is also worth noting that the stock of inventories has now grown to 630 by the end of the second period, which is substantially higher as a share of GDP or of final sales than it was at the start of period 1.  Hence, there is reason to assume that producers will likely scale back production (GDP) in the near future as long as final sales growth remains so sluggish, as there is likely little reason to accumulate even more unsold inventories on the shelves.
The second example will illustrate the case where inventories continue to rise, but at a slower pace than in the first period:
Period 1 Period 2 Change % Change
GDP 1000 990 -10 -1%
  Change in Inventories  50  20 -30 -3.0% points
  Final Sales 950 970 +20 +2.0% points
Stock of Inventories:
    Start 500 550
    End 550 570
In this example, final sales still grows by 20 to 970.  But producers here have scaled back production to just 990, or 1% below what it had been, with inventories now growing by just 20 rather than the 80 of the first example.  The change in inventories is still positive (at +20), but the change in the change in inventories is now negative, at -30.  The contributions to the -1% growth in GDP growth is made up of +2.0% points from final sales, and -3.0% points from the change in the change in private inventories.
As a final example, we will look at a case where the change in private inventories is negative.
Period 1 Period 2 Change % Change
GDP 1000 1050 +50 5%
  Change in Inventories -50 -20 +30 +3.0% points
  Final Sales 1050 1070 +20 +2.0% points
Stock of Inventories:
    Start 500 450
    End 450 430
Final sales once again grows by 20, although now from 1050 to 1070.  Sales is greater than production in each period, and inventories are drawn down by 50 in the first period and by 20 in the second period.  But while the change in inventories is negative in each period, that change is less negative in the second period than it is in the first.  That is, the change in the change in inventories is a positive 30, and this accounts for 3.0% points of the 5% growth in GDP.  It is also valuable to note that with inventories falling in each period, the total stock of inventories by the end of the second period is getting fairly low, so it is reasonable to expect that producers will aim to replenish inventories in future periods, with this then acting as a spur to growth.
Such swings in inventories are often important when economic growth is turning around, as at the start of a recovery from a downturn, or at the start of a downturn following a boom.  An example is seen at the end of the most recent recession, in the middle of 2009. The economy was in a state of collapse in 2008, the last year of the Bush Administration, and this fall carried over into the first half of 2009.  This downturn was then halted and reversed as a result of the policies implemented at the start of the Obama Administration. GDP was falling at a huge 8.9% annual rate in the last quarter of 2008, and at a still very high 6.7% rate in the first quarter of 2009.  Growth was then still negative, but at only a 0.7% rate, in the second quarter of 2009, and then started to grow at a 1.7% rate in the third quarter, and at a 3.8% rate in the fourth quarter.
The change in private inventories was negative in each quarter throughout this period. Specifically, private inventories fell by $200.5 billion in the second quarter of 2009, fell again by $197.1 billion in the third quarter, and fell again by a further $66.1 billion in the fourth quarter.  But the change in the change in private inventories was positive in the third and fourth quarters (while negative in each, they were becoming less negative), and this then accounted for a positive 0.2% points of the 1.7% growth in GDP in the third quarter, and a strong 3.9% points of the 3.8% growth in the fourth quarter (when final sales in fact declined slightly, accounting for a -0.1% contribution to growth in that period).
To summarize:  As everyone knows from their first Econ 101 class in Macroeconomics, GDP is equal to Consumption + Investment + Government Spending + Net Exports (Exports minus Imports), where total Investment is equal to Fixed Investment plus the Change in Inventories.  The change in GDP will therefore equal the change in Consumption + the change in Investment + the change in Government Spending + the change in Net Exports, where the change in Investment will equal the change in Fixed Investment plus the change in the Change in Inventories.