16 May 2014

More Than You Ever Wanted to Know About Inventory Adjustments in GDP Accounting

Austrian School, Business cycle, Economics, Shameless Self-Promotion 20 Comments

Whether it’s government debt-burdened grandchildren, marginally productive capital, or inventory adjustments in GDP accounting, I don’t rest until I have resolved the issue to my own satisfaction–even if the rest of the world has moved on by that point.

Anyway, drawing on a neat idea from “Transformer” in the comments here, I discuss this issue more at Mises Canada. An excerpt:

So what should our hypothetical analyst think, now that he has decomposed the total GDP growth figures into their final purchase and inventory components? I submit that we could tell any story we want. What matters is not the ex post figures, but what the business owners planned ex ante.

Before I explain what I mean, first ask yourself: Why do businesses carry inventory in the first place? One major reason is that they want to have a buffer in between final demand and production. The owners don’t want to lose potential sales while the factories are churning out additional units. So that desire leads businesses to accumulate inventories. On the other hand, they don’t want to carry too large of an inventory, because that ties up capital which could be earning interest. The actual desired level of inventories are an interplay of these (and possibly other) factors.

What these observations mean is that if a business owner expects sales to pick up in the future, he might intentionally bulk up his inventory. For example, the inventories carried by Halloween costume shops are certainly much higher on October 15 than on November 15. This is why we can’t derive much information from looking at changes in inventory per se.

20 Responses to “More Than You Ever Wanted to Know About Inventory Adjustments in GDP Accounting”

  1. Tel says:

    Might even be worth mentioning economic structure. Because GDP is just a single number, it cannot possibly reveal structure (use any rules for calculating GDP that you like). Consider this example:

    Suppose an economy is showing a steady 2% growth in “Final Spending on goods and services” (i.e. sales), and also showing a steady 2% growth in inventory every year. What would you expect the GDP growth to be here? Hopefully everyone got 2%, but pull out the spreadsheet and check it by all means.

    Now after several years of the above 2% growth in everything, suppose inventory starts to grow at 10% for some reason, and thereafter keeps growing at 10%, but the sales just stay at 2% growth same as before… how does this effect GDP growth? It isn’t easy to have any intuition about the answer here.

    When you try it, you see that the key year where inventory growth went from 2% to 10% shows much higher GDP growth, but every year after that, the GDP is back around 2% (depends on how large the inventory component is compared to the sales component, but with the size of inventory about 5% of the sales you don’t see the trending inventory growth as a significant part of GDP growth. Over a number of years though, the inventory becomes a larger and larger fraction of the economy (pssst wanna buy an empty shopping mall in China).

    If inventory is becoming a larger fraction of the economy, that’s important right? Some significant structural change is happening here… but a steadily growing inventory hardly shows up in the GDP growth.

    Now what happens some years down the track when for whatever reason inventory stops growing at 6% and goes back to growing at 2%? Let’s suppose that total inventory has become 10% of sales by now (yes I know that when you divide inventory by sales you get an answer in time, which is the average time an item sits on the shelf, some people do it the other way around and divide sales by inventory and that’s called “stock turns” but I digress). The one year in which inventory growth went back to normal will show a surprisingly low GDP growth, but after that we see GDP growth is back to 2% like we started with… but the structure of the economy is now different.

    • Bob Murphy says:

      Suppose an economy is showing a steady 2% growth in “Final Spending on goods and services” (i.e. sales), and also showing a steady 2% growth in inventory every year. What would you expect the GDP growth to be here? Hopefully everyone got 2%, but pull out the spreadsheet and check it by all means.

      And I hope you *did* check it, Tel, because the spreadsheet would show you that you were wrong.

      That’s one of my main themes throughout all this stuff: People are using intuition to think in terms of growth of inventory, but actually it’s the growth of *spending on* inventory.

      I.e. if you want perpetual 2% GDP growth, you need spending on final sales to grow at 2%, and spending on inventories (not inventories) to grow at 2%.

      I get your basic point, but I’m just mentioning that your confident setup is actually wrong (and misses one of my major points). This is what’s leading people to say goofy stuff in the press, like saying there’s an inventory bounce when inventories are falling, or that inventories are subtracting 57 basis points from growth when inventories are rising.

      • Bob Murphy says:

        Yikes! Sorry Tel what you were saying is a lot more defensible than my reaction this morning gave it credit for.

        It looks like you are imagining that we start with a certain inventory, then have it start growing at 2% forever. If final sales does the same, then you conclude GDP grows at 2% forever.

        That’s true. But, I thought you were imagining that it was “inventory growth” that contributes to GDP growth, when in fact it’s “growth in inventory growth.”

        It just so happens in your example, that the two are identical.

        So sorry for tut-tutting you….

        • Tel says:

          I think that with any measure of GDP, suppose all parts of the economy are growing at 2% simultaneously and no structural shift is happening then if you don’t get 2% growth in GDP itself something badly is wrong.

          However, now we have settled our arithmetic differences, the interesting bit (see PDF 2a link) is the yellow line and the blue line where a change in the inventory growth rate creates one single year of surprising out of character GDP. I stuck a chart on the end, to clarify what I’m saying here.


          Anyone casually looking at the chart would think something wonderful happened in period 5 and some disaster must have happened in period 13, but other than that, the trend is flat right?

          That’s not surprising with a second derivative, a structural shift does not reflect cleanly into a GDP value because it can’t do. That said, it would tend to have your typical NYT pundit screaming about market failure during period 13, or something.

        • Tel says:

          Last one before bed. I added “Stock Turns” to the table and the chart (representing the structural shift from high rate of inventory turnover, to lower rate). I just gumbied around with the inventory figures to produce something like a smooth curve which might be a realistic structural transition following some continuous process and including some inertia in the system.


          What you can see is that although the structural change happening does have an effect on the GDP figures, in the early stages this appears to be much better growth than the 2% long term trend line. Then around about period 12 you are back onto the long term 2% trend and that structural change is almost (but not quite) complete.

          So just picture yourself sitting in period 12 and trying to explain to Krugman that because of the structural change that already happened, we will be seeing some years of below trend growth, from period 13 to period 18.

    • Bob Murphy says:


      I’m being serious, I think you should actually plug it into Excel; I just did. If you happen to pick period 1’s starting inventory and initial spending on inventory such that the spending on inventory for period 1 is exactly 2% of inventory, then you get perpetual 2% growth in both (a) inventory and (b) spending on inventory.

      But if you make the starting values different, then the growth of inventory is either higher/lower than 2% forever, though it does converge (from either side) to 2%.

  2. not so fast says:

    “2% growth in everything, suppose inventory starts to grow at 10%”

    They use “change in private inventories” to calculate real GDP, not to calculate real GDP growth. So it is the percent change in the change in inventory that contributes to real GDP growth. Calculating how this contributes to real GDP is more complicated than you are describing.

    Usually, they simply take a weighted average to determine how a component contributes to growth. For example, in 2013, consumption contributed 1.37% to growth (table 1.1.2). Consumption was 68.5% of GDP and grew 2% from the preceding period (table 1.1.1). So 68.5% of 2% is 1.37%.

    The percent change in the change in inventory from the preceding period is not reported on table 1.1.1

    In 2013, real GDP grew 1.9%. Change in inventory contributed .16% or 8% of the real growth came from change in inventory. (table 1.1.2)

    In 2012, real change in inventory was 57.6 billion. In 2013, it was 81.5 billion (41% increase) (table 1.1.6)

    In 2012, change in inventory was .4% of GDP. In 2013, it was .6% of GDP (50% increase).

    They are not simply taking a weighted average to figure out how the change in inventory is contributing to growth. Using a weighted average ( 41% x .6%), you would get .24% contribution to real GDP growth. However, they calculate .16% contribution from the change in inventory.

    • Bob Murphy says:

      Thanks, “not so fast.” I actually called the BEA back in 2010 when I was trying to get to the bottom of their reports. I think most people naturally think of it like Tel (and plenty of other analysts), but it’s a derivative higher. And, since that’s not how you do it with the other components (like final sales or government spending), it’s super tricky.

    • Major-Freedom says:

      “For example, in 2013, consumption contributed 1.37% to growth.”

      Yet another cringe inducing facet of contemporary national accounting.

      Consumption does not “contribute” to production. Production contributes to consumption.

    • Tel says:

      If there’s weightings applied then my figures (above) don’t include anything special like that. I’m just applying simple arithmetic: change in inventory is what you finished with less what you started with… and add that change to the GDP.

      I calculate GDP growth as (this year GDP – last year GDP) / last year GDP.

      That would seem to be what happens in this example:


      When I use the same approach to Murphy’s example I get the same GDP growth numbers.

  3. Tel says:

    Speaking of inventory… the words “coordination problem” jump into my head.


  4. Major-Freedom says:

    I don’t mind people reasoning incorrectly from GDP. I don’t mind mistakes in logic.

    What I do mind is when sanctimonious pundits ground their thirst for thuggish behavior on incorrect reasonings from GDP and mistakes in logic. Then I am glad when they are embarrassed by articles such as these.

  5. Tel says:


    I’m not at my best first thing in the morning either, especially after a long week. I really did check with a spreadsheet before posting though, because I know what a disciplined house you run.

  6. Transformer says:

    Thanks for the name check!

    I think the new post describes clearly and accurately how changes in inventory are accounted for in GDP growth numbers. (I think it might have been worth having a “change in inventories” columns explicitly in your charts in the Mises Canada post, just to make it really clear)).

    On the way that the contribution is calculated: I think it may be – (change in change of inventory as a % of total change in GDP) * (% change in GDP). That formula allowed me to come up with the same number (57) as the BEA for last qtrs numbers anyway.

    This is definitely non-intuitive (you can have inventories actually falling in a given period and still contributing most of the GDP growth like in your original example). The best way to think about it in my opinion is to forget about inventory being a stock of goods and just think of “change in an inventory” as a flow (just like net import/exports would be).

    • Transformer says:

      “On the way that the contribution is calculated: I think it may be – (change in change of inventory as a % of total change in GDP) * (% change in GDP). That formula allowed me to come up with the same number (57) as the BEA for last qtrs numbers anyway. ”

      This doesn’t work for qtrs other than the last one !

      Like “just in time” , I can’t see how they calculate inventory change contribution.

  7. Major-Freedom says:

    Mises Canada:

    The real benchmark is to compare actual inventory changes with planned inventory changes–and these are subjective items in the minds of the owners.

    This is exactly right, and we are privileged in being able to speak this truth without having the kind of pressure that comes with having a politically derived income where we must find a scientistic calculation of GDP.

  8. Ken P says:

    These days, most companies use a “Just In Time” approach for their supply chain. There is an analogy of “pulling” goods from the front of the chain instead of “pushing” them from the back.

    To the extent that companies are doing a good job of using demand at late stages to pull inventory through, larger inventories should mean higher expectations of future sales.

    Inventory build could result from numerous scenarios.

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