Category Archives: Econ 101

An Increase in Government Spending Can Reduce the Debt to GDP Ratio: Econ 101

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Most people realize that it is not the absolute value of the government debt that matters, but rather the ratio of that debt to GDP.  A larger economy can support a larger debt.  But most people will also think instinctively that an increase in government spending will necessarily lead to an increase in the government debt to GDP ratio.  It is not surprising that they should think so.  But it is wrong.

Whether the government debt to GDP ratio will rise or will fall when government spending increases will depend on economic conditions and other structural factors.  In conditions of high unemployment and where the Central Bank has driven the interest rates it can control essentially to zero, such as exist now in the US and Europe, an increase in government spending will increase the demand for goods and services, and hence will increase the demand for labor to produce those goods and services.

Employment and output will then rise. How much they will rise will depend on the multiplier, but as was discussed in a previous Econ 101 post on this site, in conditions of high unemployment and close to zero Central Bank controlled interest rates such as currently exist, the multiplier will be relatively high.  The higher incomes that then follow from the higher employment and output will also then lead to higher tax revenues, as a share of the higher incomes will be paid in taxes.

Hence the addition to the deficit and thus the public debt will be less than simply the increase in government spending, due to the higher tax revenues.  With GDP higher due to the greater demand and with the debt also possibly higher but not by as much, the debt to GDP ratio could fall.  And indeed, under conditions such as currently exist in the US and Europe, the debt ratio will almost certainly fall.

To see this, one can start with a simple numerical example.  Suppose one starts with a GDP equal to 100 units (it could be $100 billion), a public debt of 50 (or 50% of GDP, roughly where it was in the US in 2009), a multiplier equal to 2.0 (a reasonable estimate for the US in recent years), and a marginal tax rate on additional income of 30% (also a reasonable estimate for what it is for US federal government level revenues; it would be higher if one included state and local government revenues).

In these conditions, suppose government spending rises by 1 unit.  With a multiplier of two, GDP will then rise by 2 units.  Tax revenues will then rise by 0.6 units, when the marginal tax rate is 30% on the additional 2 units of GDP.  The government deficit, and hence the public debt, will rise by 0.4 units, equal to the extra 1 unit of government spending less the 0.6 units of additional tax revenue.  The resulting public debt will be 50.4, while GDP will then be 102, and the ratio of 50.4/102 is equal to 0.494.  Hence the debt ratio fell from 50% to 49.4% when government spending rose by 1.  Higher government spending led to a reduction in the debt to GDP ratio.  While the total debt rose, GDP rose by proportionately more, leading to a fall in the debt to GDP ratio.

Further numerical examples will help give a feel to what is going on:

Impact on Debt/GDP Ratio from a One Unit Increase in Government Spending
        Scenario: (a) (b) (c) (d) (e)
GDP: Y 100 100 100 100 100
Public Debt: D 50 70 30 50 50
multiplier: m 2.0 2.0 2.0 0.5 3.5
marginal tax rate: t 0.3 0.3 0.3 0.3 0.3
pre-change D/Y 0.500 0.700 0.300 0.500 0.500
Change in G 1 1 1 1 1
Change in Y 2 2 2 0.5 3.5
Change in D 0.4 0.4 0.4 0.85 -0.05
Resulting D/Y 0.494 0.690 0.298 0.506 0.483

Scenario (a) is the case just discussed.  With an initial public debt ratio of 50%, a multiplier of 2, and a marginal tax rate of 30%, a unit increase in government spending will lead the debt to GDP ratio to fall to 49.4%.  This is robust to different initial debt to GDP ratios:  The debt to GDP ratio will fall with higher government spending with an initial debt ratio of 70% (scenario (b), with the debt ratio where it was in FY2012) or at 30% (scenario (c), almost what the debt ratio had fallen to at the end of the Clinton administration, before the Bush tax cuts).

Under conditions where the economy is close to full employment, so that the multiplier will be relatively small, the debt ratio could rise with the higher government spending.  GDP will not rise by much, if at all, if the economy is already producing at or close to full employment levels.  The denominator in the ratio hence will not rise by much, if at all, while the numerator (the level of debt) will rise by the level of extra government spending, with only limited or no extra tax revenues to offset this since GDP has not increased by much.   Scenario (d) provides an example, with a multiplier of 0.5.  The debt ratio will rise from 50% to 50.6% in this example, when government spending rises by 1.

At the other extreme, a very high multiplier may lead to such a large increase in GDP that the extra tax revenues thus generated are greater than the increase in government spending, leading to an actual decrease in the deficit and hence the debt.  Scenario (e) presents an example, with a multiplier of 3.5.  Debt actually falls from 50 units to 49.95 units, despite the increase in government spending by 1 unit, and the debt to GDP ratio falls from 50% to 48.3%.

One will also get this result if the extra tax revenues generated for a given increase in GDP is sufficiently high.  The above examples assume a marginal tax rate of 30%.  More generally, if the marginal tax rate times the multiplier is greater than one (e.g. 30% times 3.5 = 1.05 in the example above), then the absolute value of the debt will fall with the higher government spending.

It may well be unlikely, however, that the multiplier will be as high as 3.5, even with the current high unemployment in the US and Europe.  Thus it is unlikely that the absolute value of the debt will fall with higher government spending, even in conditions of high unemployment.  But as was discussed above, with a reasonable estimate of the multiplier at around 2, one will see the debt to GDP ratio fall, under conditions such as now exist in the US and Europe.

For those with some mathematical expertise, it is straightforward to derive the specific conditions which will determine whether the debt to GDP ratio will rise or fall with an increase in government spending.  This requires some elementary differential calculus, and I will not go through the derivation here.  But the final result is that the debt to GDP ratio will fall if:

(t + D/Y) – (1/m) > 0

and the debt ratio will fall if the sum on the left is less than zero.  That is, the debt to GDP ratio will fall if the marginal tax rate (t), plus the initial debt to GDP ratio (D/Y), minus the inverse of the multiplier (m), is greater than zero (and will rise if the sum is less than zero). Thus if t=30%, D/Y=50%, and m=2 (so 1/m=0.5), with a sum then of 0.3 + 0.5 – 0.5 = 0.3, which is greater than zero, the debt to GDP ratio will fall.

The material above is straightforward.  There is nothing deep or complex.  It also just examines the immediate impact on the public debt to GDP ratio from an increase in government spending.  For a more elaborate look at the long-term impact, see the paper of Brad DeLong and Larry Summers published in 2012.  They show there that higher government spending will not only spur GDP in the short run under conditions such as exist now, but also that such spending will likely pay for itself in the long run through its long term positive impact on growth.

But this post simply focuses on the short term, and shows that counter to what many people might at first believe, higher government spending can lead to a fall in the public debt to GDP ratio.  All this result requires is the recognition that under conditions such as exist now, when unemployment is high and Central Bank controlled interest rates are close to zero, there will be a significant multiplier effect from an increase in government spending.  The resulting increase in GDP along with the extra tax revenues thus generated could very well then lead to a fall in the debt to GDP ratio.  Indeed, with the conditions and parameters such as now exist in the US and Europe, one should expect this result.

The Fiscal Multiplier: Econ 101

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A.  Introduction

The “fiscal multiplier” (often referred to as just the “multiplier”) is simply the ratio of how much aggregate GDP will increase for a unit increase of fiscal spending.  Hence if fiscal spending increases by say $100 and aggregate GDP increases by $200 in response, the multiplier is equal to 2.  The concept is also often applied similarly to tax cuts of some dollar amount.

Under conditions where there is significant unemployment in an economy, an increase in government spending can be expected to have a multiple impact on GDP.  There will be a direct contribution to GDP from the increased production to provide for the demand from government, but also an indirect contribution as those being paid for the initial goods (whether newly employed workers or suppliers of inputs to the production of the good) will in turn spend at least some portion of their higher incomes on other goods or services in turn.  And this process will continue in further rounds.

While the concept is simple, the multiplier in practice is difficult to measure.  It is not a constant, but rather a definitional concept whose value will vary depending on the specific economic circumstances of the time and place.  It has also been controversial, as some economists both historically and even currently do not believe it is possible for an economy to be functioning at less than full employment.  For such economists, higher production from an increase in demand is not possible since the economy is already at full employment, and the multiplier must then always and everywhere be uniquely equal to zero.

But most economists recognize that it is possible for the economy to be at less than full employment.  This is especially clear today in most of the developed world, including in the US, Europe, and Japan, with unemployment high in each of these countries or regions.

The real debate, then, is about the size of the multiplier in a particular situation – whether it is low or high.  If low, then fiscal stimulus will not have much of an effect on increasing GDP, while fiscal austerity will not lead to a big reduction in GDP.  If high in contrast, fiscal stimulus will be quite effective in raising GDP, while fiscal austerity will lead to big reductions in GDP and consequent large increases in unemployment.

Recent work at the IMF, a conservative institution, on the size of the multiplier has brought this debate into the general news.  In particular, in June the IMF published a self-evaluation of the IMF supported (as well as EU and ECB supported) economic program in Greece.  It noted there (on page 21) that the fiscal multipliers assumed in that program turned out, based on actual experience, to have been too low.  This self-criticism was picked up in the general press, and many have questioned how the IMF (and the others) could have gotten this so wrong.

But judging the size of the multiplier in a particular place and in particular circumstances is not easy.  This Econ 101 blog post will discuss why the multiplier will vary in different countries and in different country circumstances.  And while it might be understandable how the multiplier might be misjudged ex ante in some concrete case, what is outrageous is not that initial misjudgment.  What is outrageous is that the policies that had been taken based on that earlier misjudgment were not then revised or reversed to reflect what had been learned.

B.  Why the Multiplier Will Vary

As noted above, the multiplier is not a constant, equal to the some particular value in all countries and under all circumstances.  Rather, it is a concept, expressing a relationship (between changes in GDP and changes in government spending) which will in general vary across different economies and across different circumstances in any particular economy.  Hence even if one had a good estimate of what it might be in one particular country under particular circumstances, one should not assume it would have that some value in another country or even in the same country under different circumstances.

Specifically, one should expect:

1)  The multiplier will vary across countries, depending on the size and structure of those countries:  In a large country such as the US, an increase in spending (both direct and indirect) will be met primarily by supplies originating in the US.  The multiplier will then be relatively large.  In contrast, higher spending in a small and open economy, such as Monaco to take an extreme example, will be met primarily by supplies originating elsewhere.  The multiplier will then be relatively small.   Most economies are in between these two in size, and one would expect the multiplier then also to be in between these two in size.

Note that this will depend not only on the size of the economy, but also its economic structure (the type of goods produced within that economy, as opposed to imported) and the nature of its trade regime.  Some economies are more open than others.

2)  The multiplier will vary depending on the current state of the economy – how far or close the economy is to full employment:  If unemployment is significant, an increase in demand can be met with an increased supply of goods, and an increase in employment of workers to produce those goods.  The multiplier will be relatively high.  In contrast, if the economy is at a time of close to full employment, an increase in demand for certain goods can only be met by reduced production of something else (with a shift in jobs from the latter to the former), so overall output might not rise by much.  In such circumstances the multiplier will be relatively low.

Hence if one had a good estimate of the multiplier in some particular economy at a point in time when the economy was close to full employment, one would greatly underestimate what the multiplier would be in that same economy at a different time when unemployment was high.

3)  The multiplier will vary depending on the form of the fiscal stimulus:  Fiscal stimulus programs can take the form of spending on newly produced goods (such as infrastructure), or on transfer programs to households (such as higher or extended unemployment benefits), or on tax cuts or tax rebates.  But while each might have a similar direct dollar impact on the fiscal deficit, the impact on GDP could vary widely.

Direct government expenditures on newly produced goods, such as new roads or school buildings, will likely have the largest impact on GDP.  The newly produced goods will, with certainty, be produced, and such product is a direct component of GDP (GDP stands for Gross Domestic Product).  And those newly employed to produce such goods (e.g. construction workers) will also then spend most or even all of their new earnings on goods they need.  The multiplier will be high.

The multiplier will also likely be relatively high on transfer programs that go to the unemployed and others who are relatively disadvantaged, as they will spend what they receive on goods that they and their family very much need. The multiplier will be less on transfer programs that benefit those who are better off (such as certain farm subsidies, for example, when they mostly benefit large and relatively well-off corporate farms), as such individuals or firms will likely save a higher share of such receipts.

And the multiplier might be quite small for tax cuts or tax rebates that go to upper income households, as they will likely save much of what they receive.

Hence the size of the multiplier will depend on the nature of the fiscal stimulus program.  Programs focussed on the direct production of goods, especially labor-intensive goods (such as the building and maintenance of much of infrastructure), or on transfers to the relatively less well off, can be expected to have a relatively high multiplier effect.  Programs focussed on transfers or subsidies going to the relatively well off, or tax cuts that accrue primarily to the relatively well off, can be expected to have a relatively low multiplier effect.

4)  The multiplier will vary depending on whether the stimulus (or austerity) programs are temporary or expected to be sustained:   Temporary tax cuts or tax rebates are a common component of stimulus programs, in part because they can be implemented quickly and easily.  However, households receiving a temporary tax cut or a one-time rebate will normally simply save a high share of what is distributed to them (or use the funds to pay down outstanding debt they might have).  The multiplier will then be relatively low or even negligible, as there would be little increased demand for goods to be produced.

5)  The multiplier will vary depending on the direction of change:  Many make the simplistic assumption that if the multiplier has some value for an increase in spending or for a tax cut, one will see the same value for the multiplier for a decrease in spending or a tax increase.  But there is no reason to assume this will be the case.  People will in general respond differently if facing an increase in income (such as from a tax cut) or a decrease (such as from an equal tax increase).  With a tax cut, the households might simply save most of what they receive, resulting in a low multiplier.  But with a tax increase (which one might see as part of an austerity program, for example), the households might be forced to scale back their consumption to pay the higher taxes, resulting in a relatively high multiplier when going in this downward direction.

Similarly, the multiplier impact when a worker is newly hired as a result of a stimulus program will likely be different than the multiplier impact when a worker is laid off as a result of an austerity program.  The multiplier impact is likely to be substantially greater (in the negative direction) when workers are laid off as such workers will likely be forced to scale back their consumption substantially.

6)  The multiplier will vary depending on the policy response of others:   While the government might launch a stimulus program, other economic actors might respond with policy changes of their own.  For example, a Central Bank might raise interest rates when the government launches a stimulus program, due perhaps to a concern on inflation (possibly a mis-guided concern, but nonetheless what they are acting on).  Raising interest rates would lead to a cut in investment, and hence the impact of the stimulus program on GDP might be constrained.  The multiplier would then be low.

Importantly, the ability of the Central Bank to respond by lowering interest rates to a cut-back in government spending, to offset what would otherwise be the contractionary effects of such a cut-back, is important to recognize and take into account.  In times like the present in the US, Europe, and Japan, when the interest rates set by the Central Bank are essentially at zero and cannot go lower, a cut-back in government spending cannot be offset by a cut in interest rates (interest rates are already as low as they can go), and the multiplier will be relatively high.  The fiscal contraction will lead to a large reduction in GDP.  In contrast, if the fiscal contraction is delayed until the economy is closer to full employment, with interest rates then positive and significant, the impact on GDP of a cut-back in government spending can be offset at that point by the Central Bank lowering interest rates, and output will not then fall.  The multiplier will at that point be close to zero.

This has extremely important implications for the design of fiscal adjustment programs.  There may well be a need eventually to reduce public debt to GDP ratios, by cutting back on government spending or increasing taxes.  But if this is done when there is significant unemployment and the Central Bank controlled interest rates are at or close to the zero lower bound, then the fiscal austerity programs will reduce demand and lead to a large fall in GDP (and consequent further rise in unemployment).  One should instead maintain fiscal demand until the economy has recovered sufficiently that one is close to full employment and interest rates are no longer at or close to zero.  At that point, a cut-back in government spending (or an increase in taxes) can be offset by the Central Bank through its management of interest rates, and GDP need not then fall.

Unfortunately, the US, Europe, and until recently Japan, have been doing the opposite since 2010.

The financial markets are another economic actor which can have an impact.  For example, in economies where the foreign exchange rate floats, the foreign exchange markets might respond to a stimulus program with a devaluation of the foreign exchange rate.  This devaluation would make exports more competitive (thus spurring production of exports), and imports more expensive (thus encouraging production of domestic substitutes for what had been imported), which would be expansionary.  The multiplier in such circumstances would then be relatively high.

7)  The multiplier will vary depending on the time frame:  So far we have not made any note of the time dimension, and have implicitly treated all the responses as taking place simultaneously.  But the time dimension does matter, as it takes time to implement programs, and then time for the multiple round responses to work themselves out.  Hence one should be clear on whether one is referring to the multiplier as the response in, say, the current quarter of a year, or over the next year, or over the next several years, or what.  The multiplier will be relatively low if measured as the impact on GDP in the current quarter, fairly large over the next year, and then begin to diminish thereafter.  And one then needs to be clear if one is referring to the multiplier in terms of the impact on GDP only within a certain period, or the cumulative impacts over a multi-year range.

C.  Conclusion

The multiplier is important, and a good deal of work has been done over the years to try to measure what it might have been in a particular time and place.  But factors such as those listed above have not always been taken into account when economists (including at the IMF) and analysts have sought to apply those results.

It has unfortunately been the case, for example, that estimates of the multiplier found when the economy was close to full employment, were then assumed to be similar when the economies at some later time were in a downturn and far from full employment.  Or cross-country differences have been ignored when the multiplier found for some small economy, say, was assumed to apply equally to a large economy.  Or the multiplier that might apply in an expansion resulting from a stimulus program was then assumed to apply similarly in a contraction resulting from an austerity program.  Or no attention was paid to how the multiplier will differ in a stimulus program depending on whether one is looking at new infrastructure work, or transfer programs, or tax cuts.  Or the multiplier for tax cut programs was treated as the same whether the tax cuts were going to the relatively poor or the relatively rich.

This has not always been the case.  Some economists and analysts have been careful.  But there has also been a lack of attention to these issues.  This does not mean one should ignore the multiplier, but rather that one needs to work with care.

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

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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.
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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.
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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.
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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).
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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.
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