Robert Barro says we double-count investment

Here is the VoxEu piece, excerpt:

Gross or net product includes gross or net investment when it occurs, and includes the corresponding present value a second time when additional rental income results from the enhanced stock of capital. Thus, from the standpoint of the intertemporal budget constraint for consumption, aggregates such as GDP and national income overstate the resources available for consumption.

I quantify the double-counting problem within a standard model used by economists, the steady state of the neoclassical growth model (Barro 2019). With reasonable parameters, GDP overstates the potential for consumption by 28%, while national income exaggerates this potential by 9%. Thus, for example, in international comparisons, countries that invest and save larger fractions of their incomes artificially appear to be too rich when gauged by per capita GDP.

And:

Using typical parameter values, the capital income share based on GDP is around 40%. With the conventional adjustment to allow for depreciation, the computed capital income share for national income is reduced to 24%. With the additional adjustment to calculate permanent income, the share falls further, to 16%. Hence, the proper accounting treatment of investment makes a major difference in calculating the division of aggregate income between capital and labour.

I wish I knew this area of national accounting better than I do — opinions?

Here is the full NBER working paper.  All via Ilya Novak.

Comments

The key quote is "Starting from GDP, net domestic product... is computed in a standard way by subtracting estimated depreciation flows." In other words, he wants to count capital deprecation as negative production, to more closely approximate the net value flow.

A logical extension of this would be to price in the whole 'broken window' fallacy and subtract all forms of property damage.

If we're talking about double counting and GDP in general, we should deduct the portion of government spending that is reclaimed from the recipient as taxes. The government effectively gets a discount compared to all other buyers; why should GDP be credited as though they paid the full price?

Would routine maintenance also be a broken window fallacy?

Does health care, massages, retail therapy, etc all consist of broken windows?

Food?

I'm not mocking your idea, just trying to understand it better and logical extensions. I've often said that GDP accounting is the Income Statement but the nation lacks a balance sheet. If government replaces a bridge prior to the end of its useful life in order to provide short term employment gains, it will have intentionally destroyed prodictive assets on its balance sheet, a form of dissaving. My point is not that we shouldnt replace the bridge early, but the cost benefit analysis is skewed if we ignore balance sheet effects and focus only on employment income.

May be don't replace the bridge early. If people are paid to enjoy leisure, at least some leisure is enjoyed. Replacing a bridge early means we pay for the destruction of some of the useful life of the bridge and at the same time the toiling of workers.

Upon having settled the matter that leisure is better than the alternative, find an alternative better than paying for leisure.

Wait a minute... VOX?!? Seriously, VOX ! Does anyone believe VOX?

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Not replacing the bridge early is a no brainer in ordinary times. I'm positing a recession where government spending would alleviate unemployment.

I know. In a recession paying for leisure is better than replacing a bridge early. In a recession paying for a tax cut might be better than paying for leisure and if you don't agree there may be alternatives.

Taxes are oppressive. Tax cuts reduce that oppression and give greater returns even to the tax man. The problem is not low taxes but high spending.

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As long as the rich are getting richer, all is right with the world.

B-B loves us all.

Rich people aren't the only ones who invest.

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I haven't read this piece yet, but the excerpts are reminiscent of the work by Basu, Pascali, Schiantarelli and Sérven, who argue that to measure welfare, we should look at TFP growth as that subtracts off from GDP the things not related to consumption and adjusts for the disutility of labor. In a similar vein, Jones and Klenow (AER, 2016) also focus on consumption as part of their "beyond GDP" framework, rather than GDP. But this new work seems to take the argument in further directions.

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The algebra is fine as it is, but I take strong issue with the idea that GDP "mismeasures" something. As any decent intro macro course will tells its students, "GDP is not a measure of welfare." Indeed, the Kuznets quotes that Barro points to are exactly of this nature; we have this high profile GDP number, but it doesn't do what you want it to do - or at least not ALL the things you want it to.

What Barro does here is construct a new measure - present discounted value of consumption - and shown how it relates to GDP (and GDP's present discounted value). In addition, he provides a capital income / labor income decomposition for both measures (GDP having such an exact decomposition because of constant returns to scale, Euler's identity for homogenous functions, and marginal-value input prices). He then says present discounted value of consumption, and its associated decompositions, are "right" while the other the construction GDP is "wrong" and thus gives "misstated" decompositions. Of course, "right/wrong" and "correct/incorrect" begs the question - right about WHAT? Correct for WHAT?

Barro says that in present discounted value terms GDP "double counts" investment. The "double counting" is only relative to how things are calculated for the present discounted value of consumption. This just reflects the fact that GDP counts production, while consumption only counts consumption. Market clearing, saving, and no storage imply that in every period consumption will be less than production. Specifically, looking at present values, future consumption in part reflects past savings i.e. past investments. GDP counts the production from the investment part (e.g. making the car) and the consumption part (e.g. driving the car), while consumption only counts the consumption part. If what you're after is welfare - sure only count consumption. If what you're after is production, well then you count production. Absolutely, GDP is higher than consumption. All Barro has done is given a more precise statement of how much bigger, in a PDV sense, GDP will be than consumption.

Noting that the "capital" share of GDP and the "capital" share of consumption are different is more word games. Indeed, assigning similar names to decompositions of different constructs is completely arbitrary. Barro doesn't explain why the "capital share" of one thing is more important than the "capital share" of some other thing. In practice, we care about the "capital share" because it tells us something about the structure of the economy - i.e. with Cobb Douglas the capital share of GDP is used to calibrate the alpha parameter. Skimming the paper, its not immediately obvious what the structural parameter linked to the "capital share" of PDV consumption is, but I wouldn't be surprised if its just alpha/2. Ok, the "capital share" of something different concept spits out a different number. For an RBC/neoclassical type, not thinking about the structural parameters is an obvious mistake...

More interesting than the LEVEL of any value is how these values change over time, and what this implies for the changing structure of the economy. Barro's attempt to say the level of the capital share is "wrong" misses the point - we aren't after the capital share per say, we're after alpha. And since the two "capital shares" are proportional, a rising GDP capital share is the same as a rising PDV consumption capital share. The mystery continues, just with scaled down numbers...

Thanks for this very good comment. One of Barro's problems, and the economics profession in general, is that they are unable to clearly communicate their ideas.

It would have been better had he not misused "begs the question".

I'm surprised that members of so status-conscious a trade as Economics don't try to get that sort of thing right.

Yes. I cringed at that too.
Also messing up per se.

But otherwise I enjoyed the comment. It certainly sounds plausible and well informed.

Reminds me of Supreme Court opinions where I read the opinion and cheer for the reasoning, then read the dissent and feel the same way.

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Grammatical comments not withstanding (no tense consistency criticism...)

Upon further reflection, Barro's article is really really pointless. As I argued earlier, we already know that consumption is the better measure of "welfare." Well, guess what - we already measure consumption too! And, to boot, when we measure consumption we do exactly what Barro says and use a "full expensing" approach!

For consumer durables, we only record the value of the good when its purchased and do not record any subsequent utility/consumption flow that this purchase may generate. With housing, on the other hand, we put construction/renovation into the Investment component of GDP and record the flow of "housing services" in consumption.

No need for special assumptions or extra modelling. We already have a measure of consumption that does what Barro wants. Maybe we should focus on consumption more than GDP (a point many have already made). Maybe we could do our direct measurement of consumption better (filling in owner occupied housing in super tricky, and how do we value "financial services" separate from realized returns?). Indeed, in the second half of the paper, these ACTUAL measurement issues are discussed (with a focus on how to properly capture investment spending and returns various hard-to-measure types of capital).

Indeed, given the consumption measure we already have, its straightforward to get a PDV for this by assuming a growth rate for consumption (equal to growth of GDP on the balanced growth path) and applying the appropriate discount rates. Again, no adjustments relative to GDP needed...

Next, his "capital share" is a purely accounting statement, and its not clear what it might mean. As other commenters have said, his decomposition mixes up an Income measure and an Expenditure measure.

First, expenditure accounting for GDP gives us:
Y = C + I
Second, income accounting for GDP gives us:
Y = R*K + w*L
and our economic model tells us R = r - delta

In turn, on a balanced growth path, capital growth equals GDP growth, so together with a basic capital accumulation we have
K_t+1 = It + (1-delta)Kt
(1+g)Kt = It + (1-delta)Kt
(delta + g)Kt = It

So combining these three, we have an accounting statement:
C = Y - I
= (r+delta)*K + w*L - (delta+g)K
= (r-g)*K + w*L

Again, this is all fine as far as it goes, what does this equation actually mean? Taken literally, its just "income after investment equals consumption, plugging in the investment that keeps capital on the BGP".

I would say this is purely an accounting equation - two quantities that will definitely add up, given our definitions. Absolutely, R*K is not equal to (r-g)*K. And absolutely R*K/Y is not equal to (r-g)*K/C. But why do I care about one and not the other? What do I learn by comparing these two values? In what sense is one "right" and the other "wrong"? To simply assert that (r-g)*K/C is "right" tells us nothing.

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Yet more evidence that economics fails to be a science. The practitioners can't even count to 2 properly.

I find this very encouraging. At this rate, economics will be a science within a few hundred years.

Half way there already: observe the casual allusion to Euler by abc above.

Hell, he may even know how to pronounce the name.

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If that's the lesson you got from this, you don't understand anything anyone said.

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Okay, let me see if I have the model right.

Nation A spends 100% of its income on almonds (consumption) with a total GDP of 100 billion USD.

Nation B spends 50% of its income on almonds (consumption) and the other 50% on improvements to almond farms (investment), also with a reported 100B GDP.

The theory is that Nation A's GDP reflects a larger actual economy than does Nation B's, because B is "double counting" some resources. Hmm. It's as if A is entirely living off the infrastructure from previous year's investments, since they are consuming twice the almonds as B - without the need to "waste" any GDP on investment.

Did I get that right? That's... really interesting.

As a non-economist but consummate bser - I don't think so; I think the contention is more like, if A and B both have 100B GDP, then because GDP "counts investment twice", potential consumption in B must adjust for this, and if adjusted B would have 66B consumption relative to A's 100B consumption*.

Whether A or B are "wasting" on investment, would be understood by looking at A and B's growth rates - and this could be per capita, per working adult, TFP- relative to the expectation of how much catch-up growth potential they have. (If B has a very high rate of investment, no higher growth rate, then yeah, to a first approximation they are "wasting" on investment, in the absence of further detail about that investment.).

Of course, in reality, investment vs consumption share does not really vary that vastly as in your example (even for countries with very strange shares, like Singapore).

*where "If, as Kuznets argued, the only final goods are consumption goods in various periods, a reasonable requirement for a measure of national product or income is that it accurately reflect, subject to data constraints, the resources available for consumption."

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I commend your attempt at a simplification, but I suspect your contrived example doesn't fully capture the essence of the problem. For example, your calculation of GDP doesn't include the present value of future consumption. Wouldnt that imply that nation B would have a GDP higher than 100?

Or maybe it is I who doesnt understand either the original model or your simplification. Not my area of expertise.

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Another fatal flaw with the present GDP methodology is the possibility that it makes Trump look good. 2Q2019 GDP growth exceeds expectations. Good economic news is problematic for democrats.

Shameless idiocy.

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A cynic might conclude that Barro is playing with the numbers (full expensing of gross investment) in order to reduce the capital-income share (why would he do that?), while tabula rasa might conclude that Barro is rearranging the numbers (full expensing of gross investment) in order to provide a more accurate accounting (an increase in the amount) of consumption, consumption being the best way to gauge the performance of the economy. I'd like to see a rearranging of the numbers in order to more accurately identify the nature of investments as between investments that increase the economy's future output and investments that generate short-term gains via rising asset prices. It's the former that are the best gauge of the economy's potential for growth and prosperity; but in a time of rising asset prices, the latter overstates both the capital share and the economy's potential for growth and prosperity. How does one gauge where the economy is headed if one doesn't accurately know where the economy has been.

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If, as Kuznets argued, the only final goods are consumption goods in various periods, a reasonable requirement for a measure of national product or income is that it accurately reflect, subject to data constraints, the resources available for consumption.
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The consumption goods available during the period, but it is not a conserved quantity. So Barro is dealing with a yield curve extension, the initiation of a new toll road promises gains tomorrow, and production of goods may increase elsewhere via tightening inventory slop. Future productivity can be partially consumed today.So Barro has to estimate that 'partial compensdation'. He has depreciation and permanent income offsetting in an adjustment somewhere. They both are equally uncertain but independent.

My best guess.

It’s the adjustment for depreciation of capital tha gets me. Surely the market price of any capital good is already adjusted for anticipated depreciation, what? So, taking yet another estimate of depreciation out of GNP estimates seems like double counting to me.

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If you take a strict productivity theory of interest view, Barro is right. The returns that come later were always priced into the initial capital value. The Austrian theory of interest treats interest as explained by time preference. Hence it isn't priced into the initial capital value. I think the latter is more consistent with every day experience (the idle wealthy can sit back and live off their returns) and would suggest there is no double counting problem.

Is the issue a divergence between accounting value and economic value?

Good question. I think accountants and economists would view the problem as largely the same. The price of capital should equal its discounted present value. The question is, does it? Productivity theorists would say yes. Austrians would say no. In the latter case, there must be some kind of market failure going on. At the most basic level, I think they are disagreeing about what's the correct discount rate.

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As abc writes, the advantages and disadvantages of GDP as a macroeconomic aggregate are very well known and pretty well taught. The G in GDP stands for "gross" meaning that depreciation is not deducted, something we never do for the balance sheet of a firm. The meaning of and reason for this are easily explained to intro macro students in a few minutes.
The main thing we want from GDP is to keep an eye on employment and business cycles and for that GDP is pretty much the best measure. There are plenty of other aggregates out there (including NDP and total consumption) which are useful for other stuff.

You claim that depreciation is never included in the balance sheet of a firm. I'm no accountant, but I necessarily dabble in balance sheets. I'm quite sure that accumulated depreciation is on balance sheets as a contra asset and certainly on the income statement that has a balance sheet implication somewhere.

I agree with your main point that GDP is a measure constructed for a singular purpose: monitoring business cycles.

I'm often challenged by students to explain why our unemployment rate doesnt include discouraged workers, and the natural rate of unemployment doesnt include frictional and structural unemployment. I explain that the measures are designed to convey information about things that monetary and fiscal policy can influence, not things that policy cannot influence.

"depreciation is not deducted, something we never do for the balance sheet of a firm"

they're not saying depreciation is not on the firm balance sheet, they're saying it's deducted on the firm balance sheet (gross pp&e - accumulated depreciation = net pp&e) whereas GDP starts and ends with the gross figure without bothering with depreciation

Thanks for the clarification.

when the big picture evades me i turn to trivial details

Modern info tech depreciates much faster than traditional capital equipment. Consequently, net capital is much smaller than the gross number reported in the GDP accounts. We have to run ever faster just to stay in the same place. This plays a significant role in why productivity growth has slowed in recent decades.

if you want to see more on net investment see Timothy Taylor at:

http://conversableeconomist.blogspot.com/2017/02/declining-us-investment-gross-and-net.html

and Spencer at:
https://talkmarkets.com/content/us-markets/productivity-and-capital-stock-per-
employee?post=123461

In particular look at his chart of the growth of net capital stock and productivity growth.

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"As an example, if a nation chooses to consume less and invest more out of a given current output, today’s permanent income does not change, even though today’s consumption falls."

isn't that precisely the point of investing? you invest to raise future output and thus your permanent income. investing now also creates more activity in the future; he's calling that "double counting" even though it's the raison d'etre of investment.

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Is the point of calculating GDP to enable policymakers and central banks to judge whether the economy is contracting or expanding, whether it needs a boost or restraint, and if a threat such as a recession or inflation looms on the horizon? If so, does expensing gross investment help achieve that goal? Many if not most economists would prefer expensing investment for purposes of tax accounting because it would induce greater investment (by lowering taxes) and with it higher productivity and economic growth. A higher calculation of GDP may well induce firms to increase investment because it would give firms greater confidence in the future. Does expensing investment in calculating GDP give firms more or less confidence?

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The excerpt switches from expenditure accounting to income accounting - this is prima facie cause to believe that Robert Barro has remorselessly driven his logic into bedlam.

The rental 'income' from previously accumulated capital stock - what is the corresponding expenditure term? E.g. owner occupied housing or rent - that's consumption, not previously consumed.

Similarly capital investment this year from an expenditure perspective was probably accounted for as labour income (or depreciation) from an income perspective.

Barro's work probably indicates the need to resuscitate a sophisticated version of the crusonia plant model, and points to the blurred lines between capital vslabour income and consumption vs. investment. But I think there's a serious error in the basic principle of his work.

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Oh dear, this looks like Barro making elementary mistakes. In particular he seems to be confusing stocks and flows. Present values are stocks, while GDP and national income are flows. Furthermore, there is no reason whatsoever to believe that what is spent to build some capital stock equals the present value of the future flows of income it will generate. Indeed there is every reason to believe they do not equal as any intelligent business person will not be building capital stock that s/he does not expect to generate future income flows whose present value does not exceed the cost of building the capital stock.

Anyway, the "cost of building the capital stock" is the investment, which is GDP generating national income today as a flow, while the income it generates in the future is future GDP and income. This is just so trivial.

Oh, and as for depreciation, we already account for that when we distinguish GDP from NDP. Again, this is just extremely trivial. Is Barro going senile?

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A residential building's value gets counted when it is produced. It generates a consumption stream that also gets counted for each year it is occupied. One might argue rather successfully that this is double counting the value of the building, since its consumption benefit is already capitalized. But if one also subtracts depreciation (i.e. use NDP rather than GDP) then I don't think there's any problem, since one now takes into account that the building gets diminished. The problem is not with the accounting treatment, but in that researchers are using GDP when they should be using NDP.

In a reply I made above, I mention that this isn't an issue if we just use the consumption measure of GDP.

Residential structures are counted once in investment (when built) and then again over time when used (rent, including owner-occupied imputed rent, is part of consumption). If you want to use GDP to measure consumption - yes, you're doing it wrong. But if you use consumption to measure consumption, then we're already doing what Barro wants.

Consumption also does the "full expensing" approach if we consider most consumer durables. When you buy a new car, that is counted in GDP at its full purchase price. Subsequently when you use the car, that consumption flow is not measured.

Indeed, in some sense, missing the consumption flow from consumer durables means that we under measure GDP in the same way that we could argue not counting home production also means we mismeasure GDP.

Once you stop thinking about how to turn GDP into something its not, and instead just use the consumption measure we already have, Barro's whole article is seen to be very useless.

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