R&D and benchmark revisions of GDP for Robinson Crusoe

Beginning with the third quarter of this year, the BEA plans to report the U.S. GDP and national income accounts on a new basis. One of the purposes of the change is to better reflect the importance of intellectual capital and technological innovation in the modern economy. These changes are expected to cause the reported value of GDP to be about 3% higher than when calculated under the present system. I have been thinking about how I would explain these changes to an undergraduate economics class, and this is what I came up with.

Robinson Crusoe, as you may have heard, lives by himself on an island, meaning his actions alone comprise the entire economy. To entertain himself (and to serve as a didactic device for students), Rob likes to calculate GDP for his little economy.

Hard Workin’ Rob works as an employee of R.C. Farms, which pays H.W. Rob \$1 for every potato he grows and harvests. In a typical year, he produces 100 potatoes, and earns \$100 in wages. R.C. Farms takes 20 of these potatoes and replants them in strategic locations around the island, a step that will make sure that the economy will have some new potatoes that will be produced next year. R.C. Farms sells the remaining 80 potatoes for \$2 each to Crusoe’s Restaurant. Hard Workin’ Rob (the laborer) does not mind the mark-up because he is also the sole owner of R.C. Farms, and any profit the company makes is also part of his income. Crusoe’s restaurant in turn takes the 80 potatoes it buys and turns them into 240 potato pancakes, which it sells to its customers (well, customer actually) for \$1 each. The restaurant has no costs other than the potatoes– it’s a prepare-it-yourself concept in restaurants that probably works best in a beautiful island setting where everybody wants to keep the accounts very simple.

So the question is, what is the island’s GDP? Clearly it’s not appropriate to add the \$160 in potatoes sold by R.C. Farms to the \$240 in cakes sold by Crusoe’s restaurant, because that would be double counting– those potatoes that R.C. Farms sold to the restaurant were used for no purpose other than to produce cakes. The concept behind GDP is that we want to calculate the market value of all final goods and services sold (in this case, \$240 in cakes), but not count sales of intermediate goods (in this case, not count the 80 potatoes used up in producing those cakes). But what about the 20 potatoes that R.C. Farms replanted rather than sold to Crusoe’s Restaurant?

Suppose first that we decided to treat those 20 replanted potatoes as just another cost of doing business, thinking of them as something that got used up in the process of creating the 240 cakes. If that’s our approach, then we’re all done– the island’s GDP would just be the \$240 in final goods (cakes) that got produced.

Again sticking with that expensing concept for the moment, Rob knows that we’re also supposed to be able to calculate GDP by adding up the income earned by everyone in the economy. So to check his math, he notes that the owner of Crusoe’s Restaurant earned \$80 in profit, the owner of R.C. Farms earned \$60 in profit, and Hard Workin’ Rob (the laborer) earned \$100 in wages, which indeed sums to \$240, which we claimed was the economy’s GDP. By the way, it was the income going to the owners of the firms that gave the restaurant’s customers the funds they needed to buy all those expensive cakes.

But it’s really not reasonable to say that the 20 potatoes replanted by R.C. Farms were used up in the process of making the cakes. In fact, those 20 potatoes weren’t used at all in producing the cakes, and they weren’t even used up, but hopefully will turn into 100 or more new potatoes for next year. The owners of R.C. Farms were enriching themselves by choosing to replant those potatoes, laying the “groundwork”, if you will, for future production and profits. So it seems more appropriate to say that R.C. Farms, and not Crusoe’s Restaurant, was the final user of those 20 potatoes, and that the \$20 the farm paid Hard Workin’ Rob for those potatoes is not an expense of getting potatoes ready to sell to the restaurant, but instead is part of the income of the owners of the farm that they decided to devote to “growing” future profits.

If we value these investment goods at cost, and regard R.C. Farms as the final user of those investment goods, we would calculate the market value of all final goods and services to be \$240 in consumption goods (the cakes) plus \$20 in investment goods (the replanted potatoes) for a total GDP of \$260. Treating capital goods as an investment rather than a current expense thus makes reported GDP higher. From the income side, since the \$20 investment spending is no longer regarded as an expense, we calculate the profits of R.C. Farms as \$80 (the \$160 revenue from sales to the restaurant minus the \$80 cost of those goods). The restaurant still earned \$80 and Hard Workin’ Rob still earned \$100, so GDP from the income side is 80 + 80 + 100 = 260, equal to what we calculated on the product side. Some of the income is now in the form of an imputed benefit the owner of R.C. Farms associates with the firm’s decision to replant potatoes. Under this accounting scheme, the island’s income now exceeds its total consumption spending, with the excess (saving) going to finance the economy’s investment.

After several years of this, Rob realizes he’s not getting anywhere (literally). So he decides to try to experiment with some new ideas to see if he can come up with a better way to do things. Can you get two viable plants if you take a potato and cut it in two before planting? Can you grow them in vessels, or other exotic locations? So, instead of just replanting all 20 potatoes in the usual way, R.C. Farms decides to just replant 15 potatoes, and use the others for experimentation– its R&D budget. Maybe these experiments will produce more potatoes, maybe they won’t– mostly they’ll just help Rob to learn if there’s a better way to do things. The question now is, how should we treat R.C. Farm’s 5-potato R&D budget?

One idea would be to say that R&D is just another expense. From that perspective, the economy’s final goods are \$240 in cakes plus \$15 in investment, for a GDP of \$255. On the income side, since we’re expensing the R&D, the profits of R.C. Farms are only \$75 (\$160 revenue from the restaurant minus \$85 in costs), which combine with \$80 income from the restaurant and \$100 income from the worker for \$255 GDP on the income side.

But the same arguments against expensing investment could be used to say we shouldn’t be expensing R&D, either. The purpose of the R&D was to produce a final good– namely knowledge– and producing this knowledge should directly benefit the owners of the firm. So if we decide instead to treat the R&D as a similar kind of activity as usual investment, we’re led to a view that GDP consists of \$240 worth of cakes, \$15 worth of investment, and \$5 worth of knowledge creation. That new knowledge in turn is going to now be counted as part of the income of the owners of the firm that conducted the R&D.

In other words, changing from expensing R&D (the current U.S. system) to treating R&D as a form of investment (the system that will be in place starting next quarter) would increase the reported GDP from \$255 as calculated under the old system to \$260 as calculated under the new. So on July 1, Rob plans to begin calculating GDP on the new basis, and report himself to be earning \$5 more each year than he used to.

But the truth is Rob won’t actually be any richer when he wakes up on July 1 than when he goes to bed on June 30.

25 thoughts on “R&D and benchmark revisions of GDP for Robinson Crusoe”

1. BenAround

Very clever, entertaining, and logically consistent. Perhaps the entertaining part is the most important part for an audience of undergrads. However, it may be a bit overly complicated. The own-account aspect of the new treatment that requires the output imputation renders the underlying rationale (not your example) less than intuitive.
It might work better to simply point out that business firms sometimes purchase R&D services in the market and that these services will no longer be treated as intermediate inputs but rather will be capitalized and treated as an investment, much the same way that purchased software was capitalized for the first time around 2000. The increase in investment on the product side will be matched by an increase in gross profit on the income side.
The R&D that firms perform on their own behalf (own-account), which is much larger, requires an imputation as it does not represent a market transaction. The only way to capture this activity is to identify and measure the costs associated with it and to then treat these costs as investment, as was previously done with own-account software. However, I think focusing on the own-account aspect distracts from the basic concept that is more intuitively conveyed by the purchased services example.

2. ppcm

Pr Hamilton good introduction and clear understanding of Public accounting and tangible and intangible assets the R&D.
The intangible assets have always been raising problems in the merchant life as testified by the hereunder French medieval story, a cooking story.
« The porters and the cook »
A porter was standing idle at the door of a public kitchen, when comes the cook outraged and calling for a public debate on the alleged crime. The porter is enjoying for free the smell of his tasteful kitchen said the cook. A fool is called as judge and asks on the substance of the prejudice. The cook repeats his complain the porter is stealing, since enjoying the smell of his tasteful cooking. The fool asks for the amount required by the cook as a settlement of the prejudice and the answer comes in currency value of the time 5 soles. The fool then asks the porter to give 5 soles, outraged the porter complies and gives 5 soles to the fool, whom then turns to the cook drops the 5 soles on the ground and says did you hear the sound of the 5 soles? The cook says yes and the fool to conclude « you have been paid »
Indeed the no one gets richer
One may look forward to read the expanded story of R. Crusoe dreaming of setting up his central bank and issuing legal tender money.

3. Ricardo

To an economist GDP should actually be a measure of production in a society and so a real economist would struggle for truth but also consistency. But GDP to a politician is a unit of propaganda. The politician could care less about real economic data concerning production. The politician wants to show that he is improving production even if he is not.
Guess who controls government statistics?
But the truth is Rob won’t actually be any richer when he wakes up on July 1 than when he goes to bed on June 30.
Thank you professor.

4. markg

JDH said “the owner of Crusoe’s Restaurant earned \$80 in profit, the owner of R.C. Farms earned \$60 in profit” and “\$240 in cakes sold by Crusoe’s restaurant”and “By the way, it was the income going to the owners of the firms that gave the restaurant’s customers the funds they needed to buy all those expensive cakes.”
The owners earned \$140, how did they buy \$240 in cakes?
I enjoyed reading the comments in your post defending R&R. More and more readers are realizing you are a clueless hack economist. My advice on teaching these changes to an undergraduate economics class – DON’T!

5. Joseph

I think it is a simple and great explanation of GDP and GDI and the new revision.
How will the revision affect international comparisons like OECD? Will there be a Roger Maris asterisk on the U.S. or will they apply a correction factor? Or will the
How the heck do they compute a number like GDP anyway in the real world and how accurate is that number? It seems that the computation must be fraught with sampling and estimate errors for a number that is reported to the decimal point. I suppose that GDI is somewhat of a cross check on accuracy.

6. 2slugbaits

JDH One of the purposes of the change is to better reflect the importance of intellectual capital and technological innovation in the modern economy.
So does this mean we should expect some differences in what gets picked up under observed multi-factor productivity?

7. Steven Kopits

Well, this being Sunday, I have time to have some problems with this model.
First of all, RC would not reduce his planted potato count by 5. Why? Because the return to each is 5x (100/20). Thus, taking out five would mean his crop would be only 80 if the R&D doesn’t pay off. From this, he’d have to take out 20 to return to his previous level of production.
Thus, the failure of his R&D program would result in a reduction of consumption by 25% (from 80 to 60). He’d be crazy to even try it.
Rather, he’d have to continue to plant his 20 potatoes and reduce his consumption by 5 (from 80 to 75), a reduction of about 6%.
Without economic growth, innovation that requires investment can only come from a reduction in current consumption.
Perhaps there is a Great Stagnation.

8. Steven Kopits

Here’s a second problem. Let assume RC takes 5 potatoes offline for R&D (let’s assume he does this out of consumption).
His R&D is successful, and the next year, his 20 planted potatos produce 110 potatoes, rather than the usual 100. GDP will now be 286 (110% of 260) under the new system. But GDP could not have been both 260 in year 0 and 286 in year 1, because five potatoes were used for research somewhere in there. So either the research needed to be expensed in year 0 or amortized in year 1.
Thus, the impact of R&D on GDP would just be the change in R&D expense, rather than its level.
Can we calculate this with any confidence for the economy?

9. benamery21

Markg:Farm income.
JDH:It might be useful to point out that whereas expensing the planted potatoes subtracted them from GDP in the same year, if they are capitalized, depreciation will subtract them the following year. This makes clearer that RC really isn’t any wealthier unless potato production actually rises.

Or perhaps you could just ask an accounting professor to explain why assets are accounted for differently than expenses are on a financial statement.
I know, asking an econ professor to understanding accounting is like asking a lawyer to understand math.

11. BenAround

2slugbaits: So does this mean we should expect some differences in what gets picked up under observed multi-factor productivity?
Not clear. Nominal output levels will be higher but so will nominal capital services input levels as a result of adding R&D to the capital stock.
MFP is measured as real output growth less real input growth, but the differences in nominal levels will not necessarily translate into differences in real growth rates.

12. JDH

Steven Kopits and benamery21: The example doesn’t state whether the 20 potatoes planted would produce 100 or 500 potatoes next year, and you don’t need to know that to calculate this year’s gross domestic product. However, it is certainly correct that depreciation should be subtracted if your objective was instead to calculate net national product or national income. If you need to plant 20 potatoes in order to produce 100 next year (that is, you have to make that investment just to maintain current production), then depreciation = \$20 per year and net domestic product or national income are just the \$240 in cakes produced.

It’s also true that if the R&D proves to be a waste, then next year’s GDP is going to be lower, because we won’t have as many potatoes being produced. But none of that means that we shouldn’t measure this year’s GDP just as stated above, namely, this year’s GDP is \$260.

13. AS

Professor Hamilton,
Do you think the change in reporting GDP will affect the FASB? Currently the FASB requires expensing of R&D costs. Accountants capitalize assets and try to match the expiration of the usefulness of limited life assets with revenue generated from the assets. It seems that the FASB must consider it too difficult to match R&D expenditures with revenue generated, thus it takes the “conservative” action of expensing R&D costs.

14. Peter N

RC Farms pays Rob \$100 for finding and digging up 100 potatoes which it puts in a warehouse to rot.
GDP = GDI = GDE, S = I = \$100
It’s wrong to confound elements of accounting identities with economic stocks and flows and use the same symbols for each. GDP is neither a stock nor a flow, nor is it the integral of a flow.
S always equals I. It’s impossible to contrive an example where it doesn’t. This implies no mechanism whatsoever.

15. EconStudent

I’ve never understood how double counting doesn’t occur with inputs/inventory/investment.
Lets say Honda has a tire it purchases in 2011 to use in the final product of a car. The car wasn’t produced in 2011 so the tire is reported as investment (inventory) for 2011. If in 2012 the same tire doesn’t get used as a part of thefinal good, is it counted again in 2012 as investment? What if the tire is used in 2012, does the cost of the tire get subtracted from the end product’s 2012 GDP contribution considering it was already counted in 2011?

16. JDH

EconStudent: It is the change in inventories that gets counted as investment. If the tire is produced in 2011 but doesn’t go into making a car, then Honda is regarded as the final 2011 user of that tire. The tire production contributed to 2011 GDP and contributed to 2011 inventory investment (i.e., the inventory went up by 1 tire). Let’s say that same tire sits around in the warehouse all of 2012. It doesn’t count in 2012 GDP (nothing was produced), and it doesn’t count in 2012 investment (there was no change in inventory during 2012). It doesn’t count for anything as long as it’s just sitting there. Let’s say it finally gets used in 2013. Then the inventory change in 2013 was negative (inventories ended up 2013 one tire lower than they started). Investment for 2013 is thus a negative number, meaning that when we add investment to other production, in effect the tire is getting subtracted from 2013 GDP. So it was added to GDP in 2011 and subtracted out in 2013, because it ultimately was an intermediate good. Counting the three years together, there was in effect only one final product (the car) and its production came in 2013.

17. Wisdom Seeker

Hmm… I think this accounting could be made more realistic if we take advantage of the second character in the original Robinson Crusoe story, his Man “Friday”. Crusoe is the capitalist and Friday becomes the labor and a whole lot more can be said about the economics between capital and labor in that context…
Meanwhile, as for this “lets account for investment and intellectual capital in GDP” new-math accounting, I think it’s extremely hokey. But, if we’re going to start “accounting” for intangibles such as “future potato-growing knowledge”, we also ought to consider the value of parents working at home for their families (either as stay-home parents or working after hours at home), and perhaps also account for the negative value of economists and financiers blowing up financial bubbles and inflicting health-degrading stress on the rest of the population… among other things!
And then go back to RFK’s well-written speech on how poor a measure of anything the GDP statistic is. And maybe ask ourselves whether we want to separate facts and opinions in our accounting schemes, and whether we might not be better off with a separate measure of well-being that is independent of accounting altogether.

18. 2slugbaits

BenAround MFP is measured as real output growth less real input growth, but the differences in nominal levels will not necessarily translate into differences in real growth rates.
Thanks, but I’m not sure this is right. And I really mean that I’m not sure. Footnote 18 in the BEA report says this:
The productivity adjustments will be based on nonfarm business multifactor productivity estimates produced by the Bureau of Labor Statistics.
I found the discussion somewhat confusing, so I’m not at all confident here, but it sounds like the multifactor productivity residual will change. The capital stock used in the BLS TPF calculation is based on estimates of fixed capital stock, and nothing in the new calculation would increase labor inputs, so I guess the higher productivity would have to fall into the residual. I’m guess’n.

19. BenAround

2slugbaits The productivity adjustments will be based on nonfarm business multifactor productivity estimates produced by the Bureau of Labor Statistics.
I agree that the discussion is confusing. In the footnote I believe that BEA is explaining how it will adjust the cost-based R&D price index for MFP growth in the production of R&D in order to approximate a true R&D output price index for deflating nominal R&D output. Because no specific data are availble to measure MFP for the R&D activity, BEA will assume that overall nonfarm MFP growth is a good proxy.
I was describing how I think the capitalization of R&D will affect overall nonfarm business MFP growth as measured by BLS. I believe the aggregate effect will be very small but cannot say a priori whether it will be positive or negative because of the variety of factors involved.
I think that BLS will eventually include R&D in the capital stock for the purpose of measuring aggregate MFP growth but that might not happen right away.

I am a bit old fashion and continue to believe that consumption is the sole end and purpose of all production; and the interest of the producer ought to be attended to, only so far as it may be necessary for promoting that of the consumer.
The new system strikes me as being rather supply side-ish and quite in line with the idea of a corporation as a person and able to consume as one. The value of investment, to the extent that it is real not speculative, will eventually show up in consumed product. There really is no good reason to count it as income or wealth ahead of time except to promote it as being of even greater value than it actually is.

21. billj

Repeating the age old confusion of exchange value and use value. In an economy with one person, there is no exchange value, as there is no possible exchange. Hence, there is no value either.

22. JDH

billj: The ratio of marginal utilities for a single consumer can be interpreted as latent relative prices or relative values even in a one-person economy with no exchange. The single person’s optimal plan could always be represented as if it was the outcome of a competitive equilibrium for which the equilibrium relative prices are those ratios of marginal utility.

23. EconStudent

Prof Hamilton:
Thank you, that’s perfectly clear. Your approach (not only in this reply but in this blog and writings in general) to explaining economics is second to none. Thanks again.

24. James Cover

I think this example explains in a simple way what the BEA is doing and why. It can easily be repeated in a farmer, miller, and baker economy that is often used to explain how GDP is related to the sum of all values added. But I do have some comments.
I have not read all of the comments, so forgive me if I am covering ground already covered.
It seems to me that the problem is a failure for the general public to appreciate the difference between gross income and net income. The change in procedure does not affect net income, just gross income. 20 potatoes were used up to produce the 100 potatoes, so net income is the 80 potatoes as well as the value added when producing the other potato-based products.
The saved potatoes, whether they are used to plant next year’s crop or used for research are used, and unless they result in more than 100 potatoes being produced the next year, Rob is not better off the next year than he was the first year. In general we don’t know whether any “investment”–whether in R&D or in planting–makes us better off until we see whether it causes the value of the output of final consumer goods to be higher in the future.
In his criticism of NIPA (back, I think in 1947) Kuznets complained that the goal of economic activity is consumption (as mentioned in a previous comment), so that all expenses used to produce income (such as commuting expenses and clothing bought for work) should not be considered a part of personal consumption expenditures and a part of the final output of goods and services. The expenses I incur when going to work are a cost of production (whether borne by me or by my employer). He also points out that there is some double counting in measuring GDP because government services are often factors of production or take the place of what would be factors of production paid for by the private sector.
Gross domestic product (or better Gross national product) ignores the depreciation of capital. It is not a measure of “income” in any meaningful sense, rather it is a measure of the output of final goods and services unadjusted for the depreciation of capital. This difference can be very important. For example, during and prior to the middle ages (according to Lopez’s “The Commercial Revolution of the middle ages, 950-1350”), it was not uncommon for a farmer to produce 2 grains of wheat for each grain planted. So, if depreciation or working capital used up during the production process is one-half of output, in what sense is GDP a useful measure income? If I use 20 potatoes to produce 100 potatoes, my income is only 80 potatoes. The 20 potatoes were produced last year.

25. Hans

This is nothing more than an accounting gimmick…The US Government, along with it’s cohorts make these changes when it is suitable for them.
R & D is now an investment? Let’s do the same for marketing and advertising because they are similar types of spending…