What Do GDP Growth Curves Really Mean?

by johnswentworth11 min read7th Oct 202151 comments

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Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced in a specific time period. - Wikipedia, GDP

 

Due to inflation, GDP increases and does not actually reflect the true growth in an economy. That is why the GDP must be divided by the inflation rate (raised to the power of units of time in which the rate is measured) to get the growth of the real GDP. - Wikipedia, Real GDP

The two quotes above reflect how I used to think about real GDP growth: it’s roughly the growth in economic production (as measured by dollar worth of outputs), discounted for inflation. This picture turns out to be extremely misleading, especially when using GDP as a growth measure. Forget complaints about how GDP doesn’t measure happiness, or leisure time, or household work, or “the health of our children, the quality of their education or the joy of their play”. Even if we accept the dollar value of goods as a proxy for whatever purpose we have in mind, GDP (as we actually calculate it) is still a wildly misleading measure of growth. In particular, it effectively ignores major technological breakthroughs.

A Puzzle

Here’s real GDP of the US for the last ~70 years, from FRED:

According to this graph, real GDP has grown by roughly a factor of 6 since 1960. That seems… way too low, intuitively. Consider:

  • I’m typing this post on my laptop (which conveniently has a backspace button and everything I type is backed up halfway around the world and I can even insert images trivially)...
  • while listening to spotify…
  • through my noise-canceling earbuds
  • and there’s a smartphone on my desk which can give me detailed road maps and directions anywhere in the US and even most of the world, plus make phone calls…
  • and oh-by-the-way I have an internet connection.

I’d expect the equivalent of any one of these things in 1960 would have cost at least a hundred times the annual income of an average person if it was even possible at all. Just from these five things alone, it seems like real GDP ought to have grown by a factor of hundreds.

… and yet, whatever formula we’re using for real GDP says it's only grown by a factor of 6. What gives? How the heck is real GDP computed that makes it so low? What exactly is it measuring?

Real GDP Is Not Nominal GDP Divided By Inflation

First things first: real GDP is not calculated by dividing nominal GDP by inflation. It’s calculated largely separately from nominal GDP; the textbook approach is to add up the total dollar value of goods (just like for nominal) but at prices from a fixed year. That way, we only count changes in total output resulting from changes in the amounts of goods produced.

An example: we have an economy with two goods, apples and brass.  In year 0, 1 unit of apples costs $1, 1 unit of brass costs $1, and people produce/consume 3 units each of brass and apples. In year 1, an amazing new technique is discovered for brass-production. Brass prices fall by a factor of 10, and people produce/consume five times more brass (15 units). Meanwhile, both price and production/consumption of apples stays roughly the same.

 Apple PriceApple QuantityBrass PriceBrass Quantity
Year 0$1/unit3 units$1/unit3 units
Year 1$1/unit3 units$0.1/unit15 units

Calculations:

  • GDP in year 0 (at year 0 prices): (3 apple-units)*($1/apple-unit) + (3 brass-units)*($1/brass-unit) = $6
  • GDP in year 1 (at year 0 prices): (3 apple-units)*($1/apple-unit) + (15 brass-units)*($1/brass-unit) = $18
  • GDP growth: $18/$6 = 3

This seems pretty reasonable. Indeed, in our puzzle about GDP growth since 1960, I said:

I’d expect the equivalent of any one of these things in 1960 would have cost at least a hundred times the annual income of an average person if it was even possible at all. Just from these five things alone, it seems like real GDP ought to have grown by a factor of hundreds.

That intuition is implicitly a calculation of real GDP at 1960 prices: I’m saying that at 1960 prices, the electronics on my desk would cost a fortune. If everybody now has goods which would cost hundreds of times the typical annual income in 1960, then that implies that real GDP in 1960 prices has grown by at least a factor of hundreds.

… but clearly that’s not how the economists at the BEA actually compute real GDP, since they only calculate a factor-of-6 increase since 1960. So what’s different?

Real GDP Is Calculated At Recent Prices

Real GDP isn’t calculated using prices from 1960 (or 1900, or some other time long ago). It’s calculated using recent prices. Wikipedia again:

… the UNCTAD uses 2005 Constant prices and exchange rates while the FRED uses 2009 constant prices and exchange rates, and recently the World Bank switched from 2005 to 2010 constant prices and exchange rates.

… wait, they switch which year’s prices are used?

Ok, before we get into baseline prices moving, let’s go back to our apples-and-brass example and see what happens if we use “recent” prices (i.e. year-1 prices) rather than “old” prices (i.e. year-0). Here’s the table again:

 Apple PriceApple QuantityBrass PriceBrass Quantity
Year 0$1/unit3 units$1/unit3 units
Year 1$1/unit3 units$0.1/unit15 units

Calculations:

  • Real GDP in year 0 (at year 1 prices): (3 apple-units)*($1/apple-unit) + (3 brass-units)*($0.1/brass-unit) = $3.3
  • Real GDP in year 1 (at year 1 prices): (3 apple-units)*($1/apple-unit) + (15 brass-units)*($0.1/brass-unit) = $4.5
  • Real GDP growth: $4.5/$3.3 = 1.36

… so rather than factor-of-3 growth (i.e. 200% growth), we see factor-of-1.36 (i.e. 36%). What’s going on here?

The key is the drop in price of brass. In year-1 prices, brass costs next-to-nothing. So, when we calculate in year-1 prices, brass has very little weight in real GDP; even a very large increase in brass production contributes a relatively small bump to real GDP. The more brass prices fall, the less brass will contribute to real GDP growth (as calculated in year-1 prices).

More generally: when the price of a good falls a lot, that good is downweighted (proportional to its price drop) in real GDP calculations at end-of-period prices.

… and the way we calculate real GDP in practice is to use prices from a relatively recent year. We even move the reference year forward from time to time, so that it’s always near the end of the period when looking at long-term growth.

Real GDP Mainly Measures The Goods Which Are Revolutionized Least

Now let’s go back to our puzzle about growth since 1960, and electronics in particular.

The cost of a transistor has dropped by a stupidly huge amount since 1960 - I don’t have the data on hand, but let’s be conservative and call it a factor of 10^12 (i.e. a trillion). If we measure in 1960 prices, the transistors on a single modern chip would be worth billions. But instead we measure using recent prices, so the transistors on a single modern chip are worth… about as much as a single modern chip currently costs. And all the world’s transistors in 1960 were worth basically-zero.

1960 real GDP (and 1970 real GDP, and 1980 real GDP, etc) calculated at recent prices is dominated by the things which are expensive today - like real estate, for instance. Things which are cheap today are ignored in hindsight, even if they were a very big deal at the time.

In other words: real GDP growth mostly tracks production of goods which aren’t revolutionized. Goods whose prices drop dramatically are downweighted to near-zero, in hindsight.

When we see slow, mostly-steady real GDP growth curves, that mostly tells us about the slow and steady increase in production of things which haven’t been revolutionized. It tells us approximately-nothing about the huge revolutions in e.g. electronics.

(Disclaimer: Real GDP Is Sometimes Computed Differently)

One word of caution, before we get to the main takeaways: real GDP at fixed (recent-year) prices is not the method used by everyone for every number called “real GDP”. In fact, the real GDP graph at the beginning of this post uses a different method - the BEA (which calculates the “official” US GDP and produced the numbers in that graph) switched from fixed prices to “chaining” in 1996. Appendix 1 of the NIPA Guide has useful details if you’re interested, and these slides give some of the reasoning. The new method is generally messier and less intuitive, but tries to correct for some of the shortcomings of fixed prices.

I played around with it a bit, and I think the qualitative takeaway is basically similar for purposes of thinking about long-term growth and technological progress (e.g. something like Moore’s law). Also, it sounds like fixed prices are still the standard thing in most places, although I haven’t looked into how other sources (like the World Bank or UNCTAD) calculate their real GDP numbers other than to notice that they’re definitely different-from-each-other-but-qualitatively-similar.

I don’t know of anyone who tries to calculate real GDP at prices from long ago. That would create a difficult operationalization problem: how does one estimate the price of e.g. a smartphone in 1960?

Takeaways

Takeaway 1: Making Predictions Based On Historical Real GDP Growth

I sometimes hear arguments invoke the “god of straight lines”: historical real GDP growth has been incredibly smooth, for a long time, despite multiple huge shifts in technology and society. That’s pretty strong evidence that something is making that line very straight, and we should expect it to continue. In particular, I hear this given as an argument around AI takeoff - i.e. we should expect smooth/continuous progress rather than a sudden jump.

Personally, my inside view says a relatively sudden jump is much more likely, but I did consider this sort of outside-view argument to be a pretty strong piece of evidence in the other direction. Now, I think the smoothness of real GDP growth tells us basically-nothing about the smoothness of AI takeoff. Even after a hypothetical massive jump in AI, real GDP would still look smooth, because it would be calculated based on post-jump prices, and it seems pretty likely that there will be something which isn’t revolutionized by AI. At the very least, paintings by the old masters won’t be produced any more easily (though admittedly their prices could still drop pretty hard if there’s no humans around who want them any more). Whatever things don’t get much cheaper are the things which would dominate real GDP curves after a big AI jump.

More generally, the smoothness of real GDP curves does not actually mean that technology progresses smoothly. It just means that we’re constantly updating the calculations, in hindsight, to focus on whatever goods were not revolutionized. On the other hand, smooth real GDP curves do tell us something interesting: even after correcting for population growth, there’s been slow-but-steady growth in production of the goods which haven’t been revolutionized.

Takeaway 2: Stagnation

On the one hand, growth has been way better than you’d think just from looking at real GDP curves. The internet is indeed pretty awesome, and real GDP basically fails to show it. Same with all the other incredible technology in our lives.

On the other hand… Jason Crawford talks about how a century or two ago, we saw incredibly rapid progress in basically every major industry. Over the past 30 years, we’ve seen incredibly rapid progress in basically one industry: information technology. That, he argues, is the sense in which progress has slowed.

To the extent that real GDP mostly shows growth in the things which aren’t revolutionized, we’d expect it to capture this kind of stagnation pretty well. We’re saying that in the “old days”, basically everything saw rapid progress, so real GDP should have seen rapid growth. Consider housing, for instance: between roughly the 1830’s and the 1960’s we saw the rise of balloon framing, standardization of lumber (e.g. the 2x4), plywood, platform framing, indoor plumbing, etc. This was the era known for bringing the “American dream of homeownership” within reach for most of the working class. It’s not one of the great industrial-era revolutions we hear much about, but economically speaking, housing technology advances were a big deal.

More recently, growth was mostly in information technology, so we should see slower GDP growth. In housing, for instance, the vast majority of new homes still use basically-the-same methods as houses from the second half of the 20th century: concrete foundation, platform frame, plywood, shingles, sheetrock, etc. And indeed, real GDP growth has been noticeably slower over the past 20 years. (Intuitively it seems like growth has been mostly in information technology for ~30-40 years rather than just 20, but with the “chaining” calculation method dramatic one-sector growth does produce pretty good real GDP growth for a few years before prices drop enough that it’s downweighted.)

Annual real GDP growth - note that's it's noticeably lower since ~2000.

UPDATE (Oct 14)

Based on the comments, I want to highlight that calculating GDP at e.g. 1960 prices would still not be a good proxy for implied-utility-growth or anything like that, any more than GDP at recent prices is. Price is just generally not a great proxy for value; as maximkazhenkov says in the comments "GDP is more of a measure of economic activity than value". I do think GDP at 1960 prices is basically the right GDP-esque metric to look at to get an idea of "how crazy we should expect the future to look", from the perspective of someone today. After all, GDP at 1960 prices tells us how crazy today looks from the perspective of someone in the 1960's. Also, "GDP (as it's actually calculated) measures production growth in the least-revolutionized goods" still seems like basically the right intuitive model over long times and large changes, and the "takeaways" in the post still seem correct.

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I.

Great post, but chaining merits more than just a disclaimer here. After all, it was introduced to deal with some of the issues your post discusses.

I highly recommend reading this 1995 article explaining the introduction of the chain-weighting approach. It's short, accessible, and has several simple concrete examples.

A few excerpts:

A major fault with [the fixed-base-year] method is that in periods of substantial economic change it results in BEA growth estimates that are highly sensitive to the arbitrary choice of the base year. ...

Although BEA has always acknowledged these problems, they have gained greater urgency in recent years because of the spectacular fall in computer prices ...

[By using chain-weighting,] BEA will, in effect, use every year as a base year.

II. Is chain weighting the norm for Real GDP?

Also, it sounds like fixed prices are still the standard thing in most places.

I get the impression chained statistics are pretty standard when it comes to "Real" GDP figures.

The System of National Accounts is a handbook of standardized best practices for measuring economic activity. Chapter 15,B-C discusses how chained indices are preferred for long time series of volume or price.

Countries don't perfectly adhere to these standards of course, but a quick websearch of Anglophone countries finds that:

According to this graph, real GDP has grown by roughly a factor of 6 since 1960. That seems… way too low, intuitively. Consider:

  • I’m typing this post on my laptop (which conveniently has a backspace button and everything I type is backed up halfway around the world and I can even insert images trivially)...
  • while listening to spotify…
  • through my noise-canceling earbuds
  • and there’s a smartphone on my desk which can give me detailed road maps and directions anywhere in the US and even most of the world, plus make phone calls…
  • and oh-by-the-way I have an internet connection.

Forgive my language, but this paragraph looks to me like an example of tech people being a bit too full of themselves sometimes. The IT-sector is clearly a cherry-picked example and cannot be extrapolated to the rest of the economy. It's also not a good proxy for utilons; a million-fold increase in transistor abundance does not correspond to a million-fold more value for society, marginal returns yada yada. One could have picked even more extreme examples, like the triple product in nuclear fusion that has improved even faster than Moore's law yet has generated approximately zero value for society thus far. On the other hand, the average life expectancy in the US has only improved by 13% since 1960 (and has begun to drop recently), arguably a measure much closer to the wellbeing of people.

1960 real GDP (and 1970 real GDP, and 1980 real GDP, etc) calculated at recent prices is dominated by the things which are expensive today - like real estate, for instance. Things which are cheap today are ignored in hindsight, even if they were a very big deal at the time.

In other words: real GDP growth mostly tracks production of goods which aren’t revolutionized. Goods whose prices drop dramatically are downweighted to near-zero, in hindsight.

And I argue that that's how it should be - a transistor is on average performing much more important tasks in 1960, like planning trajectories for moon missions or running banking systems, than in 2021, like allowing people to watch TikTok videos or play games in HD. On the other hand, people still need houses to live in no matter how fancy their smartphones become. For average people, real estate is genuinely a bigger deal now than even a massive increase in their phone's camera resolution.

In fact, the real GDP graph at the beginning of this post uses a different method - the BEA (which calculates the “official” US GDP and produced the numbers in that graph) switched from fixed prices to “chaining” in 1996.

I think this is actually an ingenious way of putting productivity figures into a historical context and thereby allowing us to track progress at all. There are ways it can break, as I will discuss later, but it's still far superior than pointing to Moore's Law and saying "Did you know you're actually trillions of times richer than the average person in 1960?".

Now, I think the smoothness of real GDP growth tells us basically-nothing about the smoothness of AI takeoff. Even after a hypothetical massive jump in AI, real GDP would still look smooth, because it would be calculated based on post-jump prices, and it seems pretty likely that there will be something which isn’t revolutionized by AI.

I agree it's silly to use GDP growth as a measure in AI takeoff scenarios, kind of like asking how big of an impact a civilization-ending meteor would have on the stock market (big, approx. 150 km in diameter). I don't expect our current concepts of private property, ownership or indeed money as a coordination mechanism to survive AI takeoff. 

But that's just AI being AI. 

Let's take a less extreme example: Suppose in the near future, a pill was invented that prolonged your healthspan perfectly by 30 years (if you buy into SENS Foundation's rejuvenation paradigm, it's actually somewhat plausible). But like all new technologies, it is very difficult to produce initially and only gradually becomes more affordable over time. 

I would expect people to be willing to pay large sums of money to access such a technology even if they could barely afford it - it's a matter of life and death after all. This would give the longevity pill an enormous initial price tag. As the price comes down and the pill becomes more widely distributed, GDP receives a big boost since it is calculated using the old price tag, until the reference point resets.

But what if the longevity pill technology does not follow previous trends and just got dumped onto the market at dirt-cheap prices? Not only would it not contribute much to GDP itself, it would also completely collapse the existing healthcare sector and render millions of people unemployed. It might actually register as negative growth.

Finally, consider the possibility that the pill made you immortal straight away. In this case, whatever the initial effects the technology had on the economy, once everybody has undergone the treatment its sales number will go to zero and its manufacturer bankrupt, all while immortality becomes a mere background fact of human existence.

So in conclusion, GDP is more of a measure of economic activity than value, and growth is only a meaningful proxy for progress under the limited context of gradual adoption and improvement of new technologies. In a way, GDP growth has slow takeoff built in as an assumption.

Forgive my language, but this paragraph looks to me like an example of tech people being a bit too full of themselves sometimes. The IT-sector is clearly a cherry-picked example and cannot be extrapolated to the rest of the economy. It's also not a good proxy for utilons...

I think you've missed a key point here. The argument did not actually rely on extrapolating to the rest of the economy. The intuitive claim was that the IT sector by itself seemed to have grown enough that GDP should have grown by a factor of hundreds. So cherry-picking is irrelevant; if there is any such sector, then that's enough for the argument.

I do agree that it's not a good proxy for utilons.

Now, this part is where I think you've correctly identified the key issue (although I disagree with the "how it should be" bit):

And I argue that that's how it should be - a transistor is on average performing much more important tasks in 1960, like planning trajectories for moon missions or running banking systems, than in 2021, like allowing people to watch TikTok videos or play games in HD. On the other hand, people still need houses to live in no matter how fancy their smartphones become. For average people, real estate is genuinely a bigger deal now than even a massive increase in their phone's camera resolution.

This is a decreasing marginal returns argument; the billionth iPhone is worth a lot less than the tenth. But it's not like there's an easily-identifiable "correct" price point to use on that curve; some iPhones do in fact provide a lot more value than others. After all, the first ten or a thousand iPhones could probably have sold for a price orders of magnitude higher (even without signalling value). If we just use current prices, then we're underestimating the iPhone's value contribution.

Your story about the longevity pill is great, and I generally agree with the conclusion at the end.

Overall, I think the right way to think about GDP growth in relation to utilons is that it's a combination of removing trivial inconveniences for large numbers of people, while solving mission-critical problems for a few people, and occasionally creating positive or negative externalities through network effects that have to be analyzed on an individual basis.

There's an argument out there that as the economy tackles low-hanging fruit, increasing innovation becomes harder to achieve. Stagnation sets in. I think this is an incomplete framing that is misleading over longer time scales.

When we think in terms of years, there are a set of tractable technological achievements, and the low-hanging fruit metaphor is appropriate here. There's a set of problems we basically know how to solve. We put in the work to solve them roughly in order of priority, and see diminishing returns on our investment.

However, one of the knock-on effects of solving these problems is that they open up formerly intractable problems and inaccessible resources.

For example, sequencing the human genome was one an expensive and time-consuming project. It came half a century after the structure of DNA was determined, and represented the culmination of our understanding of the genome to that point.

Once we'd achieved that high-hanging fruit, however, the endeavor itself created a network of highly-skilled scientists with the knowhow to make the process cheaper and more reliable. Now it's relatively cheap to sequence the genome. Cheap sequencing gives us access to massive amounts of genetic data. Cheap compute lets us gather and process big health data, and interpret it in the light of genetic data. All together, this lets us refocus our scientific efforts in more productive directions.

Doing all this would simply not have been possible at an earlier technological era. But the network effects that make the new wave of growth possible take time to accumulate. It takes time to build out the highway system or the internet, to figure out how to automate production of a useful product.

So we'll see some time delay between inventing the tech that enables a network, the growth of that network to its full potential, and the harnessing of that network to drive a new wave of technological innovation.

We can't assume that these "waves of innovation" have diminishing value over time, the way that we can assume that the automation of specific products produces diminishing value as more consumers gain access to them. They deliver value by two different mechanisms. Individual products solve particular problems. "Waves of innovation" give rise to entirely different classes of products, which may turn out to deliver widely varying average levels of utility. Even if a particular wave of innovation delivers a very high level of average utility, even an entirely efficient market can't shortcut the technological and network growth barriers to implementing that wave. It just takes time, and the work has to be done in a certain order. The exact outcomes are not predictable in advance.

So from a local perspective on the order of years, we should focus on the diminishing returns story. On the order of decades, though, we should focus on the "waves of innovation" and network effects story, where diminishing returns is not operating.

"GDP is more of a measure of economic activity than value". I think this a very good intuition.

As I understand it, a main source of confusion in discussions like this stems from mixing up the notion of "value" as (A) price*quantity=revenue and (B) the difference between the consumer's willingness to pay and the price.

"A" is what counts towards GDP -- mostly for practical reasons, since prices and quantities are, at least theoretically, are straightforward to measure on a national level. However, this definition goes against the intuition of lots of people, who usually think of value as something like the idea in definition "B".

My rephrasing of it would go something like this: (1) nowadays very powerful transistors can be had for a few cents, (2) we know that people did pay a lot of money for inferior devices in the past, (3) therefore we are very rich today (at least measured in transistors-speed-per-cent), which leads to the not totally unfounded conclusion (4): GDP is a poor measure of "value" or "national wealth" in the sense of definition "B".

This is by and large true as long as you accept definition B -- which, in turn, turns out to be the (textbook) definition of consumer surplus. Which is something that was never intended to be captured by GDP -- mostly, because consumer surplus is just very complex to measure: it is very hard to estimate how much people would be willing to pay for certain items (and how much would be sold at those prices; basically, you are trying to estimate a demand curve).

Quantifying the gain from new products is a sub-sub-field of empirical industrial organization in itself: Petrin's 2002 seminal paper that tries to do it for the market of minivans (titled, funnily enough "Quantifying the Benefits of New Products: The Case of the Minivan") is still compulsory reading in graduate IO courses. But, as you can tell from the granularity and specificity of the topic, it looks hopeless to perform these exercises for the entirety of the economy, every year. So we work what we have, which is GDP.

I've heard that minivans replaced large station wagons largely because station wagons counted as cars for purposes of fuel economy laws (which mandated that cars sold by a manufacturer achieve a "fleet average" of a certain number of miles per gallon) and minivans didn't.

GDP is more of a measure of economic activity than value

 

Upvoting for this insight.

I do agree that the distinction should be made and should be known, and that the confusion around the interpretation be reduced. At the same time calling it an "insight" appears to be due to either that very confusion or ignorance of the actual subject matter.

Since its creation, economists who are familiar with GDP have emphasized that GDP is a measure of economic activity, not economic or social well-being. In 1934, Simon Kuznets, the chief architect of the United States national accounting system and GDP, cautioned against equating GDP growth with economic or social well-being. 

https://thesolutionsjournal.com/2016/02/22/a-short-history-of-gdp-moving-towards-better-measures-of-human-well-being/

 

(Note -- I take the meaning of "value" above to refer to the more subjective utility-type meaning and not simply the price value for accounting at some aggregate level.)

Perhaps a more interesting question here might be why so many people, and specifically non-lay people who really should know better (professional economists, professional financial journalist, governmental staff and representatives), keep slipping into the error in framing/rhetoric if not flat out error in thought.

One could have picked even more extreme examples, like the triple product in nuclear fusion that has improved even faster than Moore's law yet has generated approximately zero value for society thus far.

Side note: this claim about the triple product only seems to have been true until about the early 90s. Since the early 2000s there have been no demonstrated increases at all (though future increases are projected). 

See here: https://www.fusionenergybase.com/article/measuring-progress-in-fusion-energy-the-triple-products

Lots of technologies advance rapidly at first, but Moore's Law was exceptional in terms of how long it continued even after massive research efforts had picked the low hanging fruit.

There is a standard reason why real GDP growth is defined the way it is: it works locally in time and that's really the best you can ask for from this kind of measure. If you have an agent with utility function  defined over  goods with no explicit time dependence, you can express the derivative of utility with respect to time as

If you divide both sides by the marginal utility of some good taken as the numeraire, say the first one, then you get

where  is the price of good  in terms of good . The right hand side is essentially change in real GDP, while the left hand side measures the rate of change of utility over time in "marginal units of ". If we knew that the marginal utility of the numeraire were somehow constant, then changes in real GDP would be exactly proportional to changes in utility, but in general we can't know anything like this because from prices we can only really tell the utility function up to a monotonic transformation. This means real GDP is by construction unable to tell us the answer to a question like "how much has life improved since 1960" without some further assumptions about , since the only information about preferences incorporated into it are prices, so by construction it is incapable of distinguishing utility functions in the same equivalence class under composition by a monotonic transformation.

However, real GDP does tell you the correct thing to look at locally in time: if the time interval is relatively short so that this first order approximation is valid and the marginal utility of the numeraire is roughly constant, it tells you that the changes over that time period have improved welfare as much as some extra amount of the numeraire good would have. If you want to recover global information from that, real GDP satisfies

so what you need for real GDP growth to be a good measure of welfare is for nominal GDP (GDP in units of the numeraire) times the marginal utility of the numeraire to only be a function of , which I think is equivalent to  being Cobb-Douglas up to monotonic transformation. The special nature of Cobb-Douglas also came up in another comment, but this is how it comes up here.

I think the discussion in the post is somewhat misleading. There's really no problem that real GDP ignores goods whose price has been cut by a factor of trillion; in the toy example I gave with Cobb-Douglas utility real GDP is actually a perfect measure of welfare no matter which goods have their prices cut by how much. The problem with real GDP is that it can only work as a measure on the margin because it only uses marginal information (prices), so it's insensitive to overall transformations of the utility function which don't affect anything marginal.

Curious to see what people have to say about this way of looking at the issue.

I was hoping somebody would write a comment like this. I didn't want to put a technical primer in the post (since it's aimed at a nontechnical audience), but I'm glad it's here, and I basically agree with the content.

In addition, I'm confused about how you can agree with both my comment and your post at the same time. You explicitly say, for example, that

Also, "GDP (as it's actually calculated) measures production growth in the least-revolutionized goods" still seems like basically the right intuitive model over long times and large changes, and the "takeaways" in the post still seem correct.

but this is not what GDP does. In the toy model I gave, real GDP growth perfectly captures increases in utility; and in other models where it fails to do so the problem is not that it puts less weight on goods which are revolutionized more. If a particular good being revolutionized is worth a lot in terms of welfare, then the marginal utility of that good will fall slowly even if its production expands by large factors, so real GDP will keep paying attention to it. If it is worth little, then it's correct for real GDP to ignore it, since we can come up with arbitrarily many goods (for example, wine manufactured in the year 2058) which have an infinite cost of production until one day the cost suddenly falls from infinity to something very small.

Is it "crazy" that after 2058, people will be able to drink wine manufactured in 2058? I don't think so, and I assume you don't either. Presumably this is because this is a relatively useless good if we think about it in terms of the consumer surplus or utility people would derive from it, so the fact that it is "revolutionized" is irrelevant. The obvious way to correct for this is to weigh increases in the consumption of goods by the marginal utility people derive from them, which is why real GDP is a measure that works locally.

How do you reconcile this claim you make in your post with my comment?

The main takeaways in the post generally do not assume we're thinking of GDP as a proxy for utility/consumer value. In particular, I strongly agree with:

The problem with real GDP is that it can only work as a measure [of consumer value] on the margin because it only uses marginal information (prices), so it's insensitive to overall transformations of the utility function which don't affect anything marginal.

It remains basically true that goods whose price does not drop end up much more heavily weighted in GDP. Whether or not this weighting is "correct" (for purposes of using GDP as a proxy for consumer value) isn't especially relevant to how true the claim is, though it may be relevant to how interesting one finds the claim, depending on one's intended purpose.

To the extent that we should stop using GDP as a proxy for consumer value, the question of "should a proxy for consumer value more heavily weight goods whose price does not drop?" just isn't that relevant. The interesting question is not what a proxy for consumer value should do, but rather what GDP does do, and what that tells us.

The reason I bring up the weighting of GDP growth is that there are some "revolutions" which are irrelevant and some "revolutions" which are relevant from whatever perspective you're judging "craziness". In particular, it's absurd to think that the year 2058 will be crazy because suddenly people will be able to drink wine manufactured in the year 2058 at a low cost.

Consider this claim from your post:

When we see slow, mostly-steady real GDP growth curves, that mostly tells us about the slow and steady increase in production of things which haven’t been revolutionized. It tells us approximately-nothing about the huge revolutions in e.g. electronics.

The way I interpret it, this claim is incorrect. Real GDP growth does tell you about the huge revolution in electronics, the same way that it tells you about the huge revolution in the production of wine in the year 2058. It can't do it globally for the reasons I discussed, but it does do it locally at each point in time. The reason it appears to not tell you about it is because it (correctly) weighs each "revolution" by how important they actually were to consumers, rather than weighing them by how much the cost of production of said good fell.

I think the source of the ambiguity is that it's not clear what you mean by a "revolution". Do we define "revolutions" by decreases in marginal utility (i.e. prices) or by increases in overall utility (i.e. consumer surplus)? If you mean the former, then the wine example shows that it doesn't really matter if a good is revolutionized in this sense for our judgment of how "crazy" such a change would be. If you mean the latter, then your claim that "GDP measures growth in goods that are revolutionized least" is false, because GDP is exactly designed to capture the marginal increase in consumer surplus.

The reason it appears to not tell you about it is because it (correctly) weighs each "revolution" by how important they actually were to consumers...

No it doesn't. It weighs them by price (i.e. marginal utility = production opportunity cost) at the quantities consumed. That is not a good proxy for how important they actually were to consumers.

I think the source of the ambiguity is that it's not clear what you mean by a "revolution". Do we define "revolutions" by decreases in marginal utility (i.e. prices) or by increases in overall utility (i.e. consumer surplus)?

I'm mostly operationalizing "revolution" as a big drop in production cost.

I think the wine example is conflating two different "prices": the consumer's marginal utility, and the opportunity cost to produce the wine. The latter is at least extremely large, and plausibly infinite, but the former is not. If we actually somehow obtained a pallet of 2058 wine today, it would be quite a novelty, but it would sell at auction for a decidedly non-infinite price. (And if people realized how quickly its value would depreciate, it might even sell for a relatively low price, assuming there were enough supply to satisfy a few rich novelty-buyers.) The two prices are not currently equal because production has hit its lower bound (i.e. zero).

More generally, there are lots of things which would be expensive to produce today, will likely be cheap to produce in the future, but don't create all that much value. We just don't produce any of them, To think properly about how crazy the future would be, we need to think about the consumer's perspective, not the production cost.

A technological revolution does typically involve a big drop in production cost. Note, however, that this does not necessarily mean a big drop in marginal utility.

Now, I do think there's still a core point of your argument which survives:

Real GDP growth does tell you about the huge revolution in electronics, the same way that it tells you about the huge revolution in the production of wine in the year 2058.

The thing it tells us is that the huge revolution in electronics produced goods whose marginal utility is low at current consumption levels/production levels.

When I say "real GDP growth curves mostly tell us about the slow and steady increase in production of things which haven’t been revolutionized", I mean something orthogonal to that. I mean that the real GDP growth curve looks almost-the-same in world without a big electronics revolution as it does in a world with a big electronics revolution. It "doesn't tell us about things which were revolutionized" in an information-theoretic sense - i.e. we can't tell by looking at the GDP curve whether or not there was a technological revolution. That still seems basically correct, at least for "revolutions" for which price falls more than consumption increases.

I think there's some kind of miscommunication going on here, because I think what you're saying is trivially wrong while you seem convinced that it's correct despite knowing about my point of view.

No it doesn't. It weighs them by price (i.e. marginal utility = production opportunity cost) at the quantities consumed. That is not a good proxy for how important they actually were to consumers.

Yes it is - on the margin. You can't hope for it to be globally good because of the argument I gave, but locally of course you can, that's what marginal utility means! This is modulo the zero lower bound problem you discuss in the subsequent paragraphs, but that problem is not as significant as you might think in practice, since very few revolutions happen in such a short timespan that the zero lower bound would throw things off by much.

I'm mostly operationalizing "revolution" as a big drop in production cost.

I think the wine example is conflating two different "prices": the consumer's marginal utility, and the opportunity cost to produce the wine. The latter is at least extremely large, and plausibly infinite, but the former is not. If we actually somehow obtained a pallet of 2058 wine today, it would be quite a novelty, but it would sell at auction for a decidedly non-infinite price. (And if people realized how quickly its value would depreciate, it might even sell for a relatively low price, assuming there were enough supply to satisfy a few rich novelty-buyers.) The two prices are not currently equal because production has hit its lower bound (i.e. zero).

I think a pallet of wine that somehow traveled through time would sell at a very high, though not infinite, price. The fact that the price is merely "very high" instead of "infinite" doesn't affect my argument in the least. Your claim that the two prices aren't currently equal because of the zero lower bound problem is certainly correct, but it's a technical objection that can be fixed by modifying the example a little bit without changing anything about its core message. For instance, you can take the good in question to be "sending a spacecraft to the surface of Mars and maintaining it there", which currently has a nonzero consumption. It's conceivable, at least to me, that even if the cost of doing this comes down by a factor of a billion, it won't produce anything like a commensurate amount of consumer surplus.

My problem is, as I said before, that if "revolution" is operationalized as a big fall in production costs then your claim about "real GDP measuring growth in the production of goods that is revolutionized least" is false, because there are examples which avoid the boundary problems you bring up (so relative marginal utility is always equal to relative marginal cost) and in which a good that is revolutionized would dominate the growth in real GDP because the demand for that good is so elastic, i.e. the curvature of the utility function with respect to that good is so low.

A technological revolution does typically involve a big drop in production cost. Note, however, that this does not necessarily mean a big drop in marginal utility.

How does it not "necessarily" mean a big drop in marginal utility if you get rid of your objection related to the zero lower bound? A model in which this is not true would have to break the property that the ratio of marginal costs is equal to the ratio of marginal utilities, which is only going to happen if the optimization problem of some agent is solved at a boundary point of some choice space rather than an interior point.

Nothing in your post hints at this distinction, so I'm confused why you're bringing it up now.

When I say "real GDP growth curves mostly tell us about the slow and steady increase in production of things which haven’t been revolutionized", I mean something orthogonal to that. I mean that the real GDP growth curve looks almost-the-same in world without a big electronics revolution as it does in a world with a big electronics revolution.

Can you demonstrate these claims in the context of the Cobb-Douglas toy model, or if you think your argument hinges on the utility function not having a special form, can you write down a model of your own which demonstrates this "approximate invariance under revolutions" property? In my toy model your claim is obviously false (because real GDP growth is a perfect proxy for increases in utility) so I don't understand where you're coming from here.

I think in this case omitting the discussion about equivalence under monotonic transformations leads people in the direction of macroeconomic alchemy - they try to squeeze information about welfare from relative prices and quantities even though it's actually impossible to do it.

The correct way to think about this is probably to use von Neumann's approach to expected utility: pick three times in history, say ; assume that  where  is the utility of living around time  and ask people for a probability  such that they would be indifferent between a certainty of living in time  versus a probability  of living in time  and a probability  of living in time . You can then conclude that

if an expected utility model is applicable to the situation, so you would be getting actual information about the relative differences in how well off people were at various times in history. Obviously we can't set up a contingent claims market and compare the prices we would get on some assets to infer some value for , but just imagining having to make this gamble at some odds gives you a better framework to use in thinking about the question "how much have things improved, really?"

I’d expect the equivalent of any one of these things in 1960 would have cost at least a hundred times the annual income of an average person if it was even possible at all. Just from these five things alone, it seems like real GDP ought to have grown by a factor of hundreds.

This seems wrong. Imagine some country doesn't have unobtainium, a mineral which is rare and also not particularly useful. You can't get it at any price. Then it finds some, and soon enough many citizens have unobtainium paper holders. Does this mean GDP has grown by a factor of infinity? Hell no, most people would gladly exchange their paper holders for something more useful but also previously obtainable.

Isn't it the same for computers then? You'd exchange an iphone for a house in an instant, and you can't exchange your iphone for a hundred houses. So it's just not that valuable to you, and real GDP hasn't grown by a factor of hundreds.

I ~agree with this, although there's a reverse argument which also seems true: in 1960, I think a lot of (rich) people would have traded a hundred typical houses for an iPhone. Decreasing marginals are a big deal here (the billionth iPhone is worth a lot less than the tenth), and there's not a reason to pick one point on the decreasing marginal returns curve over another.

I think the real takeaway is that using price as a proxy for value is just generally not great for purposes of thinking about long-term growth and technology shifts.

Yeah, that reverse argument doesn't work. You can sell one iphone to a 1960 businessman for the price of a hundred houses, but even in that hypothetical you can't sell a hundred iphones for a hundred houses each. You can go bigger and try to sell literally all tech advances of today, but even then 1960s US won't agree to pay you 100x its total net worth. So the hundredfold growth in GDP is wholly imaginary, no matter from which year you look at it. The only sensible method is the one you don't like: using a bunch of goods that bring about the same amount of happiness in any year, like a spoonful of jam, and measuring other goods compared to that.

I agree the hundredfold growth is a drastic overestimate, no matter how we slice it. But using using a modern price is still an underestimate: the first few iPhones really do yield a lot more value than the last few, and using a current market price misses that value. Price just doesn't work as a proxy for value.

This seems wrong. Imagine some country doesn't have unobtainium, a mineral which is rare and also not particularly useful. You can't get it at any price. Then it finds some, and soon enough many citizens have unobtainium paper holders. Does this mean GDP has grown by a factor of infinity? Hell no, most people would gladly exchange their paper holders for something more useful but also previously obtainable.

Think about it this way. Suppose we have some device that was moderately valuable which everyone needed to own exactly one of, and it costs $100 per year. I don't know- maybe all humanity has some heart disease and we need to have this medical device or we die. How much "better" does this situation get if we figure out how to cure this problem for essentially free? Say someone develops a pill that costs $.01 and it lasts for a year. In some sense, this is 10,000 times better. No one's lives are even approximately 10,000 times better, though- people are only $99.99 richer per year. 

Ignoring diminishing marginal utility, this can be attributed to the fact that people's budgets are not completely saturated with such innovations- housing isn't sufficiently decoupled from things we can't dramatically improve, like the skill of workers who operate power tools, zoning laws, and the surface area of cities.

If everything got cheaper and better at the same rate as computers, I think it would be fair to assign some ridiculous multiplier to the increase in productivity over the past 60 years. Houses would cost cents and particle colliders would circle the solar system.

Isn't it the same for computers then? You'd exchange an iphone for a house in an instant, and you can't exchange your iphone for a hundred houses. So it's just not that valuable to you, and real GDP hasn't grown by a factor of hundreds.

This example seems bad? Few of us are wealthy enough to purchase a hundred houses. More directly, I would pay up to all of my discretionary income (i.e. not required to sustain my life or support my income) for access to computers and internet. 

The situation is not such that the degree to which computers are valuable to me is appropriately represented in my decision making- computers are extremely cheap, and I am wealthy enough to not have to make any sort of compromise to own one.

I agree that real GDP or rather human productivity in the intuitively relevant sense hasn't grown by a factor of 100 since 1960.

Our world seems like a 4X game where the player min-maxed for a specific path in the tech tree (the computers path) instead of choosing e.g. biotech or construction or cities or space or energy or transportation or medicine or social science, or some more even combination thereof.

I wonder if this is a historical accident, or a natural attractor for civilizations vaguely like ours 100 years ago.

When I put on my James C Scott hat, I get a very strong answer of "natural attractor". Not sure how much I buy the model behind that (it does require some large jumps on top of the usual Scott-worldview), but it does seem potentially-interesting to dig into.

Can you elaborate?

Very oversimplified version of the Scott model: whatever surpluses exist will eventually be captured by government/managers/"people in power", except to the extent that the surpluses can be hidden by illegibility.

One thing this implies: improvements in biotech or construction or cities or space or energy or transportation or medicine are under-incentivized, since any large surpluses will likely be co-opted by government/managers/"people in power". But information technology is special, since it's directly a tool for increasing legibility. So IT is unusually high-value for governments/managers/"people in power" to invest in, and the people with the technical skills to build/run the IT systems have an unusually large amount of bargaining power.

Some examples of what this view looks like in practice:

  • "large surpluses co-opted": this includes a stereotypical libertarian picture where government regulations force all new surplus to be spent on some form of political theater (safety theater, for instance), or a stereotypical Marxist picture where landlords capture all the surplus of San Francisco's tech scene, or a Zvi-esque Mazes picture where any surplus generated by a company is gobbled up by parasitic middle management.
  • IT as a tool for increasing legibility: the modern IT industry got its start with the 1890 census tally. Creating "dashboards" for managers is still one of the main ways that people actually manage to sell B2B software today.
  • Bargaining power: Software (and data science) is itself not-very-legible to nontechnical people, so analysts end up having a surprising amount of real decision-making power (especially via how they present the data).

This comment makes me think of the novel Twig, which is set in a world that I've described as "there was a biotech revolution instead of an infotech revolution".

(Though the story simply takes this as a given and does not explore the question of how that might have happened.)

Another problem with using GDP to predict something like "continuously increasing impact on the world" is that it seems like new technologies often lead to huge surplus that wouldn't get captured in a GDP metric. Search engines are ridiculously useful, people say they would pay a lot to not lose them, and yet they're free.

(This is arguably the same problem as you identify, in that as you mention you have to quantify the value of a search engine or a smartphone to include it in a GDP metric, and there isn't an obvious way to assign a value in 1960-dollars to a search engine, so you just go with what people pay for it now.)

Personally, the main evidence I rely on for "no discontinuities in impact" is that it seems like across a range of industries / technologies, after the first zero-to-one transition in which the technology is invented, the improvements on the technology tend to be continuous / incremental, and so too is its impact on the world.

(This needs to be combined with a claim that the zero-to-one transition for AI will lead to AI systems that are subhuman and so not very impactful. My impression is that some people disagree with this, seeing current AI systems as qualitatively-different-from-AGI, and expecting a completely different zero-to-one transition to AGI, in which the resulting AGI is immediately much better than humans on some important axis, like ability to self-improve. I'm not sure why they think this, if in fact this is an accurate representation of their beliefs.)

To me, it seems like the "obvious" equivalent to a search engine in 1960 is a librarian or other professional researcher, much in the same way than the 1860 equivalent of a clothes washing machine was a domestic servant.

Curated. GDP is a measure that gets mentioned a lot. Any post clarifying what it doesn't and doesn't mean, how to interpret it, etc., is a major contribution.

If you take this definition literally, then if scientists find an extremely expensive way to make lab grown dodo meat, suddenly the GDP for when dodos existed jumps up.

Measure by old prices, and one thing we can make cheaply now that we basically couldn't make before and the numbers get huge. Measure by the old prices and one thing we could make but no longer can sends the numbers plummeting. 

There are also questions of how much you want to call two items similar. When we count the number of spoons in ancient Rome, do we compare them to modern plastic spoons, modern stainless steel spoons, or what it would cost to pay people to make authentic recreations of Roman style spoons, or the cost of an actual historical Roman spoon in modern times. 

How valuable is a slip of paper with Newtons equations written on it, 100 years before Newton was born. If you were sent back in time, you could fairly easily get some paper and pay someone to copy down these exact symbols. But if you didn't know the answer, you couldn't. You could pay someone a fair bit to look at the sky, and try to find simple equations to explain what they saw, but that's still kind of using your future knowledge to say where to look. And it may take some time. And note that 2 such slips of paper are not much more valuable than 1.

When you look closely enough, your abstractions all break down.

Ben Pace has a linkpost for the booklet "Is the rate of scientific progress slowing down?" by Tyler Cowen and Ben Southwood, which is completely about the discoveries-to-economic-measurement problem. They interrogate the signal in GDP, and conclude it is very weak; they move on to use Total Factor Productivity instead.

1960 real GDP (and 1970 real GDP, and 1980 real GDP, etc) calculated at recent prices is dominated by the things which are expensive today - like real estate, for instance. Things which are cheap today are ignored in hindsight, even if they were a very big deal at the time.

I think this part could be misleading. Gross Domestic Product only includes goods that are produced in one year. Thus, if you live in a big city where it is almost impossible to build new buildings, the variation of real estate prices in this area doesn't affect the GDP. Therefore, the fact that real estate is expensive today, which is mainly true in city center, has nothing to do with GDP, GDP growth, or the weight of the construction sector in the GDP.

Good clarification.

real GDP is not calculated by dividing nominal GDP by inflation.

What does growth look like if you do divide nominal GDP by inflation? (I might look this up at some point, but I'm more likely to remember if I write this comment.)

Do you know why it's not done this way? Presumably it has its own weirdnesses, but off the top of my head I'm not sure what they'd be. (Other than "there's lots of ways you might measure inflation", but that's true of nominal GDP too I think, and I'd guess also true of the details of how chaining is implemented.)

Well for one, I'm pretty sure that this would allow cases where a Pareto increase in production results in a decrease in (NGDP/inflation). I haven't actually tried to work out an example, though.

Also, "GDP (as it's actually calculated) measures production growth in the least-revolutionized goods" still seems like basically the right intuitive model...

I don't think this is quite right, but I think digging a little deeper here can be informative. In your apples and brass example, there was no technological progress in producing apples, but we still measured real GDP growth of 1.36 using year 1 prices. So real GDP growth doesn't just measure what's happening in the least-revolutionized goods, but it certainly does get dragged down by stagnation in one sector.

As an interesting contrast, consider what would happen if producing apples and brass both became 2x more productive in year 1, causing the price of both goods to fall to $0.50. If we still have $4.50 nominal spending in year 1 (and apples and brass have similar income elasticities), we'll spend $2.25 to buy 4.5 apples and $2.25 to buy 4.5 units of brass. Now real GDP growth calculated with year 0 prices = $9/$6 = 1.5, and real GDP growth calculated with year 1 prices = $4.5/$3 = 1.5.

This contrast sheds light on a couple points: First, the disconnect between measuring GDP growth using year 1 prices vs. year 0 prices is driven by the large change in the relative amount of each good consumed. So if the growth in our consumption of houses (and everything else) since 1960 had matched the growth in our consumption of transistors, measuring GDP growth using today's prices or 1960s prices wouldn't matter as much.

Second, and I think more interestingly, it seems that measured GDP growth can be higher when we have relatively slow growth in a lot of industries than when we have extremely rapid growth in just a few industries, even if those rapidly going industries are a significant portion of the economy. In your example, brass started off as 50% of the economy and had 10x productivity grow, and we still only measured real GDP growth of 1.36. In my example, both industries saw relatively slow productivity growth of 2x, but we measured a higher real GDP growth rate of 1.5.

This implies that to the extent that GDP growth today is (a) mostly driven by technological progress in information technology, and (b) at least in the same ballpark as historical GDP growth, it must be the case that information technology is progressing much faster than any particular industry's technology ever did during the times of stronger growth in the 19th and 20th centuries. Put another way, using this mental model as a guide, the high GDP growth rates of the 19th and 20th centuries seem to be much due much more to the broadness of technological progress at that time than to the actual rate of growth in any of the industries. This is all right in line with your point about stagnation and Jason Crawford's post, but for me it really helps to clarify how important the broadness of growth is for measured GDP growth.

This implies that to the extent that GDP growth today is (a) mostly driven by technological progress in information technology, and (b) at least in the same ballpark as historical GDP growth, it must be the case that information technology is progressing much faster than any particular industry's technology ever did during the times of stronger growth in the 19th and 20th centuries.

Great comment, and I particularly like this piece. (I'm not sure how much I buy premise (a), but it's a great illustration of what that premise would imply.)

I just want to formalize what others have mostly already commented in the context of your example, which will help draw out some of the subtleties that are missed. In this two sector economy we maximize utility from apples and brass, subject to the constraint that our spending on these items is less than or equal to our income.

This results in the condition that our expenditure on the two items is equal to the ratio of our marginal utilities between them.

In the first period you have this ratio as 1, and in the second period it equals 2. So something has changed in our preferences between the periods. If you wanted to hold preferences constant, then given the price changes you pose, brass consumption should be 10x apple consumption not 5x. This isn't necessarily a problem, technology can change preferences, let's go with that. 

Another implication of our model is that if we are maximizing utility, our income will equal our total expenditure. So in the first period total income is 6, but in the second period income is 4.5. So nominal income has actually gone down in your example. What about utility? If we posit a relatively standard functional form for utility:

To make this consistent with your example,  in period 1 and .667 in period 2. If we do the calculations, we find that U = 3 in period 1 and U = 5.13 in period 2, giving real GDP growth of 71% - somewhere in between your two numbers.

In a real economy, one issue is that new goods appear all the time, and how do we map those goods onto past preferences. I'm not sure, but I think that when economists use the more recent numbers as deflators, what they are attempting to do is get more accurate measures of the 'expenditure shares' on different types of goods in order to calibrate the utility function. Obviously this work is assumption driven, and full of pitfalls, but it's not nearly as straightforward as your example. Hal Varian has some interesting discussion of these issues:

https://www.brookings.edu/wp-content/uploads/2016/08/varian.pdf

Generally good qualitative points, although the implicit assumptions in your math are way too strong. In particular:

In the first period you have this ratio as 1, and in the second period it equals 2. So something has changed in our preferences between the periods. If you wanted to hold preferences constant, then given the price changes you pose, brass consumption should be 10x apple consumption not 5x.

This is not true in general; you're assuming constant elasticity of substitution, which is a very strong assumption. In general, it's entirely possible for the preferences/utility function to stay the same, but the elasticity of substitution to change as the amount of goods consumed changes (which is what I had in mind when writing the example).

This carries through to your example utility function. The Cobb-Douglas form you use implicitly assumes constant elasticity of substitution. Indeed, it is the only form of utility function (up to isomorphism) with constant elasticity of substitution; any other (non-equivalent) utility form whatsoever would not have that issue.

Fair enough - my point was not to come up with the exact quantitative growth rate, but to show some of the assumptions that the original post glossed over. 

I agree with everyone else: the fact that certain (important) areas of technology have progressed hugely doesn't necessarily mean that there's a huge increase in overall wealth. It's like Amdahl's law (parallelizing code can't possibly bring a speedup bigger than the ratio (all work) : (non-parallelizable work)): some things in life really don't depend much on the sort of technology that's improved hugely since 1960, and if those stay approximately the same while tech gets infinitely better, our wellbeing will be increasingly determined by the (not-much-improving) state of the things that aren't improving so fast.

Having lightning-fast calculation and high-resolution streaming video and photorealistic games and so forth is very cool, but it doesn't have much impact on how comfortably you sleep at night, or whether you have close and mutually fulfilling friendships, or how good your food tastes, or whether you die of malaria.

(Technology does impact those things, directly and indirectly. I think fewer people are dying of malaria than in 1960. But it's not the 100x-better sort of improvement we see in techier areas, and in some cases it may not be an improvement: rightly or wrongly, many people claim that today's social networking technology actually makes friendships and other social relationships worse.)

Are the issues raised here limited to GDP or do these extend to any real price/value accounting based time series? While we don't have a market value estimate for a nation/national economy it seems all the comments and the OP would directly related to pretty much all large corporation to a large extent.

So does changing the title to What do Corporate Income Growth Curves Really Mean? fit as well? (Though with some slightly different points of interest/importance._

Are the issues raised here limited to GDP or do these extend to any real price/value accounting based time series?

For basically any price/earnings-based time series, yes, similar reasoning would apply.

Someone should look into Chapter 5 of Capitalism, Socialism and Democracy (Schumpeter) - THE RATE OF INCREASE OF TOTAL OUTPUT. I think there are important insights there

I don't have that much of a problem with using the recent prices. The justification for using prices as a measure of the value of production is that price = marginal benefit (to the consumer), so a drop from $1 to $0.1 per unit of brass from year 0 to year 1 tells us that the marginal use of brass is in year 1 worth 1/10th of what it was worth in year 0. The most recent price gives you a better approximation of the current marginal value of the good.

Probably a bigger (and related) problem is that we don't have a good way to account for new products and services.

I think the underlying claim that the numbers for GDP measures are generally pretty problematic in general and particularly when attempting to make comparisons between distant points in time. Part of that is just the mechanics of designing an index. That problem is very much complicated by technology and quality improvements, both resulting in a very real apples-oranges comparison problem between the goods put in the bundle of goods.

I would expect that the errors even in the short term on that comparison aspect to compound over time.

However, I also think there is very much a  problem akin to the interpersonal utility comparison problems that exist. In some ways we can look at the examples you've mentioned and the basic consumption item is something that has been produced and consumed probable at least as long as human have lived in some form of formal civil structure. Much of your tech example is communication related. Just looking at that aspect of the GDP growth, can we really say we think we're now enjoying 100 times more value in our communications?

I think that's a bit of a hard question but just from my own perspective I might say 6 times is perhaps closer than 100 times.

But again, I do agree that what one infers from looking at GDP time series data should come with a lot of footnotes about many different caveats.

We have but one metric of the real, price-independent, value of goods and services: Robin Hanson's polls where he asks "would you own a home but die ten years early" and crap like that. You can compile his Twitter polls into some kind of constraints system and use it to fill in the true value of all things, extrapoterpoinferlating from other would-you-rather style polls. Then get Real Actual GDP

The challenge with nominal numbers is you want to put them in context. What context? OUR CONTEXT! It doesn't do us a lot of good to know what our economy would be "worth" to someone from Year 0. Prices changed over time in part for nominal (monetary) reasons and in part for real reasons. To index using Year 0 prices assumes our quantity productivity increased and everything else that affects prices is a non-factor. That's not as useful of a context. However, using recent prices solves that problem. It's what the Year 0 economy would be "worth" to us given recent valuation.

The problem isn't with RGDP, but the dual role of price - it reflects costs as well as valuation. It's only a "problem" in the sense that it is complex. Goods whose prices drop for valuation reasons rightly get downweighted in GDP - we don't want them anymore! Goods whose prices drop for cost reasons wrongly get downweighted in GDP, except oh wait, the supply curve shifts right so much that we produce a ton more to compensate. The brass example is an instance where the quantity growth didn't keep up with the price drop, and that's because the supply curve shifted faster than the demand curve, leading to a price drop in part due to valuation, which is back to a "good" downweighting. This is a feature, not a bug.

If you want further hedonic adjustments, you can do that in your choice or construction of price deflator. But let's just say at some point you're fitting your own valuation rather than an estimate of that of the general polity.

It doesn't do us a lot of good to know what our economy would be "worth" to someone from Year 0.

I disagree with this specifically for the use-case of thinking about the future. If we want to know what the future will look like to us, and we want to figure that out via extrapolation, then we need to ask what the present would look like to past people.

You're basically talking about net present value at that point, again viewing the present as the correct valuation context. Past people not needed. Maybe "training" our extrapolation paradigm on the past people problem could lead to a better approach, but I don't see why a priori. You get more mismatch between the training and test set. And that's not even what we are doing here with price-adjusting an aggregate.