Bryan Caplan  

The Solow Model and Soviet Growth Optimism

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The Moral Rot Factor... Go Quietly, Old People...
Brad DeLong makes a determined effort to explain why Samuelson and his fellow textbook writers' optimism about Soviet growth was a reasonable extension of the Solow model.  My point-by-point critique:

Economists who used PPP and production functions to predict that the Soviet Union would outstrip the United States did so through the following chain of reasoning:

  • Start with your production function: output Y as a function of technological and organizational competence A, capital K, and labor L: Y = AKαL1-α

OK.
  • The level of technological and organizational competence in the Soviet Union is lower than in the United States--centrally planned economies are inefficient, you know--but there is no strong tendency for the proportional gap in A between the US and the USSR to widen: A in the USSR will stay roughly the same fraction of A in the United States.

I'd like to see more textual evidence that Samuelson and company really thought this back in the sixties.  I'm skeptical that they gave free markets much credit for higher A.  In any case, an economist free of left-wing bias would have predicted that under capitalism, both the level and the rate of change of A would be higher for Schumpeterian reasons.
  • However, because the Soviet Union is a totalitarian state it is very good at squashing consumption--at reducing consumption C as a proportion of output Y to some near-subsistence minimum, and in channelling the extra savings into boosting the capital stock.

Ha.  An economist free of left-wing bias would have insisted that a lot of so-called Soviet "investment" was pure waste.  Keeping millions of men in uniform and building nuclear bombs were not investments; neither were the endless Siberian prestige projects, Gulags, etc.
  • Thus in the long run even though the USSR has a lower A than the US does, it will have a much higher K.

  • And that much higher K will ultimately give it a larger economy: in the end quantity has a quality all its own.

No additional complaints here.

Bottom line: Even on Brad's charitable interpretation of Samuelson and company, their argument was unreasonably sympathetic to the Soviets.  There was never a point in Soviet history when a sensible economist would have seen communism as good for growth in any meaningful sense.  (Especially in the Thirties when millions starved to death while Stalinists told the credulous West that the USSR was growing by leaps and bounds).


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COMMENTS (60 to date)
JPIrving writes:

Agreed, A is a function of time and economic liberty. If anything I imagine A would gradually drop in the USSR as the system became more and more unmanageable.

E. Barandiaran writes:

Bryan,
You're right. You can review several old studies applying Solow model to China's economic growth that made your points (I refer to studies circulated in the 1990s; I've not seen more recent studies).
BTW, since today the number of sensible economists is larger than in the 1960s, it's easier to ignore those that are not sensible (that is, those that know what other people must do and are pursuing power -as advisers or decisionmakers- to force people to do it).

Daniil Gorbatenko writes:

To second Bryan, DeLong's own analysis shows presisely why Solow and company were wrong.

The error lies in the speculation about higher K and quantity eventually resulting in quality.

Which in its turn follows from leftist meaningless
aggregate economic reasoning where heterogenous capital is reduced to K.

I wish DeLong would visit Russia where I live and go see a former Soviet mega-plant to see the K that Samuelson thought would once make USSR the world leader.

Daniil Gorbatenko writes:

Bryan, I wonder what's the use of a reasoning that reduces such a diverse phenomenon as capital to K regardless of its content?

Boonton writes:

The problem here is that the arguments against the production function are absolutely right and absolutely irrelevant to the left-right debate over the Soviet Union during the cold war.

The left's arguments were that the Soviet threat were overblown. The right argued the reverse. Take the Truman doctrine of containment. It was attacked by the right on the grounds that the Soviet Union was expanding. By giving it precious time liberals had, like Europe confronting Hitler, given it the time needed to grow its military enough to match the west. The left were more likely to make arguments like those above, that the theoretical problems with its system would force it to either reform and mellow itself or begin to rot from within.

Bryan, I wonder what's the use of a reasoning that reduces such a diverse phenomenon as capital to K regardless of its content?

Actually that reasoning would be standard marginal analysis which ranks investments based on their marginal returns. If this is your beef then your beef isn't with 'left wing economics' but classical economics since the days of Smith and Hume.

The analysis that de Long presented of the Soviet production function is actually rather conservative when you think about it. Here the west was confronting a new and unknown threat. The arguments you raise are more or less what happened but before they happened they would require some rather optimistic and unprovable assumptions to lead to the conclusion that the USSR would be of limited threat.

For example, since A is vague and even more difficult to measure than GDP there is no way to confirm that the "A gap" really was increasing as the Cold War wore on. That leaves K and L. L could be increased through forcing more of the population into labor or adding to the population through expansion. K could be increased by using less output for consumption.

This didn't require Keynesian planning. If the USSR was putting 100 million tons of steel into building tanks, it could put 20 million tons into more mines and smelting operations in order to eventually produce 150 million tons for tanks. It was irrelevant to the analysis that 'investing' 20 million tons in R&D or selling it on the market for cash or building a computer network were more profitable uses. What was relevant was that the USSR was expanding their capacity to build tanks which meant more, not less, forces threatening to sweep Western Europe.

Boonton writes:

Two more technical criticisms:

1. The original discussion was about Samuelson's textbook. At least in the short bits posted in the discussion, it seemed Samuelson was not using the production function to estimate Soviet growth but was simply presenting the then current figures for Soviet GDP, their growth rate and straight lining that out over time.

The 'lesson' did not appear to be about comparative economics but about the power of growth rates (having a higher growth rate over time is more important than your starting point). In the 76 edition he noted the weakness of straight lining a trend is that you are implicitly assuming the trend would remain constant.

2. The production function is about the max. that an economy can produce. This assumes that the economy is 'perfect' in the sense that it matches its theoretical model perfectly. For example, in the case of 100m tons of steel, it assumes Soviet planners would invest 20m tons in increasing steel production in order to build more tanks. It does not assume, though, that planners might opt to sell 20m tons of steel to raise the cash to buy their sons brand new BMWs...well actually the model does allow for that since that would be an increase in consumption and a decrease in capital.

The differing views on the Soviet Union in the last century makes for an interesting analogy to global warming today, but with the roles reversed. Soviet alarmists assumed the 'worst case' scenaro. The USSR would maximize its production function. Its decision makers would remain terrified enough of the Communist Party that they wouldn't be distracted by opportunities for petty corruption. The other side took more optimistic assumptions. Important variables like A would move against the Soviet's favor over time, for example. But what's interesting from an objective POV is that the alarmists were right. The Soviet pessismists were making assumptions that could not be verified or checked objectively. While history turned out great in the sense that they were right, risk management would still have advised being prepared for the 'perfect storm' rather than assuming perfect weather.

Snorri Godhi writes:

Why, when talking about economists, is it necessary to specify that they should be "free of left-wing bias"? I can't remember anybody insisting that biologists should be free of creationist bias; or astronomers of Ptolemaic bias.

Leaving aside the sarcasm: my point is that Bryan Caplan does not put his finger on the piece of economic theory that says that [a] the rate of growth of technological + organizational competence is slower in centrally-planned economies and [b] centrally-planned investment is wasted at a higher rate than free-market investment.

I agree that, long before 1989, a "sensible economists" would have accepted both [a] and [b], and therefore would have concluded that the Soviet model is bad for growth -- but, until somebody can pinpoint the economic theory that predicts [a] and [b] above, my tentative conclusion is that being sensible is a necessary and sufficient condition to accept [a] and [b]; and being an economist is neither necessary nor sufficient.

Koromo writes:

I would have to disagree with DeLong. If anything, the main lesson of Solow's growth model is that there is a limit on how much you can achieve via higher saving rates. And that in the long run the main determinant of growth is technological progress.
I doubt that guys like Samuelson didn't know this.

Besides, why would this be a right wing argument?

ajb writes:

One also has to distinguish between growth that was valued in terms of total GDP (including consumption) which was fictitious vs. low market value production that was still militarily valuable. One can believe that GDP measured at correct market prices is low while believing that production for purposes of fighting wars was high enough to scare us.

After all the horrible WW2 economy under Stalin managed to field thousands of tanks (the T34) which were superior to most of what the US produced. It is not clear that the US would have been capable and willing to win a non-nuclear land war against the Germans without the Eastern Front to absorb the bulk of the veteran German troops. Nukes really did make it possible for us to win the Cold War.

Boonton writes:

Actually technological change would be incorporated in the model as 'A'. But you're correct that the model assumes A is constant and growth is determined by savings. Solow made A exogenous hence 'exogenous growth model'.

But what's interesting is that Soviet collapse doesn't follow from A. The USSR achieved high growth rates in its early years mostly because it was 'catching up' to developed economies as it underwent forced industrialization. But even if you have the USSR maintain an 'A' that is constantly lower than the US's, it could remain in the game by copying the tech. innovations of the US while ploughing huge portions of its output into K. Recall Stalin's quip that 'quantity has a quality all its own'. A million Soviet tanks rolling full speed into Europe versus 50,000 more advanced Western tanks is still a competitive fight.

Basically this boils down to the West saying 'we don't have to worry about savings, new inventions will make up for it.' That's basically what happened but its quite understandable why a policy maker in the 50's, 60's, and 70's would be skeptical of counting on that as their anti-Soviet plan.

Boonton writes:

People tend to rewrite history to make it 'obvious' that things would turn out as they did. Several years after my mother-in-law died, people tell me they knew it was about to happen...even though it seemed to take everyone by surprise when it did.

In retrospect it seems 'obvious' that the USSR would have collapsed into nothingness. Yet at the time most people did not view it that way. I remember Arther C Clark has the US-USSR split going on still in 2001, 2010 and I believe even 2050. A lot of science fiction took it as a given that the US-USSR conflict would continue for decades, even centuries or would be resolved with a full scale nuclear war. Back when we had this debate on MarginalRevolution.com, many of the examples of right wingers 'predicting' the collapse of the USSR were more to the tune of an 'aspirational prediction' (set in the far off future) rather than a practical one.

This leads me to ask how much of this was just pure luck? Suppose the media and information revolutions of the 70's and 80's just happened to be one time exogenous leaps in A that capitalist economies were able to take advantage of very quickly but not things that can be expected to happen on a regular basis? Even worse, what if now that the info revolution is kind of old already authoritarian gov'ts have developed the tools to 'manage' a population with them? It may very well be that the Cold War would have ended differently if the USSR had been slightly more aggressive early on or if certain lucky things had happened a decade or two later than they actually did.

Elvin writes:

Another aspect of the debate at the time was that the US and the USSR economies would converge to some sort of mixed capitalism/centralized control system. In a sense, we could say Samuelson was right: the US has expanded government influence in health care, education, and housing and the USSR now has a lot more capitalism. However, Samuelson did not forsee how spectacularly the USSR would implode. The heavily centralized economy model is now highly discredited. Obvious now, it was not back then. It was acknowledged that the USSR didn't have the capability to match the West's material standards. The worry was expansionism. They had proxies in Africa, South East Asia, Europe, and Latin America.

Do econ departments even offer Comparative Systems courses any more? It was probably my favorite undergrad econ class back in the 1970s.

Boonton writes:

I think 'convergence' is / was a lazy reading of history. Both the US and USSR had highly centralized command economies during the 'total mobilization' of WWII. After WWII the west pulled back dramatically from command economies.

The New Deal entitlement programs of most Western economies are not about socialism as it was understood in the pre-WWII era. They are about maintaining consumption. The idea that both sides 'converged' on a mix of private and directed industrial policy after starting on opposite sides of the ring is simply not very accurate. With some exceptions like Japan's industrial policy & the UK nationalizing some industries the west, for the most part, ditched the idea of managing and directing a nation's industry. The model the west ended up with was maintaining consumption demand but letting the private sector supply that consumption.

Eric H writes:

A friend of mine from the former Soviet Union finds this debate amusing.

He has always told me that quantity, in and of itself, was never a problem in Soviet times. The country overflowed with shoes and clothes; the only problem was they were made in a narrow range of colors and sizes.

The government continually boasted that Soviet factories were the largest in the world; the only problem was that they produced mainly for industrial, not private, consumption. There were plenty of heavy haulers and earth movers but few cars for private use.

Here's an anecdote to put DeLong's assertion that a "much higher K will ultimately give it a larger economy: in the end quantity has a quality all its own":

My friend's brother jumped at the chance to purchase a new truck. To prepare for his purchase, he assembled a camping kit and a store of food to last him a few days. He gathered his meager supply of tools and set off on a journey of several hundred miles to the factory that produced his pickup. Once there, he was led to his purchase through a large lot filled with shiny, new trucks all leaking gas, oil, and coolant from their factory installed gaskets. He proceeded to repair--repair!--the brand new truck over the next few days, tightening gaskets and bolts and fasteners and making sure all the fluids were topped off.

My question for DeLong: can an economy containing a huge amount of crummy capital really be bigger than an economy containing a smaller amount of high-quality capital?

Boonton writes:

In terms of this model the answer is yes. Basically you're saying the US's 'A' was far above the USSR's. That's great but toss enough K and L into the function and sooner or later you'll get enough output to match that of the country with the better 'A'. Maybe 100 bad trucks doesn't match 50 good ones but 200 bad trucks? 300? 1,000? Its worth my time to learn how to repair gaskets if I could get 4 new trucks rather than 1 truck that's in perfect shape.

de Long doesn't assume the 'A gap' remains constant but he does assume there's no 'strong tendancy' for it to increase. It can increase from two different forces. One is the USSR's A getting progressively worse. The other is for the US's A to get progressively better. I suspect history had a lot of the first happen and some of the second. This, though, would not have been a foregone conclusion decades ago. For at least a few decades the Soviet Union appeared to at least be holding its 'A' steady behind the West. If it had been able to have kept that up, the 'catch up' scenario would have happened.

autogen writes:

Bryan, this is ridiculous. I thought your main point was that the textbooks repeated the same mistake in edition after edition? The day of reckoning just kept receding?

Boonton writes:

Well on Marginal Rev. someone had a copy of the '76 edition and in it Samuelson stated that the 'catch up' would never happen if Soviet growth started to fall below the US rate of growth. Since that did happen I'm not sure what the mistake is you think should be corrected.

Mark Bahner writes:

"L could be increased through forcing more of the population into labor or adding to the population through expansion."

Yes, and L could be decreased by killing vast numbers of people.

It's no accident of geography that the Soviet Union lost more people in WWII than all the other Allies combined. Stalin simply had no consideration for loss of human life.

Consider a tale of two canals: the U.S. effort on the Panama Canal, and the U.S.S.R. effort on the White Sea-Baltic Canal. Estimates vary, but presumably a reasonable estimate of the number of people who died constructing the White Sea-Baltic Canal is the Wikipedia estimate of 100,000 people. Contrast this with estimates of the number of people who died in the U.S. effort to build the Panama Canal: 5,600.

That's a difference of more than 90,000 people. Take all those peoples' lifetime earnings, and the lifetime earnings of all their descendants who were never born. It's going to add up.

And that doesn't even consider the value of the two canals: more tonnage was shipped through the Panama Canal last year than has been shipped through the Baltic-White Sea canal in over 70 years of operation.

Mark Bahner writes:

"Well on Marginal Rev. someone had a copy of the '76 edition and in it Samuelson stated that the 'catch up' would never happen if Soviet growth started to fall below the US rate of growth. Since that did happen I'm not sure what the mistake is you think should be corrected."

I don't think Bryan Caplan is posting on what Samuelson wrote. He's posting about what *Brad DeLong* wrote about what Samuelson wrote.

Specifically, Bryan Caplan is saying that Brad DeLong is wrong when he says that Soviet Union catching up to the U.S. was a reasonable extension of the Solow model.

Eric H writes:

So Samuelson & Co. were arguing, or DeLong is arguing, that sufficient quantities of K and L in some way compensate for an abysmal A. But that's all the function says. DeLong isn't saying anything other than what the equation says.

Why aren't coeffecients assigned to modify A for each economy to which the production function is applied?

Perversely, "A" was in fact the reason "K" was as large as it was in the Soviet Union. The Soviet's organizational competence told them to produce tons of roofing nails and underpants rather than what Soviet consumers wanted. A huge amount of poor quality stuff does not have a "quality" all its own. It's little better than the raw materials from which it's made. In fact, it's worse, because you don't have to disassemble raw materials to make them into something else.

Applying the same function to two vastly different economies is a mistake. Shoehorning a diverse world into a mathematical model doesn't tell us anything about the world or the model; it just tells us about the priors of person doing the shoehorning.

liberty writes:

Snorri Godhi said: "until somebody can pinpoint the economic theory that predicts [a] and [b] above, my tentative conclusion is that being sensible is a necessary and sufficient condition to accept [a] and [b]; and being an economist is neither necessary nor sufficient."

Not sure what kind of theory you are looking for, but basic supply and demand analysis can get you there -- many economists did even before 1917. Probably the most thorough analysis was written in the 1920s by Ludwig von Mises -- and he most certainly used economic reasoning to explain your (a) and (b) in detail enough to convince most reasonable people.

One need not be an economist, but one must consider basic economic laws - one must consider supply and demand, self interest, ownership rights, human action generally.

Boonton writes:

Specifically, Bryan Caplan is saying that Brad DeLong is wrong when he says that Soviet Union catching up to the U.S. was a reasonable extension of the Solow model.

But it is a very reasonable extension of the Solow model.

So Samuelson & Co. were arguing, or DeLong is arguing, that sufficient quantities of K and L in some way compensate for an abysmal A. But that's all the function says. DeLong isn't saying anything other than what the equation says.

I'm not following this. Basically you have a function that multiplies A*K*L (leave out the exponents). It's simple math that if one variable, like A, is low it can be compensated for with another variable being higher (like K or L).

Neither De Long nor Samuelson ever asserted that having an abysmal A could sink your economy. Clearly it can. What is clear, though, is simply having a poor A is not a surefire gurantee of economic collapse.

Perversely, "A" was in fact the reason "K" was as large as it was in the Soviet Union. The Soviet's organizational competence told them to produce tons of roofing nails and underpants rather than what Soviet consumers wanted.

Naturally if you have a poorer A you need more capital and labor to get the same stuff accomplished (like put a working pickup truck on the road).

Applying the same function to two vastly different economies is a mistake. Shoehorning a diverse world into a mathematical model doesn't tell us anything about the world or the model; it just tells us about the priors of person doing the shoehorning.

So is this a general plea to ditch math from our economic language? The model is simple, elegant and provides a lot of insights that would be very difficult without those three little variables. Imperfect? Of course it is but so is spinning endless 'just so' stories about underpants and broken pick up trucks.

Snorri Godhi writes:

Liberty: thank you for your reply. I am somewhat familiar with the concept of supply+demand (though not as familiar with it as Samuelson was), enough to realize that supply+demand can explain [b1] the efficiency of the free market. What I don't know is how it can explain [a1] the long-term growth (as opposed to static efficiency) of free-market economies. I also don't know how it can explain the slower long-term growth and lower static efficiency of centrally-planned economies. In fact, this is the entire socialist calculation debate, which in the end was solved by historical events, not by theory.

Ludwig von Mises [...] most certainly used economic reasoning to explain your (a) and (b) in detail enough to convince most reasonable people.

I might agree with that, but with an important qualification: Mises is not part of mainstream economics. In other words, most economists [including Samuelson] were not convinced by Mises. Saying that Mises convinced "most reasonable people" is to say that most economists are not reasonable.

Bill N writes:

"Calling this argument "pro-Soviet"--as Bryan Caplan does--is simply wrong. It is, as Yglesias notes, at bottom a very right-wing argument."

Brad's argument seems strained here. Is he calling Samuelson a right winger? That would certainly have surprised Samuelson and Buckley.

I recall right wingers fearing Soviet military strength, but not that their economy would overtake. By suppressing consumption, scarce resources could be diverted to military purposes. Hardly anyone considered this a recipe for economic as opposed to territorial growth. Note, this may not be true for economists and politicians who believe in the power of public spending and the multiplier.

As for his model, so what. There is opportunity for bias in
1) which model you choose to use
2) the input parameters for the model. "A" is entirely subjective. Where you set the exponent value "alpha" is critical.
3) your credulity in the model results

Boonton writes:

I'm not sure what 'opportunity for bias' means in the above comment. (BTW, it's Solow's model, not De Long's).

Economics describes the production of military goods as much as other goods. An economy that is producing more tanks than the US has overtaken the US (at least in tanks). The fear wasn't t hat the USSR's economy would 'overtake' us and we'd be buying toys in the mall saying "Made in the USSR", the fear was that the the USSR's economy could support a larger and larger military.

Eric H writes:

"So is this a general plea to ditch math from our economic language? The model is simple, elegant and provides a lot of insights that would be very difficult without those three little variables. Imperfect? Of course it is but so is spinning endless 'just so' stories about underpants and broken pick up trucks."

So...facts about Soviet overproduction of stuff no one wanted or needed or could have used are "just so stories" but claiming insight from repeating in English what the production function says in mathematical symbols is not? But yes--sort of. Not a general plea to ditch math from economics but a plea to temper it with reality-based observations.

Simplicity in and of itself is not a virtue. Just so stories aren't either, but there are enough of them in this case to cause relatively intelligent people to second-guess the virtue of applying rigid formulas to constantly changing, complex phenomena.

Maybe DeLong's right; quantity could have a quality all its own if you're talking about Kalashnikovs and nuclear warheads. Maybe in those cases, mere quantity trumps quality. It certainly did the trick for the Soviets during the siege of Leningrad and other engagements in which they armed thousands of barefoot, starving men with poor weapons and threatened to annihilate them with Katyusha rockets if they didn't advance on German tanks.

At bottom DeLong and Yglesias's arguments are about playing "find the neocon." Bryan isn't a neocon. But you don't have to be a neocon to be wary of tyranny. Is someone "right-wing" if they recognize as dangerous individuals in a government willing to go to any lengths economically or militarily to expand their power?

"Neither De Long nor Samuelson ever asserted that having an abysmal A could sink your economy. Clearly it can. What is clear, though, is simply having a poor A is not a surefire gurantee of economic collapse."

There are two sides to an equation. DeLong starts out with the assumption that the Soviet Y was as big or bigger than the American Y. I think that is a big error. Why start out with that assumption when trying to describe two economies that clearly aren't the same?

The production function is in part a tautology because K is itself a product of raw materials and organizational competence, and organizational competence on a nation-wide scale could not exist without physical and human capital.

Arbitrarily inflating Y and then saying "if Y is bigger, something has to explain it" is redundant; of course this is true, by definition of the function.

The point of my "just so stories" was that American A, K, and L are not comparable to Soviet A, K, and L.

ryan yin writes:

"Well on Marginal Rev. someone had a copy of the '76 edition and in it Samuelson stated that the 'catch up' would never happen if Soviet growth started to fall below the US rate of growth. Since that did happen I'm not sure what the mistake is you think should be corrected."

Boonton,
If Samuelson had only predicted "catch up" in 76 and had been circumspect about it, no one would have ridiculed him, Levy & Peart wouldn't have written about it, and we wouldn't be talking about this.

Boonton writes:

So...facts about Soviet overproduction of stuff no one wanted or needed or could have used are "just so stories" but claiming insight from repeating in English what the production function says in mathematical symbols is not? But yes--sort of. Not a general plea to ditch math from economics but a plea to temper it with reality-based observations.

The stories are insightful but they remain stories. Were MiG fighters as poorly made as the pickup trucks? What about the triggers on their nuclear warheads? Should we have pulled out of Europe because we trusted a country that couldn't get a gasket in a pickup right wouldn't be able to drive their tanks through?

BTW, the pickup story is actually consistent with De Long's scenaro. One way for a country with a command economy to surpress consumption is to simply make consumption unavailable, difficult to accomplish, or undesireable. I recall reading something recently about China's high savings rate and this too turned out to be one explanation. Unless you're in one of the center urban areas, there just isn't a lot of places to shop in China and as a result people don't. While it may have just been the result of economic stupidity, it is quite possible the crappy trucks were a way of indirectly taxing consumer spending in order to keep adding to K.

Simplicity in and of itself is not a virtue. Just so stories aren't either, but there are enough of them in this case to cause relatively intelligent people to second-guess the virtue of applying rigid formulas to constantly changing, complex phenomena

I agree neither gives you a full picture of reality. But put yourself in the shoes of, say, the CIA circa 1975 and you're tasked with the duty of estimating Soviet GDP for the next 5 years and its military spend. The question that I think is interesting is what should we have been able to know from the information we had at the time. It's all too easy to tell us what we should have known in 1975 when you're sitting in 2010 with wikipedia to help you!

There are two sides to an equation. DeLong starts out with the assumption that the Soviet Y was as big or bigger than the American Y. I think that is a big error. Why start out with that assumption when trying to describe two economies that clearly aren't the same?

No he doesn't he starts out with the Soviet Y being much lower than the US. That was not an 'assumption' but an emperical fact known to everyone at the time...even if you just used the 'official' numbers.

The production function is in part a tautology ..

Not sure I follow this other than to note that all equations are tautologies in some sense.

The point of my "just so stories" was that American A, K, and L are not comparable to Soviet A, K, and L.

I'm not sure why you couldn't, at least in theory, adjust the variables as needed. If a Soviet worker produces 20% less output per hour on the same type of capital, you could count that as 0.8L or represent it as an A of 20% less (since A is supposed to represent the skill at which the economy puts K and L together to make output).

ryan
If Samuelson had only predicted "catch up" in 76 and had been circumspect about it, no one would have ridiculed him, Levy & Peart wouldn't have written about it, and we wouldn't be talking about this.

1. Samuelson didn't predict in 76 that the USSR would catch up with the US.

2. 76 is coming up because it is quite hard to get copies of Economics online in various editions. I guess Google Books wasn't allowed to scan it. So I'm relying on what someone who owns the 76 edition posted on MR.


From the 1976 Text as quoted on http://www.marginalrevolution.com/marginalrevolution/2010/01/soviet-growth-american-textbooks/comments/page/3/#comments

"They [referring to 'many experts' from a previous sentence] suspect that, as the Soviet Union reaches stages of development more comparable with ours and places greater emphasis on services, she is likely to show a retardation in her rate of growth and may lose the advantage of imitation of more advanced technologies. So they caution against blindly extrapolating the data of the recent past into the future."
(After that, he remarks "Although there is much that is persuasive in such arguments, there is also the fact that they may provide temptingly optimistic rationalizations to patriots who are wishful that America can stay forever ahead." And I remark that there is also the further fact that patriots are not the only people who may be tempted by wishful optimistic rationalizations.)

From what I've been able to piece together, the point Samuelson was making served primarily a teaching purpose. Over time a faster rate of growth trumps a better 'starting point'. The discussion above actually demonstrates a lot of the points you guys are making nicely. He is saying you can't straight line models out to infinity and trust the results. He is saying you have to look at the specifics of the economy and not just crunch the numbers in the equation. BUT he is also pointing out the most important con in 'looking beyond' the model, that you may just be fooling yourself and telling yourself a story you want to hear.

China is going to provide an interesting case study in the claim that the 'information revolution' makes authoritarian gov't impossible.

As for why we are talking about it today, well it's not because there's been a sudden interest in reading 30 year old economics textbooks. Its because we insist on tossing today's template of debate on top of the past. So we assume the infinite partisanship of today was the norm back then and the things that animate the debate today were in place back then. Instead of really learning about the throught process that was happening back then, partisans today seek to enlist the past as a way to mine talking points.

Mark Bahner writes:

"BTW, the pickup story is actually consistent with De Long's scenario. One way for a country with a command economy to surpress consumption is to simply make consumption unavailable, difficult to accomplish, or undesireable."

So build a bunch of pickup trucks that nobody wants? That's consistent with the idea that the economy of the USSR would grow to match the U.S.?

Boonton writes:

So build a bunch of pickup trucks that nobody wants?

Not quite, build only enough pickup trucks for the people who really, really want them. Hence you have to spend a few days travelling to get to them when they finally become available and even then get out some tools and fix the one you want. Most people will simply not bother and keep their consumption down to the bare necessities.

A market economy might simply have a consumption based tax to encourage savings & capital formation. Also market economies that are operating in 'full wartime mobilization' act this way too. In WWII if you wanted to buy a new car, have a steak dinner, or even just buy stockings for your wife you would have found your consumption choices were either unavailable or made unappealing whereas at the same time the option to 'buy war bonds' was made as easy and fun as possible.

ryan yin writes:

As for why we are talking about it today, well it's not because there's been a sudden interest in reading 30 year old economics textbooks.

Point taken, but actually, that's pretty much why Levy & Peart are writing about it (because they're history of thought economists).

I think it's a bit odd to read that Samuelson repeatedly claimed USSR growth rates were extraordinarily high, only to revise the level but not the growth rate with each new addition, and come away with the conclusion that Samuelson was really worried about the dangers of over-reliance on a model and straight-line results.

Boonton writes:

I'd like to get my hands on one of the editions and see just what the context is that the graph is presented in. I suspect that it was serving more as an illustrative tool to demonstrate how growth rates are the real drivers of change over time. As a result, it worked as a good illustration and got attention since people thought about the US.v.USSR situation a lot in those days. AS a result no one paid much attention to its actual relationship to reality.

As came out on MR, Sovietologists, who had a bigger stake in getting at the truth about the USSR, tended to be more sceptical of the growth rates and reported GDP figures.

Today I'm sure the graph would use China.v.US as an example of competiting growth rates. What will we say 50 years from now abou that?

Mark Bahner writes:

"Not quite, build only enough pickup trucks for the people who really, really want them. Hence you have to spend a few days travelling to get to them when they finally become available and even then get out some tools and fix the one you want. Most people will simply not bother and keep their consumption down to the bare necessities."

But if there's no consumption, there's no reason to build the trucks in the first place. So in this situation, there would be either a lot full of trucks that sitting at the production plant, rusting...or the plant would need to cut back production to a level that only the extremely dedicated and resourceful would buy.

Either way, it is unlikely to ever produce as large an economy as a country in which the trucks roll off the assembly line, are transported to dealers, and driven off the dealers' lots by owners who are happy to get a more reliable (i.e., new) truck.

"A market economy might simply have a consumption based tax to encourage savings & capital formation."

That sounds like a much better idea than building trucks that don't run.

Boonton writes:

I think you're overlooking two, not one, possible reasons for non-running trucks. One is just pure stupidity. Central planners simply cannot get the incentives right to make the assembly lines work correctly.

The other is that the good engineers, high quality workers, and best management are at work somewhere else. Namely building tanks or ICBMs or MiGs.

I think the first possibility counts for a lot, but I wouldn't write the second off either.

In terms of economy, our measure of it is Y and yes there's no reason in theory why Y couldn't grow. In fact we know for periods in the USSR's history it did grow and grew rapidly.

I understand the difficulty in reducing everything to 'Y'. 100 tanks in one economy, 5,000 picks up in another. Is that equal? If it isn't then which one is bigger? That's a difficult empirical question to answer but clearly trucks have a value and so do tanks so there is an answer.

Eric H writes:

And now for a blatant appeal to authority,John Cochrane, as interviewed by John Cassidy:

What do you think the fiscal policy multiplier is?

I think it is the wrong question. In many models with positive multipliers it is socially bad to do it. Just because you get more output doesn’t mean it is a good thing. People have pointed to World War II and (said), oh, there’s a case where we had lots of output. “Well, let’s fight World War II again” is not socially good.

Cochrane's "socially bad" is my "one unit of American A, K or L is not equal to one unit of Soviet A, K or L."

Boonton, you say: "Not quite, build only enough pickup trucks for the people who really, really want them." This directive implies an internal logic absent in the Soviet system. If such a directive really existed, why did they build so much factory space and leave it unused?


Boonton writes:

The multiplier is something totally different from the production function.

The production function is the max. that an economy can product. Think of it like a weight lifter. The weight he can lift might be described as:

Y = AKL where Y is weight, L is the # of days he practices in the gym, K is the # of hours each day and A is a function of how good his trainer is in directing his practice.

The fiscal multiplier comes into effect when for some reason the economy is falling short of this maximum. To use the lifter analogy, the function may say he can lift 450 lbs but today he can only lift 400 lb because he has a cold.

The growth model is not concerned with recessions and other temporary dips from the function, it is concerned with the long run growth of the function which, over time, is what really matters.

(BTW, Cochrane's quote is pretty stupid IMO. If Germany and Japan hadn't declared war on the US it's not like anyone was going to say "let's do a world war to drive recovery". The war stimulus could have been used for massive internal improvements in the US. If WWII hadn't happened, we could have probably enjoyed 1960 in 1945 so its not like the war had no cost to us. That doesn't say anything about fiscal stimulus, though)

If such a directive really existed, why did they build so much factory space and leave it unused?

Right off the bat everyone assumed the Soviet Union's 'A' was less than the US's 'A' and was going to stay that way *because* their central planning was always going to result in less intelligent use of capital and labor. The only difference here is that De Long felt that 'A gap' was stable while Caplan felt it was doomed to increase over time. Interestingly Kling's post on the USSR's 'evil shortage' implies that he feels the 'A gap' could have been held stable or even closed a bit if Soviet leaders had the stomach to continue being as evil as Stalin.

So to answer your question the unused factory space was almost certainly due to stupidity caused by their system (aka the 'A gap'). That doesn't change the fact that the Soviet Union decided to direct their output away from individual consumption (pickup trucks) and towards military consumption (tanks) as well as to increase capital (K). The shoddy and poor quality of consumer goods in the USSR was certainly due to their 'A gap' but it was also due to their decision to inhibit consumption by making it a low priority.

ryan yin writes:

Boonton,
Can you give textual evidence for why you think no one thought Soviet multifactor productivity would ever reach or exceed US levels?

One reason why I'm really skeptical of this claim is that Samuelson was a good enough mathematician and a good enough economist to know that the Solow model pretty much tells you that you're not going to solve a substantial A problem with more K.

Another reason why I'm skeptical of this claim is because of the way Samuelson apparently kept, Ehrlich-like, just updating the date of reckoning. A third reason is that Samuelson seems quite optimistic about Soviet productivity (both its actual level and the feasibility of increasing it). Could you tell me why I shouldn't be so skeptical, or why you apparently are not at all?

Greg Ransom writes:

Let's make K = huge aggregated piles of craptastic aggregated mathematical economics.

Then let's write DeLong:

"a higher quantity of 'K' will ultimately give us a superior understanding of the world: in the end quantity has a quality all its own."

This, essentially, was the assumption of the Samuelson / Solow generation -- huge aggregated piles of homogeneous aggregated mathematical economics will make us smart.

Guess what. It didn't.

Boonton writes:

ryan

Can you give textual evidence for why you think no one thought Soviet multifactor productivity would ever reach or exceed US levels?

Actually I can't. I had to ask several times before someone came forward with a few actual quotes from Samuelson's editions. This is not something I will head to a library over.

As far as the model is concerned, the USSR's GDP could meet the US's without its productivity (the A I assume you mean) ever meeting the US's levels. In other words, the USSR would continue to do a worse job at putting capital and labor together to make output than the US but would be able to match the US in output by employing *more* labor and output.

There was never a claim made by Sameulson or anyone else of importance that the USSR would meet or exceed US productivity. If you think there was please produce it.

One reason why I'm really skeptical of this claim is that Samuelson was a good enough mathematician and a good enough economist to know that the Solow model pretty much tells you that you're not going to solve a substantial A problem with more K.

And it looks like he did recognize it, esp. as he mentioned that he was skeptical that the USSR could continue economic growth as the industrial revolution petered out and the new game for economic growth was in service based production. But then it's not like 'A' is an easy thing to measure. In theory if you have perfect measures of K and L and the exponents and GNP you can measure it but that's asking a lot...

Greg

Let's make K = huge aggregated piles....

I guess you're trying to say that reducing capital to a homogenous lump called K that can be compared in such a way that you can say K(usa)

I think you're stuck too much in the 2000's mode of thinking about this as an argument over which economic system was/is better. The argument of the cold war was which economic system would win by producing more output...namely more tanks, icbms, and hydrogen bombs.

Basically if you believe GDP is a real number then you believe K is a real number. K is simply that (aside from Labor and 'know how' (aka 'A')) which produces more GDP. Now the USSR did product output (GDP) and some of that output was consumed and some put back into more capital. Now they might have done a very bad job investing in more capital, but De Long's point is their authoritarian nature did a very good job at suppressing consumption. In other words, if $1 out of every $2 they put into K was pure waste, it's not at all obvious that would be a fatal problem for their economy since they were able to force consumption down by $3 and force Labor up by $2 through their use of forced labor and the threat of the state.

ryan yin writes:

Boonton,
It's entirely reasonable to say you're not about to run over to the library to track down what Samuelson did or did not say. But doesn't that imply agnosticism on the matter? You seem quite certain.

To me, the quotes and graphs Levy & Peart reproduce in their papers suggest Samuelson was by no means terribly skeptical of continued Soviet growth relative to the US -- after all, the amount of time he expected it to take the USSR to overtake the US kept decreasing. They seem to make a good case that far from thinking (as Delong assumes he must have) the Soviets were necessarily inefficient, Samuelson more or less figured all economies are efficient.

Boonton writes:

I suggest you reread De Long's article again. He assumes that the Soviet Union was less efficient than the US and that it would remain so into the future. Just because a country is able to match another country's GDP doesn't mean that it is equally as efficient. Countries are able to generate GDP by combining capital and labor in an intelligent way. If you're very inefficient you still have a shot in the game by being able to amass a huge amount of capital and labor....in other words making up with quantity what you lack with quality.

ryan yin writes:

Right, that's what I said -- Delong said that. What I also said was that I didn't see any evidence that Samuelson did, and I did see a lot of evidence that he didn't.

Boonton writes:

Again we don't have Samuleson's books for reference here, only some cut and pastes but:

1. Samuleson's graph straight lines what was then current Soviet and US growth rates. This would:
a. Be consistent with a constant 'A' for both countries
b. If he felt 'A' was going to change, that would show up as a change in the rate of growth.

2. In his dicussion of the projection in 76, he noted that 'experts' felt Soviet expansion would stall as it ran up against a service based economy. Presumably this would happen because central planning could not put capital and labor together as efficiently to produce services. This would be consistent with the 'A gap' expanding against the USSR's favor.


So to turn the tables:

What really has been presented to indicate Samuelson thought Soviet economics was superior to the US?

The graph does NOT indicate that. Even with the 'catch up' projection, the USSR would still be a case of 'working harder' rather than 'smarter' than the US.

Keep in mind simply having a bigger GDP does NOT mean your economic system is better. For example, India has a bigger GDP than Australia...even though Australia is known for being better off economically (granted India has been improving dramatically in the last decade or so). Australia has a better 'A' than India. They use their capital and labor together more intelligently to produce GDP. But since India has so many more people they can beat Australia in terms of raw GDP output. Observing this does NOT mean that you think Australia would do better to mimic India's economic policies.

ryan yin writes:

1. Samuleson's graph straight lines what was then current Soviet and US growth rates. This would:
a. Be consistent with a constant 'A' for both countries
b. If he felt 'A' was going to change, that would show up as a change in the rate of growth.

No, I don't think that's correct at all. The big take-away of the Solow model, in fact, is that you can't explain very much of actual growth by increased capital stocks. So, no, it's not consistent with constant A. If Samuelson thought A was constant for both, he'd have constant US GDP (b/c it's "balanced growth" and absent A-growth that means "steady state") and concave-to-flat USSR GDP.

For example, India has a bigger GDP than Australia...even though Australia is known for being better off economically

Yes, this is because India has a larger population. In fact, the Solow model tells us it's just because India has a larger population (the larger capital stock just follows from having a larger population). This needs to be emphasized. Furthermore, note that the US & USSR were roughly similar populations (as opposed to the order of magnitude-plus w/ India/Australia), so you can pretty much go back and forth between total and per-capita GDP comparisons.

What has been presented? Well, there's constant assurances of catch-up, and never a thought that "hey, it's been 20 years since I predicted they'd catch-up in about 20 years -- maybe I should rethink." There's Samuelson saying that they were on the PPF, and elsewhere making arguments that depended on that belief (quite at odds with the claim that Samuelson believed planned economies are inherently inefficient -- why, it's almost as if Samuelson didn't think much of the Austrians!). There's the straight-line graphs and the spit-balling assumption of constant growth rates for the USSR (which, again, Samuelson would know is consistent only for constant growth in A, and if he forgot he would just need to knock on Solow's door). Etc. At the very least I cannot understand why one would be very certain that Samuelson did not expect convergence in per capita GDP, total GDP, or (which is more or less implied) productivity. Yet you do seem certain. Ok, fine -- maybe you are right. Tell me why.

Boonton writes:

No, I don't think that's correct at all. The big take-away of the Solow model, in fact, is that you can't explain very much of actual growth by increased capital stocks. So, no, it's not consistent with constant A. If Samuelson thought A was constant for both, he'd have constant US GDP (b/c it's "balanced growth" and absent A-growth that means "steady state") and concave-to-flat USSR GDP.

Assuming constant A, the US GDP would only be constant if capital and labor did not change. This would require 0% population growth and 0% of investment in output towards creating new capital net of depreciation.

Yes, this is because India has a larger population. In fact, the Solow model tells us it's just because India has a larger population (the larger capital stock just follows from having a larger population). This needs to be emphasized. Furthermore, note that the US & USSR were roughly similar populations...

There's no reason in theory a country couldn't pull an India type story off but using capital instead of labor. Of course on an GDP per person basis, the country with a better A would be better off. But in a military contest, higher GDP translates into more stuff. If Australia and India bordered each other and wanted to go to war, India would have a slight advantage due to their more impressive GDP.

What has been presented? Well, there's constant assurances of catch-up, and never a thought that "hey, it's been 20 years since I predicted they'd catch-up in about 20 years -- maybe I should rethink."

As noted catching up != better economy. And note Samuelson also said they would NOT catch up if their 'A' started to decline due to their command economy being less efficient at producing the service based goods of a modern economy.

There's Samuelson saying that they were on the PPF, and elsewhere making arguments that depended on that belief...

Actually no one has presented a quote of Samuelson saying they were on their PPF. Even if he did, though, so what? Saying the USSR has a PPF is hardly saying its equal to or better than the US!

(quite at odds with the claim that Samuelson believed planned economies are inherently inefficient -- why, it's almost as if Samuelson didn't think much of the Austrians!).

Efficiency is just a relative measure which is A in Solow's model. You can be on your PPF but still be relatively inefficient compared to another economy which has a higher A.

There's the straight-line graphs and the spit-balling assumption of constant growth rates for the USSR (which, again, Samuelson would know is consistent only for constant growth in A, and if he forgot he would just need to knock on Solow's door).

Nonesense, if you have K growing at a constant rate you'll have straight lined growth. If you have A growing as well as K then you'll have accelerating growth. Your GDP won't be a straight line sloping up over time but a curve with growth accelerating expodentially higher. Catchup would happen much sooner than the straight line method would indicate. The only way you can get a straight line of GDP with a growing A is if you assume both L and K are constant. This would apply if you thought the USSR had 0% population growth and took consumed 100% of its output (except for covering depreciation on its capital). Since that's unusual for an economy I think its fair to say the critics here should present some actual evidence that Samuelson thought that.

At the very least I cannot understand why one would be very certain that Samuelson did not expect convergence in per capita GDP, total GDP, or (which is more or less implied) productivity. Yet you do seem certain. Ok, fine -- maybe you are right. Tell me why.

1. The graph and quotes are not about per capita GDP. Since nothing has yet been presented on per capita GDP I see no reason Samuelson needs a defense.

2. On total GDP we've seen quite exhaustively that you can have a less efficient economy catch up with a more efficient one by simple expansion of its labor or capital. This does not demonstrate the less efficient economy is better, only that inputs matter....that shouldn't be surprising since they wouldn't' be considered inputs if they didn't matter!

3. On productivity #1 basically applies. The quotes from Samuelson (as opposed to deLong) do not indicate that he was thinking about this question in terms of Solow's growth model. But if he was the straight line projections are simply not consistent with the Soviet Union narrowing the gap in productivity with the US. If the USSR's A grew faster than the US's (or the US's A fell while the USSR's stayed constant) we would not have straight lines except under the special condition where L and K are zero. On top of that we have the 1976 quote where Sameulson asserts that its possible the Soviet Union's 'A gap' will expand! In contrast you have nothing from Samuleson even indirectly hinting that he thought a contracting 'A gap' was likely.

Boonton writes:

Here's a simple illustration you can do in Excel. Say the US's A is 1. Say its K starts out at 100 and its L start out at 100. Say alpha is 1 so that L's exponent is 1-1=0 meaning that L remains constant at 1.

US's GDP = 1 * 100 * 1 = $100.

Let's say the USSR's A is 0.8 and its K starts out at 50.

USSR's GDP = 0.8 * 50 * 1 = $40

Note that this isn't too far off. The USSR was something like 1/2 the US's GDP at the end of WWII and the beginning of the graph.

Say the US's K increases by 5 units per year....
Over 4 years this is what I get for GDP:

GDP
$100.00
$105.00
$110.00
$115.00

Now say the USSR's K increases by 10 units:
GDP
$40.00
$48.00
$56.00
$64.00


And US - USSR GDP

Gap
$60.00
$57.00
$54.00
$51.00

Note the closing gap EVEN THOUGH I not only kept both countrys at constant productivity (A) but docked the USSR 20% in their A for their less efficient economy. I'm making a very simple assumption that K is increased in both countries by an even number of units each year. I'm sure a more sophisticated model would have K increase by some % of previous years output indicating a constant savings rate. But those simple assumptions are insightful. For example if the USSR increases its K by 10 units per year, the actual % of GDP being put into K falls from 25% in year 1 to 16% in year 4. In other words, the USSR can enjoy a little bit of consumption each year. The US would do the same, enjoying more consumption per unit of output as the years go by. But in both countries GDP goes up and the gap closes.

Now just out curiousity, let's say you are right and Samuelson thought that the USSR's A would go up 12% every year. Well look what happens to GDP:

GDP
$40.00
$52.80
$67.76
$85.18
and the Gap

Gap
$60.00
$52.20 $(7.80) change from previous year
$42.24 $(9.96)
$29.82 $(12.42)


Not that making A, relative to the US, go up, dramatically increases GDP and closes the gap much, much faster than a straight line. If Samuelson thought this then he wouldn't have a straight line model unless he had some very special behavior in mind for A where it increases by some linear amount each year (BUT why would he think this and if he did there should be some evidence to support it!)

ryan yin writes:

Boonton,

There is such a thing as exogenous growth (of A) theory, but I am unaware of any school of thought that supposes capital stocks increase exogenously (as opposed to as a result of the actions of individuals and states in response to objective functions and constraints).

With all due respect, I think you're just misreading the Solow model and its implications. When you say "there's no reason in theory a country couldn't pull an India type story off but using capital instead of labor", you're neglecting the fundamental point that, yes, there is a very good theoretical reason why this can't happen (again, that's the basic Solow result -- without A growth, investment drops to match depreciation exactly and the economy hits steady state). You are entirely right to say, "Assuming constant A, the US GDP would only be constant if capital and labor did not change," but you're missing the key point that this is precisely what the Solow model says has to happen if your A isn't growing. When you say "The graph and quotes are not about per capita GDP ..." you're forgetting that when populations are roughly equal, these are more or less the same discussion. And I think you're misunderstanding what I meant (or really, Levy & Peart meant) by "on the PPF" -- you are taking this to mean "the Soviet frontier existed", when what is meant is "the Soviet economy is on its frontier, not the interior of the set." [If you want a quote, how about 1948, p 20, “The Russians, having no unemployment before the war, were already
on their Production-possibility curve” (quoted in Levy & Peart 2006 http://pubchoicesoc.org/papers_2006/levy_peart.pdf).]

You're free to make the argument that Samuelson didn't understood the Solow model, but I find that hard to believe. You can make the argument that he understood it but didn't believe it, but it's hard to see how that could be. (For one thing, you'd have to say that he didn't believe the seminal, Nobel-prize winning work of his co-author; for another, you'd probably also have to say that Samuelson thought economies don't exhibit any diminishing returns w.r.t. capital alone and that growing economies don't actually look like a "balanced growth path", which would be extremely hard to believe.) I don't have to suppose that Samuelson is reasoning from a Y=A(K^alpha)(L^1-alpha) equation directly to know that he's not going to be saying something so deeply at odds with the optimization ideas he brought to economics in the first place.

Boonton writes:

There is such a thing as exogenous growth (of A) theory, but I am unaware of any school of thought that supposes capital stocks increase exogenously (as opposed to as a result of the actions of individuals and states in response to objective functions and constraints).

Actually in the simple model I sketched, capital is endogeneous. It increases by an even # of units every year but that's a portion of previous year's output. You can make it a bit more sophisticated and have it increase by some % of last year's output but while you get curves rather than lines the results are basically the same.

you're neglecting the fundamental point that, yes, there is a very good theoretical reason why this can't happen (again, that's the basic Solow result -- without A growth, investment drops to match depreciation exactly and the economy hits steady state).

Investment will drop as diminishing returns set in and the economy will hit a steady state. Diminishing returns basically means you've exhausted all the productive investment you can possibly make. But even in that state your GDP will expand as K and L go up, there's just no longer any advantage to trying to favor one over the other.

To bring it home to a real life picture, imagine in 1930 all Soviet farmers are using muels to plough their fields. Adding a tractor to each farm increases K while L stays the same. Using a tractor combined with L is 'A'. Because the Soviet Union isn't as good as the US, say A is only 80% of US. Adding the tractor still increases output, though. Steady state isn't reached, though, until every farm has a tractor. At the steady state output won't go up unless you add both a farmer and a tractor.

This type of analysis is rather specialized, though, since we are assuming all innovations have been exhausted. If someone figures out how to use a tractor a bit better, then A will change and the economy will grow to a new steady state. But did anyone think either the US or USSR were anywhere near a state where all possible capital investments had been exhausted at any point between the 50s to 80's?

To be honest everything yet presented indicated that Samuelson was working with a simple model where GDP is going up because of additions to K and L and for both countries the steady state was a long, long ways away. Looking at the dates, the exogenous growth models were developed as early as the late 40's and perfected through the 50's-70's. Endogenous models were developed in the 1980's (http://en.wikipedia.org/wiki/Endogenous_growth_theory). In other words, it wasn't until the 80's when economists really started putting some serious work in exploring models where A changes. Before that A was considered 'exogenous' which lends further support that Sameulson, in an undergraduate text was not pushing the model in the direction that your argument would require of him.


ryan yin writes:

Incidentally, you can kind of see a bit of what I'm talking about w.r.t. Solow by resetting alpha=.35 (pretty close to what seems to be the true value) and normalizing L to 1, even if you retain your exogenous, linear growth in K assumption. Increasing K by 10 every year just stops giving you much extra each year.

For that matter, you can see a little bit just from your own figures -- net investment exceeds GDP growth, so add a little depreciation and even constant investment eventually means C has to head towards (and beyond) zero. For constant percentage growth, this problem explodes much faster.

Boonton writes:

[If you want a quote, how about 1948, p 20, “The Russians, having no unemployment before the war, were already
on their Production-possibility curve” (quoted in Levy & Peart 2006 http://pubchoicesoc.org/papers_2006/levy_peart.pdf).]

I'd be curious to hear/see the full context of that quote. Let's assume you're talking about a very tight timescale. It's right before the war and we need more output RIGHT NOW to meet invading German tanks! Well for all the other developed nations there were lots of unemployed men left from the Great Depression. They could be pulled to add L to the function thereby increasing output. The USSR did in fact have 'no unemployment'. In such a tight timeframe you're more or less stuck with both your A and your K.

I suspect he would say the USSR's answer would be to expand L even beyond the non-existent unemployed by adding to the labor force people who were not in it originally (such as housewives and in the USSR's case political dissidents). This is more also what all the other economies did (minus the political prisoners). The US first pulled L from its unemployed population and then expanded L to include housewives.

That, though, is not quite saying the USSR was 'better'. I'd rather be an economy with a very big PPF curve but on the inside of it than to be an economy with a smaller PPF curve but right on it. Anyway you're at 1948 there when even the exogenous growth model was barely born yet.

ryan yin writes:

Actually in the simple model I sketched, capital is endogeneous.

Ok ... but investment choice is exogenous. Even in exogenous growth models they inevitably say "A grows 2% per period plus or minus a normally distributed shock"

But did anyone think either the US or USSR were anywhere near a state where all possible capital investments had been exhausted at any point between the 50s to 80's?

Yes, of course, certainly, at least in the sense that is meant here (i.e., that we're in the "balanced growth path" where absent increases in A we're more or less at a steady state). That's true of all developed economies, and has been for quite a long time now. If that weren't true, real interest rates would be falling rapidly and wages would be growing faster than the economy.

Boonton writes:

Incidentally, you can kind of see a bit of what I'm talking about w.r.t. Solow by resetting alpha=.35 (pretty close to what seems to be the true value) and normalizing L to 1, even if you retain your exogenous, linear growth in K assumption. Increasing K by 10 every year just stops giving you much extra each year.

I think I'm following what you're saying. Basically to increase capital you have to pay for it with previous GDP growth. If you're rapidly adding capital, that just increases next years depreciation bill. Your capital has to keep providing returns in the form of more output to keep this game going. But if diminishing returns are in effect, you get less and less bang for each added unit of capital.

But then why does this 'game' work for L? Why is India able to trump Australia by going huge on L? What if your economy starts out at a very primitive state so there's plenty of room to add capital before diminishing returns becomes an issue?

I suspect that the truth is that Samuelson was simply illustrating the power of growth rates by straight lining them and wasn't giving much thought to how the USSR would really sustain such growth (as were a lot of watchers at the time).

Perhaps the answer comes from A increasing for both the US and USSR. This would make sense if the US was innovating away and the USSR was always copying those innovations (but never matching US's 'A' since even copying will still leave you with inefficiencies in a planned economy)

Boonton writes:

OK I reran some numbers. I started the US with A=1 and let it increase by 1/2% each year. I set the USSR's A to be 0.8*US's A.

I started US K at 100 and US L at 100 using alpha of 0.35. For the US each year I assumed 5% of previous year's output is added to K. For the USSR 25% to represent their strategy of trying to beat the US by becoming an 'India of K'.

US
$100.00
$135.72
$175.79

USSR

$62.77
$105.13
$156.27


GAP

$37.23
$30.59
$19.52


We still get a falling gap even though the USSR is always behind the US in terms of A.

ryan yin writes:

Right, you can have higher returns to increasing your capital stock if your population is large -- basically, you want a certain amount (holding A constant) of capital per worker, so if you have lots more people you want lots more capital. A thing to note here is that A is essentially blowing up the marginal value of capital, so you'd also expect economies with higher A to have a higher steady-state level of capital per capita (if you pardon the expression). So while in principle you could see an economy compensating for lack of A by blowing up their K, in practice you'd expect the opposite: investing more output has a bigger cost for a poorer (lower A) economy (implied by diminishing marginal utility), but has a smaller payoff (since the high A of the richer economy keeps the marginal product of investment higher longer).

Or to put it another way, a low-A economy shouldn't be investing the same percentage of output every year.

Boonton writes:

Ok so I redid my Excel sheet this time using the following:

US: A=1 and stays constant
K starts at 100 and 5% of previous year's GDP is added to it (no depreciation in this model)
L starts at 100 and remains constant.

USSR: A=0.8 and stays constant
K starts at 50 and 25% of previous years GDP is added to stock.
L starts at 100 and remains constant.

Year 1 GDP is $100 US and $62.77 USSR and catch up happens around year 12 into 13 with the USSR pulling ahead afterwards.

Now at year 46 I have US GDP at $202.25 or $2.02 per person while the USSR is $274.26 or $2.75 per person. The big difference, though, is that the USSR has $19.45 of K per person while the US only has $4.28.

This tells me that while, in theory, the USSR could have out GDP'd the US by becoming an "India of K", its very expensive in terms of opportunity cost. To match the US the USSR will need almost $2 in K for every $1 the US has. In year 46 the USSR has $4.54 in K for every $1 in K the
US has yet its GDP per person is only $1.36 for every $1. per person of US GDP.

So I'm assuming here that alpha remains constant and it appears we have diminishing returns to capital at play....yet the "India of K" strategy seems at least possible in theory unless I'm making a serious mathematical error.

Of course depreciation might cause more choas to the model. Something else to consider is that consumption includes military consumption, not just consumer products. If Soviet planners opted to, say build 5,000 tanks with 100m tons of steel instead of building a new tank factory they are consuming, not investing.

I'll save the sheet if you want to take a peek at it.

Boonton writes:

OK I think I'm seeing what you mean by steady state. I added in a depreciation charge (10% of last year's K) and upped the savings rates to account for that (US 15% and USSR 35%).

At about 125 years into the model the US GDP reaches a stable point of $124.39 and the USSR $116.18. At this stable point the USSR remains forever behind the US due to its lower A.

In the early years of the model, though, the GDP gap is falling rapidly so one can see how it might appear to an observe that the USSR is going to eventually catch up to the US in GDP.

Boonton writes:

BTW, I had a hard time looking but it does appear that the USSR had a larger population than the US and a larger population in the labor force. We aren't talking about the differnce between India and Australia but it's not trivial either. While the USSR started the game with a lot less K, it appears to have had an edge on L.

ryan yin writes:

Note that even without depreciation, to get your result you need the low A country to invest five times as much as the high A country despite the marginal return to investment being half that in the US (and despite marginal utility of consumption being higher in the USSR). In the year per capita consumption is equal, the marginal product of capital in the low A country is only a third of that in the high A country and yet the program requires they invest well over 6 times as much. This is why Solow predicted K-only growth would drop off very quickly (in fact, drop to zero).

(In other words, it doesn't really make sense to have an "India of K". That's Solow's main point: sustained growth never occurs through investment alone.)

Boonton writes:

I'm not sure what I'm doing wrong (or if I'm doing something wrong) but the spreadsheet doesn't seem to pan that out.

Let's keep it easier. You're a Soviet planner. You know your K is about half the US's and your L is a bit bigger. No one is sure what your A is. Western Economists say less, your dogma says its equal or better. What do you do?

It seems pretty clear to me, build up K to match the US. We aren't really talking about an 'India of K'. So in theory if you had a country with equal K, bigger (but not much bigger) L and a smaller A you could end up with a bigger GDP or an equal one. Granted not if your A was much smaller.

But from the perspective of the 1950's, 60's and 70's what would be the USSR's A relative to the US? With the atomic and hydrogen bombs the USSR was able to match the US much sooner than expected. In the space race the USSR appeard to surge faster than the US at least up until the moon shot. Measuring 'A' as much smaller than the US's wouldn't be all that reasonable IMO until maybe the 70's and 80's. Even then, though, you need to really get 'inside' the numbers in a way which frankly would be impossible for either a Soviet or American economist.

ryan yin writes:

I'm not sure if you're still looking at this, but if you're still interested, the "long run implications" section of the wiki page on Solow (http://en.wikipedia.org/wiki/Exogenous_growth_model#Long_run_implications) lays it out pretty well. Note that these implications aren't really being driven by the particular functional form, but basically just by diminishing returns to capital.

What's going wrong in your spreadsheet is that the savings rate is arbitrarily determined (though note that when you added depreciation, even with the arbitrarily exploding investment the result was overturned). The way you have it, the Soviets are doing lots more investment when the benefit to them of investment is low (in later periods) and less in earlier periods when investment is much more valuable. Why don't they invest more earlier? Then they get more total growth for the same amount of total investment. This is the logic of growth theory: insofar as growth comes through additional capital, you should expect to see a spurt of growth at first and then leveling off. It seems extremely difficult to believe that Samuelson didn't know this. That his graph says something else implies that he wasn't figuring Soviet growth is "catch-up" (i.e., "catch-up").

Note that I'm not saying that it's mathematically impossible to come up with values of A, K, and L where output is higher despite lower A.

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