Mathing Up "Why Bubbles Are Great for the Economy" (It Has Been Done Before Department)

Hoisted from Comments: Robert Waldmann asks, apropos of Daniel Gross's book Pop!: Why Bubbles Are Great for the Economy:

Grasping Reality with Both Hands: Brad DeLong's Semi-Daily Journal: A Review of Daniel Gross's Book "Pop": Yes, but do you know an academic economist who has formalized this argument [that bubbles are good for the economy by] writing a [formal] model in which irrationality is necessary for growth? It would not be hard. And have you asked yourself "If not me, who? If not now, when?" Posted by: Robert Waldmann | May 13, 2007 at 11:55 PM.

It was done two decades ago, Robert: a model in which the introduction of investors subject to irrational exuberance and panic can either raise or lower the economy's productive capital stock and hence enhance or diminish the economic welfare of others in the economy. The model doesn't have all the channels that Gross discusses, but it has some of them--and enough to make the point.

Unfortunately, the authors were chasing the case in which bubbles and panics were socially harmful--not the case when bubbles are beneficial to the rest of society. But that case is there in the model, if the parameter ρ^∗ is big enough and the shock variance ratio (σ_η²)/(σ_ε²) is small enough.

Here's an excerpt from the core of the argument:

Size and Incidence: There are two reasons why the capital stock [in the absence of bubbles and panics] is different.... If... misperceptions... are on average bullish [i.e., prone to bubbles, investors]... on average demand [more stock].... [I]f noise traders are on average bearish [i.e., prone to panics], the equilibrium capital stock is lower.... [I]nvestors’ demands [also] depend on the risk borne.... The θ²σ_η² term in the denominator of [equation] (15) captures the reduction in the [economy's] capital stock that arises from aversion to noise trader-generated price risk.... The second term dominates, and the capital stock is lower in the presence of noise traders, if:

(17) ρ^∗/(δ -r) < (θ/((1+r)²))((σ_η²)/(σ_ε²))

For ρ^∗≤0 [i.e., a market at least as prone to panics as bubbles], it is always the case that the presence of noise traders reduces the capital stock.

Even if ρ^∗ is positive, only if both the noise trader wealth share θ is small and if noise traders’ opinions are not volatile relative to dividend risk (that is, ((σ_η²)/(σ_ε²)) relatively small) is the ratio of productive capital to wealth increased because of noise traders.

A lower capital stock implies a lower average level of consumption. Since capital gains and losses on stockholdings simply redistribute wealth from one generation to another, the average level of consumption of a generation is simply:

(18) (1+r)W + K^∗(δ-r)

which is an increasing function of the capital stock.

The reference?

J. Bradford DeLong, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann (1989), "The Size and Incidence of Losses from Noise Trading," Journal of Finance 44: 3 (July), pp. 681-696 http://www.j-bradford-delong.net/pdf_files/Noise_Traders_Incidence.pdf.

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Note: Robert's comment--that the source of utility gains to the sophisticated in DSSW (1990) is different from the source in Gross (2007)--is completely correct. Gross argues that volatility of opinions is good. DSSW argue implicitly that irrational exuberance can be good when such exuberance is not very volatile.

Comments

[CapitalistImperialistPig]

Waldman forgot he wrote this? The rest of you forgot to tell him?

[Roger Bigod]

IANAE, but isn't he just describing a bunch of externalities? Some bubbles leave cheap infrastructure around, like excess fiber cable capacity, and this subsidizes users that use the subsidy productively, like later startups. If the cost of the huge capital misallocation is outweighed by the productive use, and if capital is misallocated in underfunding of the later startups, well yeah.

I have read Kindelberger for purely economic, or at least selfish, reasons. He mentions dozens of bubbles and manias, many in real estate of particular goods like tulips. It's hard to see how these translate into net positives. IIRC, the South Sea Bubble produced a ban on joint stock companies that lasted for decades, not a vibrant capital market that others could make use use of.

[spencer]

But aren't you really missing the point that bubbles certainly seem to be an inherent feature of market capitalism that is essentially ignored by mainstream economics.

[Robert Waldmann]

Capitalist Imperialist Pig you are a capitalist imperialist pig.

Brad. Very funny. However, you are comparing steady states. It is easy to see how irrationality can increase steady state welfare (in a Solow-Swan growth model a total idiot representative agent who manages somehow to be consistently slightly optimistic about the constant marginal return on capital will have higher steady state welfare because
(delta + g + n + rho)>(delta+n+g).

I remember way back in Spring 1987 (*really* 20 years ago) arguing that the apparent welfare improvement due to noise traders in the DeLong et al 1990 model (J. Bradford De Long, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann (1990a) "Noise Trader Risk in Financial Markets," Journal of Political Economy vol 98 pp 703-738 (August 1990) which is older than the DeLong et al 1989 model (don't try to explain the miracle of publication lags with reject and resubmits to the readers) was at the expense of the first generation of rational investors when the noise traders arrive and shows that comparing steady states is not a good way to do welfare analysis.

Now who was that ? Who said that ? A yes he was named Brad DeLong.

The welfare improvement in steady state in the DeLong et al 1990 model with high rho* is at the expense of the noise traders and, in particular, the first generations of noise traders who invest too much and benefit the next generation. Also noise traders are driven from the market in the case that rho* is high enough to be steady state welfare of the rational improving.

The challenge is to find a Pareto improvement for given initial capital stock, not an improvement in steady state welfare of rational investors.

This is easy, of course. Everyone knows that an increase in steady state income can be changed into a welfare increasing increase in growth rates by adding a Marshallian spillover as in Romer 86.

I would prefer a Romer 90 type model with imperfect competition and increasing variety of capital goods (ok to be honest I would prefer a Barro and Sala I Martin simplified Rome 90 model with increasing varieties of intermediate goods) in which entry depends on the perceived value of an invention and entrepreneurs overestimate (or on average overestimate) the market for new inventions.

This will work fine, no problem and give a Pareto improvement given the initial stock of inventions. Also it wasn't published 20 (or even 17) years ago.

I'll have a manuscript ready by tomorrow.

[Brad DeLong]

Re: "The welfare improvement in steady state in the DeLong et al 1990 model with high rho* is at the expense of the noise traders and, in particular, the first generations of noise traders who invest too much and benefit the next generation. Also, noise traders are driven from the market in the case that rho* is high enough to be steady state welfare of the rational improving..."

But isn't this Gross (2007)'s case? That the investments funded by the bubblers are an act of philanthropy for the rest of us?

Brad

[anne]

Nice.

[notsneaky]

Robert, I think you mean that the idiot representative agent will have higher output. Welfare will be lower since the non-idiot outcome is "modified golden rule". And I think it's eta*g up there not just g, unless you got log utility (I'm just being pedantic on this one).

[p.lukasiak]

Geez, this is funny even tho I haven't the first clue what "((ση2)/(σε2))" means....

[Robert Waldmann]

Good point notsneeky. I was assuming log utility (blush). Steady state welfare can be increased by moving from modified golder rule towards golden rule.

To Brad. On Gross 2007 damned if I know. I would have to read it first. Now I understand my confusion, but I want a model in which irrationality is Pareto improving given the initial state (at no one's expense and not just leads to a Pareto better steady state for those who live so long).

[Barkley Rosser]

I read this paper some time ago and have forgotten what would seem to be an important detail, namely what the object of speculation by the bubblers, whether noise traders or rational investors buzzing off the noise traders.

So, there were a bunch of papers by people like Tirole that showed that bubbles would reduce steady-state welfare levels essentially because people would not be financing capital stock production (real capital investment) but would be putting their money into some unproductive speculative activity, e.g. running up the price of some object of speculation, whatever it might be (real estate, postage stamps, tulip bulb futures).

However, if the object of speculation is stocks, particularly stocks in companies involved in developing new technologies with increasing economies of scale and so forth, the speculative bubble can increase the financing in the leading growth sectors, and especially with economies of scale or tech externalities/spillovers, can lead to higher levels of steady state welfare. However, my memory is that your argument did not depend on any increasing economies of scale, either endogenously or more conventionally or anything along those lines, although this may well be the argument in the real world regarding such things as the speculation in the high tech sector stocks in the 1990s.

[notsneaky]

"Steady state welfare can be increased by moving from modified golden rule towards golden rule."

Not in Ramsey/Cass/Koopmans, which is what I understand your reference point is. Consumption can be increased in steady state by moving to golden rule. But Golden rule doesn't take into account discounting, (and you do have a rho up there), modified GR does. Given that people do discount you cannot improve upon the modified golden rule.

(Basically the costs of moving to the higher consumption steady state in terms of higher savings and foregone present consumption are not worth it since future consumption is worth less than present consumption, in case anyone cares)

And I'm not sure how one would measure the welfare of irrational agents to begin with.

[jonfernquest]

Clausewitzian total war has the wonderful side effect of destroying all capital stock.

This allows an economy to build new steel mills so we can be more competitive and productive.

Mass slaughter is only one aspect of war.

War is also a business opportunity.

Therefore, we should look at war with new fresh eyes and realise how it really isn't so bad after all.

[Michael Sullivan]

To Brad. On Gross 2007 damned if I know. I would have to read it first. Now I understand my confusion, but I want a model in which irrationality is Pareto improving given the initial state (at no one's expense and not just leads to a Pareto better steady state for those who live so long).

Robert,

That doesn't make sense to me. If those investments really represented a Pareto improvement, then they can't have been terribly noisy, no?

For any sane definition of a "bubble", we're talking about investments priced at a rate where people who buy at the top lose money. So there can't ever be a Pareto improvement from a bubble in a world that includes the investors who bought at the top.

Are our definitions of "bubble" very different, or what am I missing?

[Matt]

OK, Brad, reading your paper.