Are we seeing the end of a 15-year stock price bubble?

I spent much of the latter part of the 1990's looking at this graph:
 
During this period, Pascal St-Amour and I were trying to explain just why stock prices were so volatile; the fundamentals driving the standard C-CAPM were far too smooth to generate swings like this. Our story was based on a two-state model in which investors alternated between periods of low risk aversion (bull markets) and high risk aversion (bear markets). We made it operational with a latent Markov process and we estimated it using Bayesian MCMC techniques, which were then still relatively new to econometrics. We met with some success: our model could leverage fairly small movements in the atemporal coefficient of relative risk aversion (between 2.20 and 2.65) into swings of about 0.4 in log real asset prices.

(AER version, ungated version)

Every now and again, I've thought about updating this paper, but each time, I've decided against it. Here's why:

There was simply no way that our model could handle post-1995 data.

Which brings me to the question of whether or not there is any model that could. It's hard to imagine a model in which movements in discount rates and/or expectations about payoffs could generate those data.

Comments

[Jim Rootham]

That's because stock prices can only be described by fractal models. As is true about much else in economics.

Try reading "The Black Swan".
http://www.amazon.com/Black-Swan-Impact-Highly-Improbable/dp/1400063515

[Nick Rowe]

Add a third state, with a lower coefficient of RRA? Of course, without some independent way of explaining why RRA should change over time, you could explain anything this way. Or, you could go in reverse, and try to back out the implied RRAs from stock prices, with some sort of smoothing technique (or trying not to have too many regime switches), and see if the resulting RRA patterns make sense from (say) demographics, or something.

I can't remember, are coefficients of RRA of 2.20 and 2.65 implausibly high, given the micro data? (From the perspective of the Equity premium puzzle, it's the "bubble" prices which look rational and fundamentally based, and the "normal" (low) prices which look like a negative bubble.)

My guess is that the world always looks more predictable looking backwards than it does looking forward (I expect that's a "Black Swan" sort of observation). "Will capitalism/stock markets survive the next decade?" for example, has been a very real question at various times (like now?), whereas at other times it's been seen as social science fiction.

[Nick Rowe]

Second reaction: I am very surprised that such small changes in RRA could cause such big changes in stock prices (main point of your paper of course, but I missed seeing it the first time). So why couldn't some similar small change also fit the post-1995 data?

Is there anything special about RRAs that gives them such a big "multiplier" effect? Would small changes in the small probability of total stock market meltdown/extinction have a similarly large multiplier? Remember how much more optimistic things looked in the early 1990's than previously.

[Stephen Gordon]

Those RRA estimates are at the upper end of what you might see from micro evidence, so we were pretty happy with that. And it turns out that what drives everything is the prospect of eventually going back to the other state.

I suppose a third state could work, but until we actually saw an exit from this state, we couldn't identify an exit probability. But it'd be hard to motivate: one of the nice things about two-state latent Markov models is that the states correspond to concepts that are well-understood, but not well-defined: expansions/recessions, bull/bear markets, etc.

[Chris S]

From the records of my local public library, I've added the details of a book at the end.

I'm on dangerous ground paraphrasing, but I would apply what I've read here to your situation as follows: the pattern of disruptions to a network (of which stock prices are certainly a part) is more dependent on the network than it is on the disruptions. Thus a network can react the same way to events of varying size - large events may cause large or small changes, and small events may cause large or small changes, with the changes often taking the form of a power law distribution. This suggests that understanding the changes in a network over time will depend more on understanding the internal interconnections in the network, and less on understanding the influence of external events.

Title: Deep simplicity : bringing order to chaos and complexity

By: Gribbin, John R.

Description: In the 1980s, a groundbreaking new idea sought to explain why the world is often unpredictable. An astrophysicist describes the principles behind chaos and complexity theory, and the tremendous achievements made over the past two decades in the applications of these theories.

Publisher: Random House,
Year of publication: 2005.
Pages: 275 p.

[Cyberike]

There is actually a simple explanation of stock prices: psychology. The easiest way to see this is to look at money flows. Money flows reflect news, events, fears, hopes, expectations, and lastly, company and business fundamentals.

I have found two interesting things in my research: First, that it takes about a 6% inflow to MAINTAIN prices. Second, money flows in do not cause as large an upward tick as money flows out cause a downward tick. These are both disturbing findings, and something I would not want the general public to know.

Note: money flows into or out of any stock, fund, or market do not create consistant results. These findings are only generalized trends.

[Richard H. Serlin]

"Which brings me to the question of whether or not there is any model that could. It's hard to imagine a model in which movements in discount rates and/or expectations about payoffs could generate those data."

Yeah, because if you refuse to be realistic, and are only willing to assume perfect rationality and expertise, then your starting assumptions are so far from reality for stock prices that you can't come close to modeling them well. It's a serious flaw with academia (although there's been great improvement in the last 20 years) -- too many in control aren't using high level thinking, or just don't really care that much; their main goal is to win prizes in an academic competition, and they don't want what they're good at and known for devalued at all.

I have what I think is a nice letter on the problem of assuming too much market efficiency in the Economists' Voice at: http://www.bepress.com/ev/vol3/iss8/art3/

[Tom Grey]

Naturally, a 'more complex' model might be more accurate, but then it loses its elegance.

But all models will fail to predict human financial behavior, not too long after they become reliable enough to be used for 'making money'.

Once a model can be used to make money, thru a behavior change by the model using money maker, more folks will change behavior to make money thru that change, and then the model will break.