Archive for October, 2016

So You Don’t Think the Stock Market Cares Who Wins the Election — Think Again UPDATE

UPDATE (October 30 (9:22pm EDST): Commenter BJH correctly finds a basic flaw in my little attempt to infer some causation between Trump’s effect on the peso, the peso’s correlation with the S&P 500 and Trump’s effect on the stock market. The correlation cannot bear the weight I put on it. See my reply to BJH below.

The little swoon in the stock markets on Friday afternoon after FBI Director James Comey announced that the FBI was again investigating Hillary Clinton’s emails coincided with a sharp drop in the Mexican peso, whose value is widely assumed to be a market barometer of the likelihood of Trump’s victory. A lot of people have wondered why the stock market has not evidenced much concern about the prospect of a Trump presidency, notwithstanding his surprising success at, and in, the polls. After all, the market recovered from a rough start at the beginning of 2016 even as Trump was racking up victory after victory over his competitors for the Republican presidential nomination. And even after Trump’s capture of the Republican nomination was seen as inevitable, even though many people did start to panick, the stock markets have been behaving as if they were under heavy sedation.

So I thought that I would do a little checking on how the market has been behaving since April, when it had become clear that, barring a miracle, Trump was going to be the Republican nominee for President. Here is a chart showing the movements in the S&P 500 and in the dollar value of the Mexican peso since April 1 (normalized at their April 1 values). The stability in the two indexes is evident. The difference between the high and low values of the S&P 500 has been less than 7 percent; the peso has fluctuated more than the S&P 500, presumably because of Mexico’s extreme vulnerability to Trumpian policies, but the difference between the high and low values of the peso has been only about 12%.


But what happens when you look at the daily changes in the S&P 500 and in the peso? Looking at the changes, rather than the levels, can help identify what is actually moving the markets. Taking the logarithms of the S&P 500 and of the peso (measured in cents) and calculating the daily changes in the logarithms gives the daily percentage change in the two series. The next chart plots the daily percentage changes in the S&P 500 and the peso since April 4. The chart looks pretty remarkable to me; the correlation between changes in the peso and change in the S&P 500 is striking.


A quick regression analysis on excel produces the following result:

∆S&P = 0.0002 + .5∆peso, r-squared = .557,

where ∆S&P is the daily percentage change in the S&P 500 and ∆peso is the daily percentage change in the dollar value of the peso. The t-value on the peso coefficient is 13.5, which, in a regression with only 147 observations, is an unusually high level of statistical significance.

This result says that almost 56% of the observed daily variation in the S&P 500 between April 4 and October 28 of 2016 is accounted for by the observed daily variation in the peso. To be precise, the result doesn’t mean that there is any causal relationship between changes in the value of the peso and changes in the S&P 500. Correlation does not establish causation. It could be the case that the regression is simply reflecting the existence of causal factors that are common to both the Mexican peso and to the S&P 500 and affect both of them at the same time. Now it seems pretty obvious who or what has been the main causal factor affecting the value of the peso, so I leave it as an exercise for readers to identify what factor has been affecting the S&P 500 these past few months, and in which direction.

Rational Expectations, or, The Road to Incoherence

J. W. Mason left a very nice comment on my recent post about Paul Romer’s now-famous essay on macroeconomics, a comment now embedded in his interesting and insightful blog post on the Romer essay. As a wrote in my reply to Mason’s comment, I really liked the way he framed his point about rational expectations and intertemporal equilibrium. Sometimes when you see a familiar idea expressed in a particular way, the novelty of the expression, even though it’s not substantively different from other ways of expressing the idea, triggers a new insight. And that’s what I think happened in my own mind as I read Mason’s comment. Here’s what he wrote:

David Glasner’s interesting comment on Romer makes in passing a point that’s bugged me for years — that you can’t talk about transitions from one intertemporal equilibrium to another, there’s only the one. Or equivalently, you can’t have a model with rational expectations and then talk about what happens if there’s a “shock.” To say there is a shock in one period, is just to say that expectations in the previous period were wrong. Glasner:

the Lucas Critique applies even to micro-founded models, those models being strictly valid only in equilibrium settings and being unable to predict the adjustment of economies in the transition between equilibrium states. All models are subject to the Lucas Critique.

So the further point that I would make, after reading Mason’s comment, is just this. For an intertemporal equilibrium to exist, there must be a complete set of markets for all future periods and contingent states of the world, or, alternatively, there must be correct expectations shared by all agents about all future prices and the probability that each contingent future state of the world will be realized. By the way, If you think about it for a moment, the notion that probabilities can be assigned to every contingent future state of the world is mind-bogglingly unrealistic, because the number of contingent states must rapidly become uncountable, because every single contingency itself gives rise to further potential contingencies, and so on and on and on. But forget about that little complication. What intertemporal equilibrium requires is that all expectations of all individuals be in agreement – or at least not be inconsistent, some agents possibly having an incomplete set of expectations about future prices and future states of the world. If individuals differ in their expectations, so that their planned future purchases and sales are based on what they expect future prices to be when the time comes for those transactions to be carried out, then individuals will not be able to execute their plans as intended when at least one of them finds that actual prices are different from what they had been expected to be.

What this means is that expectations can be rational only when everyone has identical expectations. If people have divergent expectations, then the expectations of at least some people will necessarily be disappointed — the expectations of both people with differing expectations cannot be simultaneously realized — and those individuals whose expectations have been disappointed will have to revise their plans. But that means that the expectations of those people who were correct were also not rational, because the prices that they expected were not equilibrium prices. So unless all agents have the same expectations about the future, the expectations of no one are rational. Rational expectations are a fixed point, and that fixed point cannot be attained unless everyone shares those expectations.

Beyond that little problem, Mason raises the further problem that, in a rational-expectations equilibrium, it makes no sense to speak of a shock, because the only possible meaning of “shock” in the context of a full intertemporal (aka rational-expectations) equilibrium is a failure of expectations to be realized. But if expectations are not realized, expectations were not rational. So the whole New Classical modeling strategy of identifying shocks  to a system in rational-expectations equilibrium, and “predicting” the responses to these shocks as if they had been anticipated is self-contradictory and incoherent.

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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