Doing Economics: A Thought for the Day for Grad Students

A common mistake amongst Ph.D. students is to place too much weight on the ability of mathematics to solve an economic problem.  They take a model off the shelf and add a new twist. A model that began as an elegant piece of machinery designed to illustrate a particular economic issue,  goes through five or six amendments from one paper to the next. By the time it reaches the n'th iteration it looks like a dog designed by committee.

Mathematics doesn't solve economic problems. Economists solve economic problems. My advice: never formalize a problem with mathematics until you have already figured out the probable answer. Then write a model that formalizes your intuition and beat the mathematics into submission. That last part is where the fun begins because the language of mathematics forces you to make your intuition clear. Sometimes it turns out to be right. Sometimes you will realize your initial guess was mistaken. Always, it is a learning process.

Did Keynes have a Theory of Aggregate Supply?

My old classmate Nick Rowe has a new post on Chapter 3 of The General Theory.  In Nick's words,

Start with three equations.

1. The production function: Y=F(L). Output (Y) is a function of employment (L). 

2. A "classical" labour demand curve: W/P=MPL(L). The real wage (W/P) equals the Marginal Product of Labour, which is a decreasing function of employment. This is Keynes' "first classical postulate", which he agreed with. 

3. A "classical" labour supply curve: W/P=MRS(L,Y). The real wage equals the Marginal Rate of Substitution between labour (or leisure) and output (or consumption). This is Keynes' "second classical postulate", which he disagreed with (except at "full employment"). 

From 1 and 2, plus some tedious math, we can derive what Keynes calls "the aggregate supply function": PY/W = S(L). It shows the value of output, measured in wage units, as a function of employment. It is substantively identical to the Short Run Aggregate Supply Curve in intermediate macro textbooks that assume sticky nominal wages: Y=H(P/W), which uses the exact same equations 1 and 2, but presents the same solution differently. 

From 1 and 3, plus some tedious math, we can derive a second "aggregate supply function", that is not in the General Theory: PY/W = Z(L). It is substantively identical to the short run aggregate supply curve implicit in New Keynesian models, which assume sticky P and perfectly flexible W, so the economy is always on the labour supply curve and always on the production function.

From 1 and 2 and 3, plus some tedious math, we can solve for Y, L, and W/P, and derive a third aggregate supply function: Y=Y*. This is the textbook Long Run Aggregate Supply curve. It is identical to the solution we could get if we solved for the levels of Y, L, and W/P that satisfied both the first and second "aggregate supply functions".

Nick's first supply curve is the only supply curve in The General Theory. All else is due to misinterpretations by later economists who tried to make sense of what Keynes really meant (ineffectively in my view).  We don't need sticky prices (supply curve number 2) and we don't need to reintroduce the second classical postulate through the back door (supply curve number 3).  That is 1950s MIT talking and it led us down the wrong path.

My Quiz for Wannabe Keynesians

Simon Wren-Lewis has a great post today on what makes a Keynesian.  Here is my answer together with a quiz for wannabe Keynesians.

First, let me delve into a little highbrow theory.

Figure 1: The Keynesian Cross

Figure 1 is a picture that goes by the name of the Keynesian cross.  On the horizontal axis is income; the value of all wages, rents and profits earned from producing goods and services in a given year.  On the vertical axis is planned expenditure; the value of all spending on goods and services produced in the economy in a given year. Since this is a closed economy, all expenditure is allocated to one of three categories; expenditure on consumption goods, expenditure on investment goods and government purchases.  Since every dollar spent must generate income for someone; in a Keynesian equilibrium, income must equal planned expenditure.

Faust, Keynes and the DSGE Approach to Macroeconomics

DSGE models have been the subject of much attention recently on the blogs. Simon Wren-Lewis suggests that DSGE modelers made a Faustian bargain and offers a partial defense.  David Glasner is distinctly uneasy with the DSGE approach and although Paul Krugman remains eclectic he wants to retain the IS-LM model as part of his portfolio.

Like it or not, DSGE models are here to stay. I made the following argument in the First Edition of The Macroeconomics of Self-Fulfilling Prophecies in 1993.

In this book I take a point of view that is becoming less controversial but is by no means universally accepted. I will argue that the future of macroeconomics is as a branch of applied general equilibrium theory. 

Believe it or not; twenty one years ago, that was a controversial statement. I argued then that the problem with DSGE models is not the assumption that the economy is in equilibrium. The problem with DSGE models is the implication of some of these models that the equilibrium is optimal. Since then, I have consistently argued that the way forward is to reformulate Keynesian ideas with modern mathematics; that is what the DSGE agenda is all about.

Keynes and Sticky Prices: Time to Think Outside the Box

Several recent excellent posts have appeared on Keynesian economics and sticky wages and prices. David Glasner points out that

...the sticky-wages explanation for unemployment was exactly the “classical” explanation that Keynes was railing against in the General Theory.

and quoting David again

it’s really quite astonishing — and amusing — to observe that, in the current upside-down world of modern macroeconomics, what differentiates New Classical from New Keynesian macroeconomists is that macroecoomists of the New Classical variety, dismissing wage stickiness as non-existent or empirically unimportant, assume that cyclical fluctuations in employment result from high rates of intertemporal substitution by labor in response to fluctuations in labor productivity, while macroeconomists of the New Keynesian variety argue that it is nominal-wage stickiness that prevents the steep cuts in nominal wages required to maintain employment in the face of exogenous shocks in aggregate demand or supply. 

Quite!

Rational Expectations and Animal Spirits

Along with the rest of modern macroeconomics, the rational expectations (RE) assumption has gotten quite a bit of flack lately. I don’t think all of it is deserved.  It is not the rational expectations (RE) assumption that is at fault: It is the rational expectations assumption in conjunction with the assumption of a unique equilibrium. 

In standard dynamic stochastic general equilibrium (DSGE) models there is a single rational expectations equilibrium. In the models I work with there are many rational expectations equilibria. Not just one, or two or three: but an infinite dimensional continuum of them. That is not a problem. It is an opportunity that I exploit to model the idea that beliefs matter. In my work, I close my models by adding an equation that I call a 'belief function'. The belief function is an effective way of operationalizing the Old Keynesian assumption of ‘animal spirits’. It is a forecasting rule that explains how people use current information to predict the future. That rule replaces the classical  assumption that the quantity of labor demanded is always equal to the quantity of labor supplied.

You might think that adding a belief function to operationalize animal spirits allows me to dispense with the rational expectations assumption since the belief function could be arbitrary. Not so. Even though we do not live in a stationary environment, our beliefs should be consistent with the outcomes that we would observe in a stationary world.  In such a world, beliefs should obey Abraham Lincoln’s dictum that “you can fool all of the people some of the time or some of the people all of the time but you can’t fool all of the people all of the time.”  In my view, that is the rational expectations assumption.

Download my Data on the Stock Market and Unemployment

The recent drop in the stock market, if it persists, will present serious challenges for the Yellen Fed.

In a couple of recent academic papers, The Stock Market Crash of 2008 caused the Great Recession: Theory and Evidence  here and The Stock Market Crash Really Did Cause the Great Recession here I showed that changes in the value of the stock market cause changes in the unemployment rate three months later. Here is a link to a Freakonomics post that features my work.

I continue to receive requests for the data that I used in those studies. That data is available here. These are important empirical findings that establish a strong and stable relationship between changes in the value of the S&P and changes in the U.S. unemployment rate.