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.

In Chapter 4 of The General Theory, Keynes suggests that we measure output in wage units. Here is Nick again on that point...

Keynes' weird habit of measuring output in wage units had an unfortunate result: because [it implies that]  doubling the real wage, for a given level of output and real income, would exactly double output demanded. 

That is simply false. There is no unique concept of output in a multi-good economy. Contrary to Nick's assertion, there is nothing 'weird' at all about the measurement of GDP in wage units. It is a clever device that allows us to measure real GDP and to concentrate on the determinants of aggregate economic activity.

And Nick claims later in his post that

There is absolutely nothing new on the supply-side in chapter 3 of the General Theory.

Not so. Although there is no 'theory' of aggregate supply that would satisfy a micro economist, that is not the same as Nick's claim that there is nothing new. What is new is the assertion that Keynes will drop the classical second postulate. In other words: throw away the labor supply curve. Making sense of that statement is what my own work is all about.

Back to Nick...

It is the demand-side that is new. It is the idea that the demand for goods is a function of the quantity of labour that households are actually ableto sell. If households are rationed in the labour market, that will spillover and affect their demand in the output market. Because the amount of labour they are actually able to sell, and hence the income they will earn from wages plus non-wages, depends on demand. Which means that demand depends upon demand. Demand depends on itself. That was new, and interesting."

I agree that the consumption function, the idea that "demand depends on itself",  was a central element of the theory of The General Theory. But is there a Keynesian consumption function in the data? I don't think so. At least, not in the form that Keynes postulated in the GT.

Attempts to reconcile short run cross section evidence and long run time series evidence on the value of the multiplier led to permanent income theory and the Ricardian equivalence debate. That debate is what we are all so heated up over right now. If the GT is nothing but the Keynesian multiplier, and if that theory is wrong, then what is the Wannabe Keynesian left with?

The Wannabe Keynesian is left with the theory of supply; a denial of the classical second postulate. My work builds a cohesive microeconomic foundation to the economics of Keynes' theory of aggregate supply. That foundation denies Say's law, (the proposition that supply creates its own demand) and it allows us to us refocus the debate on where it belongs. What is the best way to restore effective demand?

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.

The upward sloping green line, at 45 degrees to the origin, is the Keynesian aggregate supply curve. This green line is the Keynesian theory of aggregate supply.  It says that whatever is demanded will be supplied.

The upward sloping red line is the Keynesian theory of aggregate demand.  In its simplest form, G and I, represent exogenous spending by government and by investors.  The idea that investment is exogenous, was Keynes' way of closing the system.  He thought that investment is driven by the animal spirits of investors.

The Keynesian model says, that in equilibrium, the economy will come to rest at a point where the green line and the red line cross.  There is  no necessary reason why that point should be associated with full employment, and most of the time, it won't be: Hence, the title of Keynes' book, the General Theory of Employment Interest and Money.

The jewel in the crown of Keynesian theory is the consumption function, represented by the equation,

C = A + bY,

where A is autonomous consumption spending (this is a constant) and b is the marginal propensity to consume (this is a number between zero and one). 

Figure 2: The Great Depression

Figure 2 is the Keynesian explanation for the Great Depression. The top red line, labelled X1, represents expenditure in 1929 before the stock market crash. Government purchases were equal to G and investment was equal to I1.

The lower red line, labelled X2, represents expenditure in 1932, after the stock market crash. Government purchases were still equal to G, but investment fell from I1 to I2.  This shifted down the Keynesian aggregate demand curve and led to a drop in income that was bigger than the original drop in I. Expenditure, equal to income, came to rest at point Y2.  The fall in Y was bigger than the fall in I because, as investment fell, so consumption also fell. And every one dollar of reduced consumption led to an additional drop in income of b dollars.  That at least is the theory.   

Keynes' remedy? Government must spend to replace the lost investment spending.

Figure 3: The Keynesian Remedy

Figure 3 shows how that is supposed to work. The lower dashed red line is aggregate demand in 1932 in the depth of the Depression. Government purchases did not change much during the 1930s, but as the world entered WWII, government purchases in the U.S. increased from 15% of the economy to 50% in the space of three years. As G increased from G1 to G2, the dashed red line on Figure3  shifted up and expenditure went from X2 back up to X1. Notice that  G2 + I2 on Figure 3 equals I1 + G on Figure 2.  

The increase in the size of government in war time was huge and was enough to restore full employment at Y1; but now the spending that had been carried out in 1929 by the private sector was  carried out in 1943 by the government.  We cured the unemployment problem by putting all of those unemployed people in the army.

It is also worth pointing out that private consumption expenditure fell during WWII. Keynesian theory predicts that it should have increased.  That fact is a bit uncomfortable for textbook Keynesians who appeal to the special circumstances of a wartime economy.  Here's Tyler Cowen's take on that debate.

OK: enough theory.  Here is My Quiz for Wannabe Keynesians.

1: Does demand determine employment?  Is the 45 degree line an aggregate supply curve?  And if you answered yes to this question: Is the 45 degree line a theory of aggregate supply in the short run, or in the long run?

2: Does you answer to (1) depend on the assumption that prices are sticky?

3: Is the Keynesian consumption function a good way to think about aggregate demand?  Does consumption depend on income, and if so, what is the value of the marginal propensity to consume? 

If you answered YES to all three questions, you are a bonafide card carrying Keynesian of the New York Times variety.  

Here are: My answers to My Quiz for Wannabe Keynesians

1).  YES.  The 45 degree line is an aggregate supply curve.  Further, it is a LONG RUN aggregate supply curve.  Forget about a vertical Phillips curve.  It simply is not there in the data.

2).  NO. The fact that anything demanded will be supplied has absolutely nothing to do with sticky prices or wages.  I repeat; the 45 degree line is a LONG RUN aggregate supply curve.  Prices and wages are determined by monetary factors and by beliefs and there is little or no evidence that they adjust to clear markets as classical theorists would tell us.

3).  NO.  The Keynesian theory of consumption is not a good theory of aggregate demand. The evidence for a large multiplier is weak or non existent.  I am perfectly willing to be proved wrong on that point; but I have kept up with all of the available evidence (nicely summarized here by James Hanley) and I do not find it convincing. 

Valery Ramey's work suggests that the multiplier, if anything, is slightly less than 1 and she finds that

...in most cases private spending falls significantly in response to an increase in government spending.

Perhaps things are different at the lower bound?  Nope! Ramey and Zubairy

...find no evidence that multipliers are different across states, whether defined by the amount of slack in the economy or whether interest rates are near the zero lower bound.

I am not a right wing market touting Chicago card carrying loyalist.  I want to find evidence to support effective policies to combat recessions.  But I am tired of listening to diatribes arguing that there is incontrovertible evidence that fiscal policy is effective at the lower bound. There isn't.

Am I a Keynesian? I believe I am; but you can judge for yourself.  My work explains (1). I am skeptical about (2) because the evidence suggests no stable connection between unemployment and inflation.  In my view ANY combination of unemployment and inflation can hold in a steady state equilibrium. The assertion that we must cure unemployment with traditional fiscal policy is not supported by the facts and arises from a doctrinaire approach to the evidence.

The challenge for macroeconomic theory is to understand how fluctuations in asset markets are transmitted to aggregate demand and the fact that I am skeptical about the effectiveness of traditional fiscal policy does not mean that I think that the market should be left to correct itself. There are alternative policies we can try.  But that is a story for another day.

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.

For example, I have constructed a DSGE model where 25% unemployment is an equilibrium. That model does not use, or need, the concept of sticky wages or sticky prices to explain why high unemployment  persists; persistence is implicit in the notion of an equilibrium. Unlike classical or new-Keynesian DSGE models, my work explains why 25% unemployment is a very bad thing from the point of view of society.

The use of multiple equilibrium models to understand Keynesian economics is part of a research agenda that began at the University of Pennsylvania in the 1980s. That agenda has accelerated recently and the use of multiple equilibrium models to understand data has become mainstream. Jim Bullard uses the work of Benhabib-Schmitt-Grohé and Uribe to understand the liquidity trap. Narayana Kocherlakota applies my work on incomplete factor markets to understand unemployment and the top economics journals are routinely publishing research on the importance of animal spirits as a driver of economic activity. We have moved past the IS-LM model as the true guardian of Keynesian thought.

So what’s wrong with middle brow theorizing? The IS-LM model made the best use of techniques available in 1936 when Hicks introduced it as a way of making logical sense of the General Theory. We’ve moved on since then and we now have tools for bringing dynamics into the picture and for understanding how expectations interact with realized outcomes in ways that respect the methods that have proven successful in so many other branches of economics.

The IS-LM model says nothing about inflation. It says nothing about the passage of time and it does not account for the inability of firms and workers to engage in apparently mutually beneficial trades. We now have the tools to put all of those pieces together and, despite Paul’s claims to the contrary, the result is not a simple regurgitation of 1950s macroeconomics. If a smart theorist like Krugman struggles with formalizing his intuition the problem is not with the mathematics; the problem is with the intuition.

Mathematical formalism is an indispensable tool that has been with us since the late nineteenth century. There was a major leap forward in 1947 with Samuelson’s Foundations of Economic Analysis and a further methodological surge in 1989, when Stokey-Lucas released Recursive Methods in Economic Dynamics. With the publication of Stokey-Lucas, the bar for becoming a practitioner of economics became significantly higher than it was when Adam Smith wrote The Wealth of Nations.

Some in the blogging community hearken for the days when an economist could slap together a verbal argument and publish the result in the Quarterly Journal of Economics. Paul Krugman for example, wants his…

ad hockery back — not as an exclusive approach, but as a permissible one. And that’s not a small thing, given the almost total exclusion of middlebrow modeling from academic macro for the past three decades.

The use of ‘ad hockery’ has not been acceptable in economics for quite a while. And for good reason. As Marshall argued in his 1906 letter to Bowley, mathematics is a language; nothing more. I drew attention to Marshall’s instructions in an earlier post but they are worth repeating;

1. Use mathematics as shorthand language, rather than as an engine of inquiry. 
2. Keep to them till you have done. 
3. Translate into English. 
4. Then illustrate by examples that are important in real life. 
5. Burn the mathematics.
6. If you can’t succeed in 4, burn 3. This I do often

Bloggers and researchers have each ignored Marshall’s dictum; but in different ways. Ph.D. economists have published a huge amount of mathematical junk that bears little or no relevance to any real world problem.1  Some, but not all, economic bloggers have ignored the call to check the logic with mathematics before writing down a verbal argument.

The research community ignored points (3) and (4). Paul would have us ignore points (1) and (2) and that is at least as bad.

The IS-LM model is static. It cannot explain inflation and it has no well developed theory of expectations. DSGE models are a huge methodological advance that gives us logical tools to integrate all of these pieces. There is simply no substitute for the use of mathematics to make sure that an argument hangs together.

______________________________________

1. Don’t get me wrong; mathematics for mathematics sake does play a role in economics journals.  Sometimes, the real world examples come later.  A good example of this process is Lloyd Shapley’s work on stable matches that was used by Al Roth to create markets for kidney exchanges. But the best and most enduring economics papers use the mathematics to explain real world phenomena.  

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!

Paul Krugman takes off from David's post and argues that

...even if you don’t think wage flexibility would help in our current situation (and like Keynes, I think it wouldn’t), Keynesians still need a sticky-wage story to make the facts consistent with involuntary unemployment. For if wages were flexible, an excess supply of labor should be reflected in ever-falling wages. 

Simon Wren-Lewis  takes up the torch.  He argues that

“the evidence that prices are not flexible is ... overwhelming”.

Lets look at some facts. In contrast to Simon's assertion; the evidence from the Great Depression is that wages and prices are remarkably flexible. During the first six years of the Great Depression, nominal wages and nominal prices fell by thirty percent.  Here is a graph of the normalized CPI and a normalized wage index that I constructed using aggregate data on compensation to employees (the details are in my book Expectations Employment and Prices and you can download the data here)

Of course the fact that the CPI and the wage moved in lock step means that the real wage did not fall and that, I would guess, is the fact that Paul and Simon would point to.  But that is very different from there being "overwhelming evidence" in favor of sticky prices.

The new-Keynesians have tried to discipline their models by looking at micro data on the frequency of price changes.  Here again; the NK model falls short. Klenow and Malin find that prices in the micro data are simply not rigid enough to explain the aggregate data.  Keynesians often cite Truman Bewley's 1999 study as evidence in favor of downwardly rigid nominal wages but a piece by Tomas Hirst (posted over at Pieria by Marco Nappolini) draws our attention to recent work by Elsby Shin and Solon which casts serious doubt on the relevance of Bewley's  finding. ESS find, that in the US, the wage data

...show a surprisingly high frequency of nominal wage reductions.

and for the UK,

...like the authors of previous British studies of nominal wage change, [the authors]  are struck by the apparent flexibility of British wages.

So lets get back to what's really important. High and persistent unemployment is a problem.  But it has nothing to do with inflexible wages or sticky prices. Both Classical AND new-Keynesian models are broken. It's time to think outside the box!