Posts Tagged 'J. R. Hicks'

Roger and Me

Last week Roger Farmer wrote a post elaborating on a comment that he had left to my post on Price Stickiness and Macroeconomics. Roger’s comment is aimed at this passage from my post:

[A]lthough price stickiness is a sufficient condition for inefficient macroeconomic fluctuations, it is not a necessary condition. It is entirely possible that even with highly flexible prices, there would still be inefficient macroeconomic fluctuations. And the reason why price flexibility, by itself, is no guarantee against macroeconomic contractions is that macroeconomic contractions are caused by disequilibrium prices, and disequilibrium prices can prevail regardless of how flexible prices are.

Here’s Roger’s comment:

I have a somewhat different take. I like Lucas’ insistence on equilibrium at every point in time as long as we recognize two facts. 1. There is a continuum of equilibria, both dynamic and steady state and 2. Almost all of them are Pareto suboptimal.

I made the following reply to Roger’s comment:

Roger, I think equilibrium at every point in time is ok if we distinguish between temporary and full equilibrium, but I don’t see how there can be a continuum of full equilibria when agents are making all kinds of long-term commitments by investing in specific capital. Having said that, I certainly agree with you that expectational shifts are very important in determining which equilibrium the economy winds up at.

To which Roger responded:

I am comfortable with temporary equilibrium as the guiding principle, as long as the equilibrium in each period is well defined. By that, I mean that, taking expectations as given in each period, each market clears according to some well defined principle. In classical models, that principle is the equality of demand and supply in a Walrasian auction. I do not think that is the right equilibrium concept.

Roger didn’t explain – at least not here, he probably has elsewhere — exactly why he doesn’t think equality of demand and supply in a Walrasian auction is not the right equilibrium concept. But I would be interested in hearing from him why he thinks equality of supply and demand is not the right equilibrium concept. Perhaps he will clarify his thinking for me.

Hicks wanted to separate ‘fix price markets’ from ‘flex price markets’. I don’t think that is the right equilibrium concept either. I prefer to use competitive search equilibrium for the labor market. Search equilibrium leads to indeterminacy because there are not enough prices for the inputs to the search process. Classical search theory closes that gap with an arbitrary Nash bargaining weight. I prefer to close it by making expectations fundamental [a proposition I have advanced on this blog].

I agree that the Hicksian distinction between fix-price markets and flex-price markets doesn’t cut it. Nevertheless, it’s not clear to me that a Thompsonian temporary-equilibrium model in which expectations determine the reservation wage at which workers will accept employment (i.e, the labor-supply curve conditional on the expected wage) doesn’t work as well as a competitive search equilibrium in this context.

Once one treats expectations as fundamental, there is no longer a multiplicity of equilibria. People act in a well defined way and prices clear markets. Of course ‘market clearing’ in a search market may involve unemployment that is considerably higher than the unemployment rate that would be chosen by a social planner. And when there is steady state indeterminacy, as there is in my work, shocks to beliefs may lead the economy to one of a continuum of steady state equilibria.

There is an equilibrium for each set of expectations (with the understanding, I presume, that expectations are always uniform across agents). The problem that I see with this is that there doesn’t seem to be any interaction between outcomes and expectations. Expectations are always self-fulfilling, and changes in expectations are purely exogenous. But in a classic downturn, the process seems to be cumulative, the contraction seemingly feeding on itself, causing a spiral of falling prices, declining output, rising unemployment, and increasing pessimism.

That brings me to the second part of an equilibrium concept. Are expectations rational in the sense that subjective probability measures over future outcomes coincide with realized probability measures? That is not a property of the real world. It is a consistency property for a model.

Yes; I agree totally. Rational expectations is best understood as a property of a model, the property being that if agents expect an equilibrium price vector the solution of the model is the same equilibrium price vector. It is not a substantive theory of expectation formation, the model doesn’t posit that agents correctly foresee the equilibrium price vector, that’s an extreme and unrealistic assumption about how the world actually works, IMHO. The distinction is crucial, but it seems to me that it is largely ignored in practice.

And yes: if we plop our agents down into a stationary environment, their beliefs should eventually coincide with reality.

This seems to me a plausible-sounding assumption for which there is no theoretical proof, and in view of Roger’s recent discussion of unit roots, dubious empirical support.

If the environment changes in an unpredictable way, it is the belief function, a primitive of the model, that guides the economy to a new steady state. And I can envision models where expectations on the transition path are systematically wrong.

I need to read Roger’s papers about this, but I am left wondering by what mechanism the belief function guides the economy to a steady state? It seems to me that the result requires some pretty strong assumptions.

The recent ‘nonlinearity debate’ on the blogs confuses the existence of multiple steady states in a dynamic model with the existence of multiple rational expectations equilibria. Nonlinearity is neither necessary nor sufficient for the existence of multiplicity. A linear model can have a unique indeterminate steady state associated with an infinite dimensional continuum of locally stable rational expectations equilibria. A linear model can also have a continuum of attracting points, each of which is an equilibrium. These are not just curiosities. Both of these properties characterize modern dynamic equilibrium models of the real economy.

I’m afraid that I don’t quite get the distinction that is being made here. Does “multiple steady states in a dynamic model” mean multiple equilibria of the full Arrow-Debreu general equilibrium model? And does “multiple rational-expectations equilibria” mean multiple equilibria conditional on the expectations of the agents? And I also am not sure what the import of this distinction is supposed to be.

My further question is, how does all of this relate to Leijonhfuvud’s idea of the corridor, which Roger has endorsed? My own understanding of what Axel means by the corridor is that the corridor has certain stability properties that keep the economy from careening out of control, i.e. becoming subject to a cumulative dynamic process that does not lead the economy back to the neighborhood of a stable equilibrium. But if there is a continuum of attracting points, each of which is an equilibrium, how could any of those points be understood to be outside the corridor?

Anyway, those are my questions. I am hoping that Roger can enlighten me.

Advertisements

CAUTION Accounting Identity Handle with Care

About three years ago, early in my blogging career, I wrote a series of blog posts (most or all aimed at Scott Sumner) criticizing him for an argument in a blog post about the inefficacy of fiscal stimulus that relied on the definitional equality of savings and investment. Here’s the statement I found objectionable.

Wren-Lewis seems to be . . . making a simple logical error (which is common among Keynesians.)  He equates “spending” with “consumption.”  But the part of income not “spent” is saved, which means it’s spent on investment projects.  Remember that S=I, indeed saving is defined as the resources put into investment projects.  So the tax on consumers will reduce their ability to save and invest.

I’m not going to quote any further from that discussion. If you’re interested here are links to the posts that I wrote (here, here, here, here, here, and this one in which I made an argument so obviously false that, in my embarrassment, I felt like giving up blogging, and this one in which I managed to undo, at least partially, the damage of the self-inflicted wound). But, probably out of exhaustion, that discussion came to an inconclusive end, and Scott and I went on with our lives with no hard feelings.

Well, in a recent post, Scott has again invoked the savings-equals-investment identity, so I am going to have to lodge another protest, even though I thought that, aside from his unfortunate reference to the savings-investment identity, his post made a lot of sense. So I am going to raise the issue one more time – we have had three years to get over our last discussion – hoping that I can now convince Scott to stop using accounting identities to make causal statements.

Scott begins by discussing the simplest version of the income-expenditure model (aka the Keynesian cross or 45-degree model), while treating it, as did Keynes, as if it were interchangeable with the national-accounting identities:

In the standard national income accounting, gross domestic income equals gross domestic output.  In the simplest model of all (with no government or trade) you have the following identity:

NGDI = C + S = C + I = NGDP  (it also applies to RGDI and RGDP)

Because these two variables are identical, any model that explains one will, ipso facto, explain the other.

There is a lot of ground to cover in these few lines. First of all, there are actually three relevant variables — income, output, and expenditure – not just two. Second aggregate income is not really the same thing as consumption and savings. Aggregate income is constituted by the aggregate earnings of all factors of production. However, an accounting identity assures us that all factor incomes accruing to factors of production, which are all ultimately owned by the households providing services to business firms, must be disposed of either by being spent on consumption or by being saved. Aggregate expenditure is different from aggregate income; expenditure is constituted not by the earnings of households, but by their spending on consumption and by the spending of businesses on investment, the purchase of durable equipment not physically embodied in output sold to households or other businesses. Aggregate expenditure is very close to but not identical with aggregate output. They can differ, because not all output is sold, some of it being retained within the firm as work in progress or as inventory. However, in an equilibrium situation in which variables were unchanging, aggregate income, expenditure and output would all be equal.

The equality of these three variables can be thought of as a condition of macroeconomic equilibrium. When a macroeconomic system is not in equilibrium, aggregate factor incomes are not equal to aggregate expenditure or to aggregate output. The inequality between factor incomes and expenditure induces further adjustments in spending and earnings ultimately leading to an equilibrium in which equality between those variables is restored.

So what Scott should have said is that because NGDI and NGDP are equal in equilibrium, any model that explains one will, ipso facto, explain the other, because the equality between the two is the condition for finding a solution to the model. It therefore follows that savings and investment are absolutely not the same thing. Savings is the portion of household earnings from providing factor services that is not spent on consumption. Investment is what business firms spend on plant and equipment. The two magnitudes are obviously not the same, and they do not have to be equal. However, equality between savings and investment is, like the equality between income and expenditure, a condition for macroeconomic equilibrium. In an economy not in equilibrium, savings does not equal investment. But the inequality between savings and investment induces adjustments that, in a stable macroeconomic system, move the economy toward equilibrium. Back to Scott:

Nonetheless, I think if we focus on NGDI we are more likely to be able to think clearly about macro issues.  Consider the recent comment left by Doug:

Regarding Investment, changes in private investment are the single biggest dynamic in the business cycle. While I may be 1/4 the size of C in terms of the contribution to spending, it is 6x more volatile. The economy doesn’t slip into recession because of a fluctuation in Consumption. Changes in Investment drive AD.

This is probably how most people look at things, but in my view it’s highly misleading. Monetary policy drives AD, and AD drives investment. This is easier to explain if we think in terms of NGDI, not NGDP.  Tight money reduces NGDI.  That means the sum of nominal consumption and nominal saving must fall, by the amount that NGDI declines.  What about real income?  If wages are sticky, then as NGDI declines, hours worked will fall, and real income will decline.

So far we have no reason to assume that C or S will fall at a different rate than NGDI. But if real income falls for temporary reasons (the business cycle), then the public will typically smooth consumption.  Thus if NGDP falls by 4%, consumption might fall by 2% while saving might fall by something like 10%.  This is a prediction of the permanent income hypothesis.  And of course if saving falls much more sharply than gross income, investment will also decline sharply, because savings is exactly equal to investment.

First, I observe that consumption smoothing and the permanent-income hypothesis are irrelevant to the discussion, because Scott does not explain where any of his hypothetical numbers come from or how they are related. Based on commenter Doug’s suggestion that savings is ¼ the size of consumption, one could surmise that a 4% reduction in NGDP and a 2% reduction in consumption imply a marginal propensity to consumer of 0.4. Suppose that consumption did not change at all (consumption smoothing to the max), then savings, bearing the entire burden of adjustment, would fall through the floor. What would that imply for the new equilibrium of NGDI? In the standard Keynesian model, a zero marginal propensity to consume would imply a smaller effect on NGDP from a given shock than you get with an MPC of 0.4.

It seems to me that Scott is simply positing numbers and performing calculations independently of any model, and then tells us that the numbers have to to be what he says they are because of an accounting identity. That does not seem like an assertion not an argument, or, maybe like reasoning from a price change. Scott is trying to make an inference about how the world operates from an accounting identity between two magnitudes. The problem is that the two magnitudes are variables in an economic model, and their values are determined by the interaction of all the variables in the model. Just because you can solve the model mathematically by using the equality of two variables as an equilibrium condition does not entitle you to posit a change in one and then conclude that the other must change by the same amount. You have to show how the numbers you have posited are derived from the model.

If two variables are really identical, rather than just being equal in equilibrium, then they are literally the same thing, and you can’t draw any inference about the real world from the fact that they are equal, there being no possible state of the world in which they are not equal. It is only because savings and investment are not the same thing, and because in some states of the world they are not equal, that we can make any empirical statement about what the world is like when savings and investment are equal. Back to Scott:

This is where Keynesian economics has caused endless confusion.  Keynesians don’t deny that (ex post) less saving leads to less investment, but they think this claim is misleading, because (they claim) an attempt by the public to save less will boost NGDP, and this will lead to more investment (and more realized saving.)  In their model when the public attempts to save less (ex ante), it may well end up saving more (ex post.)

I agree that Keynesian economics has caused a lot of confusion about savings and investment, largely because Keynes, who, as a philosopher and a mathematician, should have known better, tied himself into knots by insisting that savings and investment are identical, while at the same time saying that their equality was brought about, not by variations in the rate of interest, but by variations in income. Hawtrey, Robertson, and Haberler, among others, pointed out the confusion, but Keynes never seemed to grasp the point. Textbook treatments of national-income accounting and the simple Keynesian cross still don’t seem to have figured this out. But despite his disdain for Keynesian economics, Scott still has to figure it out, too. The best place to start is Richard Lipsey’s classic article “The Foundations of the Theory of National Income: An Analysis of Some Fundamental Errors” (a gated link is available here).

Scott begins by sayings that Keynesians don’t deny that (ex post) less saving leads to less investment. I don’t understand that assertion at all; Keynesians believe that a desired increase in savings, if desired savings exceeded investment, leads to a decrease in income that reduces saving. But the abortive attempt to increase savings has no effect on investment unless you posit an investment function (AKA an accelerator) that includes income as an independent variable. The accelerator was later added to the basic Keynesian model Hicks and others in order to generate cyclical fluctuations in income and employment, but non-Keynesians like Ralph Hawtrey had discussed the accelerator model long before Keynes wrote the General Theory. Scott then contradicts himself in the next sentence by saying that Keynesians believe that by attempting to save less, the public may wind up saving more. Again this result relies on the assumption of an accelerator-type investment function, which is a non-Keynesian assumption. In the basic Keynesian model investment is determined by entrepreneurial expectations. An increase (decrease) in thrift will be self-defeating, because in the new equilibrium income will have fallen (risen) sufficiently to reduce (increase) savings back to the fixed amount of investment entrepreneurs planned to undertake, entrepreneurial expectations being held fixed over the relevant time period.

I more or less agree with the rest of Scott’s post, but Scott seems to have the same knee-jerk negative reaction to Keynes and Keynesians that I have to Friedman and Friedmanians. Maybe it’s time for both of us to lighten up a bit. Anyway in honor of Scott’s recent appoint to the Ralph Hawtrey Chair of Monetary Policy at the Mercatus Center at George Mason University, I will just close with this quotation from Ralph Hawtrey’s review of the General Theory (chapter 7 of Hawtrey’s Capital and Employment) about Keynes’s treatment of savings and investment as identically equal.

[A]n essential step in [Keynes’s] train of reasoning is the proposition that investment and saving are necessarily equal. That proposition Mr. Keynes never really establishes; he evades the necessity doing so by defining investment and saving as different names for the same thing. He so defines income to be the same thing as output, and therefore, if investment is the excess of output over consumption, and saving is the excess of income over consumption, the two are identical. Identity so established cannot prove anything. The idea that a tendency for investment and saving to become different has to be counteracted by an expansion or contraction of the total of incomes is an absurdity; such a tendency cannot strain the economic system, it can only strain Mr. Keynes’s vocabulary.

Temporary Equilibrium One More Time

It’s always nice to be noticed, especially by Paul Krugman. So I am not upset, but in his response to my previous post, I don’t think that Krugman quite understood what I was trying to convey. I will try to be clearer this time. It will be easiest if I just quote from his post and insert my comments or explanations.

Glasner is right to say that the Hicksian IS-LM analysis comes most directly not out of Keynes but out of Hicks’s own Value and Capital, which introduced the concept of “temporary equilibrium”.

Actually, that’s not what I was trying to say. I wasn’t making any explicit connection between Hicks’s temporary-equilibrium concept from Value and Capital and the IS-LM model that he introduced two years earlier in his paper on Keynes and the Classics. Of course that doesn’t mean that the temporary equilibrium method isn’t connected to the IS-LM model; one would need to do a more in-depth study than I have done of Hicks’s intellectual development to determine how much IS-LM was influenced by Hicks’s interest in intertemporal equilibrium and in the method of temporary equilibrium as a way of analyzing intertemporal issues.

This involves using quasi-static methods to analyze a dynamic economy, not because you don’t realize that it’s dynamic, but simply as a tool. In particular, V&C discussed at some length a temporary equilibrium in a three-sector economy, with goods, bonds, and money; that’s essentially full-employment IS-LM, which becomes the 1937 version with some price stickiness. I wrote about that a long time ago.

Now I do think that it’s fair to say that the IS-LM model was very much in the spirit of Value and Capital, in which Hicks deployed an explicit general-equilibrium model to analyze an economy at a Keynesian level of aggregation: goods, bonds, and money. But the temporary-equilibrium aspect of Value and Capital went beyond the Keynesian analysis, because the temporary equilibrium analysis was explicitly intertemporal, all agents formulating plans based on explicit future price expectations, and the inconsistency between expected prices and actual prices was explicitly noted, while in the General Theory, and in IS-LM, price expectations were kept in the background, making an appearance only in the discussion of the marginal efficiency of capital.

So is IS-LM really Keynesian? I think yes — there is a lot of temporary equilibrium in The General Theory, even if there’s other stuff too. As I wrote in the last post, one key thing that distinguished TGT from earlier business cycle theorizing was precisely that it stopped trying to tell a dynamic story — no more periods, forced saving, boom and bust, instead a focus on how economies can stay depressed. Anyway, does it matter? The real question is whether the method of temporary equilibrium is useful.

That is precisely where I think Krugman’s grasp on the concept of temporary equilibrium is slipping. Temporary equilibrium is indeed about periods, and it is explicitly dynamic. In my previous post I referred to Hicks’s discussion in Capital and Growth, about 25 years after writing Value and Capital, in which he wrote

The Temporary Equilibrium model of Value and Capital, also, is “quasi-static” [like the Keynes theory] – in just the same sense. The reason why I was contented with such a model was because I had my eyes fixed on Keynes.

As I read this passage now — and it really bothered me when I read it as I was writing my previous post — I realize that what Hicks was saying was that his desire to conform to the Keynesian paradigm led him to compromise the integrity of the temporary equilibrium model, by forcing it to be “quasi-static” when it really was essentially dynamic. The challenge has been to convert a “quasi-static” IS-LM model into something closer to the temporary-equilibrium method that Hicks introduced, but did not fully execute in Value and Capital.

What are the alternatives? One — which took over much of macro — is to do intertemporal equilibrium all the way, with consumers making lifetime consumption plans, prices set with the future rationally expected, and so on. That’s DSGE — and I think Glasner and I agree that this hasn’t worked out too well. In fact, economists who never learned temporary-equiibrium-style modeling have had a strong tendency to reinvent pre-Keynesian fallacies (cough-Say’s Law-cough), because they don’t know how to think out of the forever-equilibrium straitjacket.

Yes, I agree! Rational expectations, full-equilibrium models have turned out to be a regression, not an advance. But the way I would make the point is that the temporary-equilibrium method provides a sort of a middle way to do intertemporal dynamics without presuming that consumption plans and investment plans are always optimal.

What about disequilibrium dynamics all the way? Basically, I have never seen anyone pull this off. Like the forever-equilibrium types, constant-disequilibrium theorists have a remarkable tendency to make elementary conceptual mistakes.

Again, I agree. We can’t work without some sort of equilibrium conditions, but temporary equilibrium provides a way to keep the discipline of equilibrium without assuming (nearly) full optimality.

Still, Glasner says that temporary equilibrium must involve disappointed expectations, and fails to take account of the dynamics that must result as expectations are revised.

Perhaps I was unclear, but I thought I was saying just the opposite. It’s the “quasi-static” IS-LM model, not temporary equilibrium, that fails to take account of the dynamics produced by revised expectations.

I guess I’d say two things. First, I’m not sure that this is always true. Hicks did indeed assume static expectations — the future will be like the present; but in Keynes’s vision of an economy stuck in sustained depression, such static expectations will be more or less right.

Again, I agree. There may be self-fulfilling expectations of a low-income, low-employment equilibrium. But I don’t think that that is the only explanation for such a situation, and certainly not for the downturn that can lead to such an equilibrium.

Second, those of us who use temporary equilibrium often do think in terms of dynamics as expectations adjust. In fact, you could say that the textbook story of how the short-run aggregate supply curve adjusts over time, eventually restoring full employment, is just that kind of thing. It’s not a great story, but it is the kind of dynamics Glasner wants — and it’s Econ 101 stuff.

Again, I agree. It’s not a great story, but, like it or not, the story is not a Keynesian story.

So where does this leave us? I’m not sure, but my impression is that Krugman, in his admiration for the IS-LM model, is trying too hard to identify IS-LM with the temporary-equilibrium approach, which I think represented a major conceptual advance over both the Keynesian model and the IS-LM representation of the Keynesian model. Temporary equilibrium and IS-LM are not necessarily inconsistent, but I mainly wanted to point out that the two aren’t the same, and shouldn’t be conflated.


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.

Archives

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 2,343 other followers

Follow Uneasy Money on WordPress.com
Advertisements