It’s time for another installment, after a longer than expected hiatus, in my series of posts summarizing and commenting on Earl Thompson’s path-breaking paper, “A Reformulaton of Macroeconomic Theory.” In the first three installments I described the shift on modeling strategy from the conventional Keynesian IS-LM model adopted by Thompson, and the basic properties of his reformulated model. In the first installment, I explained that Thompson’s key analytic insight was to ground the model in an explicitly neoclassical framework, exploiting the straightforward and powerful implications of the neoclassical theory of production to derive the basic properties of a macroeconomc model structurally comparable to the IS-LM model. The reformulated model shifts the analytic focus from the Keynesian spending functions to the conditions for factor-market equilibrium in a single-output, two-factor model. In the second installment, I explained how Thompson drew upon the Hicksian notion of temporary equilibrium for an explicit treatment of Keynesian (involuntary) unemployment dependent on incorrect (overly optimistic) expectations of future wages. While the model allows for inefficient (relative to correct expectations) choices by workers to remain unemployed owing to incorrect expectations, the temporary equilibrium nevertheless involves no departure from market clearing, and no violation of Walras’s Law. In the third installment, I described the solution of the model, deriving two market-equilibrium curves, one a locus of points of equilibrium (combinations of price levels and nominal interest rates) in the two factor markets (for labor and capital services) and one a locus of points of money-market equilibrium (again in terms of price levels and nominal interest rates) using the standard analytic techniques for deriving the Keynesian IS and LM curves.

Although not exactly the same as the Keynesian LM curve (constructed in income-interest-rate space), the locus of points of monetary equilibrium, having a similar upward slope, was assigned the familiar LM label. However, unlike the Keynesian IS curve it replaces, the locus of points, labeled FF, of factor-market equilibrium is positively sloped. The intersection of the two curves determines a temporary equilibrium, characterized by a price level, a corresponding level of employment, and for a given expected-inflation parameter, a corresponding real and nominal interest rate. The accompanying diagram, like Figure 4 in my previous installment, depicts such a temporary-equilibrium solution. I observed in the previous installment that applying Walras’s Law allows another locus of points corresponding to equilibrium in the market for the single output, which was labeled the CC curve (for commodity market equilibrium) by Thompson. The curve would have to lie in the space between the FF curve and the LM curve, where excess demands in each market have opposite (offsetting) signs. The CC curve is in some sense analogous to the Keynesian IS curve, but, as I am going to explain, it differs from the IS curve in a fundamental way. In the accompnaying diagram, I have reproduce the FF and LM curves of the with reformulated model with the CC curve drawn between the FF and LM curves. The slope of the CC curve is clearly positive, in contrast to the downward slope normally attributed to the Keynesian IS curve.

In this post, I am going to discuss Thompson’s explanation of the underlying connection between his reformulated macroeconomic model and the traditional Keynesian model. At a formal level, the two models share some of the same elements and a similar aggregative structure, raising the question what accounts for the different properties of the two models and to what extent can the analysis of one model be translated into the terms of the other model?

Aside from the difference in modeling strategy, focusing on factor-market equilibrium instead of an aggregate spending function, there must be a deeper underlying substantive difference between the two models, otherwise the choice of which market to focus on would not matter, Walras’s Law guaranteeing that anyone of the n markets can be eliminated without changing the equilibrium solution of a system of excess demand equations. So let us look a bit more closely at the difference between the Keynesian IS curve and the CC curve of the reformulated model. The most basic difference is that the CC curve relates to a stock equilibrium, with an equilibrating value of P in the market for purchasing the stock of commodities, representing the equilibrium market value of a unit of output. On the other hand, the Keynesian IS curve is measuring a flow, the rate of aggregate expenditure, the equilibrium corresponding to a particular rate of expenditure.

Thompson sums up the underlying difference between the Keynesian model and the reformulated model in two very dense paragraphs on pp. 16-17 of his paper under section heading “The role of aggregate spending and the Keynesian stock-flow fallacy.” I will quote the two paragraphs in full and try to explain as best as I can, what he is saying.

All of this is not to say that the flow of aggregate spending is irrelevant to our temporary equilibrium. The expected rate of inflation [as already noted a crucial parameter in the reformulated model] may depend parametrically upon the expected rate of spending. Then, an increase in the expected rate of spending on consumption or investment (or, more generally, an increase in the expected

futureexcess demand for goods at the originally expected prices) would, by increasedPe[the expected price level] and thusr[the nominal interest rate] for a givenR/P[the ratio of the rental price of capital to the price of capital, aka the real interest rate], shift up the FF curve. In a Modern Money Economy [i.e., an economy using a non-interest-bearing fiat money monopolistically supplied by a central bank], this shift induces a movement out of money [because an increase in the nominal interest rate increases the cost of holding non-interest-bearing fiat money] in the current market (a movement along the LM curve) and a higher current price level. This exogenous treatment of spendings variables, while perhaps most practical from the standpoint of business cycle policy, does not capture the Keynesian concept of anequilibriumrate of expenditure.

It is worth pausing here to ponder the final sentence of the paragraph, because the point that Thompson is getting at is far from obvious. I think what he means is that one can imagine, working within the framework of the reformulated FF-LM model, that a policy change, say an increase in government spending, could be captured by positing an effect on the expected price level. Additional government spending would raise the expected price level, thus causing an upward shift in the FF curve, thereby inducing people to hold less cash, leading to a new equilibrium associated with an intersection of the new FF curve at a point further up and to the right along the LM curve than the original intersection. Thus, the FF-LM framework can accommodate a traditional Keynesian fiscal policy exercise. But the IS-LM framework is unable to specify what the equilibrium rate of spending is and how that equilibrium can be determined, the problem being that there does not seem to be any variable in the model that adjusts to equilibrate the rate of spending in the way that the price level adjusts to equilibrate the market for output in the reformulated model. There is no condition specified to distinguish an equilibrium rate of spending from a non-equilibrium rate of spending. Now back to Thompson:

In order to obtain an equilibrium rate of expenditures – and thus an equilibrium rate of capital accumulation [aka investment, how much output will be carried over to next period] – a corresponding price variable must be added. The only economically natural price to introduce to equilibrate the demand and supply of next period’s capital goods is the price of next period’s capital goods. [In other words, how much of this period’s output that people want to hold until next period depends on the relationship between the current price of the output and the expected price in the next period.] This converts

Peinto an equilibrating variable. Indeed, Section III below will show that ifPeis made the equilibrating price variable, making the rate of inflation an independently equilibrating variable rather than an expectations parameter determined by other variables in the system and extending the temporary equilibrium to a two-period equilibrium model in which only prices in the third and later periods may be incorrectly expected in the current period, the Keynesian expenditures condition, the equality of ex ante savings and investment, is indeed achieved. However, Section III will also show that the familiar Keynesian comparative statics results that are based upon a negatively sloped IS curve fail to hold in the extended model just as they fail in the above, single period model.

The upshot of Thompson’s argument is that you can’t have a Keynesian investment function without introducing an expected price for capital in the next period. Without an expected price of output in the next period, there is nothing to determine how much investment entrepreneurs choose to undertake in the current period. And if you want to identify an equilibrium rate of expenditure, which means an equilibrium rate of investment, then you must perforce allow the expected price for capital in the next period to adjust to achieve that equilibrium.

I must admit that I have been struggling with this argument since I first heard Earl make it in his graduate macro class almost 40 years ago, and it is only recently that I have begun to think that I understand what he was getting at. I was helped in seeing his point by the series of posts (this, this, this, this, this, this, this, and this) that I wrote earlier this year about identities and equilibrium conditions in the basic Keynesian model, and especially by the many comments and counterarguments that I received as a result of those posts. The standard Keynesian expenditure function is hard to distinguish from an income function (which also makes it hard to distinguish investment from savings), which makes it hard to understand the difference between expenditure being equal in equilibrium and being identical to savings in general or to understand the difference between savings and investment being equal in equilibrium and being identical in general. There is a basic problem in choosing define an equilibrium in terms of two magnitudes so closely related as income and expenditure. The equilibrating mechanism doesn’t seem to be performing any real economic work, so it hard to tell the difference between an equilibrium state and a disequilibrium state in such a model. Thompson may have been getting at this point from another angle by focusing on the lack of any equilibrating mechanism in the Keynesian model, and suggesting that an equilibrating mechanism, the expected future price level or rate of inflation, has to be added to the Keynesian model in order to make any sense out of it.

In my next installment, I will consider Thompson’s argument about the instability of the equilibrium in the FF-LM model.

David

Again, I think Leijonhufvud had the answer to Keynes’s original notion of equilibrium. Equilibrium has atleast two meanings – a state that achieves macroeconomic efficiency, and a state that has no inherent tendency to change further unless you ‘prod’ it in some manner.

As a dyed-in-the-wool Marshallian, Keynes only regarded the second as equilibrium in the positive sense, the first being a normative version, deviations from which he was seeking to explain.

Re-formulating in terms of Thompson’s model, yes, investment is a function of the future price of capital. MEC is precisely that! (you can look at it in terms of cash flows, or ‘mental’ discount rates, it’s isopmorphic) A fall in MEC makes future capital goods appear less attractive. This causes a fall in investment. The fall in investment simply causes expenditure, and hence income, to fall. And that’s the Keynesian recession. Ex-post, income has adjusted to match expenditure, savings has adjusted to match investment.

Thus,the system has found an equilibrium, a new point attractor, from which it does not move unless prodded. However, it has not achieved efficiency, as the capital market is in disequilibrium, or more accurately, in an *inefficient equilibrium*.

That’s the central insight of Keynesian thought. In the aggregate, income adjusts. And it adjusts mainly on count of investment. And once income has adjusted, there is no tendency for capital prices to move any other, thus preventing the system from achieving efficiency.

If you allow the capital market an efficient equilibrium, a Keynesian recession is a logical contradiction.

Note that applying a capital market inefficiency + output efficiency model gets you the central Austrian result, I&C are negatively correlated. Which is of course not borne out by the data.

Ritwik, “And once income has adjusted, there is no tendency for capital prices to move any other [further?], thus preventing the system from achieving efficiency.”

I think you’re leaving out the next steps, i.e., the transaction demand for money falls, the interest rate falls, and, all else equal, capital prices rise. Of course, other prices are also likely falling, so real cash balances are rising, which releases some cash from hoards. Of course, Keynes’s point was: why go through all the painful adjustment when you can get here more easily by simply reducing the rate of interest.

greghill

Yes, that should be further, not other.

And, the fall in income reduces the demand for money to hit the new equilibrium without letting r fall enough to clear the capital market. We began with a state of excess money demand.

The Pigou effect is weak sauce. Here’s Leijonhufvud explaining why :

Click to access paperitma.pdf

On pg 24 of this you will find the sequence that I’ve mentioned above :

Click to access wp186.pdf

Ritwik, Can you identify for me what constitutes the inefficiency in the capital market equilibrium that you are referring to? Why is entrepreneurial pessimism an inefficiency?

David

The inefficiency is not entrepreneurial pessimism, but the refusal of the cost of risk capital to come down and clear the market at the new marginal efficiency of risk capital.

When the MEC falls, it exerts a downward pressure on the cost of capital. However, the bearish lenders go short risk capital. This creates upward pressure on the cost of capital, and before it falls down enough to match the new MEC, investment, and hence income and employment falls, reducing money demand. Now, there is no further pressure on the cost of capital. It has reached a new equilibrium level, albeit an inefficient one as it is higher than the MEC.

Note that this is not the ‘animal spirits’ argument, which claims that the volatility of MEC is higher than is socially optimal. I’m accepting the new MEC as a given.

Ritwik, OK, that’s the classic Keynesian liquidity-preference argument, which says that the lower bound on the interest rate is not zero, but some positive number, depending on where bearish speculators draw the line. Nowadays, we have more or less conflated the classic Keynesian argument with the zero-lower-bound argument. But you are right that they are not strictly the same.