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Sticky Stability, Dry Destability

Paul Krugman recently explained the contradiction of a statement like:

I don’t believe in sticky prices, or at least not except for very brief periods, and therefore I believe that the economy is almost always close to full employment.

It is important to note that the observational error of not believing in sticky prices – and evolution, too? – is orders of magnitude worse than the analytical flaws that follow. Krugman’s IS-LM framework suggests that because falling prices can’t reduce interest rates at the zero lower bound, there’s no reason to believe aggregate demand is higher at a lower price level, marginalizing the case for wage flexibility. 

The case against flexibility, though, can be extended into normal times. The argument comes from three papers by the DeLong-Summers duo – the first empirically founding theoretical results in the second, and the third as basis for my own somewhat unorthodox interpretation. All together, there’s good reason to believe the sterile, representative agent models from DeLong and Summers will make Krugman to “eat [his] microfoundations”.

Before I continue, let’s explain why understanding the effect of price flexibility is key not just to formal discourse, but policy action. Indeed there’s no reason to believe the government has any fundamental authority upon inherent rigidities in the labor market – aside from long run, secular adjustments such as systematic deunionization. Rather, this conversation is directed at the numerous, conservative critics who question Keynesians for citing sticky wages as cause for recession on the one hand, and supporting minimum wage on the other. More generally, questioning flexible wages outside of the zero lower bound, is in important counterpoint to said structural reforms such as right to work, abolishment of minimum wage, or reluctance to provide unemployment insurance.

The first relevant paper from Brad DeLong and Larry Summers considers “The Changing Cyclical Variability of Economic Activity in the United States” concluding that:

the two principal factors promoting economic stability [are Keynesian auto-stabilizers] and the increasing rigidity of prices. We attribute the latter development to the increasing institutionalization of the economy.

They also suggest a rather stylized (and ultimately unconvincing) model in which wages are set in negotiations where workers are backword-looking. Still, the Keynesian framework here brings important question to the assumption that flexibility is everywhere and always stabilizing. Another very important empirical conclusion here, which will become relevant soon, is noting that the autocorrelation in quarterly output growth rose from 0.4 before WWI to 0.8 in 1985.

This finding allowed DeLong and Summers to drop the assumption of serially uncorrelated changes in output stipulated in John Taylor’s staggered contract model. In their 1985 paper (written in profoundly unreadable font) they develop a key insight showing destabilizing effects of increased wage flexibility among perfectly rational agents. To reach this conclusion, the staggered contract model is amended in two important ways:

  1. As mentioned, serially uncorrelated output growth is a senseless assumption that ought to be dropped – allowing for a persistent nominal income shock.
  2. Elaborating the treatment of output to include real interest rates by relaxing the assumption that money demand is interest inelastic.

We can extend the latter point to note that if the real interest rate determines aggregate demand and the nominal interest rate clears the money market inflation creates a wedge between the two altering output by shifting the solution of the IS-LM system. We can qualitatively state the instability of flexibility as:

While a lower price level is expansionary, the expectation of falling prices is contractionary.

And while their model “resisted” analytical solution, the numerical results confirmed that hypothesis. They determined this by measuring the variance of the steady-state output to random demand shocks modeled by unit variant white noise. They find that price flexibility – modeled by g which measures the responsiveness of prices to changes in demand – “is destabilizing at the margin in almost all cases”. Indeed, the result is so striking that only as demand shocks approximate random noise is an increase in flexibility at the margin stabilizing, and even then only when prices are near perfectly rigid to begin with. That both conditions hold is unlikely.

To demonstrate the robustness of their result, DeLong and Summers show that it holds even if extended to Taylor’s more complete 1980 model which includes a more generalized contract length. We learn that even if price flexibility is increased by decreasing the relative length of contracts, or number of overlapping commitments, steady state variance increases. The importance of this result is hard to overstate as it suggests that even with optimizing agents, long contract lengths do not explain variability in the business cycle.

Penultimately, we are shown that this result holds absolutely except “very near” the Walrasian limit (these are mind-games as we are obviously not). They do this by altering the “time” taken in each time step t. Without explaining the math:

Keeping the parameter g [flexibility] the same in the transformed and they transformed model implies that the transformation to a period that covers half as much time involves doubling of the responsiveness of the price level to output deviations.

They suggest this is a preferable method of studying increased flexibility because of the vast inherent difference between one, two, and many period contracts arising from the naturally discrete nature. While varying g is possible, it results in meaninglessly sensitive variations at the upper bound. Therefore, by altering the “time length” of each period allows a continuous movement towards Walrasian conditions.

Quantitatively, they find that given an initial parameter set, only by altering said setup such that the periods are more than 87.5% shorter can any meaningful increases in stability from flexibility be noticed. They explain this effect qualitatively as:

The effect of a shortened period in causing more rapid price changes – and thus more of an incentive to postpone or accelerate spending by one period – approximately balances the stabilizing effects of more rapid price flexibility.

And finally, the most interesting part of the paper vindicates the claim that flexibility is destabilizing against critics who noted that with durable capital that is costly to adjust, since price flexibility leads to less erratic long run interest rates, output follows suit. They go on to show that even if since is determined by long run investment which are itself determined by Tobin’s Q, under an empirically-founded estimate of equity-risk premium with capital depreciation at 0.20, flexibility is destabilizing

They show all this within the highly stylized world of perfect rationality and atomistic agents. In reality, it is likely that flexibility is even more destabilizing considering the psychological trauma of significant deflation and cyclical adjustment. While there is a lot of leeway within representative agent setups to model – if you will – bullshit, that this exercise is developed in the context of strong empirical foundations suggesting a fall in serially correlated output and increases in rigidity moving with increases in stability and prosperity increases my confidence in its validity. Correlation is not a good reason to believe in causation. Theory founded on rigorous mathematics is not a good reason to believe in causation. But correlation with theory is a strong force.

The third paper from the duo, “Fiscal Policy in a Depressed Economy”, doesn’t mention price flexibility at all, and I’m not sure either DeLong or Summers would endorse my interpretation. That said, at the heart of their paper is the belief is the importance of hysteresis effects from fiscal consolidation, where resulting demand shortfall can create long-run unemployment decreasing future tax revenues and increase the deficit.

I suggest that hysteresis as defined in this paper will be more dangerous with greater flexibility. Let’s say all workers suddenly disemployed because of recession are to make a choice – every day – whether to remain in the labor market or not. Let’s say both wages and prices are flexible, with the latter falling more. Because workers suffer from a money illusion during short-run adjustment, they will not notice that (even with automatic stabilizers) real wages have not fallen as much. Therefore, the opportunity cost of exiting the labor market falls, and many more will fall into long-run unemployment traps.

Conversely, because of money illusion and normal irrationalities, fewer people will be tempted to reenter the labor market than if prices had remained at artificially high levels. 

Altogether, this is unorthodox because while most (not, unfortunately, all) economists agree that real wage decreases via inflation is preferable to deflation few question the idea that flexibility is bad even outside of a liquidity trap. Many accept that wage decreases via inflation are good, but note that deflation (flexibility) is preferable to nothing.

However, a more creative (and granted more liable to misinterpretation) read of DeLong and Summers (2012) suggests that wage flexibility may have perverse consequences on labor market churn, which is key to economic health. 

So ultimately I have stronger convictions than Krugman,

Even in a liquidity trap, deflation could be expansionary if it is perceived as temporary, so that deflation now gives rise to expectations of future inflation.

that wage flexibility isn’t all that important. First it’s important to note a difference between DeLong/Summers who argue about the variance of steady-state output which isn’t necessarily related to contractionary or expansionary effects per se. (Though in almost any sense, stability dampens the business cycle which is good). But if you accept my final point that deflation has adverse effects on labor market entry, it’s possible to imagine a situation wherein expectedly temporary deflation is contractionary.

Also note that I really have a tough time constructing a world where deflation is perceived as temporary, in any meaningful sense. In the long-run, very few people outside of Japan believe their central bank will tolerate deflation. So it’s basically a non-statement. In the short run, recessionary-deflationary expectations are self-confirming which makes it difficult for future expectations to clash with present expectations. 

For example, if I expect an increase in prices in some future time period, I won’t decrease production now. But if I don’t decrease production now, aggregate demand doesn’t fall and the demand-side foundations for deflation erode.

Anyway, it’s hard to believe I wrote this long piece in response to people who “don’t believe in sticky prices”. None the less, repeat after me: sticky is stable.

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1 comment
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