Sticky prices, leverage, and Pascal’s wager

May 16th, 2011
in Op Ed

Pascal by Steve Waldman,Guest Author, who writes about finance and economics for the website Interfluidity.

Caption:  Blaise Pascal

In Keynesian / quasi-monetarist of explanations of depression, sticky prices play an essential role. If prices were not sticky, a deficiency of expenditure would just lead to a reduction of the price level, and nothing very bad would happen.

Follow up:

There are (at least) two channels by which sticky prices can harm production:

  1. Sticky relative prices distort patterns of economic activity, preventing the economy from achieving the optimal level of production. Following a sharp change in nominal expenditure, the sluggishness with which some prices adjust leaves activity badly distorted, and so observed real production falls relative to the expenditure-stabilized trend.
  2. Sticky absolute prices allow changes in nominal expenditure to affect levels of economic activity more directly. Suppose we set all relative prices correctly, and then fix them in stone. Now, if we scale up the willingness of all agents to part with money, we might not observe a decline in aggregate production, but markets would fail to clear and we would observe shortages. If we scale down aggregate expenditure, we would observe a glut of capacity and a fall in production (as measured by transactions).

I’m interested here in the second channel. [1] Except under politically imposed price controls, we rarely observe what absolute price-stickiness would predict in an expenditure boom — production at capacity but shortages at offered prices. The relevant case is asymmetrical. Absolute prices adjust upward easily, but they are “sticky downward”. They do not fall.

A while back I had a post that described the price of extinguishing old debt as “the stickiest price”. After a wonderful comment exchange with Nick Rowe and others, we came, I think, to some agreement that sticky nominal debt contracts were both like and unlike sticky goods prices in important ways. However, I’ve recently come to think that, besides the direct but distinct distortions associated with rigid nominal debt, indebtedness might be an important source of downward stickiness in the prices of goods and services.

The argument is a form of Pascal’s wager. Suppose that I own a firm which generally operates at capacity. The firm is leveraged in the expectation of achieving a certain level of nominal income, out of which my debt will be serviced. Should I fail to service my debt, I will face outcomes that are very dire. Perhaps my firm will be out of business, perhaps I will have to surrender the firm to creditors. Perhaps I’ll manage to squeak by after a very radical downsizing that allows me to service my debts but destroys the long-term value of the firm. Let’s refer to any of these catastrophes as “bankruptcy”.

Suppose there is a shock to nominal demand, and people become less willing to part with money. I have two choices. I can cut prices to maintain my expected volume of sales, or I can leave prices alone. In the first case, I condemn myself to bankruptcy with certainty. I was already operating at capacity, so there is no hope that an increase in volume will save my bacon if I reduce prices.

If I do not cut my prices, my expected level of sales will fall due to the recession. On average, I will still be bankrupt. But I could get lucky. In any economic environment, sales are a fickle random variable. It is possible, if I stick with my old prices, that sales will prove robust despite the dowturn. So the rational thing for me to do is to refuse to adjust my prices and hope for the best.

Now this is a perverse outcome, from an economic perspective. Considered without regard to financing, my firm fails to maximize expected profits by failing to adjust its pricing. It instead maximizes the value of the right tail of the profit distribution, because as the owner of a leveraged firm, the right tail of the distribution is all that I have claim to. Not reducing prices is a form of screwing creditors, but I don’t care. As the owner of a highly leveraged firm operating near capacity, I will be disinclined to reduce prices.

This tale of an overleveraged entrepreneur would be insignificant, if it were an idiosyncratic occurrence. One overextended entrepreneur might refuse, but her less leveraged competitors would cut prices, and observed market prices would fall. But suppose our entrepreneur is in an industry where intense leverage is the norm. As Hyman Minsky famously pointed out, if an industry is competitive and at least some players are not foresighted about risk, levering up in good times ceases to be optional. More levered firms gain a cost-of-capital advantage that permits them to undercut financially conservative rivals over what may be prolonged periods of tranquility. So we might expect to competitive forces to drive whole industries into similar capital structures. And empirically we do find this — firms in general choose wide varieties of capital structures, but within industries, capital structures are more alike.

In highly leveraged industries then, we’d expect downward price stickiness. Following a negative shock to nominal expenditures, we would observe production losses, but not in the form of evenly distributed cutbacks. Instead, some firms would seem to thrive despite the weather, while others are forced into bankruptcy. Perhaps the firms that survive would be the “best” firms, and certainly differences in quality and ex ante leverage would affect the distribution of outcomes. But even among perfectly identical firms, if the distribution of sales is stochastic, we’d expect “consolidation” to occur. Firms that are lucky early in a depression survive. It gets easier to stay lucky as time goes on. The failure of competitors eliminates supply, helping to support your sticky price (which becomes less sticky as you retain earnings to delever).

From a macroeconomic perspective, this account suggests that, even putting aside systemic fragilities introduced by cascading bankruptcies and financial accelerators running in reverse, financial leverage leaves an economy vulnerable to depression through a price rigidity channel. This strikes me as relevant to our current situation. Policymakers have effectively guaranteed the debt of highly interconnected borrowers and successfully eliminated the threat of cascading defaults. But if my account is correct, reducing leverage at “Main Street” firms may be at least as important as ensuring the stability of interconnected financials. Policymakers have put tremendous effort into ensuring the continuous availability of credit to firms that wish to expand. But promoting debt-financed expansion may be self-defeating, if it reduces the ability of the economy to adapt to fluctuations in nominal expenditure by making prices sticky. [2]


  1. This will be an intramural point. Footnote 2 is more interesting.

    I think that explanations of the business cycle based on relative price stickiness ought not be classified as Keynesian or monetarist at all. Relative price stickiness is really a recalculation story of the sort favored by Arnold Kling (and to which I am also sympathetic). If you think of markets as calculators of equilibria, and that after a large shock computing a new equilibrium takes time, then there must be some sort of friction that prevents the computation from being instantaneous. Sticky prices offer one plausible source of friction.

    I won’t speak for Kling, but I think that some proponents of recalculation-ish theories would object to this characterization, because they view economic calculation as something deeper than a rejiggering of relative prices. They’d focus instead on inspired entrepreneurship, creative destruction, entirely new practices and products. I agree with all that, but when making up models we do have to reduce a variegated and multicolored world to symbols, and modeling recalculation as a laborious price vector computation is more expressive than it first appears. For example, we can imagine a space of potential new products whose prices begin at infinity and adjust downward with difficulty, as we learn by doing or as a stochastic function of entrepreneur effort.

    It might seem odd to expel relative-price-stickiness-based explanations from the Keynesian pantheon. After all, aren’t New Keynesian models almost defined by incorporation of relative price stickiness? Well yes, and they use relative price-stickiness to achieve monetary non-neutrality. However, at risk of stepping on toes (which is really not my intention), I think that by construction New Keynesian models are poorly suited to the analysis of extreme business cycles. New Keynesian models, like their Real Business Cycle progenitors, are usually characterized in log-linear approximation around a long-run equilibrium. Even if we believe the models to be perfectly correct, the conclusions we draw from log-linear approximations become less and less reliable as variables depart from equilibrium values. Log linearized models, if they are useful, are useful at describing near-equilibrium dynamics. If extreme business cycles involve severe departures from the presumed equilibria, or worse yet, if they involve multiple equilibria so that the economy might be durably drawn away from the presumed steady state, common New Keynesian models just aren’t helpful. To invoke Hyman Minsky again (via Steve Keen), if you want to answer questions about extreme business cycles

    it is necessary to have an economic theory which makes great depressions one of the possible states in which our… economy can find itself.
    Perhaps I am overharsh. I am certainly no expert on New Keynesian macro, and I’d be delighted to learn that I am wrong. But the New Keynesian models I have encountered simply don’t live up to Minsky’s very sensible criterion. Monetarist and Old Keynesian models, though hydraulic and not-microfounded they may be, incorporate in their design the possibility of durable and severe depressions. [ back ]


  2. The story I’ve told isn’t particularly novel. It complements commonplace accounts of why unemployment occurs in depressions. In theory, firms could simply cut employee hours and wages rather than fire people in response to a downturn. But they don’t. Employment adjusts on the “extensive” margin of layoffs much less than it adjusts on the “intensive” margin of reducing work or pay. This is often attributed to employee morale. It is better, the story goes, to have a small workforce of happy people than a big workforce of bitter people.

    But consider the same situation from employees’ perspective. Families are often highly leveraged. Even when they are not explicitly in debt, many families take on operating leverage. That is, for many families, the fixed costs of ordinary living (e.g. rent, day care, food) approach their total household income. With high leverage (whether explicit debt or operating leverage), a reduction of wages and hours translates quickly to financial and personal crisis, and ultimately to a disruptive reorganization of living arrangements. A cutback in wages and hours may leave families unable to afford their mortgage or their rent, and force a move to less desirable digs or “doubling up” with family, usually after a lot of confusion and juggling and bills and shame and collection agencies.

    Getting fired will do all that too, of course. But if firms hold wages steady and cut back by firing workers, then some workers will avoid the reorganization entirely. When firms cut wages or hours, all highly leveraged workers must reorganize. If the severity of crisis is not so different for those who are fired versus those who see pay cuts (a big if), then workers rationally prefer a layoff lottery to universal pay cuts. Their reasoning would be identical to that of leveraged firms who hold prices steady and take their chances.

    So firms find layoff lotteries to be better ex ante, because employees prefer them, and ex post because only the happy winners remain with the firm. A perennial suggestion among reformers is that we substitute some form of work-sharing for cyclical unemployment, so that the burden of downturns is evenly shared instead of falling disproportionately on an unlucky few. That sort of reform only makes sense when household leverage is generally modest. [ back ]

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