# Calvo Pricing, Precautionary Saving and Financial Frictions

I’m pretty sure the title informed potential readers that this is one post to skip. If anyone was foolish enough to read this far, I must stress that I am not arguing that standard micro founded DSGE models have false implications. I am merely noting that the effort to avoid false implications demonstrates the unseriousness of the effort to micro found macro. My conclusion is that macroeconomists write down ad hoc models, then tell stories about micro which they don’t believe, then make sure that the micro foundations add nothing and subtract nothing.

Pointless math explained with bad English and no equation editor after the jump

Standard New Keynesian macro models have sticky prices and somete have sticky wages. The stickiness is modeled using the assumption introduced by Guillermo Calvo in 1983. New Keynesians typically say they don’t like Calvo pricing and plan to replace the assumption with something more reasonable some time in the future (note 1983). The assumption is that firms can only change prices when their Calvo alarm clock rings. The opportunity to change prices is a Poisson process, which just means that the probability such an opportunity occurs in a brief interval of time is a constant times that interval of time. Obviously no one believes that Calvo’s assumption is literally true.

Calvo pricing, imperfect competition, and rational expectations imply a nice neat forward looking Phillips curve. For some reason, there is perceived to be some gain of some sort from making implausible assumptions about when prices can be changed and then getting that equation as the solution to an optimization problem. I think it is very easy to demonstrate that nothing is gained and nothing is lost due to the alleged microfounding of the pricing equation.

Later Calvo pricing was also used to model wage stickiness. Here there is the assumption that workers decide on a wage demand and firms decide how much labor to demand from them. Again no one believes this is how things really are.

What difference is there between Calvo pricing and just assuming directly that the price level and the wage level change according to the aggregate equation derived from the Calvo assumption and rational constrained maximization ? As I have told the story so far, there are two important differences. Both are due to the fact that the ringing of the Calvo alarm clock is a welcome event — it is an option to change a price or a wage. The value of an option is non-negative and, in the models, the value of this option is always positive. Calvo pricing is a source of risk for firms (and households in the model with sticky wages). This risk is not constant. If inflation (or deflation) is high, the opportunity to adjust prices (or wages) is quite valuable. If it is exactly zero, in the models, the value can be zero. This means that the rate of inflation affects the variance of firm (& household) specific risk.

Risky labor income always matters to households. Given standard assumptions, the risk causes precautionary saving so consumption grows faster than one would guess given the real interest rate. In currently popular models with financial frictions, firm specific risk is extremely important. It affects the probability of costly bankruptcy which is crucial in these models.

So the micro founded model has implications which differ in extremely important ways from the aggregate equation it was originally developed to micro found. Since no one takes the micro foundations seriously, this is a problem, a bug not a feature. The solution is the addition of another absolutely incredible assumption — the assumption that there are complete markets so people can sell contingent claims on the ringing of their personal Calvo alarm clock. This means that the difference between the micro founded model which derives the forward looking Phillips curve and the micro founded model is carefully eliminated.

Now how can it be considered an advance to replace an assumption about aggregate variables with a story about optimizing individuals if any difference between just assuming that everyone acts according to the aggregate equation is a bug to be removed ?

I think this is clearly a case of our tools using us. The difference between the model with Calvo pricing and complete markets and the ad hoc aggregate model is exactly that some fancy math appears in the model of Calvo pricing. All novel implications of the micro founded modelling exercize were carefully removed. I think it is clear that the math was just for show.