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Thursday, May 22, 2008

Menu Costs and Phillips Curves: The CalvoPlus Model and Intermediate Inputs

Awhile back, I posted a summary of a paper by Golosov and Lucas. The paper is important because it raises questions about the ability of New Keynesian models to explain fluctuations in real output. As I stated at the time:

A lot of you don't believe in a Phillips curve, but I've argued that there is a short-run inflation-output tradeoff and I've cited New Keynesian models along with supporting empirical evidence to reinforce that position. But when I make that argument, you should cite this paper by Golosov and Lucas to argue against the existence of a significant inflation-output tradeoff. The paper argues that if there is a Phillips curve, the inflation-output tradeoff is pretty steep, steep enough so that nominal shocks are "nearly neutral":

And since we believe nominal shocks matter for real GDP - there is empirical evidence in support of that claim - the fact that nominal shocks (think monetary policy) aren't able to explain much of the movement in output in the class of theoretical macroeconomic models used to assess policy and learn about the economy is a problem.

As a review, here's part of the introduction and conclusion from the Golosov and Lucas paper:

Menu Costs and Phillips Curves, by Mikhail Golosov and Robert E. Lucas Jr., Journal of Political Economy, 2007, vol. 115, no. 2 [open link]: I. Introduction This paper develops a model of a monetary economy in which firms must pay a fixed cost—a "menu cost"—in order to change nominal prices. Menu costs are interesting to macroeconomists because they are often cited as a microeconomic foundation for a form of "price stickiness" assumed in many New Keynesian models. Without sticky prices these models would not exhibit the real effects of monetary shocks—Phillips curves—that they are designed to analyze.

Under menu costs, any individual price will be constant most of the time and then occasionally jump to a new level. Thus the center of the model will be the firm's pricing decision to reprice or not to do so. Many New Keynesian models do not examine this decision but instead rely on a simplifying assumption proposed by Calvo (1983) that the waiting time between repricing dates is selected at random from an exponential distribution: Firms choose the size of price changes but not their timing.

As many others are, we are skeptical that the Calvo model provides a serviceable approximation to behavior under menu costs.[1] One reason is that the assumption of a constant repricing rate cannot fit the fact that repricing is more frequent in high-inflation environments. But a second, more important, reason was discovered by Caplin and Spulber (1987), who constructed a theoretical example of an economy with menu costs in which only a small fraction of firms reprice yet changes in money growth are neutral. In their example, there is a stationary distribution of firms' relative prices, and as a monetary expansion proceeds, the firms at the low end of this distribution reprice to the high end. The repricing rate is very low—prices are very "sticky"—but no price stickiness can be seen at the aggregate level. The key to the example is that the firms that change price are not selected at random but are rather those firms whose prices are most out of line.

The Caplin and Spulber example is well designed to exhibit this selection effect, but it is unrealistic in too many respects to be implemented quantitatively. In this paper we capture the selection effect in a new model of menu cost pricing, designed so that it can be realistically calibrated...

Our main finding is that even though monetary shocks have almost no impact on the rate at which firms change prices, the shocks' real effects are dramatically less persistent than in an otherwise comparable economy with time-dependent price adjustment. Simulations of the model's responses to a one-time impulse of inflation show small and transient effects on real output and employment..., in contrast to much larger and more persistent responses of the same model with Calvo pricing. ... In the menu cost model, a positive aggregate shock induces the lowest-priced firms to increase prices. At the same time, it offsets negative idiosyncratic shocks, and some firms that would otherwise have decreased prices choose to wait. As a result, the lowest-priced firms do most of the adjusting, their adjustments are large and positive, and the economywide price level increases quickly to reflect the aggregate shock. In the Calvo setting, in contrast, firms get the opportunity to reprice randomly, many firms reprice even though they were already close to their desired price, and the average response of prices to the shock is much smaller. It takes longer for the monetary shock to be reflected in prices, and impulse responses become more persistent. ...

VII.      Conclusions ... In summary, the model we proposed and calibrated to microeconomic evidence on U.S. pricing behavior ... does not appear to be consistent with large real effects of monetary instability. These results seem to us another confirmation of the insight provided by the much simpler example of Caplin and Spulber (1987) that even when most prices remain unchanged from one day to the next, nominal shocks can be nearly neutral...

But not so fast. The paper below develops a multi-sector "CalvoPlus Model" that maintains the mathematical simplicity of the Calvo approach, but allows state dependent pricing. In particular, in the standard Calvo model of price rigidity, firms are allowed to change prices with probability a, and prices remain fixed with probability 1-a (with the parameter a chosen based upon empirical results on the average frequency of price changes). Essentially, with probability a the cost of changing the price in a given period is zero, and with probability 1-a, the cost to change price is infinite. The CalvoPlus model changes this so that with probability a, the cost of changing a price is very low, and with probability 1-a the cost is high, but not infinite (the high-low costs vary across sectors). This introduces an element of state dependency because if a price is far enough away from its optimal value, it may be worthwhile to pay the high cost to change it since the benefit of changing the price would be even larger than the cost. It introduces heterogeneity due to the multi-sector set up (the degree of non-neutrality goes up as the number of sectors is increased, and the model is calibrated so that around 75% of price changes occur in the low cost states).

However, allowing heterogeneity across sectors in the frequency and size of price changes by itself is not enough to allow the model to generate non-neutralities large enough to be consistent with actual fluctuations in real GDP. Thus, the model also adds a second change, the introduction of intermediate inputs. As the authors note, "Intuitively, in the model with intermediate inputs, firms that change their price soon after a shock to nominal aggregate demand choose to adjust less than they otherwise would because the prices of many of their inputs have not yet responded to the shock." In the model, the price of these inputs depends directly upon the price of other goods in the economy (they are "strategic complements"). Because intermediate input prices adjust sluggishly, an increase in aggregate demand of 1%  increases input costs by less than 1%, and prices do not rise by as much as they would if intermediate inputs were not present (i.e. if input costs were completely flexible). This extra price sluggishness results in larger real effects and doubles the degree of non-neutrality in the model (i.e. the output movements attributable to CalvoPlus pricing and to the presence of intermediate inputs are about equal, and total around 25% of the total variation).

Here's part of the introduction to the paper (it's been keeping me occupied today):

Monetary Non-Neutrality in a Multi-Sector Menu Cost Model, by Emi Nakamura and Jon Steinsson, NBER WP 14001, May 2008: [Open Link] 1 Introduction Much applied work in monetary economics relies on models in which nominal rigidities are the key friction that generates monetary non-neutrality. The workhorse models in this literature - e.g., the Calvo (1983) model and the Taylor (1980) model - make the simplifying assumption that the timing of price changes is independent of firms' incentives to change prices. It has been recognized at least since Caplin and Spulber (1987) that models based on this assumption can yield very different conclusions about monetary non-neutrality than models in which nominal rigidities arise due to a fixed cost of changing prices (see...). Golosov and Lucas (2007) calibrate a menu cost model based on newly available micro-data on the frequency and size of price changes and conclude that nominal rigidities due to menu costs yield monetary non-neutrality that is "small and transient".

Given the importance of nominal rigidities as a source of monetary non-neutrality in most models that analyze the transmission of monetary policy, this conclusion poses a serious challenge for monetary economics. If realistically modeled nominal rigidity yields monetary non-neutrality that is small and transient, much of our understanding of the transmission of monetary policy is called into question. It is therefore of great importance for monetary economics to assess whether the implications of highly stylized menu cost models hold up in a richer, more realistic setting. ...

In this paper, we ... extend a simple benchmark menu cost model to include two features for which there exists particularly clear empirical evidence: 1) Heterogeneity across sectors in the frequency and size of price changes; 2) Intermediate inputs. We show that when we subject our model to calibrated nominal shocks it generates fluctuations in real output that can account for 26% of the U.S. business cycle.[1] This result of our model accords well with empirical evidence on the importance of nominal shocks for business cycle fluctuations.

Shapiro and Watson (1988) attribute 28% of the variation in output at short horizons to nominal shocks. In contrast, the Golosov and Lucas model generates fluctuations of real output that can account for only roughly 2% of the U.S. business cycle. Roughly half of the difference in monetary non-neutrality in our model relative to the model of Golosov and Lucas (2007) is due to the introduction of heterogeneity in the frequency of price change; the remaining half is due to the introduction of intermediate inputs. ...

    Posted by on Thursday, May 22, 2008 at 12:51 PM in Academic Papers, Economics, Inflation, Unemployment | Permalink  TrackBack (0)  Comments (5)

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