RDP 2007-12: Dynamic Pricing and Imperfect Common Knowledge 5. Conclusions

In this paper I have argued that, when firms have idiosyncratic components to their marginal costs, they cannot compute the current price level perfectly before they choose their own optimal price. Instead, firms have to form an estimate of the price level using the information contained in their own marginal cost and in observations of past inflation and output. This structure, coupled with the Calvo mechanism of price adjustment, results in a Phillips curve with a role for higher-order expectations of marginal cost and future inflation. Even though the pricing decision is entirely forward-looking, lagged inflation will have an impact on current inflation since lagged inflation contains information relevant to the optimal price of the firm. This effect is amplified by firms having private information about marginal costs, which induces ‘herding’, or over-weighting, of the information in the publicly-observed lagged aggregate variables. This information effect can explain the positive coefficient found on lagged inflation in estimates of the hybrid new Keynesian Phillips curve.

The idiosyncratic component of marginal costs can also help explain the fact that individual price changes are significantly larger than aggregate price changes. In addition to increasing the volatility of individual marginal costs, a higher variance of the idiosyncratic component makes it harder for individual firms to filter out the economy-wide component from the observation of their own marginal cost. This second effect reduces the responses of prices to economy-wide shocks and is a similar result to that of Mackowiak and Wiederholt (2007). They find that firms will choose to allocate less attention to aggregate variables when idiosyncratic conditions are very volatile.

The modelling philosophy of Mackowiak and Wiederholt differs from that used in this paper in their more abstract approach. They do not explicitly specify what the idiosyncratic conditions facing the firms in their model are, which makes it harder to judge whether the constraints on information processing capacity that are necessary to match the data are realistic or not. In this paper, the precision of firms' information is determined by the relative variance of individual firms' marginal costs and the economy-wide aggregate marginal cost. This explicit approach makes it possible, at least in principle, to compare variances of the model with variances in the data. It is then also possible to ask whether information imperfections are likely to be large enough in reality to be important for the dynamics of inflation. It is hard to argue that firms' own marginal costs and lagged inflation and output are the only information available to agents in reality. However, a necessary condition for explanations of economic phenomena to be plausibly based on limited information availability (or limited capacity to process information) is that quantities that are immediately and costlessly observable to agents are not too informative.

In the specific case considered here, the firm-level idiosyncratic wage variances necessary to replicate US inflation dynamics was about half of the overall variance of real wages. In principle, this could be compared to variance ratios in the data, but in practice, such a comparison is constrained by the limited availability of firm-level data. Martins (2003) is a rare study that provides some information on the relative size of firm-specific and industry-wide variances of wages paid in one industry (garment production) in one country (Portugal). If Martins' numbers are representative, actual firm-specific shocks are more volatile than what is necessary for the model to replicate the observed inflation inertia, but somewhat less volatile than necessary to replicate the observed magnitude of individual price changes. However, given the very limited availability of firm-level data, it is prudent to avoid drawing strong conclusions about what should be considered a realistic lower bound on how imperfectly informed firms can be.

The more explicit approach to information imperfections of this paper also points out directions for further research. The present model suggests an explanation for the observed higher-inflation inertia in the US relative to the euro area. European wage bargaining is often centralised, while in the US a larger fraction of wages are set at the firm level.^[14] Hence, there is thus likely to be more firm-level variation in wages in the US than in Europe which, in the model, would lead to more inertia, and could thus explain the observed differences. Comparing the predictions of the model with a larger cross-section of countries may be another way to validate the main mechanism of the model.

Finally, through the Calvo mechanism, the model is consistent with the micro evidence on the average duration of prices, but it also implies that firms need to be forward-looking when they set prices. The fact that agents in the model make dynamic choices, rather than a series of static choices, renders existing solution techniques inapplicable. The model is solved by imposing that rational expectations are common knowledge. This assumption, together with a structural model that implies that the impact of higher-order expectations are decreasing as the order of expectation increases, makes it possible to derive a solution algorithm of arbitrary accuracy. Though some of the details of the algorithm are relegated to Appendix B, it may be of independent interest to some readers.

Footnote

See OECD (1997). [14]