New Keynesian Economics and the Phillips Curve
Roberts, John M., Journal of Money, Credit & Banking
Sticky prices are an important part of monetary models of business cycles. In recent years, a consensus has formed around the microfoundations of sticky price models, and this consensus is an important part of New Keynesian economics (Ball, Mankiw, and Romer 1988). In this paper, I show that several of the New Keynesian models, including the models of staggered contracts developed by Taylor (1979, 1980) and Calvo (1983) and the quadratic price adjustment cost model of Rotemberg (1982), have a common formulation that is similar to the expectations-augmented Phillips curve of Friedman and Phelps.
I also present new estimates of this common model. Because prices are sticky in the New Keynesian models, price setting must take into account future prices, and an important issue in estimation is how to deal with expectations about future prices. Previous estimates of these models, such as those by Taylor (1980, 1989) and Rotemberg (1982), have been based on full-information techniques, in which expectations are solved under the assumption of rational expectations. As is well known, full-information estimation has the advantage of econometric efficiency if the model is correctly specified, but the disadvantage that if any part of the model is misspecified--even a part of secondary interest--the estimates will be inconsistent.
I explored two limited-information approaches. One was the technique, introduced by McCallum (1976), of using the actual future value of a variable as a proxy and then restricting the information used in estimation--such as any instrumental variables--to what was available at the time the expectations of the variable were formed. This approach has the advantage over the full-information technique that the complete economic environment need not be specified.
The other limited-information approach was to use inflation expectations obtained through surveys as proxies for expectations. This approach shares with McCallum's technique the advantage that assumptions about the structure of the rest of the economy are not necessary. But survey responses may be better measures of people's expectations than are realized future prices: I find that the key parameters of the model had the correct sign regardless of the proxy for expectations, but that the estimates were more precise when I use the surveys as proxies for expectations.
1. THE MODEL
In the New Keynesian literature, models of sticky prices have been grouped into two general categories: "time-dependent" and "state-dependent" models (Ball, Mankiw, and Romer 1988). In state-dependent models, firms change prices when underlying determinants, such as demand and costs, reach certain bounds. In time-dependent models, such as the staggered contracts models of Taylor and Calvo, firms set their prices for fixed periods of time. As I will show shortly, time-dependent models can have explicit closed-form solutions relating current price changes to future price changes and the current state of demand. State-dependent models do not, in general, have simple closed-form solutions, and in some state-dependent models, such as the one analyzed by Caplin and Spulber (1987), aggregate price adjustment may be instantaneous even if individual prices are sticky. As a consequence, I focus on time-dependent models.
1a. The Quadratic Price Adjustment Cost Model
In Rotemberg's (1982) framework, firms minimize the costs of changing prices, weighed against the costs of being away from the price the firm would choose in the absence of adjustment costs:(1)
(1) [Mathematical Expression Omitted]
where [omega] is total cost, p is the log of the actual price at time t, [p.sup.*] is the (log of the) price a firm would charge in the absence of adjustment costs, [theta] is a constant discount factor, and c is a parameter that measures the ratio of the costs of changing prices to the costs of being away from the optimum price.
The first-order condition of this problem is
(2) [Mathematical Expression Omitted]
Assume that the discount rate, [theta], is equal to one; for high frequency data, this is approximately correct. …