Behavior in Price Specifications

The seminal work of Phelps, Taylor, and Cairo developed forwardlooking models of price determination that imparted inertia to the price leveh These models incorporate expectations of future prices and excess demand by imposing constraints (typically lag-lead symmetry constrainls) that force future variables to enter the specification. In this paper, I test the empirical significance of future prices-in specifications like those of Taylor. I find that expectations of future prices are empirically unimportant in explaining price and inflation behavior. However, the dynamics of a model_that includes a purely backwardlooking inflation specification differ’ significantly-and not altogether pleasingly-from those with a forward-looking specification. 11 thank Allcia Sasser for excellent research assistance. The views expressed in this paper are those of the author and do no~ necessarily reflect positions of the Federal Reserve Bank of Boston or the Federal Reserve System. Some of the earliest and best-known macroeconomic models that impose rational expectations are the models of Sargent and Wallace (1975) . These models were widely criticized for implying that prices were completely flexible and cleared markets instantaneously. The implication of price flexibility appeared to conflict markedly with empirical observations of measures of the aggregate price level. Initially, some confusion arose as to whether the assumption of rational .expectations inherently entailed price flexibility. However, the work of Taylor (1980) and others demonstrated the critical point that it was the price specification, not the assumption of rational expectations, that led to the unlikely price behavior in the early models. Significan~ and realistic inertia could be imparted to prices in a rational expectations macro model. Yet the inclusion of expectations in the price sector of Taylor’s and others’ models arises through a set of Constraints that essentially force expectations to enter the specification. Of course, some restrictions are necessary in order to separately identify the effects of expected future variables. If the model is specified with unconstrained leads and lags, it will be difficult for the data to distinguish between the leads, which solve out as restricted combinations of lag variables, and unrestricted lags. In most cases, these constraints take the form of symmetry restrictions across past and expected future prices. This paper attempts to test the importance of the expected prices in explaining price fluctuations by relaxing these restrictions. The paper uses a variety of inflatio~ specifications that are derived from the standard contracting models of Taylor (1980) and from a new contracting specification that more accurately mimics the inertia in observed inflation rates, drawing on the work of Phelps (1978), Ball (1991), Chadha, Masson and Meredith (i1992), and Fuhrer and Moore (1995, [9] and [I0]). In addition, the paper explores the consequences of forward-looking, backwardlooking, and mixed price spedfications for the overall dynamic behavior of a macro model. To anticipate, I find that, Consistent with others, the purely foward-looking price model bears implications that are severely at odds with the data. In addition, the mixed backward-lookingl/forward-looking model implies considerably different model dynamics from a purely backward-looking model, I will argue that the purely backward-looking model’s dynamics are less plausible than the mixed model, although this conclusion may be somewhat model-specific, and depends somewhat upon prior beliefs. 1 The Analytics of the Price Models Consider three types of price specifications. The first, which I will call an expectations-augmented price-price Phillips curve, sets the current inflation rate, ~rt equal to the expected inflation rate, ~r~, adjusted for excess demand, ~ = ~+1 + V~ (1) In the usual implementation of the expectations-augmented Phillips curve, expected inflation is proxied by a distributed lag on past inflation.~ Thus equation 1 may be written