Models of staggered price adjustment with inflation inertia

Decontamination Plan

Models of the Staggered Price Adjustment With Inflation Inertia

In order to evaluate monetary policies more effectively, monetary economists has been developing quantitative models that incorporate fundamental ideas relating to time inconsistency and forward looking expectations. These monetary models have not only proved to be essential for policy evaluation but have also been shown to have common features, which include a combination of rational expectations, staggered price and wage setting, and policy rules ( Taylor & Wieland, 6-2). This paper has two principal goals. First, to present and examine the theoretical underpinnings of two models of staggered price adjustment with inflation inertia, namely, the Christiano-Eichenbaum-Evans model and the Mankiw-Reis model. Second, to elaborately analyze and compare these two models. As such, a useful perspective to begin this discussion is to present the central purpose and focus of these models.

The Christiano-Eichenbaum-Evans model

Understanding the observed inertial behavior of inflation as well as its persistence is the main goal of the work of three seasoned economists, namely Lawrence Christiano, Martin Eichenbaum and Charles Evan. In line with this goal, these economists developed a dynamic general equilibrium model, popularly known as the Christiano-Eichenbaum-Evans model (the CEE model). Their model was formulated in such a way that it incorporates staggered wage and price contracts. The basic tenet of the CEE model is that inertial inflation and consistent output movements (in response to monetary policy shock) can be generated by applying models with moderate degrees of nominal rigidities (Christiano et al., 5-50.

It is important to note here that the CEE model has two main features. First, Calvo's style nominal price and wage contracts are embedded in the model. Second, all the four departures from the standard one sector dynamic stochastic growth model are equally incorporated in the CEE model. It is worth noting here that the recent research on the determinants of consumption, productivity, asset price and investments are the factors that motivated or induced these departures. Broadly speaking, adjustment costs in investments, variable capital utilization, as well as habit formation in preferences for consumption are the specific departures that are included in the CEE model. In addition to this, the CEE model is predicated on the assumption that firms must finance their wage bills by borrowing their working capital (Christiano et al., 5-50).

It is also sufficient to note that these economists made some laudable findings while using this model. First, they used the model to project that the average duration of price and wage contracts is approximately two and three quarters respectively. Thus the model does an excellent job in terms of quantitatively accounting for the estimated response of the United States economy to a policy shock regardless of the modest nature of the aforementioned nominal rigidities. Also, in addition to accounting for the delayed, humped-shaped response in investments, consumptions, productivity and profits (as well as the weak response to the real wage), their model reproduces the dynamic response of inflation and output to such policy shocks. Second, they found that wage contracts (not price contracts) are the main critical nominal friction in their model. Broadly speaking, the estimated model as well as a version of the model with only nominal wage rigidities has similar effects. In contrast, their model performs very poorly with only nominal rigidities. Hence, unless one has to assume price contracts of extremely long duration and, consistent with the existing information covered so far in this paper, the version of their model with only price rigidities cannot generate persistent movements in outputs (Christiano et al., 5-50). It is important to note here that this problem do not arise or occur with the model with only nominal wage rigidities.

Third, they were able to document how inferences relating to nominal rigidities compare and vary across the different components and specifications of the real side of their model. They equally showed that long price and wage contracts are usually the outcome when using estimated version of their model -- a version that do not incorporate their departures from the standard growth model. Fourth, they equally found that it is crucial to allow for variable capital utilization if one want to generate inertia in inflation and persistence in the output model while, at the same time, imposing only moderate wage and price stickiness. In order to put the relevance and importance of this feature into perspective, it is necessary to note that among the maxims contained in their model is that firms set prices as a mark-up over marginal costs. Broadly speaking, wages and the rental rate of capital are the major components of the marginal costs. Thus variable capital utilization helps dampens the large rise in rental rate of capital that would otherwise occur by allowing the services of capital to increase after a positive monetary policy shock. The rise in marginal costs as well as prices will also be dampened as a result of this effect. The inflation inertia that will result implies that a persistent rise in real output will be produced by the rise in nominal spending that occurs after a positive monetary policy shock. Similar intuition equally goes a long way in explaining why the analysis of sticky wages plays critical role when using Christiano-Eichenbaum-Evans model to explain inflation inertia and output persistence. It equally explains why the assumptions made by these economists about working capital plays a critical role: marginal cost is low when the interest rate is lowered, ceteris paribus (Christiano et al., 5-50; Taylor & Wieland, 6-20).

Centrally speaking, among the hallmarks of Christiano-Eichenbaum-Evans model is that it showed that investment costs and habit formation play a critical role in accounting for the dynamics of may related variables even though they do not play a central role with respect to inflation inertia and output persistence. Their model equally showed that the reduction of a monetary policy model's reliance on sticky prices is the major role played by the working capital channel. In their views, the average duration of price contracts will increase dramatically if they estimate a version of the model that does not allow for working capital. An additional good thing about their model is that it embodies a strong internal propagation mechanisms. They equally noted that (Christiano et al., 3)

The impact of a monetary policy shock on aggregate activity continues to grow and persist even beyond the time at which the typical contract that was in place at the time of the shock has been reoptimized. In addition, the effects on real variables persist well beyond the effects of the shock on the interest rate and the growth rate of money (p.3)

As a concluding remark to this section, it is necessary to state here that these three economists did a good job of estimating and evaluating their model by pursuing particular limited information econometric strategy -- a strategy they implemented by using an identified vector auto-regression to first of all estimate the impulse response of eight key macroeconomic variables to monetary policy shock. This was followed by minimization of the differences between the estimated impulse response functions and analogous objects in the model by choosing six model parameters, some which will be briefly identified in this paper.

Having analyzed and discussed the Christiano-Eichenbaum-Evans model in this section, I will now proceed to show the applicability of the model by presenting a brief discussion of its real life applications. This will be the topic of the following section.

Real Life Applications of Christiano-Eichenbaum-Evans Model Economy

To understand the usefulness of the Christiano-Eichenbaum-Evans's model, I will gather together and discuss significant points from three studies that illustrate their practical significance and application.

In a study by DiCecio and Nelson, the authors used U.K. data to estimate the dynamic stochastic general equilibrium model of Christiano-Eichenbaum-Evans. The results of their study suggested that in United Kingdom, price stickiness is a more important source of nominal rigidity than wage stickiness. According to their observation, it is only when post-1979 observations are included in the analysis that their estimates of the parameters governing investment behavior become more reliable and practicable. It is sufficient to note here this outcome is simply a reflection of the policies adopted by the British governments until the late 1970s -- policies that, to a very reasonable extent, obstructed the influence of market forces on investments (DiCecio & Nelson).

In a related study, Schmitt-Grohe and Uribe identified the optimal interest rate rules within the Christiano-Eichenbaum-Evans model -- a model they believed to be a rich, dynamic, general equilibrium model given that it has been proved to account well for observed aggregate dynamics and other relevant variables in the post-war United States. Through their policy evaluations, which was based on a second-order accurate approximations to conditional and unconditional expected welfare, they found optimal operational monetary policy reflects a rule for targeting the real interest rate -- an interstate rate feedback rule in which a mute response to output, a unit inflation coefficient, and no-interest rate smoothening are featured. They equally observed a significant degree of optimal inflation volatility contrary to existing studies in this area. In their view, the assumption of indexation to past inflation is the key factor driving this result. According to them, when viewed in the light of indexation to long-run inflation, the optimal inflation volatility often moves closer to zero. They equally showed that for the welfare rankings of policies, the initial conditions do matter to a very significant extent.

In their work, Leeper Erik et al. examined how the conventional dynamic stochastic general equilibrium models, including the Christiano-Eichenbaum-Evans model is affected or impacted by government investments. As a way of explaining the effects of government investments in this regard, they considered two main factors, namely, the future fiscal adjustments to debt-financed spending and implementation delays for building public capital projects. In their work they demonstrated that, in the short run implementation delays can produce small or even negative labor and output responses; while for both a qualitative and quantitative positive long-run growth effects, the financing instruments and the productivity of public capital matters more in that regard. Using the Christiano-Eichenbaum-Evans model and other models with features relevant for studying government spending (which include time-to-build for private investment, utility-yielding government consumption and government production) they examined these findings and observed similar results.

Having examined the their practical significance and application of the Christiano-Eichenbaum-Evans's model in this section, I will now proceed to the next section where I will explore the Mankiw and Reis Model .

The Mankiw and Reis Model

Most monetary policy theorists are convinced that the sticky information model proposed by Mankinaw and Reis can potentially address the failures of the New Keynesian Phillips curve. In Mankiw and Reis' view, because of information acquisition or re-optimization costs, information about macroeconomic conditions tends to spread slowly (Oleg Korenok, 2). Simply put, the idea that that information disseminates slowly through a population is the basic tenet of the model presented by Mankiw and Reis (1-34). As a result of this, their model is can be termed the sticky information model.

Broadly speaking, according to the Mankiw and Reis model, some firms set prices based on old information while others compute prices based on current information. As such, some restrictions are naturally placed on the adjustment of inflation.

To promote a better understanding of Mankiw and Reis model, I will now make a more elaborate explanation of the information presented above. The explanation of the dynamic effects of aggregate demand on output as well as the price level is the main goal of the model proposed by Mankiw and Reis. As I explained above, that information about macroeconomic conditions diffuses slowly through a given population is the key essence of their model. In their view, this slow diffusion can be caused by two main factors. First, the cost of acquiring information and second, the costs associated with re-optimization. In either case, pricing decisions are not always based on current information even though prices are constantly changing. Hence, to differentiate their model from the standard sticky-price model on which the new Keynesian Phillips curve is based, Mankiw and Reis called it the "sticky-information" model (Mankiw and Reis, 1-34).

As I explained earlier, two assumptions form the basis of Mankiew and Reis model. First, a fraction of the population generally updates itself on the current state of the economy as well as computes optimal prices based on that information at each period. Second, prices are set on the basis of old plans and outdated information by the rest of the population. Hence, Mankiw and Reis model combines both the elements of Lucas model of imperfect information with that of Calvo's model of random adjustment (Keen Benjamin and Wang Yongshang, 1-11; Lucas). On a closer examination, however, it can be seen that the implications of their sticky-information model is more close to that of Stanley Fischer's contracting model. Going in line with the Fischer model, their model equally posits that the expectations of the current price level formed far in the past is the factor that determines the current price level. According to Fischer model, because those expectations are built into contract, they are considered to be very important. In Mankiw and Reis model, those expectations matter given that some of the price setters are determining their prices on the basis of old information as well as old decision.

Having presented the Mankiw and Reis model above, my next work is to make a comparative analysis of the model and the Christiano-Eichenbaum-Evans. This I will do in the following section.

Comparative Analysis of the Christiano-Eichenbaum-Evans and Mankiw-Reis Models

Generally speaking, as I have already noted before, the Mankiw and Reis model is based on the plausible assumption that information disseminates slowly throughout the population. Compare to the Christiano-Eichenbaum-Evans model, the Mankiw and Reis model displays three related properties that are, to a very significant extent, more consistent with the generally accepted views regarding the effects of monetary policy. The first property is the one that postulates that disinflations are always contractionary. This property is valid regardless of the fact that surprise disinflations are more contractionary than announced ones. The second property is the one that posits that monetary policy shocks, to a very reasonable extent, have their maximum impact on inflation with a substantial delay. The third property can be stated thus: The level of economic activity and the change in inflation are positively correlated Mankiw and Reis, 1-34).