# Models of Staggered Price Adjustment With Inflation Inertia Research Paper

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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

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for $19.77 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.

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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… [END OF PREVIEW] . . . READ MORE

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

Buy full paper

for $19.77 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.

## Research Paper on *Models of Staggered Price Adjustment With Inflation Inertia* Assignment

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… [END OF PREVIEW] . . . READ MORE

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