Excerpt

## Contents

1 Introduction

2 Stating a Standard New Keynesian Model

2.1 The Representative Household

2.2 The Price Setting Problem of the Representative Firm

2.3 The Role of the Central Bank

2.4 Log-Linearizing the Equations Characterizing the Equilibrium

3 Phillips Curve Analysis

3.1 Original Phillips Curve

3.2 Baseline New Keynesian Phillips Curve

3.3 Hybrid New Keynesian Phillips Curve

4 Inflation Dynamics and Price Rigidity Analysis

4.1 Data

4.2 Baseline Model Estimation

4.2.1 Baseline-Estimation Set-Up

4.2.2 Parameter Calibration

4.2.3 Results

4.3 Hybrid Model estimation

4.3.1 Hybrid-Estimation Set-Up

4.3.2 Results

5 Inflation Targeting Approach

5.1 Model Set-Up

5.2 One-Month Inflation Targeting Approach

5.3 Four-Months Inflation Targeting Approach

5.4 Inflation Targeting Europe vs. United States

6 Conclusion

References

Appendix

## Abstract

Following the example set by Galí, Gertler and López-Salido (2001), this paper investigates the inflation dynamics of Germany, Italy and Finland as well as the European Monetary Union as a whole, and the United States based on a Generalized Method of Moments estima- tion of the New Keynesian Phillips Curve, over the period of 1999 to 2015. We give proof of an obvious heterogeneity in inflation dynamics between the three representative Euro area countries and between the United States and Europe. Finally, we present an inflation-target- ing approach for the European Central Bank, based on the estimated degree of price rigidity. Our main findings are: (1) Inflation dynamics in Italy and the Europe area emerge to have a straight forward-looking component, (2) the backward-looking price setting behavior seems to play a dominant role in Finland, (3) Germany combines both, a backward- and forward- looking inflation characteristic, which is also true for the U.S., (4) prices in Germany are fair- ly twice as sticky as in Italy and Finland, (5) the price rigidity in Germany is quite similar to that of the Euro area.

## 1 Introduction

The price stability in the European Monetary Union^{1} is the main target of the European Cen- tral Bank (ECB). The ECB is facing a challenge changing interest rates in order to achieve the two percent inflation target that ensures price stability, regarding the variations in infla- tion among its 19 member countries at various times. Furthermore, there are not only differ- ent shapes of inflation, but also several degrees of price stickiness and inflation dynamics within the member countries that make policy decisions inflexible and rigid. Therefore, a pro- found investigation of the country-specific pricing characteristics is essential for the ECB to implement the optimal monetary policy, that combines both, price stability in the whole mon- etary union and in its member countries. Following Galí, Gertler and López-Salido (2001), we investigate the different price components and characteristics for three representative Eu- rope area member countries, proceeding as follows:

In the first part of the paper, we give an introduction of a simple standard New Keynesian DSGE model to understand the origin of the New Keynesian Phillips Curve (NKPC). After that, we show three different kinds of Phillips Curves which evolved over the last decades and motivate us for the New Keynesian Phillips Curve.

In the third part of this paper, we give proof of the heterogeneity within the Europe area, estimating the different degrees of price stickiness for Germany, Italy and Finland, with the help of a Generalized Method of Moments (GMM) estimation. We also investigate the degree of price rigidity for the United States and the Europe area as a whole.

Just like Galí et al. (2001), we use a marginal-cost based New Keynesian Phillips Curve. We show that real marginal cost and inflation have a strong co-movement for Europe area coun- tries, which justifies the usage of a marginal-cost NKPC, rather than an output-gap based NKPC^{2}. Our representative time frame ranges from the Bulletin of the ECB in January 1999 to 2015:I. For this time span, the baseline New Keynesian Phillips Curve explains inflation quite well, for all observed countries. We find that prices in Germany are fairly twice as rigid as compared to Finland and Italy. We take this as first evidence of the existence of a hetero- geneity between the three representative countries in the Europe area. For the latter, we find that prices are fairly as sticky as in Germany. According to Galí et al. (2001), there is evi- dence for a higher average price duration in the Europe area than in the United States. Our results are fairly robust in the baseline estimation regarding a change in the instrument set. Different inflation dynamics emerge if we extend the straight forward-looking baseline New Keynesian Phillips Curve with a backward-looking component, called the hybrid New Key- nesian Phillips Curve. We cannot provide proof of a backward-looking characteristic of infla- tion dynamics for Italy, while Germany and Finland combine both, a backward- and forward- looking behavior of inflation dynamics. We take this as second evidence for the heterogeneity within the Europe area. While the hybrid NKPC can be rejected in favor of the baseline New Keynesian Phillips Curve for Europe, this is not the case for the United States. Therefore, a strong difference between the Europe and U.S. average duration of prices and price-setting behavior becomes visible. In comparison to the baseline NKPC, the hybrid Phillips Curve comes with some disadvantages, especially with respect to the robustness and discount factor estimation for Finland and the United States. But yet, the hybrid model estimation confirms the estimated values in the baseline model outcome and provides sufficient and robust esti- mates for the inflation dynamics in Germany, Italy and the Europe area. From the estimated values for the price rigidity, we try to find an inflation-targeting approach for the ECB. Start- ing from the empirical fact that the ECB changes interest rates every four months, we reject a one-month inflation targeting approach in favor of a four-months inflation targeting ap- proach. More frequent changes in the rates would lead to 'inflation-jumps'^{3} because of the het- erogeneity of the European member countries. This would generate price instability. In the Bulletin from January 1999 the ECB states its "primary objective [...] to maintain price stabil- ity." In order to achieve this objective, we point out that countries with a higher price rigidity and GDP share have to be given more weight than others. From that point of view, the ECB privileges countries with a higher GDP share, as for example Germany and Italy, rather than countries with a lower share, such as Finland, because it cares more about the inflation of the former for its policy decision. We demonstrate that this unequal treatment affects the inflation progress of Finland. Although the ECB treats its member countries differently at its two per- cent inflation target, it does a good job in uniting the price stability of the whole Europe area with the price stability in our three representative member countries. With an average devia- tion of merely -0.07 % from the two percent inflation target between 1999:I and 2015:I, it de- viates only one-fourth as much as the Federal Reserve Bank. This can be seen as the success of the European Central Bank, dealing with the heterogeneity of their member countries in maintaining price stability.

## 2 Stating a Standard New Keynesian Model

Our model is a simple standard New Keynesian Model without capital. It consists of an infinite number of identical, utility-maximizing households, competitive monopolistic firms and a government sector. The representative household chooses in period *t* today's consumption of differentiated goods, labor supply and bond holdings in order to maximize its expected utility. The representative monopolistic and competitive firm is the only supplier of good *i* and maximizes its profits, given the demand of the representative household. The central bank and the fiscal authority build the government sector.

### 2.1 The Representative Household

The representative household is an infinitely living utility maximizer, deciding for every period how much to consume and how much labor to supply as well as making a plan for the future. Its utility is increasing in consuming good *i* of firm *i* and decreasing in its labor supply. Future actions are discounted by the discount factor *β s − t*:

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While maximizing today's and discounted future utility, the household faces the flow budget constraint (2.1.2). It can either save its capital into an ordinary government bond *B t*, or ex- pend in consumption good *i* of firm *i*. Its savings and expenditures must at last equal its in- come from working [illustration not visible in this excerpt], investing in bonds and dividens^{4} [illustration not visible in this excerpt] minus taxes , collected by the government. The overall amount of consumption in any period *s* - the consumption basket - depends on the sum of the consumption of each good *i* of firm *i* and evolves according to the following rule:

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The coefficient *ϵ* measures the price elasticity of demand. In the extreme case of *ϵ* = 1, the household consumes all goods *i* in the same amount. If *ϵ >* 1, the household deviates from consuming the same amount of all goods and attaches more importance to the cheaper goods. When *ϵ <* 1, the effect turns to the opposite. The solution to the following maximization problem,

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yields the household's optimal consumption decision:

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*P t* states the aggregated price of the household's consumption basket and is also known as the price index, while *C it* measures the optimal consumption of good *i* with respect to its price. Therefore, the price level can be expressed as follows:

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Per consumption level *C t P t*, the household spends the price . For this reason we can simplify the flow budget constraint in the following way:

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Equation (2.1.1) and (2.1.7) represent the maximization problem of the household. Taking the first derivative^{5} yields the following first-order conditions, characterizing the optimal behavior of the household:

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### 2.2 The Price Setting Problem of the Representative Firm

The representative firm *i* is the only supplier of the substitutable good *i*. As a consequence, each firm is a monopolist in a competitive market. The following production function defines the output as a product of technology and labor input:

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The technology input can be decomposed in a trend and stochastic component:

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In contrast to the Real-Business-Cycle Model, the New Keynesian Model introduces price stickiness. We assume that each firm can change its price in any period with a probability of (1 *− θ*) *∈* (0 *,* 1], following Calvo (1983). The fraction *θ* of firms, which cannot adjust their price in period *t*, sets the same price as in the previous period *t −* 1:

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The remaining fraction (1 *− θ*) of firms which can change their price in period *t*, chooses the optimal price in period *t*, which maximizes:

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Therefore, the representative firm sets its optimal price in accordance with its expected, dis- counted future market value and its profit. The profit of the firm can be derived from its de- mand function. The first derivation of equation (2.2.4), with respect to [illustration not visible in this excerpt], yields the follow- ing optimal price setting rule:

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### 2.3 The Role of the Central Bank

The central bank sets the nominal interest rate according to the following simple Taylor rule:

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The coefficient *φ* measures how aggressive the central bank fights against inflation. There is a positive relationship between the interes rate and the inflation, meaning that if prices are in- creasing, the central bank raises the interest rate and if prices are decreasing, rates are low- ered. Thereby, the ECB tries to keep prices stable - with an intended inflation target of two percent.

### 2.4 Log-Linearizing the Equations Characterizing the Equilibrium

It is necessary to simplify the complex, nonlinear equations above, to be able to easily combine them. For that reason, we use log-linearization. Although, the original model is no longer solved, the log-linearized approximation of the model does well. The concept of loglinearization and the log-linearized equations can be found in the Appendix. We lay our focus on the following five equations:

Households

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Firms

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Government

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As already mentioned in chapter 2.3, the central bank fights inflation measured by the 'infla- tion-fighting' parameter *φ*. For the period 1999:I to 2015:I, we calibrate^{6} this parameter equal to 1.16, meaning that if inflation in Europe rises about one percent, the ECB increases the in- terest rate by 1.16 percent. But there is uncertainty with this relation, measured by the error term *u t*. As a result, the Central Bank deviates from fighting inflation by the factor 1.16 oc- casionally.

## 3 Phillips Curve Analysis

In the past, many controversial ways of presenting inflation dynamics have evolved. In the following passage we present three of them: The original Phillips Curve followed by the New Keynesian Phillips Curve and the Hybrid New Keynesian Phillips Curve.

### 3.1 The Original Phillips Curve

The simplest original Phillips Curve is an autoregressive distributed lag model which connects today's inflation to some order *δ* of lagged inflation and some cyclical variable

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where the error term is given by *u t*. In order to avoid a long run trade-off between inflation and output, the sum of the weights on lagged inflation should equal one. Taking this as a prime measure of fit, we can evaluate the following estimates for Europe (I) and the U.S. (II) for our representative time horizon 1999:I to 2015:I:

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As opposed to the estimation of Galí et al. (2001:4), the unity condition for lagged inflation is fulfilled neither for the Europe nor for the U.S. estimate, although the Europe estimate does a better job than the U.S. one. The coefficient on lagged output is not significant and even negative in the U.S. estimate. Estimates for Germany, Italy and Finland are reported in Table I in the Appendix. They also do not support the success of the original Phillips Curve of explaining inflation over the last decade well. The sum of weights of lagged inflation and the coefficient on lagged output differ significantly from unity, for all estimates. This result is very robust to a change in the inflation lag-length.

All in all, the straight backward-looking inflation character of the traditional Phillips Curve cannot explain inflation for the period 1999:I to 2015:I sufficiently. The equation must include other factors which explain recent inflation dynamics more appropriately. Because the monetary authority and firms form price expectations about the future, it appears reasonable to include this fact in the estimation, as is done in the following paragraph.

### 3.2 Baseline New Keynesian Phillips Curve

Combining inflation dynamics, the output-gap and the price setting behavior of firms, the New Keynesian Phillips Curve is the most important equation of the New Keynesian theory. In contrast to the original Phillips Curve, the NKPC connects today's inflation with expecta- tions of future inflation and the output-gap. It can be derived from equations (2.4.1), (2.4.2) and (2.4.4)^{7}. The log-linearized price index is equal to the price of the fraction *θ* of firms which cannot adjust their price, plus the price *x t* of the fraction(1 *− θ*)of firms, which can ad- just their price:

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Rearranging and inserting equation (2.4.4) for *x t* and equation (2.4.2) yields the New Keynesian Phillips Curve:

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Equation (3.2.2) can be written in a more appropriate way, see^{8}:

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The term [illustration not visible in this excerpt] displays the inefficiency of the model caused by price rigidity. As a result, an output-gap arises, which reflects the deviation of real trend GDP from its potential level under fully flexible prices *F* - a perfect, efficient economy, as it is described by the Real-Bus- iness-Cycle Model. Therefore, a higher level of price rigidity makes monetary policy actions (as the two percent inflation target of the European Central Bank) hard to implement because changes in the interest rate do not transfer immediately into the market. The heterogeneity of the 19 members of the European currency zone and their individual degree of price inflexibil- ity require to investigate the country-specific shape of price rigidity, as will be done in sec- tion four, for Germany, Italy and Finland.

We proceed in the style of Galí et al. substituting the output-gap in equation (3.2.3) by real marginal cost, because there is a problem estimating inflation by the output-gap: The "output- gap based formulation of the new Phillips Curve cannot account for the persistence of infla- tion of the U.S. or for the Europe area." (2001:7). As a consequence, our baseline NKPC reads as follows^{9}:

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with

illustration not visible in this excerpt

where [illustration not visible in this excerpt] is the log deviation of the real marginal cost from its steady-state level.

Plot I compares real marginal cost with inflation for Germany, Italy and Finland. There is a strong co-movement between both variables, as already predicted by Galí et al. (2001) for Europe and the United States^{10}. This is especially true for Italy, which justifies the explanatory power of marginal cost for inflation in the New Keynesian Phillips Curve. We observe that the co-movement is not that strong for Germany. In fact, the fluctuations of marginal cost are too small, in comparison with deviations in inflation. This observation has an impact on the estimation results in part four. But all things considered, the marginal cost-based NKPC does a better job than the output-gap-based New Keynesian Phillips Curve. In Plot II we compare inflation with a measure of the output-gap: detrended output. We can determine an overall quite counter-cyclical movement between both variables for all observed countries. It dis- proves the success of the output-gap-based NKPC in explaining inflation^{11}, as already predict- ed by Galí et al. (2001).

### 3.3 Hybrid New Keynesian Phillips Curve

As an extension of the baseline NKPC, the hybrid New Keynesian Phillips Curve includes lagged inflation as an estimate of today's inflation, and therefore adopts the key element of the original Phillips Curve. This extension is captured by the fraction *ω* of firms, which sets their prices corresponding to preceding prices with an inflation mark-up:

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In contrast, the fraction (1 *− ω*)of firms, which acts like straight forward-looking agents, set their prices optimally, with respect to their infinite, discounted stream of future real marginal cost expectations and analogously to the calvo model:

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Hence, the amount of firms that can change their price in period *t* splits in two fractions: There are forward-looking and backward-looking price setters which are captured by the term (1 *− θ*). As a result, the parameter *θ* is still a measure for price rigidity in the hybrid model. The firms that cannot change their price in period *t* set it just as the price in the previous period (2.4.3). The aggregated price index of both, forward- and backward-looking firms, which can change their prices reads as follows:

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By combining equation (3.3.1), (3.3.2), (3.3.3) and (3.2.1), the hybrid New Keynesian Phillips Curve is acquired:

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with

illustration not visible in this excerpt^{12}

Note: If the parameter *ω* of pure backward-looking firms, is equal to, or does not differ signif- icantly from zero, the hybrid model can be rejected in favor of the baseline New Keynesian model.

## 4 Inflation Dynamics and Price Rigidity Analysis

In this section, we estimate the degrees of price stickiness and inflation dynamics for three representative countries for the European Monetary Union, Germany, Italy and Finland. Furthermore, we investigate the price rigidity for the whole Europe area and the United States. In doing so, we start with the baseline model (3.2.4), followed by the hybrid model estimation (3.3.4). For the estimate we use a Generalized Method of Moments approach^{13}.

### 4.1 Data

For the estimates we use recent quarterly data from 1999:I to 2015:I. All the data is from the OECD online database. It is seasonally adjusted, logarithmized and indexed at the base year 2010. We use the HP-filter with *λ* = 1600 to detrend data. Some variables, especially for the

U.S. estimate, are taken from the Federal Reserve Economic Database (FRED). We measure inflation by the first-difference of the GDP deflator, and real marginal cost by unit labor cost^{14}. We calculate the deviation of real unit labor cost from its mean and take the first-differ- ence as a measure of [illustration not visible in this excerpt]. For the U.S. estimate, we follow Galí and Gertler (1999:206), and use real unit labor cost of the non-farm business sector to measure [illustration not visible in this excerpt]

As a measure of detrended output, we take the first-difference of detrended real GDP from its trend. Wage inflation is measured as the first-difference of detrended nominal wage from its trend-level. We compute the interest rate as the first-difference of the cyclical short term interest rate from its steady-state level. We take real data as a measure for expected inflation. In the next paragraph we present the estimates for the baseline and hybrid NKPC. We show that the baseline NKPC successfully explains the price rigidity and inflation characteristics of all observed countries, while the hybrid New Keynesian Phillips Curve can be rejected for Italy and Europe in favor of the baseline Phillips Curve.

### 4.2 Baseline Model Estimation

In this section we start presenting the set-up of the GMM-estimation. After that, we calibrate the parameters which determine the slope coefficient *λ*. Finally, we show the key results of our estimates.

#### 4.2.1 Baseline-Estimation Set-Up

Starting from the baseline New Keynesian Phillips Curve (3.2.4), we define the following set of orthogonality conditions:

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where *z t* indicates a vector of instrument variables at time *t*.

For the instrument variables we use lagged variables of inflation, real marginal cost, wage inflation, and detrended output. In order to value the robustness of our estimates, we modify the lag-length of our instruments for the estimates I to III as follows:

(I) Inflation, real marginal cost, wage inflation and detrended output from *t −* 1 : *t −* 4.

(II) Inflation, real marginal cost, wage inflation and detrended output from *t −* 1 : *t −* 5.

(III) Inflation from *t −* 1 : *t −* 5 and real marginal cost, wage inflation and detrended output from *t −* 1 : *t −* 2.

For the first two estimates, we choose a relatively large number of lags (Z(I) = 16; Z(II) = 20) to check the robustness towards a relatively small number of lags in the last estimation (Z(III) = 11)^{15}. The lag-lengths for the different countries are all the same in order to make the results more comparable under equal restrictions.

**[...]**

^{1}. In the following we use 'Europe area' instead of 'European Monetary Union' to be short.

^{2}. Sbordone (1999) and Galí and Gertler (1999) have already shown that the "marginal cost-based" version of the NKPC "can provide a reasonable account of postwar inflation in the U.S..". Galí, Gertler and López-Salido (2001) showed, "that the same is largely true for the Euro area.".

^{3}. We introduce the term 'inflation-jumps' to make clear the effect.

^{4}. Because the household owns a firm.

^{5}. With respect to *B t* and *N t*.

^{6}. Based on recent data for inflation and the interest rate on the Main Refinancing Operations (MRO), taken from the ECB statistics database.

^{7}. A complete derivation of the NKPC is displayed in the Appendix.

^{8}.[illustration not visible in this excerpt]

^{9}. We refer to Galí, Gertler and López-Salido (2001:8f) for a detailed derivation of the marginal cost-based baseline NKPC and hybrid NKPC (2001:28f).

^{10}. (2001:11).

^{11}. We do not report results of the output-gap-based NKPC estimation, because Galí, Gertler and López-Salido already found, that "the slope coefficient becomes the wrong sign" for the United States and the Europe are (2001:14). We get the same result for Germany, Italy and Finland.

^{12}. [illustration not visible in this excerpt]

^{13}. Lars Peter Hansen (1982) - A short discussion of the main idea of a GMM-estimation is displayed in the Appendix.

^{14}. Unit Labor Cost (ULC) is calculated as the ratio of total labor cost to real GDP.

^{15}. Galí, Gertler and López-Salido (2001) emphasize that it is necessary to use a small number of overidentifying restrictions in order to minimize the potential estimation bias. Our results show that the estimated parameters are very robust towards various lag-lenghts of the instruments.

- Quote paper
- Marc Kern (Author), 2015, Inflation Dynamics Reconsidered. Inflation Targeting Europe vs. United States, Munich, GRIN Verlag, https://www.grin.com/document/317626

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