# Nonparametric Estimation and Comparison of the G7 Phillips Curves

Diploma Thesis 2004 153 Pages

## Excerpt

## Contents

List of Tables

List of Figures

List of Nomenclatures

1 Introduction

2 Remarks on the Phillips Curve

2.1 Historical Review

2.1.1 Phillips original curve and the time before

2.1.2 Lipsey’s excess demand and the first PC for the USA

2.1.3 The critiques and the failure of the curve

2.2 Summary of the Contemporary Debate - State of the Art

2.3 Discussion of Important PC Issues

2.3.1 Demand pull and cost push

2.3.2 Closed economy vs. open economy

2.3.3 Modeling two involved markets

2.3.4 Expectations

2.3.5 Proportional, derivative, and integral terms

2.3.6 Nonlinear behavior

2.3.7 Constant vs. time varying NAIRU

2.3.8 Other influences

2.4 Wage and Price Phillips Curves: The Empirical Framework

2.5 Issues to be Investigated

3 Semiparametric Regression

3.1 Some Introductory Words

3.2 Parametric Regression

3.2.1 Linear regression

3.2.2 Polynomial and nonlinear regression

3.3 Neighborhood Smoothing

3.3.1 Locally-weighted running line smoother

3.3.2 Kernel smoother

3.4 The Spline Smoothing Approach

3.4.1 Regression splines

3.4.2 Knot selection and a roughness penalty

3.4.3 Smoothing splines

3.4.4 Natural cubic splines

3.5 Additive Models

3.6 Choice of a Smoothing Model

3.6.1 Model selection

3.6.2 Automatic smoothing parameter selection

4 Analysis and Comparison of International Phillips Curves

4.1 Introduction

4.2 Preliminary Considerations

4.2.1 Seasonal adjusted data

4.2.2 The sense of multi-dimensionality

4.2.3 Wage-price spiral

4.2.4 The disregard of significant factors

4.3 The Data

4.4 Traditional 2D-view of the Two Markets

4.5 OLS Estimation of the Model Equations

4.6 Nonparametric Analysis: Fitting a GAM

4.7 Summary of the Results

5 Conclusion and Outlook

A Data Analysis Output

A.1 OLS-estimation Tables

A.2 GAM-estimation Tables

B Data Management

B.1 Source of the Data

B.2 Management

C Basic Command Code in R 1

D Baxter King Algorithm

E Data Medium

References

Eidesstattliche Versicherung

## List of Tables

2.1 The Chosen PC Specifications

4.1 Country Specific Sample Period

4.2 Comparison of the p-values for Dyn in Wage and Price PC’s

4.3 Comparison of the Coefficients of Wage and Price PC’s

4.4 Comparison of the R[2]-values of the OLS and the GAM Estimation Methods for the Wage and Price PC’s

4.5 Relative Coefficients of Wage and Price PC’s

A.1 OLS Estimates for the Wage PC Equation

A.2 OLS Estimates for the Price PC Equation

A.3 GAM Estimation for the Wage PC Equation

A.4 GAM Estimation for the Wage PC Equation

## List of Figures

2.1 The Original Phillips Curve

2.2 Wage Adjustment Function and the x-u-relationship

2.3 Expectations-Augmented Phillips Curve

2.4 Demand Pull and Cost Push

3.1 Example for Linear Regression

3.2 Polynomial Regression

3.3 The Locally-Weighted Running Line Smoothers (Loess and Lowess)

3.4 Overview of Some Important Kernels

3.5 Gaussian Kernel with Different Bandwidths

3.6 Gaussian Kernel Smoother Applied to the Motor Cycle Data

3.7 Regression splines - Piecewise Quadratic Fits to the Scatterplot

3.8 Linear and Quadratic Basis Functions with a Knot at

3.9 Fit of a Spline with Truncated Power Basis Functions

3.10 A Smoothing Spline Fit

3.11 Three Natural Cubic Spline Fits

3.12 Fit of an Additive Model to the Trees Data

3.13 Example for Cross-validation

4.1 Seasonal Unadjusted Scatter

4.2 The Influence of the Inflationary Climate

4.3 The Wage-price Spiral of the USA

4.4 The Japanese Seasonal Phillips Curves

4.5 The German Seasonal Phillips Curves

4.6 Observing the Labor Market

4.7 Observing the Commodity Market

4.8 Productivity Growth for West-Germany and Japan

4.9 Wage PC Fits by the GAM Function

4.10 Wage PC Fits by the GAM Function II

4.11 Residuals from the Wage PC GAM Fit

4.12 Price PC Fits by the GAM Function

4.13 Price PC Fits by the GAM Function II

4.14 Residuals from the Price PC GAM Fit

## List of Nomenclature

The Notation of terms and variables is following the order of their appearance within the text. For a better orientation the page, where it first appears is speci- fied in the left column. A few abbreviations have been used twice since that has not been avoidable in order to follow common notation. For instance u is unem- ployment in chapter 2 and 4, but also denotes a distance variable for neighborhood smoothers in chapter 3.

In the context of Phillips curve theory upper case letters denote absolut measures of a parameter, whereas lower case variables mark either rates of an absolute measure (in percent), indices or logs. Abbreviations are also written with upper case letters. Matrices and vectors in chapter 3 are fat and cursive, whereas R- program code (except for Appendix C) is just fat.

Nomenclatures for Chapter 1 and 2

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Nomenclatures for Chapter 3

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Nomenclatures for Chapter 4

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## Chapter 1 Introduction

The start of this century has turned out to be a crucial crossroad for macroeco- nomics on three counts. Firstly, the New Economy at the end of the last decade, often suspected to suspend the traditional economical rules (see for example Boldin (1998)) was breaking down, which gave back the belief that those rules still ex- ist. Secondly, almost at the same time the European Monetary Union experiment started, where the outcome is still uncertain, especially with regards to the goal of exclusively fighting against inflation (see the European Central Bank mission statement at http://www.ecb.int).[1] The third problem arises from the war against terrorism, which is already a serious cost driving factor because of higher security requirements, greater uncertainty faced by all economical agents and higher oil prices, whereby the latter issue has just recently been resolved for some time by the OPEC (Organization of the Petroleum Exporting Countries) having declared to increase the production of oil.

All three points are in fact strongly connected to the notorious concept of the Phillips curve (PC), which has been introduced by Alban William Phillips (1958). The main idea of it is that a positive correlation exists between, broadly speaking, the level of capacity utilization and the change of prices on a market. For instance lower unemployment rates, associated with higher production of output, would correspond to higher positive wage increases, whereas higher unemployment would lead to lower wage increases, possibly even to wage decreases (cf. Phillips (1958)).

The Deutsche Bundesbank (1987, p. 9) considered the anti-inflation policy as a requirement to produce economic prosperity and low unemployment rates, whereas Stiglitz (1997) and Hoogenveen and Kuipers (2000) strongly doubt this view.

Of course, the choice between two different situations like these does not seem to be that difficult, but one has to note that wage increases are usually strongly connected to inflation, the increase in prices, and thus to the devaluation of the national currency. This issue has been known a long time before, namely by Irving Fisher (1926), Arthur Cecil Pigou (1933) and John Maynard Keynes (1936), but Phillips’ paper has caught the most attention, partly due to the graphical representation it gave for the relation just described.

From the very beginning, the Phillips-curve (PC) was causing a big contro- versy. The model has been praised as the ”core of most large-scale macroeconomic models used by central banks, governments, and commercial forecasters” (Gali (2000)). Alan Blinder (1997) even called it ”the clean little secret” of macroeco- nomics. Similar euphoria did accompany the early 1960’s, especially when Samuel- son and Sollow (1960) encouraged policy makers to exploit the so called trade-off between inflation and unemployment. However, the critiques by Friedman (1968) and Phelps (1968), who strictly deny a stable curve in the long run, and empirical evidence get Lucas and Sargent (1978) to call the model an ”econometric failure on a grand scale”. The reason for this statement, the experience of high inflation together with high unemployment during the 1970’s, was mainly attributed to the oil price shocks in those years, but also to the change in expectations (Blanchard (2003, p. 168)) of economical agents. However, various enhancements and recre- ations of the original Phillips curve (for instance Phelps (1968), Gordon (1982) and Calvo (1983)) and its success in predicting economical measurements, as well as its ability to guide monetary policy makers (mentioning the Taylor rule (1993), see also Leeson (1997)) reinforced the relevance of the model.

One of the strengths of the Phillips curve discussion is the early tie to empir- ical observation and thereby to statistical methodology. Phillips (1958) already applied a simple fitting technique, which can be seen as some sort of nonlinear regression, as he figured the wage Phillips curve of the UK to be nonlinear. On the contrary, Gordon (1970, 1977) and others used a linear framework to be estimated. However, mainly the estimation of the functional relation between inflation and unemployment has been done in a parametric setting. This has the disadvantage of a potential loss of information due to narrowing the focus to a specific form (e.g. linear regression) beforehand. Stiglitz (1997) and Akerlof (2002) for instance suggest that the Phillips curve features important nonlinearities. Even though the polynomial and the nonlinear regression might be quite successful in tracking non- linearities, those methods still depend a lot on skills and goodwill of the analyst. In this regard nonparametric procedures generally represent a superior alternative. Its motto is: ”Let the data show us the appropriate functional form.” (Hastie and Tibshirani (1990, p. 1)). In other words those techniques attempt to extract the relation of variables exclusively data driven. During the last decades this field of statistics experienced a tremendous boom, certainly pushed by the introduction and the fast progress of the computer technology, such that today it is providing a wide range of models, smoothing procedures, fit selection criteria etc.

The goal of this thesis is to apply nonparametric methodology in order to investigate the Phillips curves of all G7 members states, the USA, Japan, Germany, Great Britain, France, Italy and Canada. Thereby it will build upon the theoretical approach of Flaschel et al. (2004), which is modeling two distinct wage and price Phillips curves, taking account of the wage-price spiral. Furthermore it includes a measure of adaptive expectations as well as myopic perfect foresight of inflation. It is expected that not only important nonlinearities of the Phillips curve will be observable in many countries, but the analysis may also provide evidence of essential differences between countries. A broad international investigation in this regard has rarely been conducted, DiNardo and Moore (1999) and Hoogenveen and Kuipers (2000) being a few exceptions. However, it promises interesting insights, namely about the behavior of the famous macroeconomic relationship in various environments.

The remainder of the paper is organized as follows. Chapter 2 is devoted to sketching the scientific history of the Phillips curve, as well as some of the more important specifications developed along the way. It then leads to the justification and the formulation of the concrete Phillips curve framework, originated by Fair (2000) and Flaschel et. al. (2004). In Chapter 3 an introduction is given in para- metric regression, neighborhood smoothing, spline smoothing, additive models, and a few model selection criteria. In doing so it concentrates on the empirical practi- cability of those techniques and it tries to sensitize the reader to understand the strength and weaknesses of the different procedures, often supported by graphical representations. In Chapter 4 parametric as well as nonparametric analyses of the Phillips curves of the G7 member states are conducted. Before, an introductory part shall shed some light on a few special issues. After the summary of the results Chapter 5 is formulating the conclusions which can be drawn from the empirical work and gives perspectives of further investigations.

## Chapter 2 Remarks on the Phillips Curve

The main objective of this chapter is to introduce a layman to the idea of the Phillips Curve, the rationale behind it, and the discussion of its various models, which then leads to the revival of one special version. A fairly appealing way of doing so is to follow a chronological order. The integration of a concept in its historical background is likely to make it easier for the reader to understand. Hence, this will be done in sections 2.1 and 2.2, the latter one summarizing the recent debate. The ensuing section deals with the possible ingredients of a Phillips Curve in a systematic way and gives justification for the choice of a special type, summarized at the end. Section 2.4 then puts this into practice by reproducing and explaining a formal framework, formulated by Flaschel, Kauermann and Semmler (2004). The closing section 2.5 announces the issues, which are to be investigated during the empirical analysis in chapter 4 and thus gives a perspective of the possible yield of this approach.

### 2.1 Historical Review

#### 2.1.1 Phillips original curve and the time before

The idea of a relation between a nominal variable - such as price changes - and a measure of real economic activity - such as the unemployment rate - has a long tradition. Already in 1752, David Hume wrote in his essay ”Of money”:

”In my opinion, it is only in the interval or intermediate situation, be- tween the acquisition of money and the rise in prices, that the increasing quantity of gold or silver is favourable to industry The farmer or gar- dener, finding that their commodities are taken off, apply themselves with alacrity to the raising of more It is easy to trace the money in its progress through the whole commonwealth; where we shall find that it must quicken the diligence of every individual, before it increases the price of labour.” (Hume (1752))

This quotation is remarkable, since Hume already considered such a tradeoff to exist only in the short run (cf. Mankiw (2001)). Three decades before Phillips (1958), Fisher (1926) empirically discovered a positive correlation between employ- ment and price changes for the United States (US) in the period 1903 - 1925. Then Pigou started chapter V of his Theory of unemployment (1933) with the statement that the quantity of employment can only be varied in accordance with variations in wage terms. Keynes’ grand General Theory (1936) postulates a minimum un- employment level, where additional aggregate demand would only result in rising prices and wages. So the topic was already around in the profession for several years when Phillips (1958) examined the relationship between the unemployment rate and rate of wage change (for simplicity in the following called ”unemployment” and ”wage inflation”) of the period 1861-1957 in the United Kingdom (UK). By some kind of smoothing procedure (chosen by rule of thumb) he found the equation (cf. Phillips (1958, p. 290)):

Dw + 0.9 = 9.638 ∗ u−[1].[394]t or log(Dw + 0.9) = log 9.638 − 1.394 log ut. (2.1.1)

Today, this could be considered a type of nonlinear regression (see section 3.2), not a nonparametric one, however. Figure 2.1 shows the trend of the relationship. High wage change corresponds to low unemployment, low wage change to high unemployment. And stable wage rates (zero wage inflation) are associated with an unemployment rate of about 5, 5% (at u∗). Of course, this insight was not new. It was the suggestion that this curve represents a stable trade-off that was new (cf. Rothschild (1978)).

Phillips’ paper strongly concentrates on the examination of an empirical fact without giving proper theoretical justification. Nevertheless, Phillips gave a first loose explanation. Similar to Fisher (1926), who attributes the correlation of price

Figure 2.1: The original Phillips Curve (cf. Phillips (1958))

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changes and employment to the incidence of good business and bad business periods, Phillips describes the rationale behind it as follows:

”...in a year of rising business activity, with the demand for labour in- creasing and the percentage unemployment decreasing, employers will be bidding more vigorously for the services of labour than they would be in a year during which the average percentage unemployment was the same but the demand for labour was not increasing. Conversely in a year of falling business activity, with the demand for labour decreas- ing and the percentage of unemployment increasing, employers will be less inclined to grant wage increases, and workers will be in a weaker position to press for them, than would be in a year during which the average percentage unemployment was the same but the demand for labour was not decreasing.” (Phillips (1958, p. 283))

#### 2.1.2 Lipsey’s excess demand and the first PC for the USA

At the same time as Phillips’ paper, Dicks-Mireaux and Dow (1959) and Klein and Ball (1959) studied the same subject, but only Phillips drew the eye-catching and now famous curve, strongly suggesting a stable trade-off, where one only has to choose alternative points on the curve. Additionally, Lipsey (1960) extended Phillips’ article by giving theoretical justification for this empirical observation. The core of Lipsey’s argumentation are the wage adjustment function (shown on the left hand side in Figure 2.2) and the x-u-relationship (see also Frisch (1983), il- lustrated on the right-hand side of figure 2.2). uf here denotes frictional unemploy- ment, the state in which labor demand is equal to labor supply. The corresponding

Figure 2.2: Wage adjustment function and the x-u-relationship (cf. Lipsey (1960))

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formula for the relationship is Dw = c ∗ND−NS, where c is a constant, N denotes NS employment, and S stands for supply as D stands for demand. An excess demand (x) of 0A in Figure 2.2 would lead to a wage change of AB. Both relationships combined reproduce Figure 2.1, the former only empirically constructed functional relation between unemployment and the rate of wage change. The triumphal procession of the Phillips Curve continued with Samuelson and Solow (1960), who analyse the first price PC for the US and carry out a first com- parison between the UK and the US. Even though the correlation was weaker than in the UK, their was evidence supporting Phillips’ results as a fairly consistent pattern from 1946 to 1960 was discovered by Samuelson and Sollow (1960, p. 189). The rest of the data gave reason to conjecture a shift of the relation in the forties and fifties. Apparently this was an innovation, since Phillips (1958) had consid- ered it to be stable at any time. Samuelson and Solow held institutional changes responsible for this shift, if it was real. In displacing the rate of wage change by price inflation and baptizing the special relationship ”Phillips Curve”, the article was setting an important milestone. But the real sensation was that Samuelson and Solow claimed this curve to be a menu for policy makers, from which one can choose different combinations of inflation rate and unemployment rate, low infla- tion connected with high unemployment and the other way around. However the simple unemployment-inflation tradeoff was soon facing opposition, which is the topic in the proceeding section.

#### 2.1.3 The critiques and the failure of the curve

The proposition of a stable price PC for the United States was mainly responsible for the success of Phillips’ concept abroad, but it also evoke the first criticism. Independently of each other Friedman (1968) and Phelps (1968) have produced a respectable refutation, which set an example that economic theory is not always dragging behind occurrences. Both authors criticize Lipsey’s interpretation for not taking into account inflationary expectations. If a monetary expansion causes the aggregate demand rising, prices are rising too. Firms observe a decrease in real wages[1] and a demand for more labor. This causes wages to rise. Workers initially assuming prices to be constant interpret this as a rise in their real wage and are willing to work more. So economic agents are fooled by the so called money illusion. If then firms and workers both identify the level of prices and wages rising in general they adjust their inflationary expectations and take it into account in bargaining. This reduces employment again to the original level. Friedman (1968) named it the natural rate of unemployment (today usually called NAIRU - Non- Accelerating Inflation Rate of Unemployment; see also section 2.4.7), bringing forward the natural rate of interest hypothesis of Wicksell (see Friedman (1968)), and predicted the Phillips curve to be unstable, meaning that by exploiting this inflation-unemployment trade-off, it will vanish over time. So he acknowledged the existence of a short-run Phillips curve (SRPC), but postulated a long-run Phillips curve being unaffected by price changes.

This is displayed in Figure 2.3, where the shift of the Phillips curve produces the vertical line, which represents the long term natural rate of unemployment. Formally those two PC types are expressed in the expectations-augmented Phillips curve Blanchard (2003, p. 169):

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The proportion of wages to prices

Figure 2.3: Expectations-Augmented Phillips Curve

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where Dpt−1 stands for expected inflation. Note that a long-run Phillips curve is associated with Dp = Dpt−1, and therefore ut = u. Frisch (1983, p. 30) regards the development of this relation as the second stage in the development of the Phillips curve theory, where the New Microeconomics approach of Phelps et al. (1971) belongs to as well. The latter further elaborates the concept of the natural rate of unemployment and studies the two components search unemployment and wait unemployment as part of the voluntary unemployment.

The third stage following Frisch’s classification is marked by the school of ra- tional expectations just evolving in the 70’s (cf. Lucas (1972, 1973) and Sargent and Wallace (1975)). For this group the Phillips curve is an ”econometric fail- ure on a grand scale” (Lucas and Sargent (1978)). Stating that expectations are formed rationally they question the money illusion argument and deny the exis- tence of a short-run PC, since economic agents are assumed to perfectly foresee prices and wages. Additionally the famous Lucas critique (Lucas (1976)) warns that the Phillips curve, as any other econometric model, will break down, if a change in the economic policy occurs. Lucas and Sargent (1978) thus declare the end of Keynesian macroeconomics and follow an approach of micro-foundations .

It didn’t take long until the critiques of the Phillips curve got a striking ev- idence. In October 1973 the first oil price shock of the 70’s caused persistent ”stagflation”, a state of high inflation along with high unemployment. But in contrast to those calling this supply shock the major change, Blanchard (2003) considers the change of expectations from about zero inflation to positive infla- tion as more important. This shift of expected inflation is probably due to a change in the monetary policy, since all of a sudden deflation seemed to disappear and a tamed inflation rate became a standard economic condition (cf. Blanchard (2003, p. 136)). All this led to the first so called ”Death of the Phillips curve” (see for instance Brinner (1977)), the broad acceptance of the failure of the sim- ple inflation-unemployment trade-off theory (the original Phillips curve). Nev- ertheless the expectations-modified PC founded by Friedman (1968) and Phelps (1968) survived much longer and still serves as a main reference in today’s Phillips curve theories (Mankiw (2001): ”it remains the theoretical benchmark for inflation- unemployment dynamics”).

The following section explains why the obituary to the PC was written a little too early. It tries to give a summary of the recent discussion and to sketch the main approaches.

### 2.2 Summary of the Contemporary Debate - State of the Art

The discussion about the PC has never really come to an end until there appeared a turning point in the late 90’s, the New Economy. The US economy faced re- peated record lows of unemployment in a long-lasting boom without any sign of accelerating inflation. So the controversy arouse once again (see for instance a series of papers to the special issue ”The return of the Phillips Curve” in the Jour- nal of Monetary Economics, October 1999, 44 (2)) and lasts until now (in 2003 a CEPR Conference took place in Berlin about that topic - http://www.phillips- curve-revisited.de).

Today a lot of new concepts and model extensions are involved (as partly becomes clear in the next section, where there will be looked at various issues more closely). Starting from Gordon and Eller (2003) it seems that one can differentiate between two main approaches: Gordon’s (1982) so-called mainstream ”triangle” model and the New Keynesian Phillips Curve.

The first evolved by amending the original equation of Phillips (1958) and Lipsey (1960) by supply shock variables and a zero long-run tradeoff, motivated by Friedman (1968). It successfully explained the movements of inflation in the 1980’s and the early 1990’s (cf. Gordon and Eller (2003)). That was the time after the tight monetary policy (from 1979 to 1982) of Paul Volcker, the former Chairman of the Federal Reserve Board of Governors, had ended the US’ inflation crisis of the 70’s and caused the worst unemployment rate since World War II. The model is called ”triangle” model because it includes three basic determinants of inflation Dpt in time period t (cf. Gordon (1997)): inertia, demand and supply. An example for such a model is (cf. Eller and Gordon (2003)):

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where the inertia is represented by the term of lagged inflation Dpt−1, xt denotes the excess demand, zt is a vector of supply shock variables and εt is a serially uncorrelated white noise error term (white noise means that the expected error E(ε) equals zero). ϱ1, ϱ2 and ϱ3 are coefficients and M is a polynomial in the lag operator. Prediction errors of this model in the mid-90s then led to an amendment by Gordon (1997) and Staiger, Stock and Watson (1997), that allowed the NAIRU to vary over time.

The second very influential approach, the New Keynesian Phillips curve (NKPC), is based on Taylor (1980), Rotemberg (1982), and Calvo (1983) and was further developed by Gali and Gertler(1999) and others (see also Gali (2000)). There are three basic relationships of the New Keynesian Phillips Curve (NKPC). The first one represents the desired price P∗t ofafirminperiodt(cf.Calvo([1983]);agreat summary of Calvo’s model is given in Mankiw ([2001])):

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which is dependent on the price level in the economy, the unemployment rate (ut) and the NAIRU (u). It is clear that this equation follows general economic intuition: the desired price falls during recessions (unemployment is increasing and aggregate demand decreasing) and it increases during booms.

Even though P∗t isthepricepreferredbyfirmsint,theactualpricedecision in t - if possible - would be different, since firms are subject to a random variable, which decides, whether a particular firm will change its commodity price or not. Despite of the unrealistic assumption of this randomness, the results are pretty similar to more realistic models (cf. Mankiw (2001)) which, moreover, have a bonus of simplicity. When such an adjustment process finally takes place, prices are formed by the following equation:

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Parameter φ in the Poisson process represents the portion of firms which will adjust prices in t; every firm has an equal probability to be one of the adjusting firms in each period. When an adjustment period takes place, firms do not set their desired price P∗t, but instead they take an average of the infinite number of prices expected to be desired in the future. That average is Psett ; and the greater j the less weight is assigned to the price P∗t+j, since desired prices in the future are subject to uncertainty of future necessities of price adjustments. The speed of decline of weights is determined by the probability of the arrival φ, for it is not necessary to have much foresight if φ is nearly 1. The circle of relationships is closed by the third equation for the overall price level in period t (Mankiw (2001)):

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The price level in the economy is an average of all prices firms have set in the past which are still relevant. φ again discounts the weight of prices set deeper in the past, since the fraction of firms not having adjusted their prices for a long time becomes less the larger j gets.

If the system of three equations just presented gets solved for inflation Dpt, which is ln(Pt) − ln(Pt−1) the result is a New Keynesian Phillips Curve (cf. Gali (2000)): Dpt = Et(Dpt+1) −

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Many variations of this concept have emerged. To name out a few: Erceg, Hen- derson, and Levin (2000), Christiano, Eichenbaum, and Evans (2001), as well as Woodford (2003). The latter approach to the New Keynesian Phillips Curve goes in the direction of separate wage and price Phillips curves. Thus it is an interest- ing parallel to the framework, which will be outlined in section 2.4. The following relations were derived in proposition 3.9. (Woodford (2003, p. 225)):

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Because of the big attention attracted by the New Keynesian PC Mankiw (2001) calls it ”the workhorse for much recent research on monetary policy” and McCallum (1997) praised it ”the closest thing there is to a standard specification”. But it does not win laurels everywhere. Mankiw (2001) mentions disinflationary booms, lack of inflation persistence, and implausible impulse response function behavior as serious shortcomings of the model. For Eller and Gordon (2003) it is even ”an empirical failure by every measure”.

Certainly, it is false to proclaim the death of the NKPC already. One way out of the misery might be the inclusion of adaptive expectations (as Mankiw (2001) states), as Fuhrer (1997), for instance, found that expectations of future prices are insignificant, empirically. Since backward-looking models are working much bet- ter in explaining the data than forward-looking models, Roberts (1997) questions the assumption of rational expectations; see also the discussion of expectations in section 2.3.4 in this regard.

Of course, it would go beyond the scope of this work to compare the various approaches theoretically (since it is an empirical work in any case) and to decide upon which one might be appropriate. Instead, section 2.3 is trying to list the main issues linked to PC modeling and gives some justification for choosing a certain set of characteristics, which are integrated into the traditional backward-looking approach of Flaschel and Krolzig (2003) and Flaschel et al. (2004). In section 2.4 a detailed description of this concept will be given formally. As it will be shown in chapter 4, it has a good explanatory power.

### 2.3 Discussion of Important PC Issues

This section will discuss a list of fundamental elements which should or should not be included in a Phillips curve model. So it is devoted to the philosophy of a potential theoretical framework, even though the list of issues provided is far from being complete. The assessment will be done as unprejudiced as possible in order to get a little closer to the truly important features, but at the end reasons shall be given to justify the choice of the approach by Fair (2000) and its further developments by Flaschel and Krolzig (2004) and Flaschel et al. (2004). A concluding table will summarize these findings to give an overview of what has been developed. The results then get a concrete formal expression in section 2.4, which will serve as the specific model tested and compared for the G7 countries in the analysis in section 4.

#### 2.3.1 Demand pull and cost push

Two fairly often discussed sources of business cycle fluctuations, and therefore rel- evant to the Phillips curve discussion as well (cf. Phillips (1958)), are Demand pull and Cost push. The first refers to stimulated aggregate demand associated with, when positive, an increase in output (GDP ) and a decrease in unemployment, caused for instance by a new fiscal policy. The second denotes a shift in the cost of production (input costs), affecting the aggregate supply side. Exemplary factors can be rising wages, higher taxes or higher import prices, e.g. when in an open economy prices of imported raw materials or goods become more expensive, often as a result of currency depreciation. The effects of such influences can be observed graphically in figure 2.4 (for a review of the theory see for instance the textbook of Blanchard (2003)).

Phillips’ (1958) first PC-equation contained the real economic parameter unem- ployment rate as a representative of demand pull and wage inflation as the nom- inal response variable. This is still the common central part for most of today’s PC-models, where often wage inflation is replaced by price inflation, assuming a one-to-one evolution of wages and prices. With respect to cost push, without ex- plicitly including a measure of it into the wage inflation formula, Phillips took into consideration the percentage increase in the retail price index and the change in

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Figure 2.4: Demand pull and Cost push: The first shifts aggregate demand (AD) to the right → the GDP (Y) rises and the general price level p (in any market) rises as well; the second causes aggregate supply (AS) to shift up → Y decreases, and p increases again, giving further momentum to inflation.

the index of import prices into consideration when explaining the behavior of the data. In this context he pointed toward the working of a wage-price spiral (cf. proceeding subsection).

Another fairly intuitive way to measuring Demand pull (also called Demand pressure or excess demand ) is excess labor (or unemployment gap) Nl − Nl (for the labor market) and excess capacity Nc − Nc (for the goods market), following the notation of Flaschel et al. (2004). Nc and Nl here denotes the NAIRU in those two markets respectively (see also Krolzig and Flaschel (2003)). Cost push (or Cost pressure) on the other side can be measured by the evolution of the term Dp − D12p, the difference between inflation and the expected inflation. Demand pressure and cost pressure terms play a major role in macroeconomic models, so that their use is hardly dispensable. The following section is concerned about another crucial specification of theoretical models in this area.

#### 2.3.2 Closed economy vs. open economy

Of course, nobody needs to argue about the fact that there are external influences on a national economy caused by international trade and cooperation. Imports and exports are having a definite impact on output, and thus on unemployment as well. Import prices and currency exchange rates do have an effect on inflation.

The affect of such terms is modeled by open economy models whereas it is ignored by closed economy models. Arbitrary examples of open economy models are for instance DiNardo and Moore (1999) and Fair (2000) (the latter uses an import price deflator). Instead Flaschel et al. (2004) applies a closed economy model for simplicity reasons. However, the decision of a closed economy model can only be justified by the evidence of good approximative properties. That would be difficult to assume for small economies as the Netherlands and Belgium, whose ratio of exports to the GDP in 2000 was 74 % and 84 % respectively , in comparison to 11 % for the USA and 10 % for Japan (Blanchard (2003, p. 375)). Since the G7 countries belong to the eight biggest economical powers, considering the GDP (China got ahead of Canada and Italy recently), in this work a closed economy model might be reasonable. It must be kept in mind though that there are in fact big differences between those countries. For instance, Germany’s ratio of exports to GDP was 33 % in the year 2000.

The choice between open and closed economy modeling is accompanied by a certain price index, usually the CPI (Consumer price index ) for the former and the GDP deflator for the latter. The reason for this consists in the CPI including a measure of import prices, whereas the GDP deflator only taks into account domestic production. Therefore, in this work the base for the calculation of inflation is the GDP deflator (see also Appendix B explaining the data management in detail).

#### 2.3.3 Modeling two involved markets

Fair (2000) observed that the discussion has recently moved away from wage and price PCs to the use of reduced form price equations, so that many models only consist of one curve. This is true if one observes for instance the so-called main- stream ”triangle” model of Gordon (1997), which considers wages only implicitly by the term of price inflation. This assumes a connection of wage and price in- flation, a - so to speak - direct and instant transfer of wage inflation in the labor market to price inflation in the goods market and vice versa. This is often formu- lated by the so called markup pricing, where prices are formed by an equation like Pt = Wt(1+μ) (cf. Blanchard (2003, p. 136). That is a pretty strong assumption.

Already Phillips (1958, p. 285) addressed the interaction of two markets in a wage- price spiral and as Fair (2000) recently stated it might be important to model two separate Phillips Curves, one for the labor market and one for the goods market in order to keep predictive accuracy. That is because adjustments of wages and prices to one another is a more complex process, involving time lags through perception difficulties, wage negotiations between employers and unions etc. So the feature of two interacting Phillips curves for two markets as in Flaschel et al. (2004) shall be applied here.

#### 2.3.4 Expectations

As Friedman (1968) and Phelps (1968) have stated and the collapse of the orig- inal Phillips curve during the seventies has shown, expectations of economical agents have to be included into a theoretical framework. This is still true today as Blanchard (2003, p. 168) presents a well-fitted linear regression line for a simple backward-looking model (with experienced inflation Dpt−1) for the United States (see also the quotation of Mankiw (2001) at the end of section 2.1). On the other hand, as presented in section 2.2 the NKPC includes measures of forward-looking expectations, for this is what many scientists associate with rational expectations (as part of rational optimizing behavior of economical agents). The opposition rather believes in adaptive expectations, the generation of expectations by means of past experience. But as Taylor (1980) shows, the world can not be divided into two sectors that easily, since backward-looking inflation inertia is not incompatible with rational expectations. Additionally, Mankiw (2001) notes that even though the data is ”crying out for” adaptive expectations, it is hard to believe that the broad media coverage of monetary policy and business sentiment indictors is ig- nored by the people when expectations about inflation are formed. So maybe a hybrid model is the solution. In this point the model of Flaschel et al. (2004) is beneficial, since it takes account of predominantly adaptive expectations (by past price inflation over a three-year window, see Rudebush and Svensson (1999); see also Appendix A) but it also includes myopic perfect foresight, for instance by present price inflation as a predictor for present wage inflation and vice versa.

#### 2.3.5 Proportional, derivative, and integral terms

As already mentioned before the terms integrated into a Phillips curve can have many different forms, in particular proportional, derivative, and integral follow- ing up the suggestions of Phillips (1954) for fiscal policy rules. For instance the unemployment rate as a predictor multiplied by a coefficient would represent a proportional term, as opposed to the change in the unemployment rate (derivative case) and the accumulated unemployment rate over let us say the last five years (integral case). A derivative control can be found in the Phillips loops as shown in Blanchflower and Oswald (1994)) and an example of the use of the integral control is Stock and Watson (1997). However, as noted in Flaschel et al. (2004, p. 8), derivative and integral terms of PCs have been identified as little significant for the US (see also Flaschel and Krolzig (2003)). This might be different for other economies and time periods, so that it is probably too early to discard variables like these. But for simplicity reasons (and, therefore, better interpretability) derivative and integral terms will be set aside in this thesis, as it is done in the standard Phillips curve as well as in Flaschel et al. (2004).

#### 2.3.6 Nonlinear behavior

Another important question is: Does inflation (as a possible response parameter) change proportionally to unemployment? Or in other words: Is the PC linear? Phillips (1958) found strong evidence that it was nonlinear for the labor market in the UK until 1957. So he imposed a special form of log-linear function on the data. In contrast, because of its simplicity and relatively good approximation properties to the real function textbooks (for instance Blanchard (2003)) tend to use linear versions. Gordon (1970, 1977) are some exemplary empirical studies based on linear PCs. In contrast Stiglitz (1997) and Eisner (1997) have suggested nonlinear behavior of inflation rates with respect to unemployment and under utilization of capacity. Akerlof (2002) is furthermore emphasizing the importance of downward stickiness of wages. His original argument: ”At very low inflation, a significant number of workers do not consider inflation sufficiently salient to be factored into their decisions. However, as inflation increases, the losses from ignoring it also rise, and therefore an increasing number of firms and workers take it into account in bargaining.” Fehr and Tyran (2001) is one of numerous empirical studies which support this hypothesis. Even if the difference between the true functional form and an OLS-estimate would not turn out to be outrageous, it might be interesting to explore some maybe small but noticeable nonlinear structure, such as the downward stickiness of wages and prices for instance. This is made possible by smart and easy to use statistical estimation techniques, which will be described extensively in chapter 3. There seems to be no striking argument to abstain from nonparametric methodology and to use crude linear regression instead. For some Phillips curves of the G7 the latter could be appropriate while for others it may not. And especially this difference could contain essential information. Nevertheless, linear regression provides a useful comparison to the estimation of nonparametric models. That is why it shall be applied in section 4 as well.

#### 2.3.7 Constant vs. time varying NAIRU

NAIRU is the abbreviation for Non-accelerating inflation rate of unemployment and it is equivalent to the so called natural rate of unemployment of Friedman (1968). The term NAIRU is often used instead of natural rate due to the some- what misleading word ”natural”, implying an unchangeable steady unemployment rate. Actually Friedman (1968) and Phelps (1968) were long understood to suggest such a constant unemployment rate in the long run, whereas Gordon (1997) and Staiger et al. (1997) argued that the NAIRU seems to be time varying. Similarly, Blanchard (2003) shows evidence for the US that the NAIRU has changed over the years.

Just considering the case of a constant NAIRU there do exist many different approaches for estimating such a measure of long-term unemployment. The textbook of Blanchard (2003) simply takes the average of all unemployment rates. Fair (2000) uses a little more appealing estimator for the NAIRU:

Abbildung in dieser Leseprobe nicht enthalten

where the δi are the coefficients of the Phillips Curve and δ0 is the absolute term. This technique was called the ”conventional method for estimating the NAIRU” by Staiger et al. (1997), namely used by the Congressional Budget Office (1994), Gordon (1990), Eisner (1995), and many others. Eller and Gordon (2003) called the concept the ”no-supply-shock NAIRU” since supply shocks are assumed to be zero at the NAIRU level of unemployment.

Staiger et al. (1997) applied a simple cubic spline with two knots for estimating a time-varying NAIRU (for reference see section 3.2). Thus Staiger’s et al. (1997) flexible method allows to get an idea of the evolution of long term unemployment and the relevant forces causing it. Beyond giving just one point estimate also provides an elsewhere rarely employed confidence interval (as Mankiw (2001, p. 47) recently lamented). Similar approaches can be found in Gordon (1997), Eller and Gordon (2003)). An extensive overview of the various NAIRU-estimation techniques cannot be given, since that is not the focus of this work. However those methods promise new insights for further investigation.

#### 2.3.8 Other influences

The relevance of additional forces was strongly suggested by Phillips (1958) already. He investigated the influence of the rate of change of unemployment (approximately du/dt, where u is unemployment and t stands for time) in his famous Phillips loops (see for a new treatment Blanchflower and Oswald (1994)) and in the Conclusion of his paper he even conjectured productivity to constitute another important factor. Since the oil price shocks and the changing inflation experience in the 70’s, mea- sures of expected inflation (Friedman (1968) and Phelps (1968)) and supply shocks (cf. Gordon (1982)) have been included. The rational expectations school (Calvo (1983)) added future expected prices and Flaschel and Krolzig (2003) recently used underemployment of capacity on the labor market and introduced additionally the wage share. Stiglitz (1997) finds demography, wage aspiration, market competi- tiveness and hysteresis (will be explained in the following sections) as important factors influencing the NAIRU. At the same time, Gordon (1997) suggests to omit wage inflation for ”the earlier fixation on wages was a mistake”.

Recapitulating, there is wide disunity within the profession, which parameters to include and which to disregard. It seems that there are no limits to phan- tasy and it would not be surprising if someone would seriously take into account the weather forecast one day. Please note that Japan for instance exhibits strong

Abbildung in dieser Leseprobe nicht enthalten

Table 2.1: The chosen Phillips Curve specifications

seasonal behavior in the analysis in chapter 4, which points toward a special tim- ing in wage inflation decisions in its economy. Flaschel et al. (2004) stated in this regard that the incorporation of parameters ”... should be the outcome of a systematic investigation and not the result of more or less isolated views and investigations. Nevertheless, it appears that the analysis must be approached from an extended perspective...”. This can be done by a simple tool, which seems to be very promising: the General-to-specific (Gets) approach, of which a review is given in Hendry (1995) could help to identify the important factors. It starts with an ex- tremely compact model including all parameters suspected to be influential. Then a reduction process involving standard testing procedures and the elimination of statistically-insignificant variables diminishes the size of the model to a much lower dimension. This probably leads to various sets of significant variables for differ- ent countries, but by analyzing and comparing those differences much information seems to be detectable.

This section has now considered a set of specifications systematically. Table 2.1 shall give a summary of the characteristics which were given some justification above and which will be the basis for the formal Phillips curve framework, rebuild (after the archetype of Flaschel et al. (2004)) in section 2.5.

### 2.4 Wage and Price Phillips Curves: The Em- pirical Framework

Having just considered to model the interaction of wage inflation and price inflation (Dw and Dp in the following respectively) by two separate but interlocking equations, one can start from the two-dimensional structural wage and price equations of Fair (2000). That is

Abbildung in dieser Leseprobe nicht enthalten

Here p and w are the logs of the nominal wage rate and the price index respectively, pm is the log of an import price deflator. The latter will be neglected, since it is aimed for a closed economy model here. Time appeared to be insignificant in Fair’s (2000) simple t-test results as well as demand pressure (expressed by ut−1) in the wage determination and wages extremely affected by ”price push”.(Note that picking the significant variables out of a large set of predictor variables can be considered as a kind of General-to-specific approach just like Hendry (1995)) Furthermore, Fair used level variables and not terms of growth rate as it is common for Phillips curves. Thus Flaschel et al. (2004) are suggesting a more general wage- price dynamic, inspired by Fair (2000):

Abbildung in dieser Leseprobe nicht enthalten

(note that the coefficient notations used in the original paper are different for eas- ier recognition throughout this section), whereNl − Nl andNc − Nc stand for excess labor demand on the labor market and excess capacity within firms re- spectirely, nW − 1 and nI − 1 denotes excess labor demand within firms (that is overtime worked) and inventory use respectively (as measures of demand pres- sure), with the Nc and Nl as the two representatives of the NAIRU. Both the overtime worked (nW − 1) and the inventory use (nI − 1) will be neglected for simplicity reasons, so that a5 and b5 are assumed to be zero. One should note, however, that under-utilization is more flexible than unemployment, since certain labor market restrictions prohibit arbitrary hire-and-fire practise, so that overtime worked is an important variable to counterbalance this effect of higher volatility of under-utilization. Therefore 2.4.3 and 2.4.4, (without the two cost-pressure terms overtime work and inventory use) are as Flaschel et al. (2004) states the ”minimum structure one should start from”.

The inflationary climate is characterized by D12p, which is calculated by

Abbildung in dieser Leseprobe nicht enthalten

So when forming expectations the last years’ average price inflation is given more weight (0,45) than the average price inflation of the two years before (0,35 and 0,2). This is an enhancement of the original version of the inflationary climate presented in Flaschel and Krolzig (2003) and used in Flaschel et al. (2004). Derivative and integral control terms as considered in section 2.3 were also incorporated into the structural wage and price equations as well as the resulting reduced form expressions of the latter paper. However, this will be neglected here since Flaschel and Krolzig (2003) found little significance of those expanding parameters, which is why it was left out in the empirical part in Flaschel et al. (2004) as well. There the model used was

Abbildung in dieser Leseprobe nicht enthalten

(including absolut terms a0 and b0 and replacing (1 − a2) by a3 and (1 − b2) by b3 regarding 2.4.3 and 2.4.4), with ul = 1−Nl and uc = 1−Nc denoting unemployment of labor and capacity respectively, and Dyn the growth rate of productivity. Except for ul and uc, the natural logarithms were taken from all other terms including W ,P and the labor productivity Y n. Dw then is the expression for the first difference of the logs (wt −wt−1), so that Dw and Dp represent wage inflation and price inflation respectively. The inflation climate term D12p is the same as above. Finally, the subscript −1 accompanies lagged parameters, that is by adding subscript t to every variable −1 means t − 1.

Abbildung in dieser Leseprobe nicht enthalten

At this point this work is departing from the implementations of the paper by Flaschel et al. (2004), which formulates and subsequently investigates additionally two varying forms for each of the formulae 2.4.6 and 2.4.7. However the two differing specifications did not reveal extra information, which is why they will be disregarded here. The theoretical framework expressed by 2.5.6 and 2.4.7 is now ready for the analysis in chapter 4.

### 2.5 Issues to be Investigated

Now that the theoretical framework has been derived it can be helpful to anticipate the possible return of the analysis to come in chapter 4. This gives focus to the investigation and provides a benchmark for its success. Nonetheless, surprises are expected and welcome. Here are the main issues which shall be explored:

1. Significance of parameters:

1.a) Which parameters (unemployment, productivity change, inflationary climate, wage inflation, price inflation) show evidence to be significant in general?

1.b) What country specific influences can be observed?

1.c) Inertia: Is the inflationary climate persistent in present wage inflation / present price inflation?

2. The values of significant coefficients:

2.a) Are wages more flexible than prices with respect to their respective demand pressure terms?

2.b) Are there any noticeable differences between countries?

3. Nonlinear features:

3.a) Is the convexity assumption true in general?

3.b) Are wages and prices sticky?

3.c) Is there a complex wage-price spiral structure or does markup pricing suffice?

4. Explanatory value of the model

4.a) What portion of the data can be explained by the model?

4.b) Is there unexplained structure left, which means autocorrelation in the resid- uals?

This list could go on, but shall stop here. Otherwise not much focus can be gained during the analysis. Note that this schedule is the pendant to 4.7, where the results of the investigation will be summarized in a similar way as stated here.

## Chapter 3 Semiparametric Regression

### 3.1 Some Introductory Words

Sir Francis Galton (1822-1911) has probably been the man, who in 1886 originally introduced the term ”regression” into science (see Draper and Smith (1998, p. 45); for a detailed historical treatment see Stigler M. (1986, pp. 294-299)). First published in the article ”Regression toward mediocrity in hereditary stature” in the Journal of the Anthropological Institute it referred to the less extreme size features Y of the offspring in comparison to extraordinary parent seed sizes X, whose relationship he expressed in a linear regression equation. The term ”regression” lost its original meaning as soon as all kinds of relationships between variables represented by such an equation were called regression. Surprisingly, the least squares method for the best unbiased fit to the data, which is inseparably associated with regression, had already been discovered independently from each other by Carl Friedrich Gauss (1777-1855) and Adrien Marie Legendre (1752-1833) around 1800, 85 years earlier.

Even though the roots of nonparametric regression do reach back to 1857 when the German economist Engel fitted a nonparametric curve in order to find the Engel’s law (Härdle (1990) notes this fact in his introduction), the methods became popular just during the last couple of decades, probably due to the highly advanced computer technology, which more and more enables one to implement elaborate statistical methods and to easily employ graphical devices for data analysis.

Many scientists have been contributing to the topic. To give a short sum- mary of a few important milestones: Whittaker (1923) is known as the inventor of smoothing splines. Local averaging smoother date back to Ezekiel (1941). Fix and Hodges (1951) gave the first initiation of Kernel density estimation and Nadaraya (1964) and Watson (1964) have independently developed from this the Kernel smoother. Reinsch (1967) introduced the penalized least squares criterion and its solutions and Good and Gaskins (1971) proposed the Penalized-likelihood estima- tion. Generalized linear models got first presented by Nelder and Wedderburn (1972). In 1973 many famous model selection approaches got proposed: Mallows Cp statistic (Mallows (1973)) and the Akaike criterion AIC (Akaike (1973)). An- other approach in this regard is the cross validation, which was strongly influenced by Stone (1974, 1977). In the same year when Cleveland (1979) developed the Lo- cally linear weighted running line smoother, Craven and Wahba (1979) proposed the Generalized Cross validation (GCV). The Backfitting procedure, originated from Ezekiel (1924) was then applied to nonparametric regression by Friedman and Stuetzle (1981). In 1982 the Supersmoother got introduced by Friedman and Stuetzle (1982). Stone (1985) developed the Additive models, which got general- ized by Hastie and Tibshirani (1986, 1990). Spline models got strongly influenced by Grace Wahba (1990). Without the claim to present a complete list main refer- ences on nonparametric regression are Eubank (1988, 1999), Hastie and Tibshirani (1990) (setting an important milestone in this field), Härdle (1990), Wahba (1990, 1991), Green and Silverman (1994) , Wand and Jones (1995), Fan and Gijbels (1996), Gu (2002), Ruppert, Wand, and Carroll (2003).

The development of the nonparametric methods did not make the parametric ones obsolete. However, for certain issues either one can provide the most adequate fitting solution. In additive models both concepts can even apply similtaneously in a multivariate setting. Therefore Ruppert et al. (2003) call the whole set of concepts Semiparametric regression and so it is called in this work as welll.

First, parametric methods will be reviewed briefly as they are still very useful first order approximations to the true relationship of variables. Then a selection of neighborhood and spline smoothers will be discussed in section 3.3 and 3.4. And as Härdle (1990, p. 24) excellently stated:

**[...]**

## Details

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