Disin�ation and the NAIRU in a New-KeynesianNew-Growth Model

Ansgar Rannenberg1

Centre for Dynamic Macroeconomic Analysis (CDMA),University of St. Andrews.

Email: ar435@st-andrews.ac.uk,Tel.: 0044/1334/462445.

03/10/2007

1The copyright for this paper belongs to Ansgar Rannenberg alone.

Abstract

Unemployment in the big continental European economies like France and Germanyhas been substantially increasing since the mid 1970s. So far it has been di¢ cultto empirically explain the increase in unemployment in these countries via changesin supposedly employment unfriendly institutions like the generosity and duration ofunemployment bene�ts. At the same time, there is some evidence produced by Ball(1996, 1999) saying that tight monetary policy during the disin�ations of the 1980scaused a subsequent increase in the NAIRU, and that there is a relationship betweenthe increase in the NAIRU and the size of the disin�ation during that period acrossadvanced OECD economies. There is also mounting evidence suggesting a role of theslowdown in productivity growth, e.g. Nickell et al. (2005), IMF (2003), Blanchardand Wolfers (2000).This paper introduces endogenous growth via a capital stock externality into an

otherwise standard New Keynesian model with capital accumulation and unemploy-ment. We subject the model to a cost push shock lasting for 1 quarter, in order tomimic a scenario akin to the one faced by central banks at the end of the 1970s. Mon-etary policy implements a disin�ation by following a standard interest feedback rulecalibrated to an estimate of a Bundesbank reaction function. About 40 quarters af-ter the shock has vanished, unemployment is still about 1.7 percentage points aboveits steady state, while annual productivity growth has decreased. Over the samehorizon, a higher weight on the output gap increases employment (i.e. reduces thefall in employment below its steady state). Thus the model generates an increase inunemployment following a disin�ation without relying on a change to labour marketstructure.We are also able to coarsely reproduce cross country di¤erences in unemployment.

A higher disin�ation generated by a larger cost push shock causes a stronger persistentincrease in unemployment, the correlation noted by Ball. For a given cost push shock,a policy rule estimated by Clarida, Gali and Gertler (1998) for the Bundesbankand the Federal Reserve Bank produces a stronger persistent increase in the caseof the Bundesbank than of the Federal Reserve. Testable di¤erences in real wagerigidity between continental Europe and the United States, namely, as pointed outby Blanchard and Katz (1999), the presence of the labour share in the wage settingfunction for Europe with a negative coe¢ cient but it�s absence in the U.S. also implydi¤erent unemployment outcomes following a cost push shock. If real wage growthdoes not depend on the labour share, the persistent increase in unemployment isabout one percentage point smaller than when it does. To the extent that the wagesetting structure is determined by labour market rigidities, "Shocks and Institutions"jointly determine the unemployment outcome, as suggested by Blanchard andWolfers(2000).

The calibration of unobservable model parameters is guided by a comparison ofsecond moments of key variables of the model with Western German data. Theendogenous growth model matches the moments better than a model without en-dogenous growth but otherwise identical features. This is particularly true for thepersistence in employment as measured by �rst and higher order autocorrelation co-e¢ cients.

Acknowledgement 1 I would like to thank Andrew Hughes-Hallett, Arnab Bhat-tachariee, Atanas Christev, Campbell Leith, Charles Nolan and the participants ofthe RES Easter School 2008 for helpful comments. All remaining errors are of coursemy own. Furthermore, I am grateful for generous �nancial support which I am re-ceiving from the Centre for Dynamic Macroeconomic Analysis (CDMA) at the Schoolof Economics and Finance at the University of St. Andrews.

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Tests of the Institutional Approach . . . . . . . . . . . . . . . . . . . . . . 43 Productivity Growth and Unemployment . . . . . . . . . . . . . . . . . . . 64 Monetary Policy and the NAIRU . . . . . . . . . . . . . . . . . . . . . . . 75 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.2 Cost Minimisation and E¢ ciency Wages . . . . . . . . . . . . . . . . 125.3 Price Setting and Nominal Rigidities . . . . . . . . . . . . . . . . . . 175.4 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.5 Introducing Endogenous Growth . . . . . . . . . . . . . . . . . . . . . 215.6 The Aggregate Equations . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Simulation Setup and Calibration . . . . . . . . . . . . . . . . . . . . . . . 257 Some Moment Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Cross Country Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4710 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5111 Appendix A - Forward Solution of the Phillips curve . . . . . . . . . . . . . 5312 Appendix B - Normalised Version of the Model . . . . . . . . . . . . . . . 54

13 Appendix C: Steady State Relations . . . . . . . . . . . . . . . . . . . . . . 5614 Appendix D: Normalised Version of the JLN Model . . . . . . . . . . . . . 5715 Appendix E: Estimation of the Wage Setting Function . . . . . . . . . . . 5816 Appendix F: Construction of the Dataset used in the Moment Comparison 63

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1 Introduction

"Short-run macroeconomics and long-run growth theory have neverbeen properly integrated. It is only a slight caricature to say that onceupon a time the long run was treated casually as forward extension ofthe short run, whereas nowadays the tendency is to treat the short runcasually as a backward extension of the long-run."Robert M. Solow/Athanasios Orphanides (1990).1

Macroeconomic analysis often draws a sharp distinction between the short andthe long run. The mainstream view is that while aggregate demand may causetemporary output �uctuations, output ultimately returns to potential as prices ad-just. What is more, potential output itself and the "non-accelerating-in�ation-rate-of-unemployment" (NAIRU) are not a¤ected. Accordingly, unemployment is thoughtto depend only on the institutions a¤ecting the wage setting power of employees andthe price setting power of �rms, like the duration and generosity of unemploymentbene�ts, union membership or product market competition. By contrast, monetarypolicy has only a short run e¤ect on unemployment.Labour market economists have applied this framework to the steady rise in conti-

nental European unemployment since the 1970s. They tried to estimate the e¤ects ofchanges in labour market institutions. The results have not been entirely conclusive.On the one hand, labour market rigidities seem to be able to explain why unemploy-ment is so much lower in the �exible labour market of the United States, than inEurope. However, when it comes to the evolution of European unemployment overtime, Blanchard notes that �explanations based solely on institutions also run intoa major empirical problem: Many of these institutions where already present whenunemployment was low, and, while many became more employment-unfriendly in the1970s, the movement since then has been largely in the opposite direction.�2

At the same time, Ball (1996, 1999) has produced evidence which links part ofthe increase in the NAIRU to a desire to disin�ate the economy and more hawkishconduct of monetary policy in Europe as opposed to the United States. Furthermore,in many countries, the increase in the NAIRU has been accompanied by a substantialslowdown in productivity growth. Early on Bruno and Sachs (1982) and more recentlyBlanchard and Wolfers (2000), Fitoussi et. al. (2000), the IMF (2003) and Nickell etal.(2005) have produced evidence for a statistically signi�cant relationship betweenthe two.

1Solow/ Orphanides (1990), p. 258.2Blanchard/ Wolfers (2000), p. C2. He recently somewhat quali�ed that statement by suggest-

ing the problem might not lie with the story but with the crude measurement of labour marketinstitutions, see Blanchard (2005), p. 417. It remains to be seen whether analysis based on newdata series yields di¤erent result.

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Blanchard (2000, 1998) suggests a role for monetary policy, arguing that the im-plementation of high real interest rates by European central banks in the 1980s inorder to reduce in�ation required the marginal product of capital to increase. Thesubsequent decline of the capital labour ratio would reduce the marginal product oflabour. If real wages are rigid, unemployment has to rise to implement the corre-sponding decline in real wages.3 However, while long-term real interest rates indeeddid rise in the 1980s, they have declined in the second half of the 1990s. They arenow at about the level they were at the end of the 60s, while unemployment in thebig European economies remains stubbornly high.This paper contributes to the explanation of this evidence -the rise in the NAIRU,

the slowdown in productivity growth and Ball�s evidence on the impact of disin�a-tions on the NAIRU- by introducing endogenous growth into a New Keynesian modelfeaturing unemployment. We implement this in a very simple fashion by assum-ing that technological progress is realised through investment and thus linking totalfactor productivity to the capital stock. We subject the economy to a 1 quartertemporary cost-push shock and let the central bank disin�ate - as happened in manyindustrialised economies at the beginning of the 1980s. It turns out the employmente¤ects can indeed be quite persistent and that unemployment might remain belowits steady state value by more than 1 percentage point for more than 10 years, whilstin�ation remains stable, that is, the NAIRU increases. A fall in the productivitygrowth rate caused by a fall in investment depresses the real wage growth rate consis-tent with stable in�ation, which, with real wage growth being rigid, requires higherunemployment.Our results resemble in some respects those of Sargent and Ljungqvist in that

the model proposed here generates an increase in unemployment without relying onchanges in labour market rigidity, while the "level" of labour market rigidity doesmatter.4 However, their approach di¤ers from ours in that in their model, unem-ployment increases via the interaction of an unemployment insurance paying bene�tslinked to past income and a permanent increase in "microeconomic turbulence". "Mi-croeconomic turbulence" is the probability that a worker looses his human capital incase his job is exogenously destroyed. The increase in turbulence creates a fraction ofunemployed workers who enjoy high bene�ts (because they used to be high skilled)but are now low skilled and thus have a low earnings potential on the labour market.Therefore they have little incentive to engage in (costly) job search, which reducestheir probability of regaining employment. By contrast, our approach is a macro-economic one in that the driving force pushing up unemployment is an in�ationaryshock and the response of the central bank to this shock.The paper is structured as follows: Sections 2 to 4 are some brief discussions

of the evidence highlighted above, namely on the role of labour market institutions(section 2), the role of productivity growth (section 3) and monetary policy (section

3See Blanchard (1998), pp. 5-18 and Blanchard (2000), pp. 2-15, and also Bean (1997), p. 95.4See Sargent and Ljungqvist (1998) and (2007).

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4) in explaining unemployment. Section 5 develops a model which coarsely encom-passes the mainstream consensus on the relationship between monetary policy andunemployment sketched above, which we coin "Jackman, Layard, Nickell", or JLNeconomy, and then add the New Growth extension whose consequences we want toinvestigate in this paper. Section 6 discusses the calibration, which is informed byempirical evidence on some of the model parameters and by the comparison of thesecond moments of a couple of model variables with their empirical counterparts inGerman data. Section 7 presents a more complete moment comparison. Section 8then discusses the response of the economy to a one quarter cost push shock calibratedto induce a disin�ation of about 4 percentage points. We also conduct a couple ofrobustness experiments in that section: We vary the output gap coe¢ cient in thecentral banks reaction function and summarise the trade-o¤ which policymakers faceby computing medium run average unemployment rates and NAIRUs. The resultingPhillips Curves are downwards sloping. Furthermore, we check the robustness of ourresults against changes in real wage rigidity and the slope of capital stock adjustmentcosts. While section 8 thus aims at establishing that our model can produce a per-sistent increase in unemployment following a one quarter cost push shock, section 9aims to add a cross country dimension to our analysis in three di¤erent ways. First,we vary the size of the cost push shock and record the resulting changes in In�ationand the NAIRU over a 10 year horizon. We then compare the di¤erences in the unem-ployment response generated by a Bundesbank and a Federal Reserve Policy rule asestimated by Clarida, Gali and Gertler (1998), and �nally we investigate the e¤ectsdi¤erences in real wage rigidity between Europe and the United States. Section 9concludes.

2 Tests of the Institutional Approach

There have been various attempts to establish an empirical link between labour mar-ket rigidities and unemployment. Most often these attempts consist of panel regres-sions of unemployment on (indicators of) labour market institutions like the durationand generosity of unemployment bene�ts or employment protection. This approachruns into problems when trying to explain the evolution of unemployment across time.A recent IMF (2003) study over the period from 1965 to 1998 concludes that insti-tutions "hardly account for the growing trend observed in most European countriesand the dramatic fall in U.S. unemployment in the 90�s": The part of the unemploy-ment rate not explained by institutions increases over time.5 Similarly, Blanchardand Wolfers (2000) noted that "while labour market institutions can possibly explaincross country di¤erences today, they do not appear to be able to explain the generalevolution of unemployment over time."6 Furthermore, it turns out that institutions

5IMF (2003), p. 134.6See Blanchard/ Wolfers (2000), p. C2.

4

are especially weak in explaining the evolution of unemployment in Germany andFrance, which are most often cited as examples of "sclerotic" economies.7

A study by Nickell (2002, 2005) shows that institutions explain virtually nothingfor Western Germany and Finland and only a minor part of the unemployment in-crease in Spain and New Zealand. Substantial movements of unemployment are leftunexplained for Ireland, France, the UK and Italy.8 The explanatory power of boththe Nickell et al and the IMF regressions rely on including lagged unemployment inthe regression, with coe¢ cients of 0.79 (IMF) and 0.87 (Nickell et al) respectively.In the words of Nickell et al,: "This re�ects a high level of persistence and/or theinability of the included variables to explain what is going on."9 A study by Elmeskovet al. (1998) con�rms this impression. They ask how much of the change in structural(as opposed to actual) unemployment from 1983 to 1995 across 19 OECD countriesis accounted for by institutional changes, and how much is explained by a countryspeci�c e¤ect.10 The country speci�c e¤ect explains most of the change in structuralunemployment in almost every country.11

Furthermore, these panel data regression results appear to be not very robust.Baker et. al (2002) survey six papers12 and �nd that the estimated e¤ects of changesto the tax wedge, bene�t duration and the replacement rate vary quite substantially:For instance, the e¤ect of an increase in bene�t duration by one year ranges from 0.7%to 1.4%.13 Baker et.al. also report that an earlier version of the Nickell et al. papercovering a slightly shorter sample produced estimates which di¤ered substantiallyfrom the �nal version, implying that Nickell et al.�s results are very sensitive to theinclusion of additional data.14 Finally, Belot and van Ours (2004) �nd that thesigni�cance of institutional variables is extremely sensitive to the inclusion of timeand country �xed e¤ects.15

One of the crucial assumptions underlying the panel data regressions cited aboveis that labour market institutions are exogenous and are not a¤ected by those forceswhich are a¤ecting unemployment or by unemployment itself. This assumption mightbe violated with respect to the tax wedge, as rising unemployment increases expen-ditures on transfers and erodes the tax base. The problem is sometimes mentionedbut is not addressed, and rarely tested for.16 The Elmeskov et a. (1998) study showsthat causality could run both ways in case of bene�t generosity and the tax wedge.

7See IMF (2003), pp. 138-141.8See Nickell (2002), pp. 44-45.9See Nickel et al (2005), p. 15.10See Elmeskov et. al (1998). This paper was part of the research following up the Job study.11See Elmeskov et. al (1998), p. 220, Table 3a.12(Nickel 1997, Elmeskov et al 1998, Belot/van ours 2002, Nickel et al 2002, Blanchard/Wolfers

2000, Bertola et. al. 2001)13See Baker et al (2002), pp.43-44.14See Baker et. al (2003), p. 35.15See Belot/Van Ours (2004), p. 635.16See for instance Nickell et al (2002), p.2, or IMF (2003). See also Blanchard (2007), p. 415.

5

Unemployment Granger causes bene�t generosity in Belgium, France, Italy, the UK,the United States and the Netherlands, while it Granger causes the tax wedge inAustria, Ireland and Norway.17

3 Productivity Growth and Unemployment

There is evidence that changes in productivity growth a¤ect unemployment. An earlyexample is Bruno and Sachs (1982), who argue that a labour productivity slowdownwhich was unanticipated by workers�wage demands caused unemployment in Britishmanufacturing to increase.18 Productivity growth or total factor productivity growthare sometimes controlled for in regressions aiming to assess the impact of labour mar-ket institutions. For instance, in the IMF study cited above, a one percentage pointreduction in productivity growth increases unemployment by 0.32 percentage points,while the Nickel et al study cited above �nds that a 1 percentage point decrease intotal factor productivity (TFP) growth causes a 1.28 p.p. increase in unemployment.Fitoussi et al. (2000) test for the role of productivity growth and other shocks, thee¤ects of which are allowed to vary across countries. For Germany, the equation pre-dicts that a one percentage point reduction in productivity growth would cause a 0.79percentage point increase in unemployment, while for France, Italy or Spain the e¤ectwould be as high as 1.6, 1.22 or 2.22 p.p.19 Ball and Mo¢ tt (2001) use a PhillipsCurve based approach and argue that di¤erences between workers wage aspirationsand productivity growth can explain the non-in�ationary unemployment reduction inthe United States in the 1990s.20 Pissarides and Vallanti (2005) use a multi equationapproach to investigate the e¤ects of a productivity slowdown and �nd an (implied)e¤ect of a 1 percentage point reduction in TFP growth on unemployment of 1.31percentage point in the EU.21

Blanchard and Wolfers (2000) estimate a speci�cation which explicitly models theinteractions of shocks and institutions, i.e. institutional variables e¤ectively becomepart of the coe¢ cient on the shocks. The shocks include TFP growth, the long runreal interest rate and a measure of labour demand, while the institutions consideredare the replacement rate as measured in Nickell (1997), bene�t duration (in years),employment protection (simple ranking from 1 to 20), the tax wedge as in Nickellet al (2002) and measures of union contract coverage, union density and bargainingcoordination.22 Both shocks and institutions are signi�cant, though concerning thelater this �nding is not robust against variations in the way the variables are mea-

17See Elmeskov et. al. (1998), pp. 248-249.18See Bruno/ Sachs (1982), p. 700/701.19See Fitoussi et al (2000), pp. 247 to 250.20Ball and Mo¢ t (2001).21See Pissarides and Vallanti (2005), p.20, table 4.22See Blanchard/Wolfers (2001), p. C19.

6

sured.23 A one percentage point reduction in TFP growth increases unemploymentby 0.71 p.p. if institutions are at the sample average. More employment unfriendlyinstitutions cause the shock to have higher e¤ects, so that the model can explain bothcross country di¤erences and the evolution of unemployment over time.

4 Monetary Policy and the NAIRU

Ball argues the change in the NAIRU during the 1980s can be explained by the mon-etary policy stance. He measures the stance of policy during that period indirectlyby the behaviour of in�ation (Ball (1996)), and directly by examining the evolutionof real interest rates (Ball(1999)) during the recessions at the beginning of the 1980s.Ball (1996) employs two measures of disin�ation: It�s size from 1980 to 1990 and thelength of the longest disin�ation during that period. The former is related to thesize of on impact unemployment increase, while the latter indicates for how long theactual unemployment rate exceeded the NAIRU.Ball �nds that while the length and the size of disin�ation explain a substan-

tial share of the increase in the NAIRU over the ten year period, large predictionerrors remain. He examines whether interaction between bene�t duration and thepolicy stance does a better job at explaining the rise in the NAIRU. 24 The �t is sub-stantially improved when the policy variables do not interact with bene�t duration,especially for the change in in�ation. 25 Ball then subjects this procedure to a seriesof robustness experiments, all of which basically con�rm the previous results.26 Thecorrelation between the change in in�ation and the change in the NAIRU emphasizedby Ball is illustrated in Figure 1, which plots the change in the NAIRU against thechange in CPI In�ation for 21 OECD countries from 1980 to 1990 and from 1990 to2000. The negative correlation is not perfect but still obvious.27

Ball (1999) measures policy by the largest cumulative decrease of short term realinterest rates in any part of the recession�s �rst year.28 He considers two dependentvariables: the change in the NAIRU from the peak before the �rst recession until �veyears after the peak, and this change divided by the change in actual unemploymentover the same time period. The later variable is called degree of hysteresis andaccounts for the fact that the severity of recessions and thus the increase in actualunemployment vary over the sample and hence one would observe di¤erent increases

23See Blanchard/Wolfers (2000), p. C31.24See Ball (1996), p. 13. The motivation for the joint role are theories of labour market hysteresis.25Ball (1996), p. 12.26See Ball (1996), pp. 13-15.27The data is taken from the OECD Outlook. The countries are Australia, Austria, Belgium,

Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Netherlands, NewZealand, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, U.S.A.28Ball notes that his dating criterion for recessions yields only two countries with two recessions

and thus is stricter than the one used with quarterly data. See Ball (1999), p. 205.

7

in the NAIRU even if actual unemployment fed into the NAIRU to the same extentin all countries, i.e. if monetary policy and bene�t duration had been the same.29 Fitis substantially better when the degree of hysteresis is used as a dependent variable,with an adjusted R2 of 0.62 as opposed to 0.43. Concerning the quantitative impactof the two variables, "The coe¢ cient on maximum easing implies that raising thatvariable from 0 to 6 (Sweden�s value, the highest in the sample) reduces the degree ofhysteresis by 0.54. Reducing the duration of unemployment bene�ts from inde�niteto half a year reduces the degree of hysteresis by 0.35. Thus policymakers can reducehysteresis through both macroeconomic and labour market policy, and the formerhas somewhat larger e¤ects."30 Hence research suggests that monetary policy a¤ectsthe NAIRU and the more so the more rigid the labour market.Ball also tries to explain reductions in the NAIRU in OECD countries by referring

to the stance of monetary policy relative to the situation of the macro economy. He�nds that to some extent, monetary policy is able explain NAIRU reductions, too.

Change in CPI Inflation vs. Change in the NAIRU: 1980-1990, 1990-2000

-10.00%

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

-20.00% -15.00% -10.00% -5.00% 0.00% 5.00%

Change in CPI Inflation

Chan

ge in

the N

AIRU

Figure 1

5 The Model

The previous section argues that there exists empirical evidence which links the mon-etary policy stance to the subsequent evolution of the NAIRU. This section developsa dynamic general equilibrium model which can explain why that might be the case.First, however, we will develop what we consider the starting point of our analy-sis. This is a model coarsely incorporating the ruling consensus of the relationshipbetween unemployment and the NAIRU. We will refer to this model as the JLN econ-omy, JLN standing for "Jackman-Layard-Nickell", as these authors have contributed

29See Ball (1999), p. 205-206.30Ball (1999), p. 207.

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in�uentially to develop the current consensus on the short and long run causes ofunemployment. This consensus has been sketched by Nickell et al. (2002) as follows:

First, unemployment in the short-run and in the long-run is deter-mined by real demand. Second, over the long term, real demand andunemployment generally tend towards the level consistent with stable in-�ation. This we term equilibrium level. Various possible mechanismsmay be at work here. For example, many OECD countries now set mon-etary policy on the basis of an in�ation target which naturally movesreal demand and unemployment towards the equilibrium de�ned above.Third, the equilibrium level of unemployment is a¤ected �rst, by anyvariable which in�uences the ease with which unemployed individuals canbe matched to available job vacancies, and second, by any variable whichtends to raise wages in a direct fashion despite excess supply in the labourmarket.31

Hence this section is structured as follows. 5.1 deals with the household optimi-sation problem whose �rst order conditions determine consumption, investment andcapital accumulation in our model in a standard fashion, but also the supply of ef-fort which determines the e¢ ciency of a unit of labour. 5.2 then shows how, giventhis e¤ort function, cost minimisation makes the representative �rm pay an e¢ ciencywage. Hence the labour supply condition is replaced by a wage setting function, thusgenerating unemployment. 5.3 introduces nominal rigidities, thus implying that out-put is demand determined. Section 5.4 speci�es a monetary policy reaction functionwhich sets the interest rate as a function of the deviation of in�ation from it�s targetand the output gap. Section 5.5 discusses how endogenous growth is introduced intothe model and how this a¤ects the model�s equations derived so far. Section 5.6summarises the aggregate equations for the convenience of the reader.

5.1 Households

Danthine and Kurmann (2004) introduce unemployment in a general equilibriummodel without moving away from the representative agent framework. In the Danthine-Kurmann setup individuals are organized in families in a zero-one continuum of fam-ilies which are in�nitely lived. All decisions regarding the intertemporal allocationof consumption and the accumulation of capital are made at the family level. Eachfamily member supplies one unit of labour in-elastically but derives disutility fromthe e¤ort G(et) he or she supplies in their job. The share of unemployed members isthe same for each family. The large family assumption means that although there areunemployed individuals in the economy, it is not necessary to track the distributionof wealth.31See Nickel et al (2002), p. 2-3. See also Jackman, Layard and Nickel (1993), p. 8-11.

9

In addition, some workers supply overhead labour, whose nature will be describedin more detail below. They can be thought of as the owners of the monopolisticallycompetitive �rms. Overhead workers never become unemployed because no �rm canproduce without managerial sta¤. A share ns of the workforce is employed by thegovernment who is assumed to pay the same wage as the private sector. They arefunded by lump sum taxes.32 All families have the same share of managers andgovernment employees.Families solve the following maximisation problem:

U = Et

( 1Xi=0

�i [u(Ct+i � habt+i�1)� (nt+i � n)G(et+i)]

); u0 > 0; u00 < 0:habt�1 = jCt�1

(1)

s:t: (nt � n)wt +Bt�1Pt

(1 + it�1) +zt + rktKt � Ct +BtPt+ Tt + It and (2)

Kt+1 = (1� �)Kt + It

�1� S

�ItIt�1

� (1 + g)��

; S (0) = 0; S (0)0 = 0; S (0)00> 0

(3)

Each period families derive instantaneous utility u (Ct � habt�1) from consump-

tion Ct+i; which is a CES consumption basket Ct =hR 10(ct(i))

(��1)� di

i ���1

: Con-sumers spread their consumption over the various goods in the CES basket Ct ina cost minimising fashion, implying that the optimal demand for good i is given

by ct(i) = Ct

�pt(i)Pt

���; where Pt denotes the price index of the consumption bas-

ket. Following Smets and Wouters (2002), we introduce external habit formation:habt�1 = jCt�1; j < 1: A family�s period t income consists wages wt, interest incomeit�1 on risk less bonds they bought in the previous period, Bt�1, the pro�ts of themonopolistically competitive �rms in the economy zt, and dividends rkt from rentingout the capital Kt they have accumulated up to time t. They have to pay lumpsum taxes Tt: Families accumulate capital by incurring investment expenditure It .Following Christiano, Eichenbaum and Evans (2005) and Smets and Wouters (2002),33 we assume adjustment costs in investment. Only a fraction of one unit of invest-32The chief reason of introducing both the share of state employees and overhead workers is to

achieve a reasonable calibration of steady state values. As is well known, the Romer model hasstrong scale e¤ects, i.e. the level of employment a¤ects the growth rate. This is due to the fact that,as shown below, the marginal product of capital becomes an increasing function of employmentand a decreasing function of the depreciation rate. The marginal product of capital governs thegrowth rate by determining the willingness of households to save and thus the economy�s growthrate. To achieve a reasonable steady state growth rate, it is thus necessary to either assume a veryhigh depreciation rate or to remove part of the labour force from "productive" sector and thus toreduce the impact of employment on the marginal product of capital, by assuming that they performnecessary tasks without which the productive sector could not operate (managerial work in case ofoverhead workers, policing etc. in case of the state employees). We opted for the second solution.33See Christiano, Eichenbaum and Evans (2005), p.12, and Smets and Wouters (2002), p.13.

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ment expenditure is actually turned into additional capital Kt , and this fractiondecreases in the investment growth rate. The assumptions on the �rst derivative ofthe S (:) function imply that adjustment costs vanish when the economy is growingat its steady state growth rate g. This implies that the steady state growth ratedoes not depend on the parameters of the adjustment cost function S:34 Setting upthe lagrangian and denoting the lagrange multipliers of the budget constraint andthe capital accumulation constraint as �t and �tqt yields the following �rst orderconditions with respect to consumption, capital and investment:

u0(Ct � habt�1) = �Et

�u0(Ct+1 � habt)

1

1 + �t+1

�[1 + it] (4)

�t = u0(Ct � habt�1) (5)

�Et��t+1r

kt+1 + �t+1qt+1 (1� �)

�= �tqt (6)

�tqt

��1� S

�ItIt�1

� (1 + g)��

� ItIt�1

S 0�

ItIt�1

� (1 + g)��

(7)

+�Et

"�t+1qt+1

�It+1It

�2S 0�It+1It

� (1 + g)�#

= �t (8)

Note that with this notation, qt denotes the present discounted value of the futurepro�ts associated with buying an additional unit of capital today, also known asTobin�s q. We assume the following functional form for S (:): S

�ItIt�1

� (1 + g)�=

�2

�ItIt�1

� (1 + g)�2:

The cost of e¤ort function of individual j G(et+i (j)) is of the form

G (et(j)) =

�et(j)�

��0 + �1 logwt(j) + �2(nt � n)

+�3 logwt + �4 logwt�1 � �5 log bt � �8 log (Yt�1= (nt�1 � n� ns))

��2;(9)

log bt = �6 log (Yt�1= (nt�1 � n� ns)) + (1� �6) logwt�1 + �7 (10)

�1; �5 > 0; 1 = �6 = 0; �2; �3; �4 < 0; �1 > ��3where Yt is private sector output. Note that the e¤ort function enters the fami-

lies�utility separately which implies that it is independent of the budget constraint.Furthermore, state employees are assumed not to perform any e¤ort while at work.The �rst order condition with respect to e¤ort is

et(j) = �0 + �1 logwt(j) + �2 (nt � n) + �3 logwt

+�4 logwt�1 � �5 log bt � �8 (Yt�1= (nt�1 � n� ns)) (11)

The structure of the cost of e¤ort function is motivated by the idea of "gift ex-change" between the �rm and the worker. The worker�s gift to the employer is e¤ort.34See Christiano, Eichenbaum and Evans, p.15.

11

The employer has to show his appreciation for the employees�contribution by payingan appropriate wage wt(j). A higher contemporary average wage wt reduces e¤ortbecause it represents a "reference level" to which the current employers�wage o¤eris compared. Put di¤erently, it requires the �rm to pay a higher wage if it wantsto extract the same amount of e¤ort. A higher average past real wage wt�1 booststhe workers�aspirations as well.35 The aggregate employment level of non-overheadworkers nt � n summarizes labour market tightness. It is thus positively related tothe workers�outside working opportunities, and thus also tends to reduce e¤ort.The terms bt and (Yt�1= (nt�1 � n� ns)) represent and a modi�cation to the Dan-

thine and Kurman (2004) cost of e¤ort function. bt denotes unemployment income.This will be chie�y unemployment bene�ts and black market income. It tends tolower the level of e¤ort.36 Workers want to be valued more than someone who re-ceives bene�ts or does not have a legal job. bt is linked both to past real wages andpast productivity in the private sector, where Yt denotes private sector output.37 Thismay re�ect both the structure of bene�ts and the manner in which the black market islinked to the o¢ cial economy. Productivity also has a direct e¤ect on morale and ef-fort as employees desire their due share of the companies�success. Unions might playa role in this to the extent that they instil a sense of entitlement among employees.The employer takes this relationship into account when setting the wage, as will

be discussed further below. The view that wages have a big e¤ect on morale andthus productivity because they signal to the worker how his contribution to theorganizational goals is valued has found considerable support by a microeconomicsurvey conducted by Bewley (1998). Bewley interviewed over 300 business people,labour leaders and business consultants in search for an explanation why wages arerarely cut in recessions.38

5.2 Cost Minimisation and E¢ ciency Wages

The production technology is a Cobb Douglas production function,

35See Danthine and Kurmann (2004), pp. 111-113. It would be desirable to have the individualworkers past real wage wt (j) in the equation but that would considerably complicate the max-imisation problem of the representative �rm dealt with later, so we follow Danthine and Kurmanin assuming a dependence of e¤ort on the average wage. For the same reason we include averageproductivity rather than the respective �rm�s productivity.36Danthine and Kurman (2007) introduce the bene�t level as a factor which, ceteris paribus,

reduces e¤ort.37The motivation for linking bene�t levels to private sector productivity rather than productivity

of the whole economy including the state sector is to simplify computation, as will become clearlater.38See Bewley (1998), pp. 459-490. A discussion of further evidence is Bewley (2004). Bewley

also argues that his �ndings contradicts essentially all theoretical justi�cations of real wage rigiditynot based on gift exchange considerations, like implicit contracts, insider outsider models or thee¢ ciency wage models based on no-shirking conditions.

12

Yt(i) = AKt(i)�(TFPtet(i) (nt(i)� n))1�� (12)

where the output of �rm i Yt(i) depends on the capital stock of �rm i Kt(i), thee¢ ciency of its workers et(i) and the number of non-overhead workers nt(i) � n: Inthe Danthine and Kurman model (2004), in a �rst stage the �rm minimises its cost ofproducing a given amount of output. Capital and labour are hired in economy widefactor market. However, the �rm does not take the real wage as given but sets ittaking into account the relationship between e¤ort and wages given by (11).39 Hencethe �rm�s problem is:

minKt(i);nt(i);wt(i);et(i)

rktKt(i)+wt(i)(nt(i)�n)s:t:Yt(i) = AKt(i)�(TFPtet(i) (nt(i)� n))1��

and et(i) = �0 + �1 logwt(i) + �2 (nt � n) + �3 logwt

+�4 logwt�1 � �5 log bt � �8 (Yt�1= (nt�1 � n� ns))

The �rst order conditions for capital and labour are

rkt = �mct (i)Yt(i)

Kt(i)(13)

wt(i) = (1� �)mct (i)Yt(i)

nt(i)� n(14)

where mct(i) and rkt refer to real marginal costs of �rm i and the capital rentalrate. It will be shown below that even though all �rms set the wage individually,�rms will �nd it optimal to set the same wage and the same e¢ ciency level. Dividingthe two �rst order conditions gives Kt(i)

nt(i)�n =�1��

wtrkt: Thus the capital labour ratio is

the same across �rms. It is then easily shown using the production function that thesame holds for the output-capital ratio and the output-labour ratio. Hence we have

rkt = �mctYtKt

(15)

wt = (1� �)mctYt

nt � ns � n(16)

This then means that the capital to (productive) labour ratio, the output per unit ofproductive labour ratio and marginal costs are the same in all �rms, as can be easilyveri�ed by dividing the two �rst order conditions. This gives the capital to productivelabour ratio as Kt(i)

nt(i)�n =�1��

wtrkt: Substituting this back into equation (15) yields an

39See Danthine/ Kurman (2004), pp. 114-115.

13

equation formct(i) containing only labour augmenting technological progress and thefactor price, implying that marginal costs are the same across all �rms:

mct =

�rkt��w1��t

A��(1� �)1��(�1TFPt)1�� (17)

We now turn to wage setting. The �rst order conditions with respect to e¤ort andthe real wage are

nt(i)� n =�t�1wt(i)

(18)

�t = (1� �)mctYt(i)

et(i)

Combining those with the �rst order condition with respect to labour yields anoptimal e¤ort level of �1. Substituting this back into the e¤ort function (11), we notethat, as the �rm�s wage depends only on aggregate variables which are the same forall �rms, it must indeed hold that wt(i) = wt . Substituting for log bt and rearrangingthen yields

(�1 + �3) logwt = (�5 (1� �6)� �4) logwt�1 + �1 � �0 + �5�7 � �2 (nt � n)

� (�5�6 + �8) log

�1=

�Yt�1

nt�1 � n� ns

��Subtracting (�5�6 + (1� �5)) logwt�1 on both sides and dividing by (�1 + �3) thenyields

logwt =�1 � �0 + �5�7

�1 + �3� �2�1 + �3

(nt � n) +�5 + �8 � �4�1 + �3

logwt�1

�(�5�6 + �8)

�1 + �3log

�wt�1 (nt�1 � n� ns)

Yt�1

�(19)

Hence with the coe¢ cient restrictions imposed above, the wage depends positivelyon the past real wage and non managerial employment. It will be above its marketclearing level and thus there is unemployment in the economy.Note that the last term in brackets is in fact the private sector labour share.

If this were constant in the steady state, as it would be at a constant employmentlevel, equation (??) could be solved for a long run real wage if �5+�8��4

�1+�3< 1: As

mentioned above however, in our model, Danthine and Kurmann�s, is a growth model.Therefore the real wage must be growing in the steady state. Thus a wage setting

14

function simply relating the wage level to employment would not be consistent witha stable employment level. The easiest way to deal with the issue therefore is to set�5+�8��4�1+�3

= 1. This does not seem too restrictive: It simply says that an increase inthe log of the time t real wage in the economy (including �rm i) has in absolute valuethe same net e¤ect on e¤ort (remember we have �1 + �3 > 0) as an increase in theexogenous reference as represented by logwt�1, log bt and log (Yt�1= (nt�1 � n� ns)) :Thus we arrive at a real wage Phillips Curve with a labour share term:

logwt � logwt�1 = a+ b � (nt � n) + c log

�wt�1 (nt�1 � n� ns)

Yt�1

�;

with a =�0 � �1 + �5�7

�1 + �3, b = � �2

�1 + �3> 0 and c = �(�5�6 + �8)

�1 + �3< 0 (20)

Equation (20) is a real wage Phillips Curve plus an "error correction term" rep-resented by the log of the labour share. It is very close to a speci�cation derived byBlanchard and Katz (1999) from intuitively plausible relationships between averagewages, the reservation wage and productivity.40

Empirical estimates of (20) (usually replacing nt with the unemployment rate) orvariants thereof repeatedly �nd c=0 for the United states but c < 0 for Europeancountries.41 The di¤erence could be due to �8 being close to zero in the U.S. butpositive in Europe because of a larger in�uence of unions who establish the idea thatthe reference wage should be linked to productivity, as is also argued by Blanchardand Katz (1999). Using individual data on compensation matched with �rm leveldata on performance and inputs, Abowd et al. (2001) �nd that the relationshipbetween �rm level wages and performance measures like value added and sales peremployee is stronger in France than in the United States.42

The di¤erence could also be due to �6 being close to zero in the U.S but not inEurope. In this case, bene�ts grow (or fall) with wages rather than productivity. Thiswould imply that the U.S bene�t system is designed to keep a solid wedge between theincome of the unemployed and the income of workers. By contrast, unemployment

40Blanchard and Katz (1999) specify the wage as a function of productivity and the reservationwage, which in turn is a convex combination of average wages and productivity, as in our model.41See Blanchard and Katz (1999), p.73, and Cahuc and Zylberberg (2004), p.484-486. Note that

(20) di¤ers from the empirical speci�cation in that it is the private sector labour share, assumingthat overhead workers are essentially the self employed. This is done to simplify calculations. Notethat in (20) we can very easily replace the labour share term by (1� �)mct�1. This manipulationwould not be possible if we were using the labour share for the total economy, including the statesector (assuming that the value added of state employees would be measured with the wages theyare paid, as is common practice in national accounts). However, it can be shown that the e¤ect ofan employment change on the labour share would be even greater if we included state employees.This would essentially make persistent reductions in real wage growth even harder and thus, which,as will become clear later, would be expected to enhance the e¤ects we are interested in showinghere.42See Abowd et al. (2001), pp. 429-433.

15

bene�ts in Europe would track average productivity. This could be due to a desireto combat relative poverty among the unemployed rather than absolute poverty.Estimation of (20) will later provide a way to distinguish real wage rigidity between

the United States and Europe within our simulation. This will become importantwhen we turn to the cross country aspects of our analysis.Steady state employment in this framework will depend on labour market in-

stitutions like payroll taxes and the level of unemployment bene�ts, but also onproductivity growth and the size of the mark-up. As we will assume imperfect com-petition later, in the steady state, marginal cost equal the inverse of the mark-up �;i.e. mc = ��1: From (17) ; it is easy to see that in the steady state, with rk andmc constant, real wages grow at the same rate as total factor productivity, which wedenote as gTFP . (17) is essentially a textbook price setting function, giving the realwage consistent with �rms realising their mark-up. Assuming that there is a tax rate� on real wages, implying a net wage of (1� �)wt; substituting (16) into (20) forwt�1, and noting that in the steady state, mc = ��1; yields

nt = �(�5�6 + �8)

�2log

�(1� �) (1� �)

�

�� �2�1 + �3

log (1 + gTFP )+�0 � �1 + �5�7

�2+n

Clearly, an increase in payroll taxes and a reduction in product market competition(i.e. an increase in the mark-up) both decrease employment if �5�6 + �8 > 0: Thusif and only if we have a labour share term in the wage setting function will payrolltaxes and the degree of product market competition have an e¤ect on employment.This was already noted by Blanchard and Katz (1999).43 An increase in total factorproductivity growth increases employment, while an increase in the level of bene�tsfor given wages and productivity (i.e. �7) will again decrease employment. Thusour model embeds the textbook e¤ect of some important labour market institutionson the NAIRU and is thus in line with the mainstream approach sketched at thebeginning of this section.It remains to determine the size of the overhead labour force. Following Rotemberg

and Woodford (1999), we assume that in the steady state, all economic pro�t gener-ated by employing productive labour and capital goes to the overhead sta¤. Hencethe �rm ends up with zero pro�ts.44 This is justi�ed because setting up productionis impossible without overhead labour and the �rms pro�t is thus essentially equal tothe collective marginal product of its overhead sta¤. We assume that the overheadsta¤ splits this pro�t equally. We assume the amount of overhead workers required toenable production is such that the real wage for overhead and non-overhead workerswill be exactly the same in the steady state. These assumptions allow for a straight-forward way to determine the amount of overhead and non-overhead workers as a

43Blanchard and Katz (1999), p.72.44See Rotemberg/ Woodford (2004), pp. 15-16.

16

function of total employment. Zero pro�t requires

�� 1�

Yt � wtn = 0

where ��1�is the share of �rms pro�ts in output. Substituting wt = (1� �) 1

�Yt

n�ns�ngives, after some manipulation

�� 11� �

=n

n� ns � n� s

This is the ratio of overhead labour to productive labour, which we call s: Solving forn then gives

n =s

1 + s(n� ns)

5.3 Price Setting and Nominal Rigidities

Each �rm produces one of the variants of the output good in the CES basket. Invest-ment expenditure stretches over these variants in precisely the same way as consump-

tion demand, we can write yt+i(j) = Yt+i

�pt+i(j)Pt+i

���. Following Rotemberg (1983)

we assume that the representative �rm faces quadratic costs if it alters its individualprice in�ation from a reference level � � 1. This is the steady state level of in�a-tion in the economy. These cost arise because frequent price changes are bad forthe reputation of the company. Convincing customers to remain with the companynevertheless is costly.45 Additional costs arise because deviating from the "standard"level of in�ation requires the �rm to engage in a costly re-optimisation process. Thishas to be carried out by high paid marketing professionals, while price changes closeto average in�ation can be decided by lower paid "frontline" sta¤. Both kinds of costsare likely to increase in the �rms output as well. We assume the following functionalform:

ACt+i(j) ='

2(pt+i(j)

pt+i�1(j)� �)2yt+i(j) (21)

The �rm j chooses its price pt+i(j) in order to maximise

1Xi=0

Et

��t;t+i

�pt+i(j)

Pt+iyt+i(j)�mct+iyt+i(j)� ACt+i(j)

��(22)

where �t;t+i denotes the discount factor used to discount real pro�ts earned in periodt+i back to period t. Note that because households own the �rms, we have �t;t+i =

45See Rotemberg (1983), p. 269.

17

�i u0(Ct+i)u0(Ct)

: Di¤erentiating with respect to pt(j) and noting that, as all �rms are thesame, pt(j) = Pt holds ex post, yields

(1� �) + �mct � '

�PtPt�1

� ��

PtPt�1

+ �'

2(PtPt�1

� �)2

+Et

��t;t+1'

Yt+1Yt

�Pt+1Pt

� ��Pt+1Pt

�= 0 (23)

which is a nonlinear version of the standard New Keynesian Phillips curve. It relatescurrent in�ation to expected future in�ation, and implies a steady state value formarginal cost ( for Pt

Pt�1= Pt+1

Pt= �) of ��1

�: It is, however, a consistent feature of

empirical estimations of Phillips curves that speci�cations which include lagged in�a-tion as well ("hybrid" Phillips curves") perform better than purely forward lookingPhillips Curves. This is because in�ation has inertia.46 Backward looking elementsare easily introduced into the price setting considerations of the �rm by assumingthat the reference level of in�ation does not remain constant over time. Instead,we assume that it equals last periods in�ation, i.e. �t =

Pt�1Pt�2

: If the in�ation ratebecomes higher for several periods, �rms will mandate frontline sta¤ to handle priceincreases of that size in order to keep costs low. Customers will get used to the dif-ferent pace of price changes as well, making a higher rate of price change less costlyfor the individual �rm. Hence we have

(1� �) + �mct � '

�PtPt�1

� Pt�1Pt�2

�PtPt�1

+ �'

2(PtPt�1

� Pt�1Pt�2

)2

+Et

��t;t+1'

Yt+1Yt

�Pt+1Pt

� PtPt�1

�Pt+1Pt

�= 0 (24)

The experiment we want to conduct later is a disin�ation. In�ation is brought into theeconomy by a so called "cost-push shock" ut :This shock increases current in�ation,holding the values of past in�ation and marginal costs constant, and is added directlyto the Phillip�s curve equation:

(1� �) + �mct � '

��PtPt�1

� ut

�� Pt�1Pt�2

��PtPt�1

� ut

�+�

'

2(

�PtPt�1

� ut

�� Pt�1Pt�2

) + Et

��t;t+1'

Yt+1Yt

�Pt+1Pt

��

PtPt�1

� ut

��Pt+1Pt

�= 0(25)

While it would certainly be desirable to derive such a shock from �rst principles, likefor instance explicitly including energy in the production function, the road takenhere has the advantage of simplicity and is in line with the New-Keynesian literatureas well.47

46See for instance Gali and Gertler (2000).47See for instance Clarida et al (1999), pages 1665 and 1667.

18

Although we will simulate a non-linearised version of the model below, it is stillinsightful to linearise the Phillips Curve for purpose of comparison with other spec-i�cations found in the literature and in empirical studies. This is all the more soas simulating a model with a linearised Phillips Curve does yield results which arepretty close to the model featuring the non-linearised Phillips Curve. Linearising (24)around the steady state gives

�t =�t�1

1 + (1 + g)�+

(� � 1)cmct' (1 + (1 + g)�)

+(1 + g)�

1 + (1 + g)�Et�t+1 (26)

The steady state discount rate � can be replaced by � u0(Ct+1�Habt)u0(Ct�Habt�1) : Assuming loga-

rithmic utility (u(Ct) = ln(Ct � Habt�1)) and noting that consumption, habit andoutput will all grow at the same rate in the steady state, yields

�t =�t�11 + �

+(� � 1)cmct' (1 + �)

+�

1 + �Et�t+1 (27)

for the hybrid Phillips Curve. Note that these equations resemble very closely spec-i�cations which are obtained by Woodford (2003) under the assumption of Calvocontracts and full indexation of the prices of those �rms which can not re-optimiseprices to past in�ation. In fact, the coe¢ cients on expected future in�ation and thecoe¢ cient on lagged in�ation exactly match Woodfords�results.48

(27) implies that disin�ation is always costly in terms of output and employmentbecause as � < 1; the weight on lagged in�ation exceeds 0.5.49 Costliness is a featureof real world disin�ations, and recent estimates the hybrid Phillips Curve by Jon-deau and Bihan (2005) suggests that the coe¢ cients on past and expected in�ationexceed 0.5 in France, Germany and the Euro area as a whole and are in fact quantita-tively close to the values in equation (27), assuming � = 0:99:50 There is also furtherevidence supporting the hypothesis of full indexation to past prices among non opti-mising �rms within a Calvo price setting framework. This is provided by estimationsof complete general equilibrium models with the goal of matching impulse responsefunctions of monetary shocks from a restricted VAR. Examples of this are Woodfordand Giannoni (2003) and Christiano, Eichenbaum and Evans (2005).51

It is instructive to add the cost push shock to (27)and solve forward, which yields

�t � �t�1 =� � 1'

1Xi=0

(Etcmct+i) + (1 + �)1Xi=0

Etut+i (28)

48See Woodford (2003), p. 215.49As was shown by Chadha et al (1992), this is a su¢ cient condition to prevent the path of

disin�ation from being completely costless. Intuitively, a reduction in expected in�ation reducesin�ation today, and a lower coe¢ cient on expected in�ation means that today�s in�ation will bereduced by less for any given output level. See Chadha et al (1992), p. 403.50See Jondeau/ Bihan (2005), pp. 521-550.51See Woodford (2003), p. 351 and Christiano, Eichenbaum and Evans (2005), pp. 30-32.

19

This shows that, up to a linear approximation, (25) is in fact a forward lookingaccelerationist Phillips Curve. If present and future marginal costs are at their steadystate level and present and future values of cost push shock are zero, in�ation willremain constant. It will accelerate or decelerate otherwise. Hence the model has awell de�ned NAIRU.

5.4 Monetary Policy

Monetary Policy is assumed to follow a simple Taylor type nominal interest rate rule.The exact speci�cation will vary across simulations. However, all speci�cations willinclude a lagged dependent variable in order to account for the interest rate inertiaobserved in the data. In the baseline, the interest rate reacts to current in�ation andthe lagged output gap:

it = (1� �) i+ (1� �) ��t + (1� �) Y4gpt�1 + �it�1 (29)

i; � and gpt denote the long-run real interest rate (recall that in�ation is zero in thesteady state), the degree of interest rate smoothing and the output gap, respectively. � and Y denote the long run coe¢ cients on in�ation and the output gap. Thecentral bank responds to the lagged value of the output gap but current values ofin�ation. We choose this form because it matches the speci�cation estimated byClausen and Meier (2003) on a real time output gap. We will discuss later why thisis more consistent with our model than the alternatives. However, our basic resultsare not sensitive to changing the form of the policy rule.The output gap is the percentage deviation of total output, i.e. private sector plus

the output of government employees, from its natural level. We calculate the outputof government employees by simply adding up their wages, following the conventionof national accounts. We assume that government employees earn the same wage asin the private sector. For total output, we then have Yt + wtn

s, while total naturaloutput is given by Y n

t +wnt n

s. wnt and Ynt denote the wage rate and the private sector

output level consistent with natural employment, or the NAIRU. Thus we have

gpt =Yt + wtn

s � Y nt � wnt n

s

Y nt + wnt n

s(30)

Y nt denotes the private sector output level which would set marginal costs equal to

its long run level ��1; given the capital stock and the previous period�s real wage. Ascan be obtained from equation (28), this would ensure that in the absence of cost pushshocks, in�ation is neither rising nor falling. The employment level corresponding tothis output level will be referred to as "natural employment" nnt . The natural levelsof output and employment are derived by substituting the equation for the rental oncapital (15) and the wage setting equation (20) into (17) and setting mct = ��1: The

20

natural levels of output, employment and the real wage are then given by the valuesof Y n

t nnt and wnt solving

��1 =(nnt � ns � n)�wnt

A (1� �) (�1TFPt)1��K�

t

logwnt � logwt�1 = a+ b � (nnt � n) + c log

�wt�1 (nt�1 � n� ns)

Yt�1

�Y nt = AKt

�(TFPt�1 (nnt � ns � n))1�� (31)

Note that given the past real wage, the capital stock has a positive e¤ect onnatural employment given the past real wage. This e¤ect works through the negativee¤ect of a higher capital stock on the capital rental. This tends to lower marginalcosts and thus accommodates a higher real wage given the mark-up. This allows theemployer to meet the demands of wage setters associated with higher employment.

5.5 Introducing Endogenous Growth

The basic idea in the knowledge spill-over model of Romer (1986) is to start o¤with astandard neoclassical production function with labour augmenting technical progressas above.52 An additional feature is that labour augmenting technological progressmight be �rm speci�c. Thus the output of �rm i is given by

Yt(i) = F (Kt(i); TFPt (i)nt(i)) (32)

Romer then makes two crucial assumptions:

� Increasing it�s physical capital simultaneously teaches the �rm how to producemore e¢ ciently. This idea was �rst suggested by Arrow (1962). For simplicity,in the Romer setup, TFPt (i) is simply proportional to the �rm�s capital stock.

� Knowledge is a public good. Hence each �rm�s knowledge is in fact proportionalto the aggregate capital stock rather than to its own.53 However, the impact ofthe �rm�s capital stock on the aggregate capital stock is so small that they canbe neglected. Thus the production function of �rm i becomes

Yt(i) = F (Kt(i); Ktnt(i)) (33)

This implies that there are now constant returns to capital at the economy widelevel, allowing per capita output to grow. However, there are still decreasing returnsto capital at the �rm level. In the Romer model, this leads to a growth rate which is

52The exposition here follows Barro and Sala-i-Martin (2004), pp.212-222.53See Barro/ Sala-i-Martin (2004), pp.21-22.

21

ine¢ ciently low. This is because saving is to low as the individual return on capitalfalls short of the social return on capital.Note that the steady state in the learning by doing model satis�es the famous �ve

stylized facts of growth: Output per capita and capital per labour keep increasing,the capital output ratio is trendless, the real wage per unit of labour keeps increasing,the rate of pro�t is trendless and the share of GDP going to capital and labour aretrend less as well. Thus from an empirical point of view, there is no reason renderingthe neoclassical production function superior to the alternative employed here.Thus we set TFPt = Kt in the equations derived in the previous section. The

marginal cost equation (17) and the aggregate production function become

mct =

�rkt��w1��t

A��(1� �)1��(�1Kt)1��(34)

Yt = AKt(�1 (nt � ns � n))1�� (35)

To arrive at from the production function (12) ; after setting TFPt = Kt, we divideby nt(i)�n: As the capital labour ratio and the output per unit of productive labourratio are the same across all �rms, we arrive at (35) :The capital stock now has a stronger e¤ect on both marginal costs and output than

in the JLN economy. An increase in the capital stock by 1% for a given employmentlevel (implying that output expands at the same rate) reduces marginal costs by1%: In the absence of endogenous growth the e¤ect is only �% This can be see bysubstituting the capital rental out of equations (17) and (34) and then substitutingYtKtusing the respective production functions.Accordingly, the capital stock also has a greater e¤ect on natural employment and

the NAIRU. The equivalents of equations (31) are

��1 =(nnt � ns � n)�wntA (1� �) (�1)

1��Kt

logwnt � logwt�1 = a+ b � (nnt � n) + c log

�wt�1 (nt�1 � n� ns)

Yt�1

�Y nt = AKt(�1 (n

nt � ns � n))1�� (36)

Clearly, an increase in the capital stock now accommodates a larger increase innatural employment than in (31) :

5.6 The Aggregate Equations

This section summarises the models aggregate equations developed above for conve-nience of the reader and introduces explicit functional forms where that has not yetbeen done above. As many of the economy�s variables are growing in the steady state

22

(Yt;Ct; It; wt; Kt), simulation of the model requires normalising those variables witha cointegrated variable. It is very convenient from a technical point of view to nor-malise with respect to the capital stock. How that is done is shown in the appendix,as well as the computation of steady state values of the stationarised variables.Aggregate demand is the sum of consumption, investment, the amount of price

adjustment costs and government expenditure:

ADt = Ct + It +'

2(�t � �t�1)

2Yt + wtns (37)

We will assume logarithmic utility so that the consumption Euler equation be-comes

1= (Ct � habt�1) = � (1 + it)Et

�1

(Ct+1 � habt) (1 + �t+1)

�(38)

The level of habit is given byhabt�1 = jCt�1

Investment expenditures is governed by the following equations:

�t =1

Ct � habt�1

�Et��t+1r

kt+1 + �t+1qt+1 (1� �)

�= �tqt

�tqt

" 1� �

2

�ItIt�1

� (1 + g)�2!

� ItIt�1

�

�ItIt�1

� (1 + g)�#

(39)

+�Et

"�t+1qt+1

�It+1It

�2�

�It+1It

� (1 + g)�#

= �t

while capital accumulation is given by

Kt+1 = (1� �)Kt + It

1� �

2

�ItIt�1

� (1 + g)�2!

(40)

The capital rental is given in both models by

rkt = �mctYtKt

(41)

However, with endogenous growth, we can write rkt as a function of employment andmarginal costs alone, namely as

rkt = �mctA(�1 (nt � ns � n))1�� (42)

23

Marginal cost in the JLN economy becomes

mct =

�rkt��w1��t

A��(1� �)1��(�1TFPt)1�� (43)

while in the presence of endogenous growth, we have

mct =

�rkt��w1��t

A��(1� �)1��(�1Kt)1��(44)

Wages are set according to equation (??):

logwt � logwt�1 = a+ b � (nt � n) + c log

�wt�1 (nt�1 � n� ns)

Yt�1

�(45)

Total output in the absence of endogenous growth is given by private sector outputYt plus the output of state employees:

Outputt = AKt�(TFPt�1 (nt � n� ns))1�� + wtn

s (46)

while in the presence of endogenous growth, we have

Outputt = AtKt((nt � n� ns)�1)1�� + wtn

s

Markets clear:ADt = Outputt

The evolution of prices is determined by the Phillips Curve, where we replace thestochastic discount factor by its de�nition �t;t+1 = � u

0(Ct+1�habt)u0(Ct�habt�1) = � Ct�habt�1

Ct+1�habt

(1� �) + �mct � '

��PtPt�1

� ut

�� Pt�1Pt�2

��PtPt�1

� ut

�+ �

'

2(

�PtPt�1

� ut

�� Pt�1Pt�2

)2

+�Et

�Ct � habt�1Ct+1 � habt

'Yt+1Yt

�Pt+1Pt

��

PtPt�1

� ut

��Pt+1Pt

�= 0 (47)

Finally, policy is speci�ed by equation (29)

it = (1� �) i+ (1� �) ��t + (1� �) Y4gpt�1 + �it�1 (48)

with gpt as de�ned in (30) with natural output as determined in (31) for the JLNeconomy and as determined in (36) for the New Growth economy.

24

6 Simulation Setup and Calibration

We conduct two types of simulations. In the �rst one, we aim to create a scenarioakin to the one faced by central banks in Western Europe at the end of the seventiesand the beginning of the 1980s. That means we would like to create a situationwhere annual in�ation increases several percentage points above its target level forsome time and is then subsequently reduced. Therefore ut is set equal to 0.03for the �rst quarter and a forecast conditional on this being the case is computedfor all the variables. To put it di¤erently, we have a 3 percentage point increasein quarterly in�ation given marginal costs, or 12 percentage point increase at anannualised rate. In the baseline simulation, this will give rise to a disin�ation of a bitmore than 4.6 percentage points over 5 years, which is at the lower end of disin�ationsactually experienced during that period. For instance, in Germany, annual in�ationwas at 6.3% in 1981, which was then reduced to -0.1% in 1986, which is a rathersmall disin�ation compared to the UK, France or Italy were in�ation declined by 8.6,10.8 and 13.7 percentage points over the same period, respectively. Note that thereis no endogenous persistence in the shock itself beyond the �rst quarter, implyingthat any persistence in the path of the variables and in particular unemploymentbeyond that point is endogenous. The models are solved employing a second orderapproximation to the policy function using the approach of Schmitt-Grohe and Uribe(2004).54 We consider the second order approximation appropriate because the modelhas multiple distortions (unemployment, imperfect competition, external e¤ects ofcapital goods production). Therefore precautionary savings e¤ects which would belost if the policy function were approximated to �rst order might matter. The onlysource of uncertainty we consider arises from random draws of the cost push shock.The solution and the simulations are conducted using the software Dynare.55

The calibration of the model parameters for the experiment described above ispresented in table 1. It was arrived at as follows. We distinguish between fourdi¤erent types of parameters. The �rst set is calibrated according to standard valuesin the literature. It consists of the utility discount factor �; the output elasticityof capital �; the elasticity of substitution between varieties of goods � (our choiceimplies a mark-up of 1.2 and a share of overhead labour of 17.93%), the depreciationrate �, the price adjustment cost parameter ' and the share of government employeesns. ' is calibrated as to generate marginal cost coe¢ cient in the Phillips whichwould also be generated in a Calvo Phillips Curve with full backward indexing ofunchanged prices and a probability of no re-optimisation is 2/3. ns is based on dataof the German statistical o¢ ce on the number of full time equivalent employees in thepublic sector and on total hours worked in the economy in 2006.56 Employment in

54See Schmitt-Grohe and Uribe (2004), pp.755 to 775.55The programme and useful recourses on how to use it can be downloaded from

http://www.cepremap.cnrs.fr/dynare/.56The number of full time equivalents is calculated by adding up employees where each employee

25

the German public sector has been shrinking for years and our estimate of its share intotal employment will therefore be rather conservative. The second set of parametersare the coe¢ cients on employment and the labour share in the wage setting function,a, b and c. b and c are calibrated to be consistent with an estimate of that functiondiscussed in the appendix. We estimate (45) on Germany quarterly data on hourlylabour costs, unemployment and the labour share in GDP ranging from 1970 to 2000by two stage least squares to account for possible endogeneity of employment. Wethen calibrate the intercept a to achieve a steady state unemployment rate of 4%.This procedure is also used by Danthine and Kurman (2004).57

The three "free" parameters A, and j the production function multiple, the pa-rameter indexing adjustment costs and the degree of habit formation were calibratedto match second moments of a couple of variables in the New Growth Economy. Wealso apply this set of parameters to the JLN economy and report the resulting secondmoments as well. We generate the moments by setting standard deviation of the costpush shock equal to 0.003, thus producing a sample of 200000 observations generatedby random draws of the stochastic cost push shock. Since we are chie�y interested inrelative measures, the absolute size of the cost push shock is of little importance. Wechoose it so that the standard deviation of employment is close to it�s value in thedata. j was then calibrated primarily to match the persistence of the consumptioncapital ratio (all trended variables are normalised with the capital stock) as measuredby the autocorrelation coe¢ cient up to �fth order, while A and were calibrated toapproximate the standard deviation of the investment output ratio relative to theoutput capital ratio.Table 1: Calibration of non-policy Parameters� � j A � � �1 ' a b c u1 n0.33 0.99 0.4 0.38 6 0.025 0.452 30 -0.1123 0.08 -0.1 0.65 0.03 0.1793ns i gTFP �0.18 0.0181 0.0079 0.003The baseline calibration of the monetary policy reaction function is taken from

Clausen and Meier (2003), who estimate a Bundesbank policy rule over the periodfrom 1973 to 1998 for quarterly data. They use a real time measure of the outputgap in order to account for the fact that the central bank�s information set doesnot include future levels of GDP. Therefore they argue that the estimate of potential

is weighted with the fraction of the 40 hour working week he or she is working. This gives a numberof 4.6 million full time equivalents in 2006, see Statistisches Bundesamt 2007, table 2.3.4. This doesnot include employment in incorporated government owned companies. Assuming an average yearlyholiday of a month, this gives an estimate of 8794.76 million hours (=40*4.6*365/7*11/12). Thetotal number of hours by non-self-employed workers for that year was 56001 million, see StatistischesBundesamt (2007), table 2.7. With a calibrated unemployment rate of 4%, we then get a share ofgovernment employment in the total labour force of 15.26%. Assuming that about 3% of the labourforce are employed in government owned �rms, we arrive at our calibrated share of governmentemployees of 18%.57See Danthine and Kurmann (2004), p.120.

26

output underlying the output gap measure should be based only on GDP levels knownup to the quarter when the decision on the interest rate is made.58 An importantadditional bene�t of this procedure with respect to the model at hand lies in the factthat the potential output estimate will evolve in a manner depending more stronglyon past values of actual output than in a procedure which uses the full sample ofoutput values. This is what we would expect to be the case in our endogenousgrowth/ sticky price model. In this model, past levels in actual output, to the extentthat they are due to investment expenditure and trigger further investment, wouldbe expected to more strongly correlated. Thus the method of Clausen and Meier toestimating potential output seems to be more consistent with our model�s de�nitionof the output gap than an estimate based on the full GDP sample.Clausen and Meier�s best performing procedure for estimating potential output,

a linear trend, yields the statistically signi�cant coe¢ cients on output, in�ation andthe lagged interest rate reported in table 2 which in fact correspond to the originalcoe¢ cients proposed by Taylor (1993) to characterise the policy of the Federal Re-serve.59 Their estimate of the output gap coe¢ cient is of particular interest becausethe Bundesbank was often perceived as paying much less attention to output thanthe Fed. This was also borne out by other empirical estimates of the Taylor, one ofwhich we will discuss below.60 For the purpose at hand, we consider using as baselinecoe¢ cients for the policy rule the least hawkish ones in the literature of BundesbankTaylor rule estimates a prudent approach. It will become clear why this is the casewhen we discuss the simulation results.Table 2: Baseline Calibration of the Policy Rule: Clausen and Meier

(2003)61

� Y �1.5 0.52 0.75However, it is well known that estimating potential output, and in particular

obtaining output gap measure consistent with the underlying theoretical model isa tricky business.62 Furthermore, some would argue that the central bank reacts toforecasts of in�ation rather than current values. To check the robustness of our resultsboth with respect to the speci�cation of the interest rate rule, potential output mea-surements and estimation methodology, we perform both the disin�ation experimentand the moment comparison also for an alternative forward looking interest rate ruleestimated by Clarida, Gali and Gertler (1998) for the G3. Their rule is estimated

58See Clausen/ Meier (2003), p. 2. Note that because Taylor rules are usually estimated usingannualised in�ation and interest rate data, the coe¢ cient on the output gap has to be divided by 4to adapt it to quarterly frequency.59See Clausen/ Meier (2003), pp. 11-12 and p. 22.60See for instance Clarida et. al (1998), p. 1045, who estimate a statistically insigni�cant coe¢ -

cient on the output gap of 0.25/4.61See Clausen and Meier (2003), p. 22.62See Gali (2001), p. 12 and Gali and Gertler (1999), pp. 200-205.

27

using monthly data. A quarterly data version of their speci�cation amounts to

it = (1� �) i+ (1� �) �Et

��t+1 + �t+2 + �t+3 + �t+4

4

�+ (1� �)

Y4gpt + �it�1

(49)Hence the central bank responds to a one year forecast of in�ation, the current outputgap and the lagged interest rate.63 They measure potential output using a quadratictrend of a West German industrial production index and their data set stretches from1979 to 1993 and estimate the policy rule using the general method of moments.64

The point estimates are replicated in table 3. Clearly, the small coe¢ cient on theoutput gap corresponds more to the conventional wisdom on how the Bundesbankwas conducting policy.Table 3: Forward looking interest rate Rule: Clarida, Gali and Gertler

(1998)65

� Y �1.31 0.25 0.91

7 Some Moment Comparison

We now report the results of comparing the second moments generated by stochasticsimulations of the model economy to the corresponding empirical moments for Ger-man data. The moment comparison forms an important part in the calibration ofthe model. The three free parameters ; A and j where calibrated with an eye onthe empirical standard deviation of the investment/capital ratio to the output capitalratio and the persistence of employment and consumption, both as measured by the�rst to �fth order autocorrelation. We report some selected second moments of otherimportant variables to give an idea how the model in the chosen calibration matchesthe data. We carry out the same comparison for the JLN economy, and for both thebaseline policy reaction function and the Clarida, Gali Gertler (1998) estimate.We consider the following variables: The ratios of (total) output, consumption,

investment and real wages to capital, denoted as Ft; Dt; Rt and Ht respectively (recallthat we have to normalise all the trended variables with the capital stock to renderthem stationary) and employment nt (measured as linearly detrended log hours), thenominal interest rate it, in�ation �t (measured as the change in the GDP de�ator),productivity growth pt (measured as change in real GDP per hour worked), capitalstock growth gt, and the investment/ savings rate I=Y: From those, we computethe following moments: The coe¢ cient of variation for output, the relative standarddeviations of Dt, Rt and �tto Ft, the standard deviations of employment, the savingsrate and capital stock growth , the cross-correlation of all variables with Ft and

63See Clarida, Gali and Gertler (1998), p. 10439 and 1042.64See Clarida, Gali and Gertler (1999), p. 1040.65See Clarida, Gali and Gertler (1998), p. 1045.

28

the autocorrelation of each variable up to the �fth order. We conduct the momentcomparison for both the baseline case and the reaction function estimated by Clarida,Gali and Gertler.The construction of the data for Ft; Dt; Rt and Ht are discussed in the Appendix.

The raw data was obtained from the Statistische Bundesamt, except for the nominalinterest rate and the in�ation data which was obtained from the "International Fi-nancial Statistics" CD-ROM. The data set ranges 1970:Q1 to only 1990:Q4 becausereuni�cation is associated with a big drop in Ft; Dt and Rt; which would distort themoments. Furthermore, there are strong theoretical reasons to believe that all vari-ables other than employment, in�ation and the nominal interest rate are stationary.This is why we do not detrend or �lter them. However we adjust the sample to inducestationarity if stationarity is not con�rmed for the full sample by either an ADF test(by rejecting the null of a unit root) or a KPSS test (by not rejecting the null ofstationarity). Where we have to detrend, we use a linear time trend.The null of stationarity is rejected at the 5% level for Dt and Ft:After removing

the years 70 to 73, we are not rejecting the null of stationarity anymore at the 10%level for these variables. For Ht, the null of stationarity is not rejected at the 5%level for the full sample:For Rt; the unit root can be rejected over the entire sampleat the 5% level, as is the case for gt and the savings rate. The same holds for thenominal interest rate, and so we do not detrend this variable either. We do detrendthe in�ation rate, because the null of stationarity is rejected for this variable.Table 4 reports the various standard deviations, relative standard deviations and

cross-correlations with the output capital ratio Ft listed above. Column 1 contains thedata, while column 2 and 3 refer to the baseline policy reaction function. The standarddeviation of employment for the New Growth economy is on the mark because we havecalibrated the standard deviation of the cost push shock accordingly. The resultingcoe¢ cient of variation of Ft for the New Growth Model (NGM) is smaller than in thedata. It is in fact almost equal to the standard deviation of employment, which is infact also true for the JLN economy. The relative standard deviation of Dt in the NewGrowth model is very close to the data, while in the JLN economy, it is far too low.The relative standard deviation of Rt with respect to Ft is close to the data in bothmodels but closer in the New Growth economy. The standard deviations of capitalstock growth is very close to the data in the New Growth economy. The same holdsfor the standard deviation of capital stock growth relative to the standard deviationof employment (0.0766 as opposed to 0.0714 in the data). This is important becausemovements capital stock growth rates drive the results (and in particular employment)in the New Growth economy discussed in the next section. Therefore we would likethe standard deviation of capital stock growth relative to employment to be close tothe data. In the JLN economy, this relative standard deviation is too high.Turning to the cross-correlations, what is most striking is that for the JLN

economy, corr(it; Ft); corr(�t; Ft); corr(pt; Ft) are wrongly signed. They are nega-tive where the data is positive. The New Growth model produces wrong signs for

29

corr(�t; Ft); though the absolute value is much smaller than for the JLN Economy,and corr(Ht; Ft): The magnitudes of corr(Dt; Ft) and corr(Rt; Ft) are not too faraway from the data for both models, while for corr(nt; Ft); both models produce con-siderably too high values. It is particularly interesting that the New Growth modelproduces a positive correlation between the output capital ratio and the nominalinterest rate. Correctly matching the correlation of output with in�ation and thenominal interest rate is generally perceived as a di¢ culty in New Keynesian modelsif demand shocks are absent.66

Table 4: Relative Standard Deviations and Cross-CorrelationsMoments Data JLN NGM CGG: JLN CGG: NGMsd:Ft=meanFt 0.0272 0.0115 0.0192 0.0077 0.0215sd:Dt=sd:Ft 0.6179 0.4447 0.5936 0.4619 0.5910sd:Rt=sd:Ft 0.4888 0.5783 0.4540 0.6072 0.4812sd:nt 0.0196 0.0112 0.0209 0.0074 0.0235sd: (It=Yt) 0.0092 0.0048 0.0053 0.0035 0.0061sd:�t= (sd:Ft=meanFt) 0.208 0.3645 0.2001 0.8801 0.1982sd:gt 0.0014 0.0012 0.0016 0.0009 0.0018corr(Dt; Ft) 0.8658 0.95 0.9923 0.8863 0.9906corr(Rt; Ft) 0.9102 0.9317 0.9953 0.8898 0.9948corr(nt; Ft) 0.5921 0.950 0.9990 0.8001 0.9991corr(it; Ft) 0.1557 -0.6772 0.0830 0.0188 0.8804corr(�t; Ft) 0.2001 -0.5071 -0.0901 0.1471 0.2263corr(pt; Ft) 0.2653 -0.1966 0.7587 -0.2452 0.8262corr(Ht; Ft) 0.4924 0.4476 -0.6729 0.4468 -0.7258Table 5 reports the autocorrelation up to the �fth order for the data and the

baseline case. For those variables which we do not reject the null of stationarity overthe full sample we use the dataset starting in 1970 rather than the reduced datasetstarting in 1974 in order not to unnecessarily sacri�ce information. When the i-thorder autocorrelation of a variable is within �0:1 of the corresponding autocorrelationin the sample, it is printed in bold. A number in italics means that the value is closerto the data than the i-th order autocorrelation of the same variable in the competingmodel. Concerning the variables Ft; Dt;and nt; we observe that the New Growtheconomy is matching the persistence the data quite closely. By contrast, Rt; gt, itand It=Yt are considerably less persistent in the New Growth model than in the data,although they are still considerably closer to the data than in the JLN economyConversely, all these variables show far too little persistence in the JLN economy(and for all variables less than in the New Growth economy): The autocorrelationsare dying o¤ too quickly.For �t; both models produce very similar autocorrelations. They match the �rst

order autocorrelation but all the remaining ones are incorrectly signed. For pt; both

66See for instance Nolan and Thoenissen (2005), p. 25-26.

30

models produce incorrectly signed �rst and second order autocorrelations. The JLNeconomy then does match the sign of the third order autocorrelation but produceswrong signs for the remainder. The New Growth economy produces a wrong signfor the third order autocorrelation but almost matches the fourth and matches thesign of the �fth. For the real wage to capital ratio Ht; both models match the �rstto fourth order autocorrelation, though the JLN economy comes closer to the data.The New Growth economy fails match the �fth order autocorrelation, while the JLNeconomy does.Thus the New Growth model does mostly better than the neoclassical at matching

the data�s second moments for the baseline central bank reaction function, with veryfew exceptions.Table 5: Autocorrelations, BaselineOrder of Autocorrelation Data NCM NGM Data NCM NGM

Ft Ft Ft it it it1 0.86 0.89 0.93 0.9 0.8 0.842 0.75 0.65 0.82 0.75 0.49 0.583 0.65 0.4 0.71 0.58 0.22 0.384 0.56 0.22 0.63 0.39 0.06 0.255 0.47 0.08 0.58 0.23 -0.00 0.2

Dt Dt Dt �t �t �t1 0.93 0.88 0.94 0.35 0.45 0.422 0.9 0.65 0.85 -0.16 0.1 0.073 0.85 0.4 0.76 0.21 -0.07 -0.094 0.79 0.22 0.71 0.6 -0.11 -0.115 0.73 0.11 0.68 0.17 -0.08 -0.07

Rt Rt Rt pt pt pt1 0.96 0.9 0.94 -0.03 0.53 0.842 0.92 0.68 0.82 -0.18 0.07 0.673 0.86 0.45 0.7 -0.02 -0.21 0.534 0.81 0.24 0.6 0.37 -0.31 0.475 0.74 0.1 0.54 0.04 -0.27 0.42

nt nt nt Ht Ht Ht

1 0.93 0.88 0.94 0.92 0.99 0.992 0.84 0.65 0.84 0.89 0.95 0.973 0.73 0.34 0.74 0.85 0.9 0.944 0.62 0.20 0.66 0.82 0.84 0.925 0.51 0.08 0.62 0.78 0.78 0.89

31

Order of Autocorrelation Data NCM NG Data NCM NGg g g I=Y I=Y I=Y

1 0.97 0.9 0.94 0.95 0.91 0.942 0.94 0.68 0.82 0.91 0.71 0.823 0.89 0.45 0.7 0.87 0.49 0.694 0.85 0.24 0.6 0.82 0.3 0.585 0.79 0.1 0.54 0.75 0.15 0.51We now turn to the reaction function estimated by Clarida, Gali and Gertler

(1998). The relative standard deviations and cross correlations can be obtained fromcolumns 4 and 5 of table 4. Again the standard deviations of Ft and nt are quite closeto each other for both models, unlike in the data. The New Growth economy stillclosely matches the relative standard deviation of Dt and Rt (the later even betterthan before). In the JLN economy the relative standard deviation of Dt is still agood deal too low and the relative standard deviation of Rt is even further from thedata than before. corr(Dt; Ft) and corr(Rt; Ft) are almost equal while corr(nt; Ft)is considerably reduced (and thus brought closer to the data) for the JLN economy.corr(Ht; Ft) and corr(pt; Ft) also show some change in magnitude but not in signs. Bycontrast, corr(�t; Ft) becomes positive in both models, with the New Growth modelcoming very close to the data. Concerning the autocorrelations, which are reportedin Table 6, note that they generally increase somewhat in the New Growth model,much so in case of it; but decrease in the neoclassical model, with the exception of itand �t: Thus we conclude that the New Growth model is still better at matching thesecond moments discussed here, in particularly the persistence in the data, than theJLN economy.

32

Table 6: Autocorrelations, Clarida, Gali Gertler Reaction FunctionOrder of Autocorrelation Data NCM NGM Data NCM NGM

Ft Ft Ft it it it1 0.86 0.84 0.96 0.9 0.91 0.992 0.75 0.57 0.87 0.75 0.73 0.983 0.65 0.30 0.77 0.58 0.55 0.964 0.56 0.10 0.69 0.39 0.42 0.935 0.47 -0.01 0.64 0.23 0.34 0.91

Dt Dt Dt �t �t �t1 0.93 0.77 0.96 0.35 0.66 0.492 0.9 0.46 0.90 -0.16 0.36 0.143 0.85 0.23 0.83 0.21 0.12 -0.064 0.79 0.13 0.78 0.6 -0.03 -0.135 0.73 0.12 0.74 0.17 -0.1 -0.11

Rt Rt Rt pt pt pt1 0.96 0.92 0.96 -0.03 0.34 0.92 0.92 0.72 0.86 -0.18 -0.00 0.763 0.86 0.48 0.75 -0.02 -0.20 0.644 0.81 0.26 0.65 0.37 -0.26 0.555 0.74 0.08 0.58 0.04 -0.23 0.49

nt nt nt Ht Ht Ht

1 0.93 0.82 0.96 0.92 0.99 0.992 0.84 0.53 0.88 0.89 0.95 0.983 0.73 0.24 0.8 0.85 0.91 0.954 0.62 0.03 0.73 0.82 0.85 0.935 0.51 -0.1 0.68 0.78 0.8 0.90Order of Autocorrelation Data NCM NG Data NCM NG

g g g I=Y I=Y I=Y1 0.97 0.92 0.96 0.95 0.94 0.952 0.92 0.72 0.86 0.91 0.78 0.853 0.88 0.48 0.75 0.87 0.58 0.734 0.83 0.26 0.65 0.82 0.37 0.625 0.78 0.08 0.58 0.75 0.19 0.54

8 Simulation Results

We can now turn towards discussing the results of some simulations. In discussingthe results we will focus on the dynamics of employment and the NAIRU, in�ation,marginal costs and the capital stock.

33

JLN Economy - Unemployment and NAIRU

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0 10 20 30 40 50 60 70 80Quarters

UnemploymentNAIRU

Figure 2

We will discuss the results from the JLN economy �rst. Figure 3 plots the responseof actual unemployment (blue diamond) and the NAIRU (the pink square). In all�gures, the period zero value will be the steady state value of the respective variable.Unemployment increases by about 3 percentage points on impact but starts recoveringafter rising to 10.4 percentage points above its steady state value. It then quicklyrecovers and in quarter 8 practically returns to its steady state value. Employmentwould be expected to decrease because the cost push shock will increase in�ationwhich will ultimately lead to an increase in ex ante real interest rates via the policyrule (29). As consumers and investors are forward looking, this causes a contractionof aggregate demand on impact. Figure 2 plots the in�ation rate, which peaks inquarter 1 at a value of 3.8% and then quickly declines back to zero.

34

JLN Economy - Inflation

-1.00%-0.50%0.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%4.00%4.50%

0 10 20 30 40 50 60 70 80

Quarters

Inflation

Figure 3

There is then some overshooting in employment, because after employment hasrecovered, the e¤ective labour ratio ( Kt

ntTFPt) has decreased as capital stock growth has

slowed down during the recession. The resulting increase in the marginal product ofcapital increases capital stock growth above trend, which can be obtained from �gure4. This increases the demand for labour. The path of natural employment shows thatthis overshooting can be accommodated without an acceleration in in�ation. Naturalemployment increases in line with actual employment because the real wage declinesrelative to total factor productivity during the recession (see (31)). The higher levelof employment does then imply higher real wage growth. However, the fact thatcapital stock growth is above trend puts downward pressure on rkt which works tolower marginal costs (see equation (43)) and thus counters the in�ationary e¤ect ofabove trend real wage growth.

35

JLN Economy - Capital Stock Growth

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

0 10 20 30 40 50 60 70 80Quarters

Capital Stock Growth

Figure 4

Baseline - Unemployment and NAIRU

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0 10 20 30 40 50 60 70 80

Quarters

UnemploymentNAIRU

Figure 5

36

Baseline - Inflation

-1.50%-1.00%

-0.50%0.00%

0.50%1.00%

1.50%2.00%

2.50%3.00%

3.50%

0 10 20 30 40 50 60 70 80

Quarters

Inflation

Figure 6

We now turn towards the New Growth economy. Figure 5 plots unemploymentand the NAIRU for quarter zero to quarter 80. Unemployment increases by 5.7percentage points on impact. This is a bit strong, however big on impact jumps arecommon problem in forward looking models whose solution lies beyond the scope ofthis paper. It is clear that the shock has far more persistent e¤ect on employment thanin the neoclassical model. After about 11 quarters (10 quarters after the end of theshock), when employment is already overshooting in the JLN economy, only a bit morethan half of the on-impact loss in employment has vanished and employment is stillabout 3.2 percentage points below its steady state value. What is more, employmentgrowth soon comes to a halt: quarterly increases are now in the order of magnitude0.06 percentage points per quarter or less. As can be obtained from table 7, after40 quarters, or 10 years unemployment is still about 1.7 percentage points above itssteady state value, while after 60 Quarters (15 years) the di¤erence is still about 1percentage point. Furthermore, Figure 5 reveals that the persistent increase in actualunemployment is matched by an increase in the NAIRU, as after six quarters, actualunemployment rises above the NAIRU, which gradually increases during and afterthe recession. A glance at Figure 6 shows that in�ation (after peaking in quarter 1at a quarterly rate of about 3.3 percentage point) indeed stops declining at about thesame time actual unemployment falls below the NAIRU, as we would expect fromequation ?? and the de�nition of the NAIRU in this model.

37

Table 7: Baseline -Unemployment deviation from the Steady State for selected Quarters10 20 30 40 50 60 70 803.1 2.7 2.2 1.7 1.3 1 0.7 0.5We know from equation (45) that an increase in unemployment will reduce real

wage growth which would tend to lower marginal costs, so there must be a strongcountervailing force pushing marginal costs up in order to explain why in�ation stopsfalling. Figure 7 shows that while real wage growth drops sharply, in quarter 2 thegrowth rate of the capital stock falls by even more and remains considerably belowreal wage growth for about 9 quarters, after which they are about equal. Slowercapital stock growth entails slower technological progress and thus slower growth oflabour productivity, which will tend to generate a higher trajectory of marginal costfor a given level of real wage growth. In the New Growth model, the movement of realwages relative to labour productivity for a given employment level is thus capturedby the evolution of the wage capital ratio. Therefore this variable matters a lot formarginal cost, which is also borne out by equation (44). Figure 8, which plots thedeviations of marginal cost and the wage capital ratio from their steady state valuescon�rms that it is the movement of the real wage capital ratio which drives marginalcost back up, as both move broadly in parallel.By contrast, in the neoclassical model, the e¤ect of the capital stock on mar-

ginal costs is much weaker. The major determinant of marginal costs apart fromreal wages, TFPt, grows exogenously no matter whether output and investment arecontracting or growing. Thus marginal costs or, to put it di¤erently, the permissi-ble, non-in�ationary rate of real wage growth are much less a¤ected by changes tothe capital stock. Furthermore, the neoclassical model has an in-built stabilisationmechanism for investment, because unlike in the New Growth economy the marginalproduct of capital increases in the labour-capital ratio. This is not the case in theNew Growth economy, where at the economy wide level, the capital rental dependson employment alone, as can be obtained from equation (43).

38

Baseline - Capital Stock Growth and Real Wage Growth

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

0 10 20 30 40 50 60 70 80Quarters

Capital Stock GrowthReal Wage Growth

Figure 7

Baseline - Real Wage Capital Ratio and Marginal Costs

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%

1.00%

2.00%

3.00%

0 10 20 30 40 50 60 70 80

Quarters

Real Wage - Capital RatioReal Marginal Cost

Figure 8

Turning back to the New Growth economy, the recovery of actual employment hasto slow down after about 6 quarters because unemployment arrives at a level beyondwhich any reduction would cause in�ation to accelerate as it would push real wagegrowth above the growth rate of the capital stock and thus push up marginal cost.This would trigger interest rate increases via the policy rule. In fact this is alreadyhappening as actual unemployment is falling below actual unemployment and in�a-tion starts to pick up. To put it di¤erently, the central bank does not have a reasonto boost employment by aggressively lowering interest because although in�ation issomewhat below target, the output gap is closed as marginal cost equals its steadystate value. Figure 9 shows that the central bank stops lowering the real interest rate

39

(i.e. Et (it � �t+1)) after 8 quarters, when it is 0.45 percentage points (about 1.81percentage points at an annualised rate) below the steady state value, and begins totighten again. This is not very expansionary because the capital rental is depressedand expected to remain so, too. Figure 10 summarises the bene�ts from investing byplotting the present discounted value of an additional unit of capital, qt (this meaningof qt can be picked up from equation (39) ; where the relevant discount factor is thestochastic discount factor of households � u

0(Ct+1�Habt)u0(Ct�Habt�1)). Tobin�s Q recovers quickly

after the shock has passed and reaches its steady state value of one after 5 quarters,then exceeds it�s steady state level for . However, this is not su¢ ciently high to moveup the capital stock growth rate quickly because of the presence of investment ad-justment costs. The investment �rst order conditions (39) determine the investmentgrowth rate, which due to fast recovery of qt moves much closer to it�s steady statevalue as well. However, the capital stock growth rate depends on the investment cap-ital ratio, as can be seen from equation (40) ; which has declined during the recessionand the subsequent period of slow growth. Thus a faster recovery of capital stockgrowth would require an investment growth rate exceeding the steady state, whichwould have to be induced by a higher qt which in turn would require a lower realinterest rate.

Real Interest Rate

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

0 10 20 30 40 50 60 70 80Quarters

Real Interest Rate

Figure 9

40

Baseline - Tobin's q

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

0 10 20 30 40 50 60 70 80Quarters

Baseline - Tobin's q

Figure 10

The speed of recovery is then governed by the relative growth rates of real wagesand the capital stock. From quarter 9 onwards, the capital stock grows very slightlyfaster than real wages. This causes a slow decline in the wage-capital ratio, as canbe obtained from �gure 8, and allows for a slow reduction in unemployment becausehigher productivity growth implies �rms can accommodate the increased real wagegrowth associated with a tighter labour market without facing an increase in marginalcosts. This, in turn, again increases capital stock growth by increasing the marginalproduct of capital.Thus the disin�ation engineered by the central bank, while clearly successful, has

come at a cost beyond a temporary reduction in employment: The unemploymentlevel consistent with constant in�ation, or cmct = 0; has increased. Just as foundby Ball, a successful disin�ation during which the economy goes into a recessionis followed by an increase in the NAIRU. Furthermore, there is also a persistentslowdown in labour productivity growth. It is easily shown that labour productivitygrowth across all employees pt in the New Growth model can be written as pt =OutputtOutputt�1

nt�1nt� 1: If quarterly employment changes are negligible, output growth is

essentially equal to capital stock growth, and such is pt. From quarter 9 onwards,it can thus be obtained from �gure 6. At this point it falls short of its steady statevalue by about 0.23% per quarter or 0.92% at an annualised rate, while 40 quartersafter the shock it is still about 0.11% lower than in the steady state (0.44% at anannualised rate).These results provoke the question how changes to the central banks reaction

function a¤ect the long-run paths of employment and in�ation. Intuition wouldexpect that a stronger weight on the output gap in the reaction function would leadto a smaller decrease in employment not just in the short but also in the long run.As investment would be squeezed less, there would be a smaller decline in capital

41

stock growth which could accommodate higher of non-in�ationary employment afterthe recovery from the recession. Therefore we increase the coe¢ cient on the outputgap, Y ; to 5, leaving all other parameters the same. The corresponding evolutionof unemployment can be obtained from �gure 11. Indeed unemployment not onlyincreases considerably less in the short run (in fact it decreases on impact), but after40 quarters, it is still about 0.8 percentage point lower than in the Baseline case,as can be obtained from table 8. Hence a less hawkish monetary policy has indeedvery long-lasting benign e¤ects on employment. Figure 12 shows that capital stockgrowth declines less than in the baseline case. It�s post-shock plateau value exceedsthe corresponding baseline value ( in quarter 9) by about 0.05%, or about 0.2% at anannualised rate, and also recovers faster subsequently.Table 8: Y = 5 - Unemployment deviation from the Steady State for

selected Quarters10 20 30 40 50 60 70 801.8 1.4 1.1 0.8 0.7 0.5 0.4 0.29

Output weight=5 - Unemployment and NAIRU

0.00%

2.00%

4.00%

6.00%

8.00%

0 20 40 60 80Quarters

UnemploymentNAIRU

Figure 11

42

Output Gap Weight=5: Inflation

0.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%4.00%4.50%5.00%5.50%

0 10 20 30 40 50 60 70 80Quarters

Inflation

Figure 12

Output Gap Weight=5 Capital Stock Growth and Real WageGrowth

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

0 10 20 30 40 50 60 70 80Quarters

Capital Stock GrowthReal Wage Growth

Figure 13

The lower increase in unemployment comes at the cost of a considerably strongerin�ation surge during the lifetime of the cost-push shock. While in the baseline sim-ulation, in�ation peaks a (quarterly) rate of 3.3%, it now increases as high as 5.1%in the �rst quarter, as can be obtained from �gure 12, while the annual in�ationrate over the �rst year amounts to 15%. Note however that the increase in in�ationis only temporary. After 10 quarters, it has already decreased to 0.42%. Thus the

43

stronger acceleration in in�ation is a short run phenomenon. The gain in employ-ment is of more persistent nature. Whether this is desirable or not would require awelfare analysis which is beyond the scope of this paper. However, it is illustrativeto summarise the long-run trade-o¤s policymakers are facing by continuing to varythe output gap coe¢ cient and to plot the resulting average annualised in�ation ratesagainst the corresponding average unemployment and natural unemployment rates.This done in Figure 14 over 60 quarters, for values of Y between 0.3 and 5. Bothcurves are clearly downward sloping. As with traditional Phillips Curves, both curvesbecome steeper as unemployment becomes lower. The unemployment Phillips Curveis always �atter than the NAIRU-Phillips Curve. This is because monetary policya¤ects the path of actual unemployment in the short run more strongly than theNAIRU. It�s slope varies from -0.77 to -2.7 as unemployment falls, while the slopeof the NAIRU Phillips curve varies from -0.9 to -3.3. Over the range of policy rulesconsidered here, a 1.5 percentage point reduction in the average NAIRU is associatedwith a 2.4 percentage point increase in in�ation. Hence there is a trade-o¤ betweenin�ation and unemployment over an extended period of time. By contrast, similarexperiments with the neoclassical version only produced the short run trade-o¤ be-tween the variation of in�ation and the variation of employment familiar from NewKeynesian models.From an empirical point of view, 5 is arguably not a reasonable value for Y :

However we will see in the next section when we turn to the cross country dimensionthat the e¤ect of an increase in the output gap coe¢ cient depends very much on theform of the policy reaction function. We will draw on the estimates of Clarida Galiand Gertler (1998) of their forward looking rule for the Bundesbank and an estimateof the same rule for the Federal reserve. We will see to which extent the estimateddi¤erences in the reaction function coe¢ cients can help to explain the di¤erence inthe evolution of unemployment.

44

Phillips Curves: 60 Quarter Averages of Inflation, NAIRU andUnemployment for different Output Weights

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

2.00%

4.50% 5.00% 5.50% 6.00% 6.50% 7.00% 7.50%

Infla

tion

UnemploymentNAIRU

Figure 14

We will next consider how these results change if real wages are less �exible.Intuition would suggest that less �exible wages would cause a more persistent responseof unemployment, because any given increase in unemployment leads to a smallerreduction in real wage growth than before. This will enhance the drop of the capitalstock growth rate relative to the real wage growth rate. Hence only a higher rate ofunemployment can be accommodated without triggering an acceleration of in�ation.Higher unemployment in turn reduces the marginal product of capital, implying lessinvestment, reducing capital stock growth and thus limiting the room for employmentexpansion.To investigate the quantitative implications of these mechanisms, we reduce the

slope of the real wage growth function b to 0.07. Figure 15 shows that both ac-tual unemployment and the NAIRU fall much slower than in the baseline case. Themaximum NAIRU is about 0.6 percentage points higher than the maximum in thebaseline simulation, thus reducing the room for an immediate non-in�ationary recov-ery. As a result, after 40 quarters, as can be obtained from table 9 the deviationfrom the steady state is 2.5 percentage points as opposed to 1.7 percentage points inthe baseline case. To the extent that real wage growth is more �exible in the UnitedStates than in continental Europe, this results o¤ers an explanation why the increasein American unemployment during the disin�ation in the early 1980s has not beensustained.However, empirical estimates of (45) ; usually replacing nt with the unemployment

rate, frequently �nd no signi�cant di¤erence between the coe¢ cient on unemployment

45

between European countries and the United States. However, it seems that there isa signi�cant and robust observable intercontinental di¤erence in the value of c; thecoe¢ cient on the labour share:67 We will examine the consequences of setting c equalto zero in the following sectionTable 9: b = 0:06 - Unemployment deviation from the Steady State for

selected Quarters10 20 30 40 50 60 70 803.6 3.4 2.9 2.5 2.1 1.7 1.4 1.2

b=0.07 - Unemployment and NAIRU

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

0 10 20 30 40 50 60 70 80Quarters

UnemploymentNAIRU

Figure 15

As a �nal robustness experiment, we change the slope of the adjustment costfunction by reducing : It is clear and can also be veri�ed from equation (39) thatif adjustment cost react slower to It

It�1, investment will be more a¤ected by changes

in the present value of an additional unit of capital and thus will decrease more inresponse to a fall in qt: Thus an increase in the the real interest rate and a reductionin the marginal product of capital will have a bigger e¤ect on capital accumulation,too. This would be expected to increase unemployment in the short as well as inthe long run. On the other hand, lower adjustment costs also imply that investmentgrowth will by more when interest rates fall and employment recovers. This wouldbe expected to speed up the recovery of employment. The simulation will tell whichforce dominates.Reducing from 0.65 to 0.4 generates the employment path displayed in �gure

16. As expected, both actual unemployment and the NAIRU increase by more thanin the baseline case. Unemployment increases by more both in the short and in themedium run, as can be obtained from table 10.

67See Blanchard and Katz (1999), p.73, and Cahuc and Zylberberg (2004), p.484-486.

46

Table 10: = 0:4 - Percentage point Deviation of unemployment fromits Steady State for selected Quarters

10 20 30 40 50 60 70 803.8 3.2 2.5 2.0 1.5 1.2 0.9 0.6

gamma=0.4 - Unemployment and NAIRU

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

0 10 20 30 40 50 60 70 80Quarters

UnemploymentNAIRU

Figure 16

9 Cross Country Aspects

The previous section shows that our New Keynesian model with endogenous growthis able to produce a persistent increase in unemployment as a consequence of a dis-in�ation. This is an important result because economists have been struggling toexplain the evolution of unemployment in continental Europe over time. This begsthe question whether we can also use the model to (coarsely) replicate di¤erencesin unemployment evolutions across countries. We address this issue in three di¤er-ent ways in this section. For that purpose, we will draw on the di¤erences in thesize of the disin�ation across the OECD, in (estimates of) the policy reaction func-tion coe¢ cients between the Bundesbank and the Federal Reserve and in real wagerigidity.We have mentioned before that there is an apparent, if not perfect, negative

correlation between the change in in�ation and the change in the NAIRU. Ball (1996)investigated this for the 1980s and we plotted it earlier over to decades and across21 OECD countries. We will now try to replicate this by varying the size of thecost push shock. Cross country di¤erences in the size of the cost push shock usedin our model can be interpreted as di¤erences in the responsiveness to global supplyshocks (for instance di¤erences in the dependence on oil in case of an oil price shock),di¤erences in the past record of monetary policy (in the sense that some central banks

47

have let in�ation spiral more out of bounds than others, leading to larger deviationsof in�ation from target), di¤erences in the choice of how much to disin�ate (a centralbank might just be willing to accept a higher in�ation rate following a supply shock)and di¤erently sized exchange rate shocks, or some combination of all of these factors.We are being deliberately unspeci�c about what exactly creates the di¤erence betweenthe in�ation target of the central bank and the actual in�ation rate.To generate observations, we vary the size of the cost push shock from 0.01 to

0.05, leaving all other parameters unchanged. Then we calculate the change fromyear 1 to year 10 of the in�ation rate during those years and the NAIRU in the �rstquarter of those years, and plot the later against the former in �gure 17.68 Thereis obviously a clear negative correlation. The slope of the line varies between -0.41and -0.56, which not too far away from the simple regression coe¢ cient of -0.33 (or-0.36 if, like Ball we exclude Greece) resulting from a regression of the change in theNAIRU on the change in in�ation using the OECD data presented earlier.

Change in Inflation vs. Change in the NAIRU over 10 years

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

-8.00% -7.00% -6.00% -5.00% -4.00% -3.00% -2.00% -1.00% 0.00%

Change in Inflation

Chan

ge in

the N

AIRU

Figure 17

Let us now take a look at the e¤ect of empirically observable di¤erences in thepolicy rule. To get a proper idea of the e¤ects of these it is obviously important tohave comparable estimates. Therefore we make use of the fact that Clarida, Gali andGertler (1998) estimated the same policy rule using the same methodology for severalcountries, including Germany and the United States. We would have liked to draw onreal time estimates as in the previous section but to our knowledge, internationallycomparable estimates of this kind do not exist. The coe¢ cient estimates of Clarida,

68We take the di¤erence of the �rst quarter of both years since the NAIRU moves up very fastduring the �rst four quarters. Di¤erencing the annual averages of the two years would create amisleading impression of the correlation between the medium run change in the NAIRU (by undulyreducing this change) and the change in in�ation. The quarterly movements of the NAIRU in theOECD data are very slow and redoing �gure one with the di¤erence in the NAIRU between 1980quarter1 1990 quarter 1 rather than with the di¤erences in the annual averages as is the case nowwould not change the result.

48

Gali and Gertler of equation (49) for the Federal Reserve are reproduced in table 10.We now repeat the same experiment we conducted in the last section for both theestimates for the Bundesbank reaction function and the coe¢ cients of the FederalReserve. The �rst two lines of Table 11 shows the deviation of unemployment fromis steady state for both set of coe¢ cients. Note �rst that the persistent increase inunemployment with the policy rule as speci�ed and estimated by Clarida Gali, andGertler for the Bundesbank is substantially higher than the increase we saw with thepolicy rule used in the Baseline. This illustrates that, in terms of the unemploymente¤ects which are the subject of this paper, we were quite conservative in specifying andcalibrating our Baseline policy rule. Apart from that, unemployment is persistentlyhigher under the Bundesbank rule than under the Federal reserve one, though thedi¤erence is for the most part less than one percentage point. For instance after 40quarters, or 10 years, unemployment and the NAIRU are about 0.7 percentage pointshigher under the Bundesbank Rule than under the Federal Reserve rule.It is, however, informative to take a look at the standard errors associated with

Clarida, Gali and Gertler�s estimate. For instance, the standard error associated withthe coe¢ cient on the lagged interest rate � has as standard error of 0.03. Thus a valuefor � of 0.06 is still consistent (at a 5% level of con�dence) with Clarida, Gali andGertler�s estimate. The third row of table 11 shows the implied evolution of unem-ployment if we set � = 0:91: The resulting unemployment trajectory is substantiallylower than before. After 40 quarters, the unemployment and the NAIRU are now1.3 percentage points lower than under the Bundesbank rule, while after 50 quarters,the di¤erence is still 1 percentage point. In the same manner, we can also make useof the standard error of the estimate of Y , which equals 0.16. Increasing Y to0.88 yields the employment trajectory shown in the �nal row of Table 11, which isagain lower than with the point estimate: after 40 quarters, unemployment is and theNAIRU are about 1.1 percentage points lower than under the Bundesbank policy rule.Thus in the New Growth model, di¤erences in policy function parameters consistentwith the Clarida Gali and Gertler evidence can contribute to explaining the di¤erentevolutions of the unemployment rate in Germany as compared to the United States.

49

Table 10: Coe¢ cient Estimates of Clarida, Gali and Gertler for theFederal Reserve.69

� Y �1.83 0.56 0.97Table 11: Clarida, Gali and Gertler Policy Rule: Unemployment de-

viation from the Steady State for selected QuartersQuarter 10 20 30 40 50 60 70 80Bundesbank 4.2 4.1 3.2 2.6 2.0 1.6 1.2 0.9Federal Reserve 3.0 3.1 2.5 1.9 1.5 1.1 0.8 0.6Federal Reserve, � = 0:91 2.2 2.1 1.6 1.3 1.0 0.8 0.6 0.4Federal Reserve, Y = 0:88 2.4 2.4 1.9 1.5 1.1 0.9 0.6 0.5Finally, we explore the e¤ects of the observed cross continental di¤erences in the

nature of real wage rigidity. Estimating (45) on U.S. data con�rms the �nding ofother researchers that c = 0; while the U.S. estimate of b is not signi�cantly di¤erentfrom the value we employed so far (0.08). Therefore, in our �nal experiment aimedat highlighting cross country dimensions, we set c = 0 in the Baseline calibration,leaving everything else as in the Baseline, including the policy rule and its calibra-tion. The resulting deviation of unemployment from its steady state can be obtainedfrom table 12. Clearly, the increase in unemployment is persistently lower: After 40quarters, unemployment is only 0.6 percentage points higher than in the steady stateas compared to 1.7 percentage points in the Baseline.Remember that within our model, c = 0 would arise from �5�6 + �8 = 0; where

�5; �6 and �8 denote the (negative of the) e¤ect of the level of unemployment bene�tson e¤ort the e¤ect of productivity on unemployment bene�ts and the (negative ofthe) e¤ect of productivity on e¤ort. We suggested above how these results might berooted in di¤erences in the labour market setup, i.e. the greater strength of unions andperhaps a stronger link between unemployment bene�ts and productivity in Europe.Thus, our result should also be seen as theoretical support to Blanchard and Wolfers(2000) empirical �nding that both shocks and institutions a¤ect unemployment inthe medium run.The di¤erences in reaction function coe¢ cients and the di¤erences in real rigidity

examined here also contribute to explaining why some points in �gure 14 are "o¤the regression line". The three coe¢ cient vectors for the federal reserve investigatedhere all imply lower NAIRU increases than under the Bundesbank rule but largerdisin�ations for an equally sized cost push shock, as can be obtained from the �rstfour rows of table 13. Similarly, if we remove the labour share term from the wagesetting function in the baseline calibration, the increase in the NAIRU drops but thesize of the disin�ation over ten years does not.

69See Clarida, Gali and Gertler (1998), p. 1045.

50

Table 12: c = 0 - Percentage point Deviation of Unemployment fromits Steady State for selected Quarters

10 20 30 40 50 60 70 800.9 1.0 0.8 0.6 0.4 0.3 0.2 0.1Table 13: Change in the NAIRU vs. Change in in�ation for various

Scenarios��annualt �NAIRU

CGG, Bundesbank -0.6 2.50CGG, Federal Reserve -3 1.9CGG, Federal Reserve, � = 0:91 -9.1 1.2CGG, Federal Reserve, Y = 0:88 -6.3 1.4Baseline, c = 0 -5.2 0.5

10 Conclusion

This paper aims to put forward an explanation to long lasting, persistent swings inunemployment which does not rely change in labour market rigidities or other struc-tural parameters of the economy, but on a temporary nominal shock and the waymonetary policy deals with the resulting �uctuations in output and in�ation. We�rst developed a micro founded model embodying consensus features with respect tothe short and medium run e¤ect of a disin�ation on unemployment. This model hasunemployment, and a natural rate of unemployment, or NAIRU which is essentiallyindependent of monetary policy. Output is demand determined as prices are sticky.The central bank follows a standard interest feedback rule relating the interest rateto the output gap and in�ation, calibrated to an estimate of a Bundesbank reactionfunction. Correspondingly, an adverse one quarter cost push shock a¤ects increasesunemployment only over a horizon of about 8 quarters. We then incorporated en-dogenous growth in this model and calibrate by comparing the second moments ofkey variables to their counterparts in the Western German economy.We apply the same cost push shock and �nd that the NAIRU is a¤ected over

relevant horizon. Under the baseline calibration, unemployment will still be about1.7 percentage points above its pre-shock value after about 40 quarters, or 10 years. Atthe same time, in�ation stops declining soon after the cost push shock has vanished.Thus the increase in unemployment represents an increase in the NAIRU.The increase in the NAIRU is brought about by the decline in investment during

the recession required to disin�ate the economy. The capital stock in the endogenousgrowth economy has a much stronger e¤ect on marginal costs than in the "consensus"model, which has a neoclassical production function. Thus, although wage growthdeclines as employment contracts, marginal cost returns back to their steady statelevel soon after the shock has vanished. This stops the disin�ation. The subsequentrecovery is very slow because the central bank has no reason to lower interest rates.

51

Its reaction function dictates that it reacts solely to in�ation, being close to target,and the output gap, de�ned as the deviation of output from the level consistent withconstant in�ation, which is zero.The model also shows that the central bank faces a trade-o¤between preventing a

strong acceleration of in�ation and quickly bringing in�ation back to target on the onehand and preventing a persistent increase in unemployment on the other. A highercoe¢ cient on the output gap has substantial and lasting benign e¤ects on the path ofunemployment. We also show that varying the output gap coe¢ cient and plotting theresulting average unemployment rates and NAIRUs against the associated averagein�ation rates creates a downward sloping Phillip�s Curves. Thus the model cancontribute to explaining the evolution of European unemployment during the 1980sand beyond. Rising NAIRUs would be the consequence of the disin�ations engineeredas a response to the in�ationary shocks of the late 1970s, as would be part of theslowdown in productivity growth.Apart from generating a persistent increase in unemployment, the model proposed

here also contributes to explaining cross country di¤erences in the evolution of unem-ployment. Varying the size of the cost push shock generates a relationship betweenthe change in the in�ation rate and the change in the NAIRU over a ten year horizonsimilar to a relationship in the data �rst observed by Ball (1996). Using comparablepolicy rule estimates of Clarida, Gali and Gertler (1998) for the Bundesbank andthe Federal Reserves while holding the cost-push shock constant creates higher per-sistent unemployment with the later than with the former. Finally, taking accountof a well established cross-continental di¤erence in the structure of the wage settingfunction, namely the absence of a labour share term if the function is estimated forU.S. data also proves informative. In the absence of the labour share term, we see alower increase in the NAIRU. The size of the labour share term in wage setting canbe linked, if coarsely so, to features of the labour market like the presence of unionsor the bene�t system. Thus the paper lends support to the view that, as suggestedby Blanchard, it is both "shocks and institutions" which are at the heart of explain-ing the evolution of unemployment across time and the observed di¤erences acrosscountries.In addition, the comparison of second moments of the model with German data

ranging from 1970 to 1990 shows that the New Growth sticky price model is matchingthe data of that time period much better than a sticky price model with an identicalcalibration but with a standard neoclassical production function. In particular, theNew Growth sticky price model is much better at matching the observed persistencein important macroeconomic variables like employment, output and consumption,and other second moments as well.An obvious extension of the analysis presented here would be compute optimal

monetary policy within the framework proposed here. The common policy prescrip-tion arising from maximising welfare in sticky price DSGE models is for the centralbank to react strongly to in�ation but little to output. The signi�cant costs of a

52

disin�ation in the sticky price - New Growth model pointed out above suggest thatthis prescription might change.Another interesting extension would be to introduce non Ricardian consumers or

distortionary taxation to allow for expansionary e¤ects of debt-�nanced governmentexpenditure. While disin�ation was somewhat less an issue in Europe during the1990s than during the 80s, the "road towards Maastricht" forced those EU countriesaiming to adopt the Euro in 1998 to pursue an austere �scal policy which entailed bothreducing budget de�cits and sometimes the public debt-GDP ratio. By contrast, theReagan administration hugely increased public expenditure �nanced by debt, duringthe 1980s. While this policy is commonly accepted to have a¤ected employment inthe short run, it would be interesting to analyse their potential long run e¤ects withina suitably modi�ed version of the model proposed here.

11 Appendix A - Forward Solution of the Phillipscurve

The Hybrid Phillips Curve of this model is

�t =�t�11 + �

+(� � 1)cmct' (1 + �)

+�

1 + �Et�t+1 + ut

This can be rearranged to get

�t � �t�1 =(� � 1)cmct

'+ (1 + �)ut + � (Et�t+1 � �t)

De�ning �t � �t�1 � St; we have a forward looking �rst order di¤erence equation.Using the forward operator F , which is de�ned such that FXt = Xt+1 we can write

(1� �F )St =(� � 1)cmct

'+ (1 + �)ut

70

Using the fact that Xt1��F =

1Xi=0

��iXt+i

�if � < 1; we arrive at

�t � �t�1 =� � 1'

1Xi=0

(cmct+i) + (1 + �)

1Xi=0

ut+i

12 Appendix B - Normalised Version of the Model70See Leslie (1993), pp.94-95.

53

In this appendix we show how the normalisation of Ct; Yt; It and wt by the capitalstock changes the aggregate equations of the model. The resulting equations are thosewhich have been simulated. We de�ne Ct

Kt; habt�1

Kt

Yt+wtns

Kt; ItKtand wt

Ktas Dt; Habt�1; Ft;

Rt and Ht; while the gross capital stock growth rateKt+1

Kt� 1 is de�ned as gkt+1:

We directly apply the normalisation to the equations of the aggregate demandblock:

Ft = Dt +Rt +'

2(�t � �t�1)

2 (Ft �Htns) +Htn

s (50)

Consumption (remember habt�1 = jCt�1; thus Habt�1 = jDt�11+gkt

1= (Dt �Habt�1) = �Et�(1 + it) =

�(1 + �t+1) (Dt+1 �Habt)

�1 + gkt+1

���(51)

Habt = jDt

1 + gkt+1(52)

Investment:

�Et

1

(Dt+1 �Habt)�1 + gKt+1

� �rkt+1 + qt+1 (1� �)�!

=1

Dt �Habt�1q t

1

Dt �Habt�1qt

" 1� �

2

�RtRt�1

�1 + gkt

�� (1 + g)

�2!� RtRt�1

�

�RtRt�1

�1 + gkt

�� (1 + g)

�#

+�Et

"1

Dt+1 �Habtqt+1

�Rt+1Rt

�1 + gkt+1

��2�

�Rt+1Rt

�1 + gkt+1

�� (1 + g)

�#=

1

Dt �Habt�1(53)

gkt+1 = �� +Rt

"1� �

2

�RtRt�1

�1 + gkt

�� (1 + g)

�2#(54)

From (40) we have

gkt+1 = �� +Rt

1� �

2

�RtRt�1

�1 + gkt

�� (1 + g)

�2!(55)

The rental on capital remains unchanged:

rkt = �mctAt((nt � ns � n)�1)1�� (56)

Multiplying (43) K�

1��t

K�

1��t

54

mct =F

�1��t Ht

X(57)

where X = A1

1�� (1� �)�1.

Wage Setting: lnwt = lnwt�1+a+b (nt � n)+c log�wt�1(nt�1�n�ns)

Yt�1

�can be rewrit-

ten as (using equation (16) lnHt = a+b (nt � n)+

�wt�1

Kt�1(1+gkt )

�+c log ((1� �)mct�1) =

a+ b (nt � n) + ln

�Ht�1

(1+gkt )

�+ c log ((1� �)mct�1)

Ht = exp(a+ b (nt � n))Ht�1�1 + gkt

� ((1� �)mct�1)c (58)

Employment: from Outputt = AKt((nt � n� ns)�1)1�� + wtn

s; we have

Ft = A((nt � n� ns)�1)1�� +Htn

s (59)

The Phillips Curve and the Policy rule do not contain any trended variables andtherefore does not need to be normalised. However, we will substitute the real pro�tsstochastic discount factor by its de�nition, i.e. �t;t+1 = � u

0(Ct+1�Habt)u0(Habt�1)

= � Ct�Habt�1Ct+1�Habt ;

which gives

(1� �) + �mct � '

��PtPt�1

� ut

�� Pt�1Pt�2

��PtPt�1

� ut

�+ �

'

2(

�PtPt�1

� ut

�� Pt�1Pt�2

)2

(60)

+�Dt �Habt�1

Ft'Et

�Ft+1

Dt+1 �Habt

�Pt+1Pt

��

PtPt�1

� ut

��Pt+1Pt

�= 0 (61)

Replacing Pt+iPt�1+i

= 1 + �t+i gives

(1� �) + �mct � ' ((�t � ut)� �t�1) (1 + �t � ut) + �'

2((�t � ut)� �t�1)

2 (62)

+�Dt �Habt�1

Ft'Et

�Ft+1

Dt+1 �Habt(�t+1 � (�t � ut)) (1 + �t+1)

�= 0 (63)

For natural output, natural employment and the natural real wage from equation

��1 =(F nt )

�1�� Hn

t

X(64)

F nt = At((nnt � n� ns)�1)

1�� + nsHnt

Hnt = exp(a+ b (nnt � n))

Ht�1�1 + gkt

� ((1� �)mct�1)c (65)

55

given last periods wage/ capital ratio Ht�1 and this periods capital stock growth rategkt (which was also determined in the t-1 by the then investment decision). As canbe obtained from the equations, both F nt and natural employment can change overtime. In particular, an increase in gkt will increase natural employment and F

nt by

lowering Hnt as it is now possible for �rms to accommodate a higher real wage. The

output gap gpt is then calculated as

gpt =Outputt �Outputnt

Outputnt

�Kt

Kt

�=Ft � F ntF nt

(66)

13 Appendix C: Steady State Relations

This Appendix shows how to calculate the steady state values for the system devel-oped in Appendix B. We will �rst derive a steady state relation between the level ofemployment and the steady state growth rate for the New Growth Economy.First we make use of the properties of the adjustment cost function and its deriv-

atives in the steady state and apply these to the third of the equations in (53) ; whichyields q = 1:We plug this into the second equation of (53) and make use of thefact that in the steady state all trended variables (including the level of habit andconsumption) grow at the same rate g to arrive at

��rkt+1 + (1� �)

�= (1 + g) (67)

In the New Growth economy, we now replace the capital rental with equation (42),noting that in the steady state we have mc = ��1; to arrive at

g =���(1� �) + ���1A((n� n� ns)�1)

1����� 1Clearly, g is increasing in n.

This is the steady state growth rate which is borne out by the marginal productof capital in the endogenous growth economy. It is easily veri�ed that it is concave inemployment. It is straightforward to show that the real wage implied by the desiredmark-up grows at the same rate as output and the capital stock by using mct = ��1

on 44. This yields

wt = Kt�1

���1A��(1� �)1��

(rk)�

�1=(1��)� lnwt = � lnKt � g (68)

Hence in the steady state, the real wage has to grow at the same rate as the capitalstock. This means that equation (68) actually the dynamic, endogenous growthversion of the familiar macroeconomic textbook price setting function: It gives the

56

real wage growth rate compatible with marginal costs remaining constant and at it�slong run level. Unlike the textbook price setting function, this real wage growth rateis not constant but increases in employment: A higher steady state employment levelimplies a higher marginal product of capital, which triggers higher investment andthus faster capital stock- and thus productivity growth. Accordingly, the steady statelevels of employment an the growth rate are determined by the intersection of (68)with the wage setting function (20), making again use of the fact that mc = ��1:In practice, we choose a desired steady state employment rate (here 0.96) and

then compute the wage setting function intercept a to support this value, given g, band � and n:Having determined g and n; the determination of the steady state values of

Ft; Dt; Rt; Ht; rkt and it is now straightforward. For F we have

F = A((n� n� ns)�1)1�� (69)

from the production function. ForRt; we have from the capital accumulation equationin (39)

R = g + � (70)

D can then be determined as a residual via

D = F �R (71)

H is computed using the cost-minimisation �rst order condition for labour (16)

H = (1� �)��1F

n� n� ns(72)

rk is computed viark = ���1A((n� n� ns)�1)

1�� (73)

The steady state value of it is computed from (51)

i =1 + g

�� 1 (74)

Note that this is also the intercept of the interest rate rule i of the central bank.

14 Appendix D: Normalised Version of the JLNModel

Most of the equations from Appendix B just carry over to the neoclassical model.However, there are a few changes related to the production function and the marginal

57

cost equation. The aggregate production function is nowOutputt = AK�t (TFPt�1 (nt � n� ns))1��+

wtns: Dividing both sides by Kt gives

Ft = (lt�1 (nt � n� ns))1�� +Htns (75)

where lt is de�ned as TFPtKt. This variable evolves according to

lt =1 + gTFP1 + gKt

lt�1 (76)

In the JLN model, it convenient to normalise the real wage with respect to TFPtrather than with respect to Kt, while all the remaining normalisations carry over tothe JLN model. Denoting wt

TFPtas Hnc

t ; we have from (43) ; after making use of (41)

mct =F(�=(1��))t Hnc

t

A1=(1��) (1� �)�1(77)

Concerning the capital rental, we employ the JLN expression for Ft to have

rkt = �mctAl1��t ((nt � n� ns)�1)

1�� (78)

Finally, the normalised wage setting becomes

Hnct = exp(a+ b (nt � n))

Hnct�1

(1 + gTFP )((1� �)mct�1)

c (79)

All the remaining equations are just the same as in the New Growth version. Thecomputation of the steady state values in the neoclassical model is slightly di¤erent.The steady state growth rate (of output, consumption, the capital stock, the realwage) is now given by the parameter gTFP rather than being endogenously deter-mined, which means we have g = gTFP : Hence we can compute the steady state realinterest rate from 74, while we compute rk from (67). From (79), we have the steadystate employment rate. Setting mct = ��1in (78) then gives the steady state valuefor lt as

l =1

(nt � n� ns)�1

�rk�

�A

�1=(1��)(80)

which allows us to compute F from (75). Rearranging (77) then yields Hnc:

15 Appendix E: Estimation of the Wage SettingFunction

We estimate the real wage growth function using German data ranging from 1970Q1to 2000Q4. Our dataset includes Western German data up to 1991Q4 and following

58

that data for the uni�ed country. All data is taken from a publication of the Ger-man "Statistisches Bundesamt", all of which has been seasonally adjusted.71 Whenestimating the function, we replace the employment rate with one minus the unem-ployment rate. As a measure for labour costs, we use the "Arbeitnehmerentgeld" perhour worked, which is employee compensation including the full tax wedge. Thisis de�ated using the GDP price index. The labour share is given by total nominalcompensation (i.e. total "Arbeitnehmerentgeld") divided by total nominal GDP. Wethen estimate � logwt = a+ b � Unemploymentratet + c log (LSt�1) + d92Q1; whereLSt�1 denotes the previous periods labour share in GDP, d92Q1 denotes an interceptdummy equalling one in 1992Q1 and zero everywhere else. The later is to account forreuni�cation. We use two stage least squares to account for the possible endogeneityof employment. As instruments, we choose � log realwaget�1; unemploymentratet�1(following Danthine and Kurman (2004)); c and d92Q1:72

Note that we use Newey-West Standard Errors serial correlation consistent stan-dard errors because the Breusch-Godfrey LM test for serial correlation rejects thehypotheses of no serial correlation at the 5% level. The result is reported in table E1,where WG denotes the change in log real wages and U denotes the unemploymentrate.

71See Statistisches Bundesamt (2006) and Statistisches Bundesamt (2007a).72See Danthine/ Kurman (2004), p. 121.

59

Table E1Dependent Variable: WGMethod: Two-Stage Least SquaresDate: 06/03/08 Time: 12:27Sample (adjusted): 1970Q3 2000Q4Included observations: 122 after adjustmentsNewey-West HAC Standard Errors & Covariance (lag truncation=4)Instrument list: WG(-1) C U(-1) LOG(LS(-2)) D92Q1

Variable Coe¢ cient Std. Error t-Statistic Prob.

C -0.042273 0.018893 -2.237531 0.0271U -0.120587 0.046582 -2.588689 0.0108LOG(LS(-1)) -0.089599 0.032530 -2.754342 0.0068D92Q1 -0.112300 0.002188 -51.33630 0.0000

R-squared 0.574362 Mean dependent var 0.005890Adjusted R-squared 0.563541 S.D. dependent var 0.014077S.E. of regression 0.009300 Sum squared resid 0.010205F-statistic 52.46032 Durbin-Watson stat 2.535359Prob(F-statistic) 0.000000

Note that our calibrated value of b is lower than the point estimate of 0.12. How-ever, it is not statistically di¤erent from 0.12 with any reasonable level of con�dence,in fact it is less than one standard deviation away from the point estimate. The rea-son for this choice is that while it is possible to preserve the results of this paper inface of higher wage �exibility, this calibration has certain undesirable features. If weaim to achieve a steady growth rate of GDP in the order of magnitude of a reasonableorder of magnitude (and one that makes lifetime utility converge), we would have tochoose either relatively high depreciation rates or a lower individual discount factor�, the later implying a very high steady state risk less rate. We think that theseconsiderations justify the choice of a value smaller than the point estimate.The reason why the coe¢ cient of the labour share c also falls short of the calibrated

coe¢ cient, though the distance is again less than one standard deviation. This is dueto the fact that we have experimented with di¤erent computations of the labourshare in GDP. The alternative computation was based on real values of GDP andemployee compensation. The later computations methods generated a value of -0.12than the -0.1 we use in the simulations. It is not a priori clear which measure is moreappropriate. In fact to is common to interpret the labour share term as real wagesdivided by productivity (i.e. real GDP/hour or real GDP/ employee) and enter thesevariables separately.73 Furthermore, a reduction of c by 0.01 has only small e¤ects.

73Cahuc and Zylberberg (2004), p. 486 and OECD (1997), p. 21.

60

For the United States, we estimate the wage setting equation using the BLS serieson real hourly compensation, BLS series PRS85006153, to calculate � logwt; theseasonally adjusted unemployment rate, series LNS14000000Q, nominal GDP fromthe BEA NIPA table 1.1.5 and total nominal employee compensation from the BEANIPA table 2.1. In order to get a signi�cant coe¢ cient on the unemployment rate,we were forced to include �ve years more than in our estimate for Germany, and wethus started in 1965. The result can be obtained from Table E2. As expected, theLS is not signi�cant, which was result robust to adding and excluding observations.Re estimating the equation after dropping log (LSt�1) leads to an almost unchangedestimate of the coe¢ cient on the unemployment rate. Note that the coe¢ cients onthe unemployment rate in Germany is not statistically di¤erent from the coe¢ cientestimated for the U.S. at any reasonable level of con�dence.

61

Table E2Dependent Variable: WGMethod: Least SquaresDate: 06/03/08 Time: 16:03Sample: 1965Q1 2000Q4Included observations: 144Newey-West HAC Standard Errors & Covariance (lag truncation=4)

Variable Coe¢ cient Std. Error t-Statistic Prob.

C 0.005364 0.033562 0.159838 0.8732U -0.066995 0.033021 -2.028888 0.0444LS 0.003206 0.059322 0.054043 0.9570

R-squared 0.030102 Mean dependent var 0.003202Adjusted R-squared 0.016345 S.D. dependent var 0.006138S.E. of regression 0.006088 Akaike info criterion -7.344412Sum squared resid 0.005226 Schwarz criterion -7.282541Log likelihood 531.7977 F-statistic 2.188064Durbin-Watson stat 1.642216 Prob(F-statistic) 0.115927Table 13Dependent Variable: WGMethod: Two-Stage Least SquaresDate: 06/03/08 Time: 13:15Sample: 1965Q1 2000Q4Included observations: 144Instrument list: WG(-1) C U(-1)

Variable Coe¢ cient Std. Error t-Statistic Prob.

U -0.067605 0.032425 -2.084951 0.0389C 0.007253 0.002008 3.612856 0.0004

R-squared 0.030069 Mean dependent var 0.003202Adjusted R-squared 0.023238 S.D. dependent var 0.006138S.E. of regression 0.006067 Sum squared resid 0.005226F-statistic 4.347020 Durbin-Watson stat 1.643279Prob(F-statistic) 0.038864

62

16 Appendix F: Construction of the Dataset usedin the Moment Comparison

This appendix explains the construction of the dataset for Ft; Dt; Rt and Ht. TheGerman federal statistical o¢ ce ("Statistisches Bundesamt") supplies annual datafor the capital stock in constant prices of the year 2000.74 Thus we had to constructquarterly observations for the capital stock. We decided on the following method.We �rst calculated the annual change. Than we allocated the total changed to thefour quarters according to the share these quarters had in real gross �xed investment.This gave as a beginning of quarter value for the capital stock.Our data on real output, consumption and investment expenditure was preferably

also to be in prices of 2000. However, the Statistisches Bundesamt only supplieschained indices for these variables.75 We therefore used nominal GDP, consumptionand investment 2000 to recursively calculate our series in absolute numbers. As theindices for post and pre reuni�cation years have di¤erent bases, we used the ratioof uni�ed Germany to Western Germany from 1991 to downscale the index for eachvariable.Furthermore, as the total labour force in our model is normalised to one, Output,

consumption and investment are essentially expressed in per capita terms in ourmodel, as is the capital stock. Hence case of Ft; Dt and Rt; the number of inhabitantscancels out and we can divide real GDP by our capital stock measure, and accordinglyfor Dt and Rt. By contrast, Ht is computed by multiplying the real wage as measuredin the previous section times the average number of hours worked across the sample.We tried a linear trend for hours worked instead but this would have turned ourmeasure of Ht non-stationary.

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