Peter Stuart
email: p.stuart1@nuigalway.ie

Conall J Hawkins

D P Sleeman

Colin Lawton

J Conall

D P Hawkins

Colin Sleeman

Lawton

First record of Skrjabingylus petrowi (Nematode: Metastrongyloidea) in a pine marten Martes martes from Ireland

Keywords: Skrjabingylus petrowi, Martes martes, Nematoda, Parasite, Ireland

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Members of the family Mustelidae are the definitive hosts of the Metastrongyloid nematode of the genus Skrjabingylus Petrov, 1927. Skrjabingylus spp. are found within the frontal sinuses of their definitive hosts, and infection can result in abscesses, perforations and other damage to the skull [START_REF] Hansson | Cranial Helminth parasites in species of Mustelidae: I. Frequency and damage in fresh Mustelids from Sweden[END_REF]). Following [START_REF] Heddergott | First record of Skrjabingylus petrowi (Nematoda: Metastrongyloidea) in a pine marten (Martes martes) in Germany[END_REF] first record of the nematode Skrjabingylus petrowi in pine martens Martes martes from Germany, we identified S. petrowi in a pine marten from Ireland. Due to new legal protection of the pine marten in Ireland, its population is thought to be increasing and expanding into new areas [START_REF] Marnell | Ireland red list no. 3: terrestrial mammals, national parks and wildlife service. Department of the Environment, Heritage and Local Government[END_REF]. This is the first record of S. petrowi in Ireland and makes it the fifth record of S. petrowi outside Russia, where it was first described [START_REF] Heddergott | First record of Skrjabingylus petrowi (Nematoda: Metastrongyloidea) in a pine marten (Martes martes) in Germany[END_REF]). Prior to this, the only Skrjabingylus spp. reported from Ireland have been Skrjabingylus nasicola which was only found in the Irish stoat Mustela erminea hibernica [START_REF] Sleeman | Skrjabingylus nasicola (Leuckhart) (Metastrongyloidea) as a parasite of the Irish stoat[END_REF]). The skull we investigated was taken from a male (first-year age class by cementum analysis) road kill pine marten found in Roscrea, Co. Tipperary (52°57′ 0″ N, 7°49′ 0″ W). It has previously been reported that 90% of Russian pine martens from the first-year age class were infected with Skrjabingylus spp., decreasing to 50% once they passed 3 years of age [START_REF] King | The effects of the nematode parasite Skrjabingylus nasicola on British weasels (Mustela nivalis)[END_REF]. No perforations were observed in the skull. The skull was frozen, cut sagittally and immersed in a 0.7% saline solution so that nematodes could be extracted under a dissection microscope following the methods of [START_REF] Hansson | Cranial Helminth parasites in species of Mustelidae: I. Frequency and damage in fresh Mustelids from Sweden[END_REF]. All nematodes were examined with a light microscope to take morphological measurements and to determine sex. Twenty-three nematodes were removed, 13 from the right sinus frontalis (five males, eight females) and ten from the left sinus frontalis (five males, five females). The anatomical measurements taken were in agreement with those previously taken for S. petrowi (Table 1). One of the diagnostic features that distinguish Skrjabingylus spp. from each other is spicule length (Fig. 1). S. petrowi spicules have been previously recorded with lengths of 410 to 605 μm [START_REF] Heddergott | First record of Skrjabingylus petrowi (Nematoda: Metastrongyloidea) in a pine marten (Martes martes) in Germany[END_REF]. Spicule lengths measured in the specimens from the present study ranged from 410 to 500 μm (Table 1). This also puts the spicules measured outside the 150 to 324 μm range of measurements previously recorded for S. nasicola [START_REF] Heddergott | First record of Skrjabingylus petrowi (Nematoda: Metastrongyloidea) in a pine marten (Martes martes) in Germany[END_REF], the Skrjabingylus species previously recorded in Ireland. It is possible that S. petrowi was recently introduced to Ireland carried by an introduced host species. However, it is more plausible that it went undetected in Ireland until now. Apart from [START_REF] Sleeman | Skrjabingylus nasicola (Leuckhart) (Metastrongyloidea) as a parasite of the Irish stoat[END_REF] examination of two pine martens, we are not aware of any other investigation into the presence of Skrjabingylus spp. in pine martens in Ireland. The need for anatomical measurements of the nematodes to identify Skrjabingylus spp. to the species level is in agreement with [START_REF] Heddergott | First record of Skrjabingylus petrowi (Nematoda: Metastrongyloidea) in a pine marten (Martes martes) in Germany[END_REF] statement that cleaned skulls are not suitable for accurate diagnosis of infections of Skrjabingylus spp. This investigation also presents further evidence of [START_REF] Heddergott | First record of Skrjabingylus petrowi (Nematoda: Metastrongyloidea) in a pine marten (Martes martes) in Germany[END_REF] assumption that S. petrowi has a host preference for Martes spp. and that earlier records of S. nasicola in Martes spp. may have been erroneous.

Acknowledgements Thanks to Simon White who donated the pine marten. We are grateful to Mike Heddergott for confirming the nematode as Skrjabingylus petrowi. Thanks to Albert Lawless for help in preparing the photo and advice on microscopy. Thanks also to Heikki Henttonen for advice on preserving the nematodes. Peter Stuart is funded under the Research Stimulus Fund Programme by the Irish Department of Agriculture and Food. Conall Hawkins is sponsored by IRCSET, through the Embark Initiative. Thanks to two anonymous reviewers for comments on the manuscript.


Keywords: unemployment, work-sharing, VECM, France, forecasting E24, E27, C32 unemployment, work-sharing, France, VECM, forecasting

We analyze the macroeconomic impact of the French work-sharing reform of 2000 (a reduction of standard working hours in combination with wage subsidies). Using a vector error correction model (VECM) for several labor market variables as well as inflation and output we produce out-of-sample forecasts for 2000/2001. A comparison of these forecasts -which serve as a benchmark simulation without structural shifts-to the realized values (with shifts) suggests significant beneficial employment effects of the policy mix. Other shifts were absent and thus cannot explain the outcome. Output, productivity, hourly labor costs, and inflation are only transitorily affected or not at all.

Introduction

At the turn of the millennium, the French unemployment rate decreased by 2. 2%points (1999-2001) after more than a decade with stubbornly high unemployment.

The rest of the Eurozone experienced a decline as well, but the amount of 1.2%-points was markedly lower (see table 1 below for this and other basic data). An analogous feature can be observed in employment figures: after growth rates below average in 1995-1998, France experienced above average growth rates from 1999 to 2002. The rest of the Eurozone shared the tendency of the movement, but not quite its extent.

This development may partly be attributed to the above Eurozone-average real GDP growth in France (3.1% p.a. for France against 2.5% p.a. for the rest of the Eurozone in 1997Eurozone in -2001)). However, another event that had an important influence on the economic environment of France during this period was a "work-sharing" reform. A brief summary of the complex institutional setting could read as follows: On the one hand, the standard workweek was reduced from 39 to 35 hours, first on a voluntary basis coupled with incentive schemes conditional on employment creation (Robien act 1996, Aubry I act 1998), then on a compulsory basis (Aubry II act 2000). On the other hand the following alleviations were offered to firms: Greater managerial flexibility w.r.t. working time allocation (Robien, Aubry I), payroll tax cuts through lower social security contributions for employers (in all acts), and a negotiated mid-term wageincome growth restraint.

The explicit aim of this policy mix was to reduce unemployment levels. Thus it is interesting to analyze if the reform had any noticeable effect or if it was just ordinary economic growth that did the work. Also from the perspective of economic theory it is still an unsettled issue whether a reduction of standard hours (alone) will lead to more or less unemployment since in most models the outcome is in general ambiguous.

Earlier studies provided mixed results, see below, and a general consensus has not been reached. Recent empirical assessments of other work-sharing reforms have not been positive, see [START_REF] Hunt | Has Work-Sharing Worked in Germany?[END_REF] or Crépon and Kramarz (2002). But the respective German and French/1982 reforms included persistent hourly wage hikes as income compensation for workers and no alleviation for firms, such that the negative outcome is perhaps not too surprising. However, the institutional environment of the recent French reform was quite different which provides an interesting new perspective on the issue of work-sharing.

The existing literature in the context of the recent French reform falls into roughly three classes: First there were ex-ante simulations of several scenarios within macro models (see e.g. DARES-BDF-OFCE 1998), second there is descriptive evidence (e.g. [START_REF] Dares | L'approche par les modèles économétriques (Simulations à partir du modèle Mosaïque de l'OFCE et du modèle de la Banque de France)[END_REF], and finally micro data for selective samples of firms have been thoroughly analyzed [START_REF] Bunel | Les déterminants des embauches des établissements à 35 heures: aides incitatives, effets de sélection et modalités de mise en oeuvre[END_REF], Passeron 2002). For those studies that allow drawing conclusions with respect to employment effects, the results are mostly optimistic.

Our aim is to complement the literature by shedding some light on the macroeconomic consequences of the recent French work-sharing reform. To this end we estimate an empirical system of labor market variables (as well as inflation and output) using a vector error correction model (VECM) up to 1999. As there are two competing possible break dates (namely 1999q4 and 2000q1, see section 3 for detailed results), we actually estimate two slightly different models. With these models we can produce forecasts for the subsequent period, acknowledging the fact that those forecasts are based on the previous institutional regime. A comparison to actual observations after the introduction of the 35h work-week allows us to pinpoint significant changes.

For both models we get very similar results; we find that unemployment was reduced throughout the analyzed horizon at the cost of a transitory depression of total hours worked reflecting a short-run rise of hourly labor costs. Labor costs and inflation remain somewhat higher than their forecasts, but not significantly so. Output is forecast quite well in every period and in general seems unaffected by the break.

These results can be attributed to the work-sharing-cum-lower-costs reform because other forces that could have had an influence on the unemployment rate were absent: For example, the labor supply grew at normal rates (see [START_REF] Boulard | Comparison of Forecast and Actuality[END_REF], which makes our estimates even slightly conservative. National accounts data show that other stimuli such as an expansionary fiscal policy did not occur, and not even ECB officials or other pro-Euro economists claimed that the introduction of the Euro would fight unemployment; instead they have always called for structural labor market reforms. (Also recall that the Euro was adopted already in the beginning of 1999, not in 2000.) But even if these arguments are disputed, our real output forecast turns out to be surprisingly accurate, such that potentially stimulating business-cycle effects would be controlled for.

The rest of this contribution is structured as follows: In the next section we provide a brief survey of the relevant literature, we describe some institutional details of the reform, and we discuss estimates and implications of existing studies. Section 3 presents the data and explains our model specification along with the resulting forecasts. The final section summarizes the main findings.

[Tables 1 and2 about here] 2 Theory, institutions, and existing evaluations

A glimpse at the recent work-sharing debate

Economists are usually very critical about work-sharing due to the "lump-of-labor" fallacy, i.e. the assumption of a fixed labor input volume that is often implicitly made in public debates on the issue [START_REF] Layard | Unemployment -Macroeconomic Performance and the Labour Market[END_REF]Jackman 1991, Snower 1997).

But most of the theoretical studies yield ambiguous predictions depending on what the precise model or parameter values are.

For example, in the reference model of [START_REF] Calmfors | Work Sharing and Overtime[END_REF] even the most skeptical model variant predicts a definitely negative response of output and employment only if the overtime premium is constant. If a progressive premium system is allowed instead, the response becomes uncertain. The predictions of the model by [START_REF] Fitzroy | Working Time, Taxation and Unemployment in General Equilibrium[END_REF] are more optimistic, although it coincides with the conclusions in [START_REF] Marimon | Employment and Distributional Effects of Restricting Working Time[END_REF], where the possible employment creation would lower firms' profits. In contrast to that, a possible Pareto improvement is found in the matching models by Rocheteau (2002) and by [START_REF] Ortega | Working-time Regulation, Firm Heterogeneity, and Efficiency[END_REF], where lower standard hours may offer a firm more flexibility to react to demand shocks.

On the empirical side, the results are also mixed. Crépon and Kramarz (2002) analyze the reduction of 40 to 39 hours in 1982 for France. At that time full wage income compensation without reorganizational possibilities were the norm. Not surprisingly, they find a negative effect on employment. In [START_REF] Hunt | Has Work-Sharing Worked in Germany?[END_REF], a similar work-sharing reform without wage moderation is analyzed for West Germany in 1984-1994. De-. De-pending on the data set and method used she finds mostly insignificant coefficients of both signs. On the other hand, after conditioning on wages Franz and König (1986) find a positive partial effect of normal hours reduction on employment for West Germany (p. S241), although it is not mainly a study about work-sharing. 1 In contrast to former experiences, the reforms that recently took place in France implied working-time reduction against tax cuts and subsequent wage growth restraint. This policy mix therefore may have been more effective than earlier work-sharing attempts.

The institutional background in France

The shortening of the standard work-week was implemented in several stages. A first act to reduce working-time (named Robien) was passed in June 1996. This voluntary measure had only very little impact, covering only 0.3m employees between June 1996and June 1998(Passeron 2002).

The main reform project was implemented in two stages. First the Robien act was replaced by the Aubry I act in June 1998 which lowered the legally standard work-week to 35 hours. (Martine Aubry was the minister of labor between June 1997 and October 2000.) However, while it became effective for firms with more than 20 employees on January 1 st , 2000, smaller firms would not be affected until January 2002. Additionally an incentive scheme was introduced to promote a quicker effective work-week reduction. The most important exception in this legislation was the civil The Aubry I incentive scheme provided reductions of social security contributions for firms that effectively reduced the work-week and guaranteed a certain level of employment. A useful source for details is Passeron (2002). Among the firms with a work-week reduction up to the end of 2001, 58% participated in the Aubry I incentive scheme (this covers 28% of all workers that had their working time reduced).

The second stage (Aubry II, passed in December 1999/January 2000) confirmed the 39 to 35 hours transition and instated a system of structural aids. For bigger firms the Aubry I scheme was being phased out, whereas for smaller firms the end date is 2002. The structural aids depend on wage levels; the average tax reduction per year and employee was EUR 1067 (Passeron 2002); it was not conditional on guaranteed employment levels anymore. Furthermore the flexibility of varying weekly hours over the course of a year was increased. For a transition period of one year, the overtime premium for the first four hours was reduced from 25% to 10% (the next four hours remained subject to a 25% premium and hours beyond that must be paid at 150%). This working-time reduction was mostly accompanied by an initial wage income compensation (Pham 2002). For example, in 2000 98% of all employees covered by Aubry II enjoyed a full wage compensation; however, 1/3 had to accept a wage stagnancy and 14% a wage growth moderation for the following one to three years.

Finally it should be noted that in some sense the work-sharing experience is already history, because right after its election in early 2002 the new center-right government started to reverse the reform.

Previous evaluations

Apart from the already mentioned descriptive evidence in DARES (2002), the macroeconomic studies for France were based on ex-ante simulations e.g. within the macro models of the OFCE institute, the central bank (BdF), and the ministry of finance [START_REF] Plan | Réduction du temps de travail: les enseignements de l'observation[END_REF]. Depending on the various assumptions the assessment of the employment effects range from optimistic (up to 700,000 additional jobs in the simulations of the OFCE and of the BdF) to more sceptical (between 200 and 300,000 according to MINEFI, even negative if a blockade between unions and employers is assumed).

The existing microeconomic studies (based on observed data) use samples of firms with specific characteristics, apparently due to data limitations. Passeron (2002) for example only analyzes firms in the Aubry I scheme. He concludes that the employment gain induced by the work-week reduction is between 6 and 7.5%. (Effects where firms become eligible for subsidies without having been induced to meet the criteria are supposedly not included in those numbers.) The resulting productivity gain effect in his study is 4% which is a little more than what is often assumed on theoretical grounds. According to Passeron the government subsidies decreased total labor costs of the Aubry I firms by 4%. In addition to that, Passeron estimates a beneficial "anti-seniority" effect of 1%, because newly hired workers are cheaper relative to their productivity. Wage moderation is seen as 0.8%, such that altogether the work-week reduction was approximately cost-neutral over the horizon until 2002. This study is not representative for aggregates, and even the sign of the bias is ambiguous: Firms that waited until 2000 to reduce their work-week receive less subsidies but also have less restructuring costs. Another study for selected firms is [START_REF] Bunel | Les déterminants des embauches des établissements à 35 heures: aides incitatives, effets de sélection et modalités de mise en oeuvre[END_REF], who uses a special data set ("Passages") to compare all firms that reduced their effective weekly working time to 35 hours.

The existing macro evidence is only for scenarios, and it is not clear what the selective micro studies imply for the aggregate level. An empirical macro analysis therefore seems useful, and we now turn to it.

Variables and data

In the context of imperfect competition, prices and wages are set simultaneously by economic agents, see e.g. [START_REF] Layard | Unemployment -Macroeconomic Performance and the Labour Market[END_REF], where the unemployment rate gives some feedback to the system. Therefore we require the following variables: wages, prices, an employment measure, real output, and the unemployment rate.

For wages there are basically three possibilities: 1. Total compensation including social security contributions paid by employers, which represents the total cost of a labor unit; 2. "gross" wages that include only social security contributions and taxes paid by the worker herself; 3. net wages without taxes or contributions. For price setting and the labor demand total compensation is clearly the appropriate variable.

For wage setting the level of net wages could also be relevant, but we restrict ourselves to the total compensation measure, not least because net wages is a time series which is difficult to obtain.

Prices: For labor demand and price setting it is the GDP deflator which is important, while adding the consumer price index (CPI) would make sense for wage setting analysis. Here we chose to include only the GDP deflator. Note that both price indices display roughly the same development (not shown), such that the exclusion of the CPI is not problematic.

Employment can be the labor volume (in hours) or the number of employed people, where average working time links the two concepts. As the hours worked per person is a central variable for the present study we include both employment measures. For real output it is natural to choose real GDP, and the chosen unemployment rate is the one according to ILO definitions. W.r.t. the selected variable set it might be argued that potentially important variables are missing. Apart from the price/tax wedge and import prices, there are many possible extensions. For example capital user costs may play a significant role as part

F o r P e e r R e v i e w
of marginal costs, and labor demand could also depend on the sectoral composition of output. However, in this paper we do not follow up on these issues because our aim is to work with a manageable labor market model. By analyzing the described data set we have tried to follow a pragmatic middle-of-the-road approach.

The data are from the following sources: OECD, the French statistical office (IN-SEE), and the statistical department of the French labor ministry (DARES); all series are seasonally adjusted. The variable names, a survey of the sources and calculation methods are given in table 3. We present the analyzed time series in figure 1 with some anticipated transformations: LW Real t = LW t -LP Y t will denote the hourly real wage, and Inf l t = ∆LP Y t ( * 400) is essentially the first difference of the log price level, i.e. the inflation rate.

Our general sample choice is determined by two facts: Data on hours worked are only available from 1980 on, and it turns out that there is instability in the unemployment rate equation already towards the end of 1999, see the system analysis below for more details. Thus the estimation period is set to 1980q1-1999q3, where the first observations will be used as starting values for the necessary lagged regressors.

[Table 3 about here] [Figure 1 about here]

Preliminary univariate data analysis

Obviously the inflation rate displays a very persistent behavior, such that using the price level in the model would be difficult. But the inflation rate itself can well be included as an integrated series (I(1)) in the multivariate system. Instead of the nominal wage we therefore include the real wage "LWReal" (≡ LW -LP Y ) in the system.

The variable vector is thus given by:

y t = (U R t , LEM P t , LY t , Inf l t , LW Real t , LV ol t ) (1)
The results of standard unit root tests are shown in table 4. For all series the null

F o r P e e r R e v i e w
hypothesis of a unit root cannot be rejected, with the possible exception of the labor volume. This does not pose any problems per se, but another test in the system context would still be interesting (see below).

[Table 4 about here]

Before moving to the system analysis we perform a simple univariate forecast of unemployment after the reduction of standard hours. Here we apply the standard ARIMA model for the sample 1978q2-1999q3. We impose the unit root restriction and after eliminating insignificant terms arrive at an ARIMA(3,1,2) specification. The forecasts derived from this model beyond 1999q3 are displayed in figure 2 along with the forecast error confidence bands and the actually observed development. The development of UR is clearly overestimated; actually, this model treats the unemployment rate more or less as a random walk and thus simply sets the forecast close to the last observed value. This automatically raises the question whether the information contained in other variables enables us to produce better forecasts, or if the forecast failure is due to a policy-induced structural break.

[Figure 2 about here]

The multivariate forecasting model

Our statistical framework is the vector autoregressive model (VAR) with Gaussian innovations that is widely used in empirical macroeconomics. 2 We combine the n = 6 variables in the column vector y t for t = 1, ..., T , where in our case T refers to 1999q3 or 1999q4, depending on the model variant, see below. Then the VAR has the following shape:

y t = K k=1 Φ k y t-k + τ t + µ + t (2)
As deterministics a constant µ and a linear trend (serving as a proxy for technical progress etc., with coefficient τ ) are allowed. After the appropriate reparametrization

∆y t = Πy t-1 + K-1 k=1 Γ k ∆y t-k + τ t + µ + t (3)
We adopt the conventional denomination for the matrix of the cointegration vectors, β, and the matrix of adjustment coefficients, α, both of dimension n × r for a given cointegration rank r, such that Π = αβ . The linear trend can only appear in the cointegrating relations, i.e. we impose τ = αρ (ρ freely varying).

First a choice about the number of lags in the VAR needs to be made. We use a maximum of six lags, as this already means estimating 36+2 parameters in each equation. The Schwartz and HQ information criteria suggest K = 2, only the (inconsistent)

Akaike criterion chooses K = 6. However, because of remaining residual autocorrelation with two lags we are led to a choice of K = 3. A single outlier in 1984q1

(especially in the unemployment equation) distorts the otherwise Gaussian properties of the innovations, such that we include a restricted impulse dummy for that observation. 3 Then the residual diagnostics are fully satisfactory, see table 5.

[Table 5 about here]

The rank of the matrix Π is an important property of the system, although it is not as crucial for forecasts as it would be for other analyses. We apply the well-known

Johansen procedure accounting for a restricted trend, see table 6. [START_REF] Johansen | A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model[END_REF] shows that this test procedure is unbiased if the rank tests are interpreted as a sequence, starting from rank zero and stopping at the first insignificant test statistic. At first sight the standard trace test statistics (in the third column) are all significant, and thus the conclusion would be a (trend) stationary VAR without any unit roots in the system.

Apart from the fact that this would contradict the univariate unit root test evidence, it would be a highly unusual finding for macroeconomic time series.

However, the rank test is substantially oversized in small samples (i.e. it rejects too often although the null hypothesis is true), and thus this nominal result may be exaggerated. Fortunately, there exists a novel method to investigate this suspicion. for given models in small samples, compare that to the asymptotic value and derive the corresponding correcting factor. It is obvious that this factor depends on nuisance parameters that are asymptotically (and hence for the standard test setup) irrelevant.

The factor is applied to the measured test statistic and thereby the bias of the test is decreased. Simulation studies show a beneficial effect.

In order to calculate the Bartlett corrections for the last four null hypotheses, we estimated the VAR four times with the respective rank under the null to obtain the necessary estimates of the parameter matrices. These were entered into the program of [START_REF] Johansen | A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model[END_REF]; the lag length is still fixed at K = 3. The results of this procedure are provided in the last column of table 6, and the test conclusions change considerably:

We have to stop at H 0 : r = 4 when interpreting the sequence of corrected trace tests, as this is the first non-rejected hypothesis. This choice implies that n -r = 2 independent stochastic trends drive the system which is a reasonable property of such a model. The results are not entirely straightforward because of the fact thatviewed in isolation-H 0 : r = 5 is also rejected. However, this is irrelevant for the appropriate testing strategy of the Johansen procedure as explained before. Unreported evidence about the estimated characteristic roots of the system also supports the choice of exactly two unit roots. Therefore we proceeded with an imposed cointegration rank of r = 4.

[Table 6 about here]

It is beyond the scope of this paper to provide a structural analysis of the French labor market. This aspect and the relatively high cointegration rank induced us to refrain from an economic identification of the cointegrating relationships. However, we checked that no harmful normalizations were used, e.g. no zero parameters were normalized to unity.

We can now investigate a number of hypotheses within the cointegrated VAR:

First we return to the trend stationarity of the (log) labor volume. We test this as the The corresponding exclusion is clearly rejected (χ 2 (4) = 32.1, p = 0.00), so the trend is essential for an adequate model. Finally, note that output does not adjust to any equilibrium deviations (tested as a zero row in the α matrix, χ 2 (4) = 3.56, p = 0.47),

and is thus weakly exogenous for the long-run parameters. This partly explains why we find that output is mostly unaffected by the structural break, see below.

Stability of the model and choice of breakpoint

The final check of the model is about its stability. Especially for our purposes a stable specification in the estimation period is obviously a desirable feature because an unstable model would not yield meaningful forecasts.

Several recursively estimated test statistics indicate that parameter stability for the described sample up to 1999q3 clearly holds, see figures 3 through 5. This means that the quantitative impact of the previous reforms -Robien and Aubry I as described before-was small and could easily be subsumed under the error term.

[Figures 3,4, and 5 about here] However, based on the a priori information about the beginning of the reform we originally conjectured that any potential structural break should have happened in 2000q1. But when we add the observation 1999q4 to the estimation period, there is clear-cut evidence for instability at least in the unemployment equation (see figure 6), reflecting an unusual decline of the unemployment rate. As the coming reform was publicly known in the end of 1999, this suggests that announcement effects were already at work; the favorable product demand environment during that time probably helped, too.

[Figure 6 about here] Given these findings, our strategy for the forecast test is to check both breakpoints until T = 1999q3 as described before and start our system forecast immediately afterwards. For the 2000q1 break date variant, we extend the estimation period until T = 1999q4, but introduce an impulse dummy for the last observation to account for the significant stability failure documented in figure 6. (This impulse dummy is not restricted to the cointegration space.) Note that the second variant is quite conservative in the sense that no movements before 2000q1 are attributed to the work-sharing reform.

Before we apply the forecasting model, note also that several robustness analyses were done in the course of preparing this paper, varying both the number of lags, the cointegration rank, and applying several model reduction strategies. The forecasts on which our interest is centered were always very similar.

Forecasts and reality

Now we are in the position to answer the central question of this study, namely if the policy of reducing standard hours in combination with wage subsidies had a significant influence on the unemployment rate and other variables. To this end we compare the observed development of the vector y t until 2001q2 (i.e. y T +h , h = 1...H) and the corresponding dynamic forecasts y f T +h = E T (y T +h ), which are conditional on sample information up to T . These are computed recursively using the estimated VECM coefficient matrices. For the first variant we have T = 1999q3 and H = 7, whereas the second variant uses T = 1999q4 and H = 6 (with an impulse dummy in 1999q4).

Our approach is related to the test of Box and Tiao (1976) which however is about the joint significance of the forecast errors; a more detailed interpretation is possible by considering the forecast errors separately. (The variance formulae for the entire sequence of forecast errors can also be found in Clements and Hendry (1998).)

In line with our strategy of considering both 1999q3 and 1999q4 as potential breakpoints, we present two sets of corresponding graphs in figures 7 and 8. There are some quite interesting results to be pointed out: • The forecast of the unemployment rate (UR) falls slightly, but its confidence bands drift apart quickly and become extremely large. In spite of this the observed development of unemployment is significantly lower than the forecast.

• Consequently, the employment development (LEMP) is consistently underestimated. At the end of the forecast horizon the discrepancy of the forecast w.r.t.

reality constitutes about 0.5 million additional employed workers.

• The real output (LY) is forecast surprisingly well, so in this sense no extraordinary goods market developments were responsible for the fall of the unemployment rate.

• There is nothing important to be seen in the inflation path, especially no dramatic rise because of rising labor costs. However, the reliability of the forecast is very low, given the extremely wide confidence bands stretching far into the negative range.

• W.r.t. real hourly labor costs (LWReal) there is an unpredicted increase in the beginning despite the paid subsidies. (The maximal difference between reality and forecast is about 2%.) This is not surprising since an initial income compensation had been negotiated which represents a short-run hourly wage hike.

However, this is gradually eliminated by subsequent wage growth restraint.

• Finally we observe a quite drastic slump of the labor volume (LVol) especially in 2000q1, although this is slowly offset in the following quarters. It seems as if the path of the labor volume relative to its forecast were partly a mirror image of the development of labor costs. One would probably not have expected that the labor volume after seven quarters is hardly distinguishable from its (forecast) normal path.

During the forecast horizon higher labor costs correspond to higher productivity (LY -LV ol) and somewhat higher inflation, although not all these deviations are significant. Towards the end of the forecast horizon average hourly productivity is These developments make sense in a model where the increased individual productivity due to less working hours is subsequently offset by lower productivity of the formerly unemployed. It also implies that the labor cost subsidies were an important factor of the policy mix.

As was already mentioned in the introduction, other obvious effects that might have affected unemployment were not present during the forecast period. For example, there was no hidden expansion of active labor market policies; the number of the covered workers even dropped in 2000 [START_REF] Boulard | Comparison of Forecast and Actuality[END_REF]. Overall fiscal deficits were also reduced in comparison with the 1998-1999 period (source: INSEE national accounts data). There was no sign of other labor supply shifts happening (again, see the labor force developments in table 1), and the overall economic climate is captured quite well by our implicit empirical output model.

Hence we conclude that there exists relatively strong evidence that the French work-sharing-cum-labor-cost-subsidies reform was responsible for the lower unemployment rate at least in 2000-2001 and in this sense was successful.

Summary

As the effects of a reduction of standard hours are not predictable on purely theoretical grounds, it is the task of empirical studies to determine the efficacy of such policy options. The present paper provides evidence for the case of France, where a reduction of weekly standard hours in the beginning of 2000 was accompanied by subsidies of the social security contributions.

Detailed firm level data only exist for subgroups of firms that are not representative; also, labor demand is only part of the story behind unemployment and wage developments. Therefore we used aggregate data to measure possible influences of the reform. We specified an empirical macroeconomic labor market model and examined the differences between observed data and the dynamic model forecasts in the horizon between the end of 1999 and mid 2001. Given that the economic environment is either captured within our model (most importantly demand conditions) or remained stable in France during our forecast period (most importantly active labor market policy), the effect can only be attributed to the mentioned reforms.

Our analysis of the development of unemployment and other variables in France imply that the reduction of standard hours in combination with the offered wage subsidies was at least partly successful. This finding is significant in the sense that it holds after accounting for the forecast uncertainty. Although there was a short-term wage push and the labor input volume (in hours) displayed a sudden slump (implying higher productivity in the short run), wages and labor demand afterwards slowly recovered from this disturbance. Together with the shorter working hours, this meant that the employment level grew faster than its forecast. But above all, the unemployment rate fell more than would have been predicted on the basis of the old policy regime. Real output as well as the inflation rate seemed relatively unaffected.

Given the various preceding stages of the work-sharing reform project, our approach of dating the structural break not earlier than 1999q4 may be criticized, although the average working time data in table 2 reveal that notable changes only occur around 1999q4/2000q1. Furthermore, our model is empirically stable until the end of 1999 which also suggests that the effects of the preliminary reforms are not quantitatively important. But even in a broader sense an earlier and "smoother" structural break would not invalidate our analysis, either: The observed decrease in unemployment in 1998-1999 is not counted as caused by the reform by choice of our breakpoint date.

Therefore, our tests are actually somewhat conservative in the sense that the overall impact of the reform in terms of unemployment reduction was probably even bigger.

All things considered, the mix of imposing restructuring costs on firms while at the same time offering cost alleviation in favor of unemployed workers apparently was a good choice. But of course this relatively radical reform only helped roughly one fifth of all unemployed, and unemployment in France remained a mass phenomenon. This list of empirical studies is of course not complete, but conveys the status quo of the research, namely that evidence is diverse, and that a consensus has not been reached. Further references are given in [START_REF] Ortega | Working-time Regulation, Firm Heterogeneity, and Efficiency[END_REF], [START_REF] Marimon | Employment and Distributional Effects of Restricting Working Time[END_REF], and [START_REF] Hunt | Has Work-Sharing Worked in Germany?[END_REF]. The link between actual hours and legal hours was studied for the U.S. by Trejo (1991) and [START_REF] Costa | Hours of Work and the Fair Labor Standards Act: A Study of Retail and Wholesale Trade, 1938-1950[END_REF], arguing that work-sharing is irrelevant if firms and workers negotiate a constant compensation/workload-package. They find non-neutrality of lower working hours, whereas in Trejo ( 2001) irrelevance of worksharing cannot be rejected.

2 For a textbook treatment see Lütkepohl (1991), and for the theory of a VAR with cointegration [START_REF] Johansen | A Small Sample Correction for the Test of Cointegrating Rank in the Vector Autoregressive Model[END_REF]. The reported results were computed mainly with Pc-Give 10, see [START_REF] Doornik | Modelling Dynamic Systems Using PcGive 10[END_REF], with the exception of the Bartlett correction of the rank test which was performed with the program for RATS mentioned in Johansen (2002).

3 "Restricted" means that the impulse dummy i84q1 t ({. . . , 0, 0, 1, 0, 0, . . .}) is only allowed in the levels of the data and not in the differences. This is achieved by including i84q1 t in the cointegration space and its difference ∆i84q1 t unrestrictedly in the VAR.

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A Data Appendix

The DARES publishes the average working time of full-time employees in each quarter on the basis of the ACEMO survey carried out among employers. However, this data covers only plants with more than ten employees in the non-agricultural private sectors (hereafter competitive sector, excluding civil service, health services, etc. with about 6

to 7 million employees in the 1990's). This is equal to the average working-time of all employees under two assumptions: first full-time employees of small plants (less than 10 employees) work as long as those in medium and large companies, and second, the working time in the competitive sector is the same as in the rest of the economy. (As we use the log of the data, a weaker assumption is actually sufficient, namely that the ratio of the different working hours is constant.)

The INSEE provides the number of full-time equivalent employees, thus part-time effects are corrected for.

The volume of paid hours is thus the product of the average working time of all full-time employees and the number of full-time equivalent employees. Remarks: Test statistics based on forecasts from a fixed date on the left of the x-axis until the respective dates on the x-axis, and scaled relative to the 5% critical value which is normalized to unity.

  not state-owned firms). There were about 16m employees potentially affected by this reform[START_REF] Dares | L'approche par les modèles économétriques (Simulations à partir du modèle Mosaïque de l'OFCE et du modèle de la Banque de France)[END_REF], of which about one third worked in small firms. (The overall number of employees in France in 2001 was about 22m people.)

  . For a survey see Conseil Supérieur de l'emploi, des revenus et des coûts (1998), DARES-BDF-OFCE (1998), or Commissariat Général du

  error correction model (VECM) is obtained:

  1999q4 and 2000q1 in the following way: For 1999q4, we simply estimate the model 13

[

  Figures 7 and 8 about here]

  Figures

Figure

  Figure 3: Recursive eigenvalues

  Figure 4: Chow breakpoint tests

Figure

  Figure 5: Chow forecasts tests

  Figure 6:

  table 1), if not faster than usual. The coverage of active labor market policy actually declined somewhat

	during our forecast period
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Page 13 of 32 Editorial

  hypothesis that LVol alone is one of the components of the cointegration space. The LR test of this restriction cannot reject, with χ 2 (2) = 3.76, p = 0.15. A second interesting question is whether the linear trend is actually needed in the cointegrating relations.

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19 of 32 Editorial

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Table 1 :

 1 Comparison of the macroeconomic context between France and the Eurozone All numbers are growth rates (yoy) in %, except for the unemployment rate, which is in level and in %. "EU" is the Euro area. 1 AMECO, own calculations 2 EUROSTAT, own calculations 3 harmonized 4 labor force statistics 5 measured as output per head Source: AMECO, Eurostat, own calculations

	1up CHOWs system	1%
	Remarks: The Chow test statistics are based on recursive 1-step forecast errors that are scaled
	relative to the (1%) critical value which is normalized to unity.

Table 2 :

 2 Different measures of working time

Table 3 :

 3 Description of the data Tests are for the 5% and 1% level, an asterisk denotes significance at the 5% level. Lags refer to lagged differences. Several results per variable are reported if the lag specification is ambiguous.

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	Abbrev.	Meaning	Source / details
	UR	unemployment rate	Standardized unemployment rate (ILO
			concept) from the OECD.
	LEMP	number of employed workers	Source INSEE.
		(log of)
	LY	real GPD (1995 prices, log of)	From OECD Main Economic Indica-
			tors (MEI).
	LPY	GDP deflator (log of)	From OECD MEI. The first difference
			(times 400 to achieve approximate an-
			nual growth rates) is the inflation rate
			measure, Inf l t ≡ 400 * ∆LP Y t .
	LW	hourly wage (log of)	Total compensation taken from the
			quarterly national accounts of the
			OECD (QNA) and then divided by the
			labor volume, see below.
	LVol	labor input volume of employed	See the appendix.
		workers (hours, log of)
		30

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK * Remarks:

Table 5 :

 5 Diagnostic tests for the levels VAR with three lags ∆U R t ∆LEM P t ∆LY t ∆Inf l t ∆LW Real t ∆LV ol t absence of autocorrelation (1-5), F(5,47)

	.23	.82	.44	.28	.81	.34
			normality, χ 2 (2)
	.42	.16	.63	.25	.41	.22
			absence of ARCH (1-4), F(4,30)
	.49	.83	.61	.42	.54	.14

Remarks

: Sample 1981q2-1999q3

. The levels VAR with K = 3 lags is unrestricted in terms of cointegration. Deterministics: linear trend, constant, an impulse dummy for 1984q1 and its difference (see text). Numbers are marginal significance levels

(p-values)

.

Table 6 :

 6 Johansen cointegration test eigenvalue H 0 : r ≤ trace stat. nominal pvalue

	Bartlett corrected
	trace stat.

Remarks:

Sample 1981q2-1999q3, 3 lags (i.e. 2 lagged differences)

, restricted trend and restricted impulse dummy for 1984q1 (see text). Significance denoted by * (5%) and ** (1%). For the Bartlett correction see the text.

Acknowledgments: We wish to thank participants of the Berlin Econometrics Seminar, EALE, Ecomod, and EEA meetings as well as Michael Funke, Bernard Salzmann, and an anonymous referee for helpful comments, and Nathalie Fourcade for help with the data. We remain responsible for any mistakes.


Simulation < E3 -Prices, Business Fluctuations, and Cycles < E -Macroeconomics and Monetary

Keywords: inflation variability, factor models, combination of forecasts

The combination of individual forecasts is often a useful tool to improve forecast accuracy. The most commonly used technique for forecast combination is the mean, and it has frequently proved hard to surpass. This paper considers factor analysis to combine US inflation forecasts showing that just one factor is not enough to beat the mean and that the second one is necessary. The first factor is usually a weighted mean of the variables and it can be interpreted as a consensus forecast, while the second factor generally provides the differences among the variables and, since our observations are forecasts, it may be related with the dispersion in forecasting expectations and, in a sense, with its uncertainty. Within this approach, the paper also revisits Friedman's hypothesis relating the level of inflation with expectations uncertainty at the beginning of the 21st century.

Introduction

It may be common to have several sources of information that can be used to build different forecasts for the same economic indicator. The combination of such forecasts might be a useful tool to improve forecast accuracy. This paper considers the combination of individual forecasts for US inflation from the Survey of Professional Forecasters, provided since 1990 by the Federal Reserve Bank of Philadelphia.

The combination of individual forecasts is known to improve forecast accuracy since the work of [START_REF] Bates | The combination of forecasts[END_REF] and [START_REF] Newbold | Experience with forecasting univariate time series and the combination of forecasts[END_REF], among others. Recent surveys on this topic can be found, for instance, in [START_REF] Clemen | Combining forecasts: A review and annotated bibliography[END_REF], Diebold and Lopez (1996) and Newbold and Harvey (2002). There are a large number of alternatives to combine forecasts. The most commonly used is the equal weights for all the panelists (mean), that has been proved hard to beat by most sophisticated alternatives, like basing the weighting mechanism in the variancecovariance matrix of the forecast errors or ridge regressions, among others, (see, for instance, [START_REF] Stock | Combination forecasts of output growth in a seven-country data set[END_REF].

One of the most frequently tools used to achieve dimensionality reduction is Factor Analysis.

In the context of time series analysis, some references related to this topic are, for instance, [START_REF] Anderson | The use of factor analysis in the statistical analysis of multiple time series[END_REF], [START_REF] Priestley | Applications of principal component analysis and factor analysis in the identification of multivariable systems[END_REF], [START_REF] Box | A canonical analysis of multiple time series[END_REF], [START_REF] Geweke | Maximum Likelihood Confirmatory Analysis of Economic Time Series[END_REF], [START_REF] Brillinger | Time series Data Analysis and Theory[END_REF], [START_REF] Velu | Reduced rank models for multiple time series[END_REF], [START_REF] Peña | Identifying a simplifying structure in time series[END_REF], Stock and Watson (2002a), [START_REF] Tiao | Model specification in multivariate time series[END_REF], [START_REF] Reinsel | Elements of Multivariate Time Series Analysis[END_REF] and [START_REF] Ahn | Inference of vector autoregressive models with cointegration and scalar components[END_REF], among others. Some applications using price data are [START_REF] Stock | Forecasting inflation[END_REF] and [START_REF] Nath | Relative importance of sectoral and aggregate sources of price changes[END_REF].

As the combination of forecasts can be seen as a dimension reduction problem (from I panelists forecasts to just a single forecast), we consider the use of factor analysis as a tool to extract the common information to produce a consensus forecast and to reveal the degree of disagreement Figlewski (1983) and Figlewski and Urich (1983), who focused on forecast errors, and by [START_REF] Chan | A dynamic factor model framework for forecast combination[END_REF] who used an approximated factor model for the forecasts from different time series approaches. In this paper we compare the forecast accuracy of one and two factor models to combine forecasts of US inflation. Our endogenous variables in the factor model will be the predictions provided by different panelists. The first factor is usually a weighted mean of the observations (in this case, the individual forecasts), so with this factor we expect similar results to the equal weights approach. The second factor generally provides the differences among the variables and, since our observations are forecasts, our conjecture is that it may be related with the dispersion in forecasting expectations. We will analyze the potential usefulness of the second factor as a proxy of uncertainty in inflation, and check its relationship with the level of inflation and its ability to improve forecasting performance. In this sense, we would revisit [START_REF] Friedman | Inflation and Unemployment[END_REF] hypothesis.

The paper is organized as follows. In section 2 we describe the data. In section 3 we present the factor model and the forecasting combination rule. In section 4 we report the estimation and initial forecasting results of the one and two factor models. In section 5 we explore the capabilities of the second factor as a measure of uncertainty and check its forecasting performance with the previous models. Finally, in section 6 we conclude. the Consensus Forecast do not fill our requirements because of their periodicity or because they provide the forecasts for the mean of the year and, in that case, the forecasts are updated for the same time period but with different information sets.

The data

The Survey of Professional Forecasters was thoroughly analyzed by [START_REF] Zarnowitz | Twenty-two years of the NBER-ASA quarterly economic Outlook Survey: Aspects and Comparisons of Forecasting Performance[END_REF] who found that the forecast combination of many of these individuals provided a consensus forecast with lower average errors than most individual forecasts. Also, the survey performed favorably in forecast accuracy in comparison with a variety of econometric and time series models.

For instance, [START_REF] Batchelor | Empirical measures of inflation uncertainty: a cautionary note[END_REF] analyses a variety of proxies for inflation uncertainty based on survey and time-series approaches and they find that survey-based proxies for inflation seem less misleading than the time series proxies. [START_REF] Dutt | Inflation expectations: are they rational? An empirical examination[END_REF] have also assessed the rationality of inflation expectations from this survey, though in a weak form. Engsted (1991) and [START_REF] Berk | Measuring inflation expectations: a survey data approach[END_REF] have found the same conclusion using data from surveys in the UK and the Netherlands, respectively. Most recently, [START_REF] Baghestani | On the rationality of professional forecasts of corporate bond yield spreads[END_REF] 3 The model Let y t+1|t,i be the one period ahead forecast, with information up to time t, given by individual forecaster i, i = 1, 2, ..., I. Let y t+1|t = (y t+1|t,1 , ..., y t+1|t,I ) 0 be an I-dimensional vector of inflation forecasts. We use a factor model to separate the common information contained across the I forecasts, from the specific one to each forecaster. Consider the r-dimensional vector of common factors m t = (m t,1 , ..., m t,r ) 0 , r < I. Then, it can be assumed that the forecasts can be generated by a linear combination of the common information plus the specific components or error terms, such that

y t+1|t = Λm t + e t , (1)
where Λ is an I ×r factor loading matrix, and e t = (e t,1 , ..., e t,I ) 0 is the vector of specific errors.

Therefore, all the common correlated information comes through the common factors, m t , and the vector e t contains information specific to each time series forecast. The error terms are assumed to have a diagonal variance-covariance matrix, since if there were any information correlated among two terms in e t , it should be captured by the term Λm t . We assume, furthermore, that cov(m t , e t )=0. As it is explained in [START_REF] Chan | A dynamic factor model framework for forecast combination[END_REF], this assumption is not restrictive if joint normality is assumed.

We will follow [START_REF] Forni | The generalized factor model: Identification and estimation[END_REF] and Stock and Watson (2002a) who use the principal components to consistently estimate the dynamic factors. In this case, the factor models are known as approximate factor models and the procedure consists in estimating the r common factors through the first r principal components of the variance-covariance matrix of y t+1|t .

Approximate factor models have been proven useful in forecasting macroeconomic variables (see Stock andWatson, 2002b andFavero et al., 2004). Let v i be the eigenvector associated to the ith largest eigenvalue of the variance-covariance matrix of y t+1|t . Then, the i-th principal component (which is a consistent estimate of the i-th

common factor) is estimated as b m it = v 0 i y t+1|t . Let b m t = ( b m 1t , ..., b m rt ) 0 be the first estimated r principal components.
The factor combining rule to produce a single one step ahead forecast b y * t+1|t from all the sources of information is given by

b y * t+1|t = b β 0 + b β 1 b m 1t + • • • + b β r b m rt , (2)
where b β = ( b β 0 , ..., b β r ) 0 is the ordinary least squares estimate from the regression

π t = β 0 + β 1 b m 1t-1 + • • • + β r b m rt-1 + error t ,
with π t the observed inflation at time t. Notice that b y * t+1|t are true ex-ante forecasts since the coefficients β i are estimated only with information up to time t and do not include any information of the forecasting sample.

Estimation and initial forecasting results

We consider one period ahead forecasts from the first quarter of 1991 until the last quarter of 2002. The initial number of panelists was approximately 30 but it had to be reduced to 14 as we had to choose those individuals who systematically collaborate, that is, they have been in the panel for a minimum of seven years and did not miss more than four consecutive forecasts. This might introduce some selection bias, but it is done in this way in order to treat the missing data and obtain a balanced panel of forecasts. This has been done previously in the literature since it avoids biases due to changes in panel composition. See, for instance, [START_REF] Batchelor | Empirical measures of inflation uncertainty: a cautionary note[END_REF] who restrict their analysis to the 21, from 60 original respondents, forecasters who contributed consistently over the sample period they analysed.

As regards missing data, in this setup, they are one step ahead inflation forecasts that were not given by some individuals in a particular period of time.

As every individual provides one to four periods ahead forecasts, we can substitute the missing data by the forecast that the same individual provided for that period in the previous quarter, that is, the two period ahead forecast. If this datum were also unavailable, we would consider the three period ahead forecast and so forth. This is the reason why we can only consider panelists that do not miss more than four consecutive forecasts. This procedure is intended to preserve the special features of each forecaster. As an alternative to this option we could take the average of the remaining forecasts at that point of time. But this would annihilate the panelists own characteristics and would provide a downwards bias in the estimation of the forecast dispersion. With these considerations in mind, the final sample considered goes from 1991-III to 2002-IV and for this period both inflation and one period ahead inflation forecasts might be considered as stationary.

The model is estimated with one and two common factors. It is common practice in the literature to take as benchmark, for comparison purposes, the average of forecasts (see, for instance, [START_REF] Batchelor | How useful are the forecasts of intergovernmental agencies? The IMF and OECD versus the consensus[END_REF] and this is the approach we have taken. Our benchmark forecast will be the average forecast of the 14 panelists. Therefore, the procedure to analyze the different forecast combinations is as follows:

1. We use the data, 1991-III to 1999-IV to fit one and two factor models, as well as the benchmark forecast.

2. Then, the fitted models will be used to generate one-step-ahead forecasts for the years in be reestimated adding one data point at the time, using all previous data prior to each forecast period.

3. Forecast errors will be computed for each forecast period. The root mean squared errors (RMSEs) by model will be computed to verify the forecasting performance of alternative forecast combinations.

Trying to verify the robustness of our forecasting exercise, a similar procedure is also repeated later, for different estimation and forecasting samples.

To illustrate the estimation results, figure 1 shows the factor loadings for the 1st and 2nd common factors using the whole sample. It can be seen that the first factor is a weighted mean of the observations. The interpretation of the second factor is as follows: in figure 1 it is shown that the second eigenvector gives positive weights to some individuals and negative to others, so this second factor opposes the expectations in forecasting inflation of the different panelists. As our observations as forecasts, a measure of the magnitude of this second factor might be related to the expectations uncertainty on the future of inflation.

To decide on the number of common factors we follow Stock and Watson (2002b) who considered factor models until they account for more than 50% of the total variance. In our case, the first factor accounts for 45% of the variance and the second one adds 13%, so with these two common factors together more than 50% of the total variance is explained.

Figure 1 goes around here. show the RMSE ratios of the 1 and 2 common factors forecast combination methods respectively.

The fifth column will be analyzed in the next section.

Table 1 should be around here

These results point out that just one factor is not enough to beat the mean, and that the second factor seems necessary to improve forecast accuracy. Nevertheless, in the next section we will explore in more detail the potential contribution of the second factor.

5 Uncertainty in inflation expectations [START_REF] Friedman | Inflation and Unemployment[END_REF] remarks the importance of uncertainty in inflation expectations, suggesting a positive correlation between the level of inflation and inflation uncertainty. Since then, many articles have attempted to measure inflation uncertainty. [START_REF] Engle | Estimates of the variance of US inflation based upon the ARCH model[END_REF]), Capporale and McKiernan (1997), Belton et al. (2002), or more recently [START_REF] Kontonikas | Inflation and inflation uncertainty in the United Kingdom, evidence from GARCH modelling[END_REF] employ ARCH and GARCH techniques to estimate this uncertainty with mixed results. [START_REF] Bomberger | Interest Rates, Uncertainty and the Livinsgston Data[END_REF], [START_REF] Bomberger | Disagreement as a Measure of Uncertainty[END_REF] and [START_REF] Shoesmith | A further interpretation of Friedman's hypothesis: the cointegration of component CPI indexes[END_REF] interpret inflation uncertainty in terms of the intramarket price variability and [START_REF] Cukierman | Differential Inflationary Expectations and the Variability of the Rate of Inflation: Theory and Evidence[END_REF] and [START_REF] Zarnowitz | Consensus and Uncertainty in Economic Prediction[END_REF] take the variance of inflationary expectations from survey data as a proxy for the variance of the inflationary process. We proceed as in [START_REF] Cukierman | Differential Inflationary Expectations and the Variability of the Rate of Inflation: Theory and Evidence[END_REF] and [START_REF] Zarnowitz | Consensus and Uncertainty in Economic Prediction[END_REF] relating the dispersion in the survey data with uncertainty in inflation in the context of our two factors model.

We have seen that the first factor is a weighted mean of the forecasts. The contemporaneous correlation between the first factor and the mean of the forecasts is 0.96. Given such a high correlation between the first factor and the mean it explains why there should not be much gain in using just one factor models. The second factor opposes the expectations in forecasting inflation of different panelists, so a measure of the magnitude of this second factor might be related to the uncertainty in forecasting. The contemporaneous correlation between the squared second factor and the variance of the inflationary expectations forecasts is 0.71 which gives and idea of the strong relationship between both measures; and it is a little smaller between the absolute value of the second factor and the standard deviation of the inflationary expectations.

During most of the nineties, US inflation rates have become lower and less variable, but relevant events have occurred in our forecasting sample (years 2000, 2001 and 2002) that could have introduced a higher level of uncertainty in inflation expectations. We propose to test Friedman's hypothesis introducing the absolute value of the second common factor as an additional regressor to explain the level of inflation

π t+1 = β 0 + β 1 b m 1t + β 2 b m 2t + β 3 | b m 2t | + error t+1. (3)
We expect β 3 to be positive if the level of inflation is positively correlated with the level of uncertainty.

The fifth column of table 1 shows the ratios of the RMSE of the factor model accounting for uncertainty over the RMSE of the benchmark forecast. The big improvement -the ratio is 0.54obtained in the last part of the sample might be seen in the context of greater uncertainty of the economy during the period analyzed. 43% to 47% after its inclusion. However, this might be due to the characteristics of the sample period analyzed where inflation during the nineties has been most of the time under control, except perhaps for the last two years, where the forecasting improvement is clear as we have seen previously.

Concluding Remarks

Factor analysis seems a reasonable alternative to combine US inflation forecasts, but as it has been seen just one factor may not be enough to beat the forecasts average. A second factor seems necessary to improve forecast accuracy, measured in terms of the RMSE. This second factor is interpreted as a measure of dispersion in inflationary expectations since it gives positive weights to some panelists and negative to others, pointing out the differences amongst them. The magnitude of this dispersion, measured as the absolute value of the second factor is also helpful when forecasting the level of inflation.

Inflation during the nineties became lower and more stable with the absence of economic recessions (except for the one in 1991), but the beginning of the 21 st century was shocked by relevant social events, like September 11 th terrorist attacks, that introduced higher levels of uncertainty in the whole economy and, therefore, in US inflation.

  forecasters. The one factor model has previously been used in forecast combination by

  has found that the multiperiod forecasts of the corporate bond yield spread from the Survey of Professional Forecasters are generally unbiased and consistently outperform the comparable ARIMA forecasts.

5

  Page

  our forecasting sample, 2000-I to 2002-IV. In order to obtain one step-ahead forecasts,

9

  Page

For a better understandingPage

  of this improvement in forecasting, we present the estimation results by OLS of the model with the whole sample where t-values are given in parenthesis. The highest correlation coefficient between the estimated 10 (less than 0.1), so | b m 2t | adds valuable additional orthogonal information when trying to explain inflation. The positive value of the coefficient related to |m 2t | might be interpreted in the sense of Friedman's hypothesis meaning the relationship between uncertainty and higher inflation rates. The coefficient for |m 2t | is not highly significant, the reduction of the estimated residual standard error goes from 0.754 to 0.738, and the R 2 increases only from

Figure 1 :

 1 Figure 1: Factor loadings for the 1st and 2nd common factors (left and right panels respectively).

  This paper considers the individual forecasts for US inflation from the Survey of Professional Forecasters, provided since 1990 by the Federal Reserve Bank of Philadelphia. This Survey gives It is distributed free of charge and its forecasts are widely watched as they are reported in major newspapers like the Wall Street Journal and on financial newswires. The forecasts are anonymous and do not reflect the ideas of the institutions they belong to. It is conducted quarterly and, at each moment in time, it provides the last observed value and forecasts for one to five quarters ahead of the annualized growth rate, that allows us to have real one period ahead forecasts. Other surveys like the Livingston Survey, the Blue Chip Economic Indicators, the National Association of Business Economists (NABE) or

	regular inflation forecasts from private sector economists (Wall Street financial firms, banks,
	economic consulting and other private firms).
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  Table1compares the forecasting results in terms of the ratio of the RMSE of the different factor models over the RMSE of the average forecast (benchmark forecast) for different samples.

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	8

Table Table 1

 Table Friedman's hypothesis to check if the uncertainty in inflation expectations is nowadays still related to the level of inflation. We have found that including a measure of uncertainty resulted in more accurate forecasts.Further work should include the extension of our results to forecast other macroeconomic aggregates and check wether factor analysis still appears as a reasonable alternative to combine expectations. Also, it would be desirable to analyse deeper the interpretation of the two first common factors, both, from a theoretical and an empirical points of view. Engsted, T. (1991) A note on the rationality of survey inflation expectations in the United Kingdom, Applied Economics, 23, 1269-1276. Favero, C., Marcellino, M, and Neglia, F. (2004) Principal components at work: the empirical analysis of monetary policy with large data sets, Journal of Applied Econometrics, forthcoming. Figlewski, S. (1983) Optimal Price Forecasting Using Survey Data, The Review of Economics and Statistics, 65, 13-21. Figlewski, S. and T. Urich (1983) Optimal Aggregation of Money Supply Forecasts: Accuracy, Profitability and Market Efficiency, The Journal of Finance, 28, 695-710. Ratios of the RMSE of the different factor models over the RMSE of the average forecast (benchmark forecast).

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	8 Initial Estimation Sample Forecasting Sample 1 Factor 2 Factor 2 Factor + Uncert. 9 Figures
	0.4
	F o r F o r F o r F o r F o r F o r F o r 1991-III to 1999-IV 1991-III to 2000-IV 1991-III to 2001-IV F o r	2000-I to 2002-IV 2001-I to 2002-IV 2002-I to 2002-IV	1.00 0.96 1.28	1.00 0.94 0.89	0.99 0.92 0.54
	P e e P e e P e e P e e P e e P e e P e e P e e
		r r r r r r r r
		R e v R e v R e v R e v R e v R e v R e v R e v
		i e i e i e i e i e i e i e i e
			w w w w w w w w
				In this sense, we revisited
		11 18

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK 12 Page 13 of 20 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Submitted Manuscript


R11 -Regional Economic Activity: Growth, Development, and Changes < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics, R12 -Size and Spatial Distributions of Regional Economic Activity

On the basis of a relatively free trade world and global economy, specialisation tends to increase the comparative advantages of a country. But in this scenario, not countries but cities are the territorial organization that play the main role. Cities concentrate the economic activity and political influential household that reflects economic changes.

The purpose of this study is to explore the principles underlie the distribution of population on a territory and the likely effect of economic development on redistributing population geographically.

Introduction

Many attempts have been made to explain the distribution of population over territory.

Recently this question has become more significant, especially for less developed countries as they experience the rapid urbanization following World War II, which is today qualitatively different from the patterns followed in developed countries [START_REF] Kirsi | Agglomeration Economies in the Finnish Manufacturing Sector[END_REF]Taylor,1998;Tolley and Thomas, 1987). Urbanisation, city size, and migration have been seen only as demographic problems.

Cities are considered synonymous with poverty, pollution and so on. Governments have made various efforts to control population size in cities, however, most attempts have not taken into account what determines the distribution of population over territory. The main objective of this paper is to discuss the relationship between economic development and population distribution.

For centuries, city locations depended on the presence of natural resources (water, fertile soil, coal, etc.). Nowadays, changes in population distribution appear to be more complex. Many scholars who wrote about the genesis of urban concentration affirm that the formation of cities resulted from technological innovations in the countryside. The new technology increased agricultural production and generated a On the other hand, [START_REF] Kirsi | Agglomeration Economies in the Finnish Manufacturing Sector[END_REF] and Keyfitz (1965) argue that although this process was a necessary condition for the creation of cities, it was not sufficient. Some additional kind of social organization was needed to enable people in the city to appropriate, directly or indirectly, part of the production that kept them alive.

According to Keyfitz, surplus can only be extracted after it has been insitutionalised through taxes, trade, and other means adopted by the state (Keyfitz, 1965). He further argues that in the early stage of cities' development, agricultural products were needed to support and finance the creation of new activities such as manufacturing.

The creation of new cities and the expansion of the already existing ones was made possible by the construction of roads, the widespread use of money, and the political power of the cities over the territory.

As a result of this process, city economies experienced a structural change from agricultural to non-agricultural production. That is to say, economic development implies a radical shift in the composition of national output of goods and services 1 National Resources Committee, 1937, cited in Keyfitz, 1965. from sectors of relatively low productivity to those with higher ones (Morris, 1994, p.16;[START_REF] Harris | Environmental Issues in the cities of the Developing World. Development Planning Unit (DPU) Working Papter[END_REF].

At this point it is relevant to ask these questions: What principles underlie the distribution of population over a territory? And, what is the likely effect of economic development on redistributing population geographically?

In classical political economics, it was argued that the division of the labour has an impact on the distribution of the population. Towns are defined as the places that have a greater degree of division of labour, productivity, and specialization [START_REF] Chang | Financial Development and Economic Growth: the Case of Taiwan[END_REF][START_REF] Harris | E c o n o mi c De v e l o p me n t a n d Ur b a n i s a t i o n[END_REF]. However, these concepts by themselves do not explain what mechanism distributes people over territory2 .

During the 1960s the view that dominated research on the distribution of population in developing countries suggested that migration was the result of the deterioration of living conditions in the countryside. However, it has been demonstrated that migration and urban concentration are more closely correlated with economic development rather than rural poverty. For example, Keyfitz expounds that in South and Southeast Asia, as in Europe ' …the expansion of cities was a function of the demand for labour within them, rather than of a lack of opportunities in rural areas' (Keyfitz, 1965, p.285).

As the national output composition changes there are transformations in the shares of labour demand by economic sectors. Since cities are the traditional sites of industrial activities, industrial expansion attracts workers and their families to urban areas. With the rise of the number of migrants to the cities there is an increase in the demand for manufactured goods and services. As a consequence, this creates a greater demand for labour [START_REF] Yuanliang | Aggregate Cigarette Demand and Regional Differences in China[END_REF]O' Sullivan, 2000;Verma, 1986).

As the output of goods and services changes, relative city sizes change. Therefore, the mechanism linking economic development and urbanization is the labour market (Taylor, 1998, pp.28-65;[START_REF] Harris | Environmental Issues in the cities of the Developing World. Development Planning Unit (DPU) Working Papter[END_REF].

Economic development requires a continuing rise in productivity. Many authors have argued that productivity is higher where urban agglomeration economies are more prominent. For example, Verma (1986) explains that in Indian States during the 1970s, productivity was related to the increase of migration into urban areas and to the percentage of states' urban populations. According to Verma, productivity was affected by the number and the size of urban agglomerations as well as by the populations of the largest cities. Yet, while the contribution of large cities to productivity declined, it increased in medium-size cities. This means that since the 1970s, large cities in India have grown at a slower pace than medium-size cities.

City size and urban growth are related to scale and agglomeration economies. In order to satisfy the growth of output during economic development, it is necessary to have a labour force concentration. This in turn affects city size. On one hand, large population concentrations make it possible to have scale economies and larger markets. [START_REF] Harris | Environmental Issues in the cities of the Developing World. Development Planning Unit (DPU) Working Papter[END_REF] argues that sectorally different potentials for scale economies generate and sustain different settlement sizes. In other words, scale economies determine the distribution of urban populations between settlements of different sizes, and the patterns of specialization by localities. On the other hand, concentration of economic activities generates agglomeration economies by permitting innovations in transport and communication networks that reduce the costs of access to national and international markets (Lee& Wills, 1997;William et al, 2000;[START_REF] Henderson | Urban Development, Theory, Fact and Illusion[END_REF].

Economic development enhances territorial specialization. It is evident that in some areas economic, social, and natural conditions play an important role in producing cheaper commodities. As a result, many less-developed countries have lost their agricultural self-sufficiency as they engaged in manufacturing export goods that allowed them to gain from international specialization. " The sharp difference in productivity between sectors and subsectors of the national differentiation (and territorial differentiation in turn enhances the growth of productivity)" (Harris, 1990, p.10).

According to Mukkaala (2004), [START_REF] Henderson | Urban Development, Theory, Fact and Illusion[END_REF] and Tolley (1987), city size and the proportion of urbanised population are affected by demand conditions within the country, and changes in the degree of international specialization that occur during development. All cities have patterns of specialization that depend on their participation in national and international markets. Large cities are more complex than small ones. Hypothetically, a c i t y ' s pattern depends on its contribution to the national and international output. " Different population sizes of cities indicates different ' peak sizes' for the complex of specialization in a city' s externally traded output of goods and services" [START_REF] Chang | Financial Development and Economic Growth: the Case of Taiwan[END_REF]O' Sullivan, 2000;[START_REF] Henderson | Urban Development, Theory, Fact and Illusion[END_REF].

It should have become evident that there is a close relationship between a high rate of Tolley and Thomas demonstrated that urban population growth rates have a tendency to decline with a rise of income. They predicted that the high rates of urbanization observed in developing countries would decline as their income levels rise. In regard to urban concentration, they argue that there have been significant differences between developed and developing countries. In the case of developing countries, large proportions of the population tend to be concentrated in one or few cities, while in developed countries the share of the population that lives in large cities tends to be lower.

In the same direction, Harris explains that in some countries the association between economic development and urbanisation is weak. On the one hand, many developing countries with low levels of per-capita GNP have high urban population 3 Urbanisation is the change in the proportions of rural and urban populations. growth rates, whereas, developed countries have low rates of urbanization. On the other hand, immigration levels are lower in developed countries, although they have high rates of economic growth, while in developing countries with low levels of economic growth, immigration levels may be high. This means that " the association of economic activity and urbanization varies with the " stage of development" (Harris, 1990, p.4).

According to [START_REF] Harris | Environmental Issues in the cities of the Developing World. Development Planning Unit (DPU) Working Papter[END_REF], the size and distribution of land holding, household income, and colonial heritage, among other factors, seem to have an impact on population distribution. For example, during the 1980s, sub-Saharan Africa went through an economic crisis, which was manifested in a negative rate of agricultural growth, severe declines in export commodities, and a significant fall in urban incomes.

Sub-Saharan Africa had rapid urbanization, but poor rates of economic growth.

Theoretically, there is a close relationship between economic development and redistribution of the population, however, empirically, there are examples that do not support this general proposition. The maquiladora industry started developing in many Northern Mexico cities in the 1960s. This activity is based on using a cheap labour force and low capital investment to produce manufactured export goods. The maquiladora sector imports raw material and parts 4 , without restrictions, and its output is exported (Harris, 1993 andPradilla, 1993). Taking into consideration the concepts expounded in the preceding section, the objective of this section is to analyse, in broad terms, the relationship between economic development and urbanization in Northern Mexico.

When they began in Mexico, the government considered maquiladoras only as a transitional process that would alleviate the unemployment generated by the United S t a t e s ' s u s p e n s i o n o f t h e " braceros' programme. However, during the 1980s, as Mexico went through an economic crisis 5 , the government changed its policy and liberalized the economy, promoting export activities. Since then, the maquiladora industry has been seen as a strategic activity to help recovery of the Mexican economy (Pradilla, 1993). 4 According to INEGI, between January and October of 1991 the maquiladora sector along the northern border imported 99.0% of its raw materials and parts (INEGI, 1992, cited in Pradilla, 1993). 5 The Mexican economy was highly affected by the rise of real interest rates on loans from international banks, Mexico being the most indebted Latin America country; the drop in oil prices, the main export product of Mexico; and two million U.S. dollars were taken out of the country. The pace of maquiladora growth has been dependent on international market conditions, especially those in the United States, because of its particular features and border location. For instance, between 1975-1976 many plants in the northern states were closed as the result of the economic crisis in USA. In the oil boom period maquiladoras experienced stagnation and lost international competitiveness. Since 1989, as a consequence of the North American economic recession, the pace of growth of the maquiladora sector has been slower than expected (Paradilla, 1993). Yet, between 1975[START_REF] Harris | Environmental Issues in the cities of the Developing World. Development Planning Unit (DPU) Working Papter[END_REF], the maquiladora sector has grown in size. The number of establishments increased from 454 to 2,033 and the number of employees from 67, 214 to 465, 800. Maquiladoras created 88% of the new national industrial jobs, between 1985 and 1990, and the northern Mexico states of Baja California Norte, Sonora, Chihuahua, Coahuila, and Nuevo Leon y Tamaulipas accounted for 86.9 % of the total number of establishments, 90.2% of the employment, and 87.1% of the total maquiladora production value 6 .

The maquiladora sector in Mexican border cities increased significantly between 6 INEGI, 1992, cited in Pradilla Cobos, Emilio, 1993. 1 shows, employment and value-add growth rates were over 7.0% and 6.5%, respectively, which exceeded the national economy growth rate of 0.9% between 1980-1988(Garza, 1992)). The maquiladora sector is considered very important in terms of international trade because it produces about a quarter of the value of the country' s manufactured exports (Harris, 1993).

As consequence of the continuous maquiladora industrialization process, the economic structure of the northern cities has been transformed. As Table 1 shows, in the period 1975-1989 Cd, Juarez, Tijuana, Matamoros, Nogales, and Reynosa y Mexicali had the highest concentration of employment and value add in Mexico.

Economic development has also affected the size of the cities along Mexico ' s northern border as expansion of the maquiladora sector attracted workers. Between 1980-1990, the population growth rates in northern cities were much higher than the growth rate at the national level, as Table 2 shows; the only exception was Matamoros City. Tijuana (7.6%) and Ensenada (8.0%) are the most significant examples.

To conclude, it should have become evident that the case of Mexico ' s northern border shows a clear correlation between economic growth and urbanization. That is not to say that the maquiladora development is the only factor behind the rapid urbanization 13 in northern cities. Other determinants, such as regional location and individual city conditions that affect the level of urbanization 7 should also be considered. Note also that the maquiladora industry is highly linked with international markets, therefore, the future of most of these cities depends on fluctuations in world trade markets.

Conclusions

To understand the territorial distribution of population and to improve national productivity, the role each city plays in the national and international economy must be considered. Nowadays, cities are the key factors in economic development and the globalization process since they concentrate the labour force, economic activities, and infrastructure 8 , which are important in elevating productivity and being competitive in international markets.

Cities such as maquiladora are marked by territorial specialization. This specialization indicates the strengths and weaknesses of the city and its manufacturing 7 For instance, the northern cities of the Mexico attracts people from both countries that want to cross the border (legally or illegally) for several reasons: tourism, business, trade, services and so on. 8 For instance, business and professional services, financial resources, transports, market information, all kind of consumers, and so on. Economic development enhances productivity and territorial specialization, which underlie the distribution of population. Among the factors that must be considered are first, concentration of the labour force and productivity and specialization levels, second, the effects of national and international markets on the distribution of population, these should include openness in a city' s trading system, third, the national and regional conditions that determine the pattern of development and urbanization; and fourth, noting that the relationship between economic development and population distribution is not an historical process, it occurs only under specific circumstances. 1987, 1988, 1989, Mexico, cited in Pradilla (1993).

  Thus, people released from agricultural activities were able to move to cities and work in non-agricultural enterprises. 1

  urbanisation 3 . However some authors point out that in addition to the level of economic development, regional localisation and individual country conditions have an impact on the level of urbanisation. For that reason, they affirm that there is no " simple association between economic development and the degree to which a country is u r b a n i z e d "(Tolley and Thomas, 1987, p.4).

"

  Maquiladora" , Economic Development and Urbanisation in Northern Mexico.

  . In order to promote local economic growth, local authorities have to analyse the patterns that follow such activities. Their dynamics and evolution will depend strongly on the policies implemented by the city government.

Page 11 of 18 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	1975 and 1989. As Table
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Table 1 : Maquiladora Sector: Employment and Value Add by Northern Border Cities, 1975-1989

 1

	Ciudades		Personal			Valor
			Ocupado			agregado*	T.C.%
		1975	1989	T.C.%	1975	1989
	Ensenada, B.C.N.	314	1 556	12.1	12.6	45.6	9.6
	Mexicali,B.C.N.	6 324	21 374	9.1	363.4	1 228.8	9.1
	Tecate, B.C.N.	803	4 640	13.3	44.1	236.0	12.7
	Tijuana, B.C.N.	7 844	58 029	15.4	472.4	2 774.3	13.5
	Cd. Acuna, Cuah.	1 900	13 173	14.8	52.9	407.3	15.7
	P.Negras, Coah.	2 561	8 051	8.5	90.7	254.2	7.6
	Cd. Juarez, Chih.	19 775 124 386	14.0	1 048.9	6 047.5	13.3
	Agua Prieta, Son.	2 636	6 806	7.0	98.9	255.7	7.0
	Nogales, Son.	6 794	22 635	9.0	390.5	955.6	6.6
	Cd. Reynosa, Tamps.	1 255	23 938	23.4	53.4	1 215.2	25.0
	Matamoros, Tamps.	9 778	38 132	10.2	400.7	2 024.2	12.3
	Nvo. Laredo, Tamps.	1 928	14 747	15.6	69.8	770.1	18.7
	Total en la frontera	61 912 339 319	12.9	3 098.3	16 307.3	12.6

Source; INEGI, Estadisticas de la Industria Maquiladora de

Exportacion, 1975-1986, Aguscalientes Mexico, 1983

and INEGI, Avance de Informacion economica. Industria Maquiladora de Exportacion,

Table 2 : Population growth rate of the main border cities with maquiladora activity, 1970-1980, 1980-1990

 2

	1970-1980	1980-1990

Source: CONAPO, Demografia de la Frotera Norte cited in

Pradilla, 1993

In many traditional activities there is a high level of division of labour, and this situation does not imply necessarily a change in population redistribution.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

< R1 -General Regional Economics < R -Urban, Rural,