Michael Funke
email: funke@econ.uni-hamburg.de.

Declan Curran

Roberta Colavecchio

DRIFTING TOGETHER OR FALLING APART? THE EMPIRICS OF REGIONAL ECONOMIC GROWTH IN POST-UNIFICATION GERMANY

Keywords: C14 -Semiparametric and Nonparametric Methods Regional economic growth, Germany, Convergence, Desnity estimation Regional economic growth, Germany, convergence clubs, density estimation, modality tests JEL-Classification: C14, R11, R12

whether they are published or not. The documents may come

Introduction

When, on October 3 rd 1990, the 60 million Germans in the West were formally re-united with the 16 million Germans in the East, the two parts could hardly have been more different. Despite a common culture and language, after forty years of development with radically different economic institutions and incentives, the Federal Republic of Germany and the German Democratic Republic (GDR) were characterized by substantial disparities in physical and human capital, labour productivity, incomes and wealth. According to [START_REF] Sinn | Jumpstart. The Economic Unification of Germany[END_REF], GDP per person in East Germany in 1989 was only 60 percent of the West German level. The West was one of the technologically most advanced and richest countries in the world; the East was economically shattered after four decades of communism and nearly bankrupt. In the years leading up to unification, real GDP growth was steady in the former West Germany and the unemployment rate was stable. After unification, the western states experienced sharper business cycle fluctuations: a modest upturn in 1990-91 was followed by a sharp recession in 1992-93, both of which were mainly due to the unification process. The initial economic boom was led by "exports" to the eastern states, where consumers were switching to cheaper and better quality goods produced in the West. The subsequent recession was also closely related to unification. Restrictive measures were implemented to reduce the fiscal deficit and the Bundesbank tightened monetary policy to cap the rising inflation. These policy responses, coupled with a contraction in foreign demand, had a dampening effect on the economy and the postunification boom gradually turned into a deep recession, with GDP growth rates well below the historical average for western Germany.

The problem of uneven regional developments has been closely monitored in post-unification policy debates and in recent years there has been a surge in empirical work on growth and convergence. When considering regional convergence, various empirical approaches have been implemented in the literature: from simple plots of measures of dispersion over time to intra-distributional dynamics using Markov chains applied to GDP per capita. Numerous studies have revealed persistent differences in per capita income among regions. Evidence shows that some regions managed to sustain high per capita income over a long time span while other regions seemed to be trapped in a low income growth path. These persistent differences are strikingly at odds with the standard neoclassical growth model, which predicts that poorer countries usually develop faster than richer ones and that there is a tendency toward convergence in levels of GDP per capita. On the other hand there exists an opposing growth paradigm [see, for example, [START_REF] Azariadis | Threshold Externalities in Economic Development[END_REF]] explaining multiple steady states in the growth rate of per capita income. According to [START_REF] Azariadis | Threshold Externalities in Economic Development[END_REF] and Aghion and Howitt (1998, chapter 10), multiple locally stable equilibria can be attributed to differences in initial conditions. [START_REF] Faini | Increasing Returns, Non-Traded Inputs, and Regional Development[END_REF] has initially considered multiple steady states in the context of regional development issues. In all these models, different initial conditions may cause regions to get stuck at different self-perpetuating levels of economic activity. As Quah (1996[START_REF] Quah | Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs[END_REF] and [START_REF] Paap | Distribution and Mobility of Wealth of Nations[END_REF], this may lead to a polarisation into clubs of rich and poor countries or regions. 1 Research on convergence has accommodated cross-regional heterogeneity in a sequence of stages.

At first, conventional cross-section analysis [see, for example, [START_REF] Barro | Economic Growth in a Cross-Section of Countries[END_REF] and [START_REF] Mankiw | A Contribution to the Empirics of Economic Growth[END_REF]] assumed complete homogeneity in steady state growth rates. Recently, [START_REF] Lee | Growth and Convergence in a Multi-Country Empirical Stochastic Growth Model[END_REF][START_REF] Lee | Growth Empirics: A Panel Data Approach -A Comment[END_REF] allowed complete heterogeneity in steady state growth rates. However, as pointed out by [START_REF] Islam | Growth Empirics: A Panel Data Approach -A Reply[END_REF], extensions that allow varying growth rates run the risk of robbing the concept of convergence of any economic meaning. Instead of assuming complete heterogeneity, we set a structure of an intermediate form: we advocate techniques which focus on the evolution of the entire cross-sectional distribution in addressing the question of convergence across German districts in the first decade after German unification. 2 In this context, a convergence process occurs if, for instance, a bimodal density is detected at the beginning of the sample period and over time there is a tendency in the distribution to move towards unimodality. Alternatively, if there already is a unimodal distribution after German unification, convergence occurs when the dispersion of this density and therefore per capita income declines over time. To the best of our knowledge, no papers have attempted to formally test the convergence club hypothesis across East and West German regions after unification. 3 It is our purpose to detect whether clubs exist and which regions are associated with which clubs. A natural approach to assess the evolution over time of the dispersion of the regional per capita income is to estimate the cross-section distributions by using kernel density estimation.

The remainder of the paper is structured as follows. Section 2 describes the data set used for this study together with the non-parametric estimates of the per capita regional GDP over time. To support the visual impression given by kernel density estimates, and to provide further insight on the features of the underlying density, we have performed multimodality tests, whose results are presented in section 3. Section 4 concludes. 1 The obvious difficulty here is to figure out in the data which countries are in the bad and which ones are in the good equilibrium. Barrier to getting out of such a trap can be the lack of a "big push" [see [START_REF] Murphy | Industrialization and the Big Push[END_REF]]. [START_REF] Rodrik | Coordination Failure and Government Policy: A Model with Applications to East Asia and Eastern Europe[END_REF] has argued that the East Asian miracle may have depended on a state-assisted process of overcoming coordination failure, and a consequent shift between two different equilibrium output levels (or a virtuous circle). It is also worth noting that the possibility of non-uniqueness is discussed informally even in Solow´s (1956) original exposition of the neoclassical growth model. 2 In this paper we add to the contributions of [START_REF] Bianchi | Testing for Convergence: Evidence from Non-Parametric Multimodality Tests[END_REF], [START_REF] Corrado | Identifying and Interpreting Regional Convergence Clusters across Europe[END_REF], [START_REF] Laurini | Income Convergence Clubs for Brazilian Municipalities: A Non-Parametric Analysis[END_REF]), Lopez-Bazo et al. (1999) and [START_REF] Pittau | Fitting Regional Income Distributions in the European Union[END_REF] testing for "two-club" or "twin-peak" convergence of GDP per capita across countries and EU regions by analysing data which do not overlap with the data of existing papers. 3 [START_REF] Funke | Threshold Effects and Regional Economic Growth -Evidence from West Germany[END_REF] have demonstrated the existence of two clubs across West German regions prior to unification using threshold estimation techniques. The opportunity to assess spatial disparity trends in per capita income indicators is limited by the availability of consistent and comparable data. Long and dense time series for small geographic units are difficult to obtain, and in many cases not existent. In this section, we briefly present the spatial distribution of our data which are at the heart of our analysis. There are three levels of administration in Germany: (1) the Federal Republic at the national level; (2) 16 federal states (Bundesländer) on the regional level and (3) 439 districts (Kreise) or towns with autonomous administration (kreisfreie Städte), both on the local level. Smaller municipalities belong to the districts. In our empirical work below we focus on these 439 districts covering the entire economy. 4 Our data run from 1992 to 2001. Data for 1993 are missing. The source of our data is the "Arbeitskreis Volkswirtschaftliche Gesamtrechnung der Länder". 5 The GDP per capita data are at constant 1995 prices and are obtained dividing the GDP of the German districts by their population. Ideally, we should deflate district-level per capita incomes using district-level deflators but, since districtlevel price indices are not available, we follow the usual practice and simply use the 16 state-level GDP deflators.

Nonparametric density estimations can reveal several features of the data and therefore help to capture the stylised facts that need explanation, exploring which specifications match with the data.

The kernel estimator for the density function f(x) at point x is (1)

( ) ∑ =       - = n i i h x K nh x f x 1 1 ˆ
where x = x 1 , x 2 , …, x n , is an independent and identically distributed sample of random variables from a probability density f(x) and K(·) is the standard normal kernel with window width h. The window width essentially controls the degree to which the data are smoothed to produce the kernel estimate. The larger the value of h, the smoother the kernel distribution. A crucial issue is the selection of this smoothing parameter. In order to solve the trade-off between oversmoothing and undersmoothing, i.e. the trade-off between bias and variance, we have first used Silverman´s (1986, 4 We focus on district-level data because state-level data tend to "aggregate away" important differences between smaller geographic entities within the 16 states. For example, in the dataset that we analyse below, the ratio of GDP per capita between the richest (Hamburg) and the poorest state (Sachsen-Anhalt) was 2.63 in 2001, while the corresponding ratio for the richest (Landkreis München) and the poorest district (Mittlerer Erzgebirgskreis) was 7.30. On the other hand, one has to be aware that district-level GDP per capita figures may be affected by a commuting bias. Especially, commuters could overstate GDP per capita in agglomerations and city regions. Hamburg and Berlin are classified as a single region. This was forced on us because of lack of district-level data for both states. We also run the Kernel estimates excluding Berlin and Hamburg. Qualitatively, results are unchanged and the pattern is not much affected. 5 See http://www.statistik-bw.de/Arbeitskreis_VGR/publikationen.asp. The distributions have been fitted to the logarithm of real per capita income. In Figures 1 and2 are plotted the kernel density estimations for the (log) GDP from 1992 to 2001 obtained using the two abovementioned bandwidth selection methods and by transforming the income variable to the original scale. The figures show similar patterns, validating the fact that the estimates are robust with respect to the bandwidth specification. Nevertheless, as expected, the [START_REF] Silverman | Density Estimation for Statistics and Data Analysis[END_REF] rule of thumb returns a slightly larger optimal smoothing parameter and therefore the relative density estimate (Figure 1) appears oversmoothed compared to the one obtained used the Sheather and Jones (1991) plug-in method (Figure 2). A preliminary inspection of the estimated densities reveals several noteworthy aspects. First, the snapshots show pronounced triple peakedness at the beginning of the considered time span. This evidence indicates that the German districts in 1992 can be separated into three groups, poor, rich and middle income. Second, as time passes this triple peakedness becomes less visible as the mode corresponding to low-income level recedes somewhat, without disappearing entirely as Figure 1 would have us believe. 6 As we will see, this bimodal/trimodal ambiguity recurs later when we utilize statistical tests for multimodality. Either way, this smoothing of the third mode is indicative of an improvement in economic conditions of the German poorest districts. In particular, this smoothing of the initial trimodality supports the notion of a catching-up process of eastern Germany at the beginning of the 1990s, i.e. the poorest districts did not stay as poor as they were immediately after unification. That said, despite the tendency of initially poor units to increase relative incomes, on there is a visible tendency for the remaining two peaks to move apart, with the third mode moving to the right towards a higher income level. Moreover, the variability of the "low-mean distribution" has been declining over the decade from 1992 to 2001 and in 2001 appears to be considerably smaller than the spread of the "high-mean distribution". This evidence reveals that cross regional income disparity has become larger rather than smaller as predicted by absolute convergence.

Furthermore, we use the methodology of distributional dynamics to model the evolution of the relative distribution of per capita incomes for Germany districts. This approach models directly the evolution of relative income distributions by constructing transition probability matrices that track changes over time in the relative position of districts within the distribution. This is an exercise that a number of authors have undertaken (see Quah, 1996aQuah, , 1996b[START_REF] Quah | Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs[END_REF]. The modelling of distribution dynamics assumes that the density distribution φ t has evolved in accordance with the following equation:

(2) ,

1 φ φ t t M = +
where M is an operator that maps the transition between the income distributions for the periods t and t+1. Since the density distribution φ for the period t only depends on the density φ for the immediately previous period, this is a first-order Markov process. In our estimates below we have assumed that the distribution φ has a finite number of states. For the Markov transition matrices we assume that the probability of variable s t taking on a particular value j depends only on its past value s t-1 according to the first-order Markov chain (3)

{ } P i s j s P ij t t = = = -1 | ,
where P ij indicates the probability that state i will be followed by state j. As (4) 1 ...

2 1 = + + + P P P in i i
we may construct the so-called transition matrix 7 In particular, the growth rates of the real GDP per capita over the decade from 1992 to 2001 were negative in 66 districts. Out of these 66, seven districts (Delmenhorst, Landkreis Holzminden, Landkreis Sigmaringen, Landkreis Soltau-Fallingborstel, Landkreis Unterallgäu, Neustadt an der Weinstrasse, Wilhelmshaven) have even experienced two-digit negative growth rates. Following Jones (1998, p. 4) these districts might be labeled "growth disasters". where line i and column j give the probability that state i will be followed by state j. In our modelling approach, the probability P ij measures the proportion of districts in regime i during the previous period that migrate to regime j in the current period.

The transition probability matrix in Table 1 reports transitions between the 1992 and 2001 distributions of GDP per capita relative to the German average. The main diagonal of the matrix gives the proportion of districts that were in the same range of the distribution immediately after German unification as a decade later. Table 1 also provides information about n, the number of districts that begin their transitions in a given state. Furthermore, we provide the classes that divide up the state space.

The salient characteristics of the transition probability matrix in Table 1 reveal a number of noteworthy behavioural patterns in the distribution of real GDP over time. First, as indicated by the first element of the main diagonal (0.03), districts which originally reside in the lowest range of the distribution (i.e. with a GDP per capital of 50% or less of the German average) appear to be very unlikely to remain in this category at the end of the period in question. Such districts display a strong tendency to either move forward to the second category (0.68) or jump to the third category (0.27).

Second, the third and fourth elements of the main diagonal (a real GDP of 65%-80% and 80%-100% of the German average, respectively) indicate a relatively high probability for the regions within this range to maintain their status quo over the period. That said, regions in the third category appear to be relatively open to backward or forward movements (with probabilities of 0.13 and 0.22 respectively) while those in the fourth seem decidedly more backward looking, as illustrated by the 0.26 probability of moving a step back but only a mere 0.04 probability of moving forward one step.

Finally, the districts residing in the fifth category (with a real GDP of 100-125% of the average) appear to be more likely to either retain this position or fall back by one category. These districts marked inability to move forward (a probability of 0.02) suggests there comes a point where incremental increases in real GDP become harder and harder to sustain. Furthermore, those districts that reside in the highest income category at the beginning of the time period display a very high probability (0.83) of consolidating their position of affluence.

The forementioned characteristics support the findings of kernel density estimation, namely: the tendency of the poorest districts to catch-up; the middle income districts retaining their status quo (despite a small number of their ranks back-peddling); and the consolidation of the richest districts of their position.

0] [1.0-1.25] [1.25-∞]
In Table 1, the operator M has been constructed by assuming that the distribution φ t has a finite number of states. This discrete modelling approach leads to the problem that the researcher has to determine the number of intervals and the limit values of each interval in an arbitrary and ad hoc way. Furthermore, the discretisation process may eliminate the property of Markovian dependence in the data, as [START_REF] Bulli | Distribution Dynamics and Cross-Country Convergence: A New Approach[END_REF] has pointed out. The solution addressing these shortcomings consists of carrying out a continuous analysis of transition, which avoids discretisation through the use of conditional densities that are estimated non-parametrically and referred to as stochastic kernels. A stochastic kernel amounts to a transition matrix with an infinite number of infinitely small ranges.

The results from this tool are displayed as three-dimensional graphs in Figure 3 and a twodimensional contour map in Figure 4.

The three dimensional stochastic kernel graph yields a number of valuable insights, which are both additional and complementary to those of the static kernel illustrations of Figures 1 and2. In order to fully exploit the information content of this construct we firstly adjust the viewer's perspective by rotating the illustration (Figure 3, top left and top right). We then provide further insights by tilting the graph downwards, as if looking down on the three dimensional distribution from above. This "aerial view" is further enhanced by means of contour images of the distribution (Figure 4). Rotating the graphs in Figure 3 (top right and top left) highlights two features: the pronounced peaks at the beginning and end of the distribution; and middle section of the distribution which, while relatively lower, still suggests the possibility of either slippage or enhancement of one's relative position.

This aerial view of the income distribution, highlighting as it does the diagonal pattern of the distribution over time, illustrates the tendency of regions residing in low income categories in 1992 to remain there in 2001, while high income regions retain their affluent status throughout the period in question. That said, a further more subtle nuance can be gleaned from Figures 3 and4

Tests for Multimodality

The discussion above has relied heavily on the visual impression and shape of the non-parametric income densities. In practical terms, looking at Figure 1234, the first question to ask is: are those districts randomly drawn from an unimodal distribution, a bimodal distribution or is there any kind of trimodality? In order to ascertain the significant number of modes present in our estimated density functions, we employ Silverman´s (1981,1986) nonparametric test for multimodality and peakedness. 8The non-parametric procedure tests the null hypothesis that a density f has k modes (or peaks, bumps) against the alternative that f has more than k modes, where k is a non-negative integer. The test statistic in this case is the critical window width, defined by

(6) ( ) { } modes most at has | inf k f h k hcrit = .
For h < h crit (k), the estimated density has at least k+1 modes. The basic idea of the test is intuitive and simple. Specifically, if the series has k modes, then h crit (k-1) should be 'large' because substantial smoothing is required to generate a (k-1)-mode density. For example, if the data possess two strong modes, a large value of h will be needed to obtain an unimodal estimate. An illustrative calculation of the critical window widths h and the corresponding number of modes (peaks) in the kernel density estimates for the year 1999 is plotted in Figure 5. Thus, the technique forms a natural hypothesis-testing framework since large numbers of h crit (k) indicate more than k modes. The crucial question, then, becomes how large is "large" when the chosen bandwidth is concerned. The value of h crit (k) is computed through a binary search algorithm, and its significance level can be assessed by the bootstrap procedure attributable to [START_REF] Efron | Bootstrap Methods -Another Look at the Jack-Knife[END_REF]. In particular, the bootstrap test requires a statistic test t(x) and an estimated null distribution for the data under H 0 . Given these, the p-value of the test is

(7) { } ) ( *) ( prob ˆ0 bootstrap x t x t p F > = where (8) ( ) ′ = * * * x x x n x ,..., , * 2 1
is the bootstrap drawn from the null distribution F ˆ0 . To approximate p bootstrap , bootstrap samples have to be drawn from a rescaled density estimate obtained by setting + is the rescaling factor, y i * are sampled with replacement from the original sample, y * its mean, σˆ2 its variance and ε is assumed to be distributed as a standard normal since the kernel is Gaussian. 9 In the spirit of the analysis of Hall (1992), the bootstrap method treats the available sample as the population, and through repeated re-sampling of this sample, obtains the distribution of statistics of the test. A sample is taken of the original series (with replacement) and transformed to have the same first and second moments. Critical values are then obtained by generating a large number of samples. 10 This is not a nested test and its results should therefore be interpreted as a hierarchical set of significance tests.

We execute the [START_REF] Silverman | Using Kernel Density Estimates to Investigate Multimodality[END_REF][START_REF] Silverman | Density Estimation for Statistics and Data Analysis[END_REF] test for each year, with null hypotheses of one, two and three modes (hence alternative hypotheses of more than one, more than two and more than three modes). The results are listed in Table 3, with the first row for any given year indicating the values of h crit (k);

the p-values associated with the corresponding critical value widths are given in parentheses; and k* representing the number of modes detected. Taken together, the Silverman test suggests a persistent ambiguity between trimodality and bimodality over the time period, consistent with the "eye-ball evidence" drawn from Figures 1234.

In order to geographically illustrate the clusters detected in the Kernel density estimations, we have produced a set of maps, Figures 6 and7, which create a visual impression of the spatial structure of the real GDP per capita across German districts. The categories are defined such that in each income range there resides an equal number of districts. To be consistent with the results of our empirical analysis we have chosen to identify three and six categories of the real GDP per capita in 1992 and in 2001, the first and the last year of the considered time span. The presented maps provide evidence that spatial clusters do exist for the variable under consideration. 11 For the correct interpretation of the maps it is important to bear in mind that they are not suitable to assess the absolute growth performance of the 439 German districts: in particular, it is not possible to say whether over the last decade the poorest areas caught up with the richest ones or whether some areas got richer or poorer as they switched from a cluster to another. (The reason for that is that the thresholds defining the identified categories have changed over time). Looking at those thresholds -which all rose considerably -it is indeed possible to state that the average German GDP has risen between 1992 and 2001.

12 Data for Mecklenburg-Vorpommern (18 Kreise) is not available for 1992. However, their per capita income level is found to reside within the lowest income category as soon as these figures become available in 1996. A further piece of information that can be gleaned from the visual inspection of the maps is that approximately 40 percent of West Germany belongs to the high-income cluster, both in 1992 and in 2001, with a high concentration of rich districts localized in the Hamburg area to the North, as well as in the western and southern parts of West Germany. One surprising feature that emerges is the marked downturn in the fortunes of 24 western districts, who experienced an erosion of their per capita GDP from above 21,300 euros in 1992 to 17,200 euros in 2001. 13All in all, the comparison between 1992 and 2001 shows that the spatial structure of the real GDP per capita of German districts over the last decade has indeed changed. Figure 6 shows that the relative income position of the East German districts has remained at the bottom of the ranking whereas districts located in the South-West and in the Hamburg area were still included in the richest group. In other words, the relatively "poorer" districts have remained clustered in the eastern part of Germany and the "wealthier" areas have remained localized in the South-West. That said, the emergence of a number of wealthier eastern districts concurrently with the fall-back experienced by a pocket of western regions suggests that the overall picture may be more complex than first thought.

Figure 7 paints the same picture in greater detail as six different income groups are identified. This 6-category map allows a more precise view of the spatial structure of real GDP per capita across the German districts, while retaining a natural consistency with the 3-category map of Figure 6. Of the two lowest income ranges, the very poorest range is observed only in East Germany in 1992. By 2001, however, it is apparent from the more detailed 6-category maps that a number of West

German states now reside in this lowest category, particularly in the north and south-west. Within the East there is also a discernible movement from the lowest income range to the second lowest, over the period in question. In the middle income ranges there has been a perceptible emergence of middle-income category districts in the East German states over the 1992-2001 time period, whereas in the West those regions residing in the middle income ranges in 1992 have broadly retained their status throughout the period. Similar to the trends observed in Figure 6, the relatively wealthier regions tend to be concentrated in the west and southern areas of the country in both 1992 and 2001.

One can also discern the emergence of a sprinkling of relatively wealthy regions in the East by 2001, due perhaps to real GDP growth associated with urban, commercial areas such as Berlin and Dresden.

Taken as a whole, the visual impression created in Figures 6 and7 of the spatial structure of the real GDP per capita leads one to conclude the following: over the period 1992-2001 there has been a noticeable catching-up process in terms of the real GDP of East German regions; West German regions that have been residing in middle income ranges tend to have retained this status throughout the period in question, though as illustrated by the 6-category maps a small number of western regions which were in the lower income categories in 1992 have fallen back somewhat by 2001; the relatively richer clusters in the western and southern areas of the country have consolidated their position over the period in question, while a sprinkling of relatively wealthy regions has also emerged in the East.14

Conclusions and Further Comments

The objective of this paper is to address the question of convergence across German districts in the first decade after German unification by drawing out and emphasising some stylised facts of regional per capita income dynamics, rather than estimating any particular economic model. We achieve this by employing techniques which focus on the evolution of the entire cross-sectional income distribution. In particular, we follow a distributional approach to convergence based on nonparametric kernel density estimation and implement a number of tests to establish the statistical significance of our findings. The visual inspection of the estimated densities indicates the following:

the presence of trimodality in 1992; in subsequent years less pronounced trimodality, supporting the notion of a catching-up process of eastern Germany in the early 1990s; and a tendency for the remaining two peaks to move apart, resulting in a swelling of the middle income mode and a more pronounced high income mode. 15 An alternative approach to investigating the presence of convergence clubs would be to track in more detail the performance of each geographical unit. This may provide another dimension of disparity that is relevant for economic policy making. From a policy perspective, besides having information about the entire cross-section of observations, it is also important to know how likely is each district to improve its conditions, how many did so and what are their characteristics. In other words, whether or not districts that were rich (poor) a decade ago are the same ones that are rich (poor) now has relevant policy implications. If the poor regions are persistently poor, one may want to consider public programs aimed at enhancing the performance of these districts. On the other hand, if the incomes per capita are rotating over time, one would be less concerned about overall geographical income distribution. Our approach has not conceptualised this alternative mixing or ranking change aspect of disparity. Further consideration should be given to such indicators in future research. 15 The exact nature of multimodality, however, is still surrounded by some degree of uncertainty. At first glance, it might seem promising to consider growth model with multiple equilibria in the tradition of Aghion and Howitt (1998, Chapter 10), [START_REF] Azariadis | The Economics of Poverty Traps Part One: Complete Markets[END_REF], Drazen and Azariades (1990) and [START_REF] Matsuyama | Increasing Returns, Industrialization and Indeterminancy of Equilibrium[END_REF] when trying to explain "job-poor" versus "job-rich" growth experiences. In such models, a country may be trapped in a "job-poor" equilibrium when, in principle at least, an alternative and superior equilibrium is also feasible. However, the recent literature has cast doubts on the robustness of multiple equilibria. [START_REF] Frankel | Resolving Indeterminacy in Dynamic Settings: The Role of Shocks[END_REF] analyse a two sector model with increasing returns, based upon [START_REF] Matsuyama | Increasing Returns, Industrialization and Indeterminancy of Equilibrium[END_REF]. They show that if the wage is stochastic and arrives as a Poisson process, the muliplicity property may be eliminated because some of the deterministic equilibria are more robust to perturbations than others. A similar conclusion has been established by Herrendorf et al. (1999) for heterogeneous agents. They show that sufficient heterogeneity of agents will lead to a refinement in the set of observable equilibria and uniqueness in models like that of [START_REF] Matsuyama | Increasing Returns, Industrialization and Indeterminancy of Equilibrium[END_REF].

  ) "first generation" rule-of-thumb for a Gaussian kernel. Additionally, we consider the twostage direct plug-in bandwidth selection method of Sheather andJones (1991).

Figure 1 :

 1 Figure 1: Non-parametric densities of per capita GDP (constant 1995 prices) across German districts using Silverman´s (1986) "first generation" rule-of-thumb

  the considered decade, several districts experienced negative growth rates. 7 Third,

  . The hint of concavity visible in both the three dimensional graph (bottom right) and contour representation are movement in the status of the lower income regions; a finding which is explored further below.

Figure

  Figure 3: Stochastic Kernel Estimates, 1992 -2001

Figure 4 :

 4 Figure 4: Stochastic Kernel Contours

Figure 5 :

 5 Figure 5: Number of Modes in the Kernel Density Estimate as a Function of the Window Width Size h, 1999

  Figure 6: Real GDP per capita 1992 and 2001

  Figure 7: Real GDP per capita 1992 and 2001

Table 1 : Transition Probability Matrix Relative to the German Average

 1

				GDP PER CAPITA 2001
		n	4	61	79	128	74	73
		63 [0-0.5]	0.03	0.68	0.27	0.02	0.00	0.00
	GDP	30 [0.5-0.65]	0.07	0.40	0.33	0.17	0.03	0.00
	PER	45 [0.65-0.8]	0.00	0.13	0.53	0.22	0.11	0.00
	CAPITA	106 [0.8-1.00]	0.00	0.00	0.26	0.70	0.04	0.00
	1992	90 [1.00-1.25] 0.00	0.00	0.00	0.41	0.57	0.02
		85 [1.25-∞]	0.00	0.00	0.00	0.01	0.15	0.83
			[0-0.5] [0.5-0.65] [0.65-0.8] [0.8-1.

Table 2 : Silverman´s Multimodality Test

 2

	YEAR	CRITICAL BANDWIDTHS AND P-VALUES	k*
		h crit(1)	h crit(2)	h crit(3)
	1992	2490	2240
		[0.00]	[0.00]

  11 In particular, as one would expect, the poorest district are concentrated in East Germany. In 1992, all districts, except Berlin, Kreisfreie Stadt Potsdam and Kreisfreie Stadt Erfurt, belong to the "poorest" group, 12 whereas only 10 percent of the West districts are included in this low-income cluster. By 2001, the proportion of eastern districts that still reside in this same cluster has shrunk to 80 percent of the total eastern districts. However, a number of districts have switched to the richer groups, showing an improvement in their relative income level. In particular, the districts Landkreis Teltow-Fläming and Landkreis Dahme-Spreewald in the greater Berlin area have moved from the low-to the middle-

	income group. Furthermore, 8 percent of the eastern German districts (Kreisfreie Stadt Dresden,
	Kreisfreie Stadt Rostock, Kreisfreie Stadt Cottbus, Kreisfreie Stadt Neubrandenburg, Kreisfreie
	Stadt Jena, Kreisfreie Stadt Erfurt, Kreisfreie Stadt Schwerin, Kreisfreie Stadt Zwickau, Kreisfreie
	Stadt Potsdam) have gained a foothold amongst the richest elite by 2001.

A "mode" is meant here to be a point on the empirical density estimate around which the tangent to the curve changes its slope from positive to negative.

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

This test of multimodality has been used by[START_REF] Bianchi | Testing for Convergence: Evidence from Non-Parametric Multimodality Tests[END_REF] to test the hypothesis of income convergence for a group of 119 countries between the years of1970[START_REF] Murphy | Industrialization and the Big Push[END_REF][START_REF] Bianchi | Testing for Convergence: Evidence from Non-Parametric Multimodality Tests[END_REF] rejects the hypothesis of convergence in favour of the formation of convergence clubs.

In 2001 the share of western districts included in the low-income group over the total number of West German districts rose to 18 percent (58 out of a total of 326 West German districts) from 10 percent in 1992.

These results are consistent with the empirical evidence in[START_REF] Bayer | Convergence in West German Regional Unemployment Rates[END_REF] and[START_REF] Villaverde | Productivity Convergence in the European Regions, 1980 -2003: A Sectoral and Spatial Approach[END_REF] showing moderate speed of ß-convergence across German and European regions.


Harris Neeliah

Bhavani Shankar
email: b.shankar@reading.ac.uk

Ozone Pollution and Farm Profits in England and Wales

come

Ozone Pollution and Farm Profits in England and Wales

I. Introduction

Concern over environmental degradation worldwide has triggered the setting up of a number of fora and commissions to look into ways of assessing the extent of damage, with a view to devising new environmental standards and/or modifying existing ones. Over the last decade there has been much associated research activity in Europe, looking into a wide range of pollutants, their impacts and their respective standards. One such important pollutant is tropospheric (groundlevel or low-level) ozone.

Tropospheric ozone (TO) is produced by the interaction of solar radiation with the oxides of nitrogen (NO x ) and Volatile Organic Compounds (VOCs, such as methane and carbon monoxide). Although the precursor NO x and VOC gases are also produced by natural processes, combustion in industrial production and motor vehicle operation have contributed significantly to elevated ozone concentrations in Europe. Such levels can potentially affect human health, crops and materials. Research on these effects is being conducted under the aegis of the United Nations Economic Commission for Europe's (UNECE) Working Group on Effects (WGE). One of these research avenues concerns the externality of TO on crop production.

European research in this area has concentrated on establishing dose-response relationships for various crops using experimental methods, and establishing and F o r P e e r R e v i e w 3 refining critical levels beyond which crop yields are affected. Rather than use ambient (mean) ozone concentrations, the so-called 'Level 1' approach adopted by European researchers was based on the 'AOT40' concept, i.e., the cumulative ozone exposure over 40 parts per billion, over a fixed growing season. Based on critical levels derived from a 'Level I' concept, it seems that 91% of the arable acreage in the UK is exposed to potentially harmful ozone concentrations [START_REF] Porg | Ozone in the United Kingdom. Fourth Report of the Photochemical Oxidants Review Group[END_REF].

Recognising that dose-response can be modified by several factors such as pests, rainfall, etc, 'Level II' research efforts are underway to fine-tune critical levels, taking these factors into consideration [START_REF] Karlsson | Establishing ozone critical levels II[END_REF]. But given the multitude of factors that interplay, much more work needs to be done yet to come up with a reliable 'Level II' index. Even when sophisticated Level II indices are ultimately developed, they may not be able to capture the true farmlevel impact of ozone. Farmers have a variety of mitigatory options available to them, and not all crops are equally susceptible to high TO levels 1 . Consequently, farmers may react to changes in the level of TO by changing land allocated to crop production, changing the levels of other inputs, by altering the output mix, etc. Such mitigatory behaviour is the result of economic decision-making, and is not taken into account even in the most sophisticated physical experiments or by a 'level II' index. Biological experiments usually fix the levels of all other inputs at levels where their marginal products are zero, so that the productivity effect of the variable under investigation, such as the ozone level, is not confounded with the effects of these other inputs. By doing so, however, the actual productivity 1 Wheat, potatoes and sugarbeet are key UK crops that are more likely to suffer following high ozone concentrations. This study attempts to overcome this shortcoming inherent in using biological dose-response models to estimate the economic impacts of ozone. It does so by intersecting panel datasets on pollution and farm variables, and directly estimating the effect of ozone on profits and supply based on a profit function approach.

The previous literature on the farm-level economic effects of ozone on can be divided into two strands:

(i) The larger strand feeds biological dose-response experimental data into mathematical programming models. The models are then run to optimise farm profits at varying levels of ozone exposure. A number of empirical studies were carried out in the US in the mid-80's using such an approach (see [START_REF] Heck | Assessing the impacts of ozone on agricultural crops: Overview[END_REF] for a review).

(ii) A much smaller strand uses observations on ozone, and farm inputs, outputs, costs and profits, to directly estimate the effects of ozone on farm-level outcomes using dual methods. This includes [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF] for the US and Young and Aidun (1993) for Canada. Our research belongs to this latter strand.

This study offers the following advantages and innovations compared to previous work: 2 We are grateful to a referee for point this out. (b) It benefits from employing the AOT40 cumulative exposure index, which is considered by European researchers to be a better predictor of the impacts of ozone on vegetation than seasonal mean measures that have been used by studies conducted in North America.

(c) In contrast to previous work, we control for farm-specific effects in isolating the effects of ozone on profits and supply. As is well known, farm level outcomes are often strongly influenced by unobserved heterogeneity, and controlling for such heterogeneity is important for accurate estimation (d) By employing a multi-output approach, we allow for a more realistic representation of how ozone affects farm outcomes in comparison to singleoutput representations.

The paper is organised as follows. Section II introduces the duality concept, sections III and IV outline the econometric methods and data, section V presents the analysis of the results and section VI concludes.

II. Multi-output dual profit function

Producers are characterised as maximising short-run profits with respect to variable inputs, given stress brought about by external factors, including ozone.

In our particular case, if there is an observed depression in yields, it is expected that profit-maximising farmers will adjust their practices [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF].

In the short-run, they can alter their variable input mix to mitigate the effect. This will affect variable input costs, and ultimately profits. In the short to medium term, farmers can alter both their input and output mixes and choose to farm a crop that is less susceptible to ozone. This behaviour can be represented by a dual profit function. For any output-input combination (y, x), the profit function is defined as:

( , , ) max[ ' ' ] = p w k p y w x (1)
where w and x are vectors of factor prices and factor demands, p are the output prices, and y are the output quantities respectively. k represents fixed and quasifixed inputs. If the profit function satisfies certain regularity conditions, it is dual to the production function and its parameters contain enough information to describe the farmer's short-run production behaviour. The profit function should be: decreasing in w, increasing in p, convex in all prices and be linearly homogeneous in all prices [START_REF] Mcfadden | Cost, revenue, and profit functions[END_REF][START_REF] Chambers | Applied production analysis: A dual approach[END_REF]. These regularity conditions are testable. (3)

(2) and (3) are uniquely defined as profit maximising output and input quantities and they are the behavioural relationships that underpin the dual analysis of production decisions. The empirical strategy involves the simultaneous estimation of the profit function, the output and input share equations as a system.

III. Methods

The translog specification 3

The multioutput translog profit function to be estimated can be written as:

= = + + + µ (5)
where r S = the share of netput r in total profit, it is positive for outputs (r=1, 2)

and negative for inputs (r=3…..7). r it µ is the error term for the respective share equations.

If the profit function satisfies the conditions of monotonicity, convexity, symmetry and homogeneity, it is dual of the transformation function and its estimated parameters contain sufficient information to describe the farm's production technology at profit maximising points in the production possibility set. Symmetry of the profit function is imposed by using nested cross-equation restrictions and appropriately constraining relevant coefficients in the profit function and the share equations. Linear homogeneity implies that profit will remain unchanged if all variable inputs and outputs prices increase by the same proportion. Linear homogeneity is routinely imposed prior to profit function estimation in the literature. We impose homogeneity by using an input price as a numéraire to normalise the profit and price variables, as in common practice (eg. Sidhu and Baanante (1985); [START_REF] Kheralla | The sequencing of agricultural market reforms in Malawi[END_REF]). This has the added

The WITHIN-SURE model

The multi-output profit function system is estimated using a fixed effects model on a panel dataset. This allows the control of unobserved farm and farmer characteristics that do not change over time. Fixed effects are chosen over random effects because of extensive evidence in the agricultural context that individual characteristics (e.g., managerial ability) may be correlated with the explanatory variables (e.g., level of output) and treating them as uncorrelated may lead to bias. The error terms in the system (4) and ( 5) can thus be described as follows:

µ d it = 4 d i + u s it (d = pf, 1…7) (6)
where 4 d i is the farm(er)-specific effect, and the u d it is iid error for equation d.

The Within-SURE method involves first subtracting farm means from all variables in equations sets (4) and ( 5), thereby removing the farm-specific effects 4 s i. . Subsequent to removal of means, Seemingly Unrelated Regression (SUR) methods (Zellner, 1962) are applied to the de-meaned equations.

Ozone-related elasticities The ultimate objective of this paper is to estimate the impact of changes in tropospheric ozone concentration on variable profits and on the supplies of cereal output. Such information can be obtained by considering the elasticities of variable profits and profit-maximising output-supply with respect to changes in ozone concentration. The elasticity of variable profits with respect to ozone can be computed as:

7 , 1 ln 1 ln 2 k it d itd d p k = = + + (7)
and the elasticity of supply of output v with respect to ozone can be estimated using:

7 , 1 ln ln v v k it r itr r v p k S = = + + + , (8)
where v indexes the outputs and S v is the output share. and v are estimated parameters.

IV. Data

Cereals

The data used for estimation come from a series of economics studies on cereals window [START_REF] Ollerenshaw | Impacts of ozone on the growth and yield of field-grown winter wheat[END_REF]. The AOT40 is computed as:

1 ( 40) 40 . = > n i i i x for x in ppb h (9)
where i x is the hourly TO concentration in parts per billion and n is the number of hours for which 40 i x > . According to [START_REF] Lefohn | A comparison of indices that describe the relationship between exposure to ozone and reduction in the yield of agricultural crops[END_REF], using a cumulative exposure index results in a better predictor of the impacts of ozone on vegetation as compared to seasonal mean measures of the type that were used in [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF] and Young and Aidun (1993). The spatial locations of the monitoring stations and the ozone data were input in a Geographical

Information System (GIS) so that ozone levels for farms could be estimated through interpolation. Summary statistics are presented in Table 1.

[Table 1 approximately here]

V. Results

Pre-testing for output price separability and input non-jointness

The fixed effects model is tested for output price separability and input nonjointness. A log-likelihood test is used to check whether restrictions imposed on the system hold. This is a 2 test, with the number of restrictions being the degrees of freedom. The null hypotheses are that separability and input non- 2.

[Table 2 approximately here]

The hypothesis of separability in output prices is rejected at 5% level. The existence of price and quantity indexes that satisfy the adding-up property, and therefore the scope for aggregating wheat and barley as a single output, is rejected. It is therefore theoretically and empirically more appropriate to use a multi-output specification to evaluate wheat and barley profits. The hypothesis that the technology is non-joint in inputs is also rejected at the 5% level. This further suggests that the wheat and barley enterprises are closely synergistic, and any attempt to model either wheat or barley in isolation would have been inappropriate.

Estimates and Diagnostics

We used the Lagrange multiplier (LM) test of Breusch and Pagan to check the hypothesis of a diagonal residual correlation matrix. We obtained a 2 value of 407.4, which was significant at the 1% level and therefore reject the null hypothesis of a diagonal residual correlation matrix. The use of SURE over an OLS is consequently warranted. An F test was also carried out to test whether all slopes coefficients were simultaneously zero. This hypothesis was also rejected at the 1% level.

Results from the Within-SURE estimation of the system of equations comprising the multi-output profit function and the share equations are shown in Table 3. 3 approximately here]

The number of significant parameters at 1%, 5% and 10% significance levels are 23, 24 and 25 out of 30 estimated parameters. Thus most parameters in the model appear to be reasonably precisely estimated. Symmetry restrictions are tested conditional on imposed homogeneity. The results are shown in Table 4.

[Table 4 approximately here]

The results from the likelihood test are encouraging. At the 5% level the property of symmetry conditional on homogeneity is not rejected. Therefore, the parameters of the model in its most restricted form are used to compute the share values and the elasticities.

We next turn to checking monotonicity and convexity in prices. As Table 5 shows, monotonicity is satisfied as the fitted output and input shares are respectively positive and negative. Convexity in prices is satisfied when ownprice elasticities are confirmed to have the correct signs. Elasticities evaluated at sample means values are presented in Table 6. As the table confirms, all ownprice elasticities display the correct sign. The main theoretically implied restrictions are seen to be satisfied, therefore the estimated profit function is dual to the transformation function and its parameters contain sufficient information to describe the farm's production technology at profit maximising points. We therefore turn to computing ozone elasticities with reasonable confidence in model performance. 5 approximately here]

[Table 6 approximately here]

Ozone elasticities and their implications

The major aim of this study has been to estimate variable profit and cereal supply elasticities with respect to ozone using equations ( 7) and ( 8). Computed elasticities are reported in Table 7. At the sample mean AOT40 of 3090 ppb.h, the estimated elasticity of profits with respect to ozone is -0.134. This elasticity conforms to prior expectations and suggests that a 10% increase in the ozone index above its mean value would correspond to a 1.3% decrease in variable farm profits. The elasticity is significant at the 10% level.

[Table 7 approximately here]

There are no European farm-level studies with which to compare our results.

The closest comparable studies are those of Young and Aidun (1993) and [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF]. Young and Aidun (1993) estimated an elasticity of -2, which is fifteen times the magnitude of the present estimate. This disparity could be explained by numerous factors. The Alberta study by Young and Aidun modelled ozone effects on profits from a single enterprise, wheat. In our case, involving farms jointly cropping wheat and barley, there are likely more avenues available for farmers to mitigate the effects of ozone on overall profits. In this regard, our results appear more comparable to [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF] and [START_REF] Mjelde | Using farmers' actions to measure crop loss due to air pollution[END_REF], who computed profit elasticities of -0.476 and -0.408 respectively, exposures. This could have attenuated the average deleterious effect of ozone that could have occurred with a more geographically localised sample. The levels of TO experienced in Alberta were also of higher magnitude that those experienced in England and Wales from 1993 to 1998. Given that the effect of ozone on crop output is likely to be increasing in ozone levels, wheat production and therefore profits may have been relatively more affected in Alberta as compared to England and Wales. There is also the possibility that the wheat varieties cropped in Alberta could have been more susceptible than those under cultivation in England and Wales.

Possibly, the key reason for the significant difference in magnitudes is that we account for heterogeneity via the use of panel methods. A significant body of research now shows that economic outcomes across farms are strongly influenced by unobserved heterogeneity, including farmer efficiency, soil quality and topography effects, etc. Lack of control for such effects has the potential to significantly bias the estimated effects of variables such as ozone. (1993) and [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF] an elasticity of -0.134 can still be of economic significance. The effect is inelastic, but when evaluated at average variable profits, it corresponds to a loss of £ 1465 for a 10% increase in the mean AOT40 index, for an average farm in the sample. Fluctuations significantly larger than 10% are common both across space in a given year, and across years.

For example, in 1995, England and Wales suffered a strong TO episode and many counties experienced AOT40 values greater than 4635 ppb.h. This represented a 50% increase in the average sample concentration. Extrapolating the profit elasticity with respect to TO to this average ozone value would suggest a 6.7% reduction in the average variable profits. This equates to a £ 7325 reduction in variable profits for an average cereal producer in the year 1995.

Thus the losses can be significant even though the estimated magnitude is smaller than previous studies have indicated.

The wheat supply elasticity with respect to TO is -0.1006 and is significant at the 10% level. The negative sign on the elasticity is validated by biological science studies [START_REF] Buse | An Assessment of Crop Losses in Europe due to Ozone[END_REF], which show that wheat is susceptible to high ozone levels. A supply elasticity of -0.1006 implies that a 10% increase in the average ozone index depresses wheat supply by 1.006%. Young and Aidun (1993) obtained an output elasticity of supply of -0.73 on wheat farms in Alberta. The same explanations discussed for the difference in profit elasticity magnitudes across studies apply here. Somewhat surprisingly, barley supply elasticity is larger, at -1.25. Barley is less sensitive to TO than wheat, and hence 18 the a-priori expectation would have been that the effect on wheat supply would be more pronounced. However, a variety of adjustments at the margin are likely to take place in response to ozone exposure over time. This includes changes in variable input applications, changes in land cropped, and changes in the output mix, as producers compensate for ozone-induced losses [START_REF] Garcia | Measuring the benefits of environmental change using a duality approach: The case of ozone and Illinois cash grain farms[END_REF].

VI. Conclusion

This study sought to identify the economic impact on and adjustments in the behaviour of cereal producers due to changing TO concentrations. Previous economic evaluations of the impacts of ozone in European settings have largely relied on extrapolations from experimental data. However, farmers have an array of behavioural economic responses available to mitigate the effects of ozone, and so such extrapolations can result in overstatement of economic impact. In this paper, we have instead directly relied on farm level data and estimation of a set of behavioural economic equations to investigate the impact of ozone in England and Wales. We have also tried to improve estimation precision compared to the existing literature in this area from North America, by using a more relevant pollution index, and by controlling for heterogeneity.

Our results have confirmed a statistically significant impact of ozone on farm profits and wheat and barley supply in England and Wales. However, the effect is relatively small compared both to what is implied by experimental evidence, and also compared to estimates from North America. Despite the small The main message from this research is that great caution is warranted in freely extrapolating from experimental data to carry out economic impact assessment.

Experimental evidence is extremely valuable in several ways, but there can be a significant gulf between experimental and economic outcomes. Farmers as economic agents can and will carry out mitigatory actions to cope with external shocks to productivity, thereby cushioning the impact of the shock. Even the estimates that we have derived cannot be extrapolated to a regional or national

  obtain in the 'real world' where other inputs are not so constrained, are mis-estimated 2 .

  To our best knowledge, it is the first application of dual methods to investigate farm-level effects of ozone using European data.

  the number of variables to be estimated. Later, symmetry is tested conditional upon homogeneity.

  undertaken in the UK from 1993 to 1998. The survey was conducted by the Land Economy Department of the University of Cambridge on behalf of the Department of Environment, Food and Rural Affairs, U.K. Wheat and barley constitute the major cereals in the region. Farms having complete production data on winter wheat and barley and that are present in all six years were included in the sample. This constituted a balanced farm level panel dataset of farms, resulting in 396 observations. The prices for wheat and barley were determined by dividing the total respective enterprise revenues by the quantity of the outputs. The total revenue also included revenue received from the sale of straw and set-aside payment. Farm level prices for seeds and fertiliser were calculated by dividing expenditures by respective quantities. In the present context the different seed varieties and different types of fertiliser were aggregated, to ultimately derive a price for seed and a price for fertiliser.Variable profits, output and input prices were respectively deflated using input and output specific price indices for agricultural production, obtained from DEFRA However, as far as crop protection inputs were concerned, only expenditure data were gathered. Hence the price index for crop protection input, constructed by DEFRA under the 'Agriculture in the UK' data series(DEFRA, 2002) was used. The DEFRA national average agricultural wage rates also enter the model as an explanatory variable. Land rental rates were computed by dividing expenditure on land rent by area and expressed as £ per ha. Variable profits and prices were then normalised by the price of crop protection input to impose homogeneity.Tropospheric ozoneOzone data were obtained from the UK national air quality information archive, which covers 50 monitoring stations spread across the UK. The reported data are in parts per billion per day. They were downloaded for each day from the 1 st day of May till the last day of July of each year covered in the study. This choice is based on previous experimental research, which reveals that the winter the UK is more susceptible to ozone damage during this particular

  . The test statistics for the hypotheses are presented in Table

  these studies also modelled a multi-output scenario (wheat, soybeans and corn 4 ). Also, Young and Aidun (1993) used ppb as ozone units and this could have resulted in an overestimation of the ozone effect. Experimental research in Europe has clearly demonstrated that there is a threshold effect to the effect of ozone pollution on crop production, as captured by the AOT40 index we have used. The current sample had a broader spatial coverage, with wider ozone

  present estimate is lower than those obtained by Young and Aidun

  elasticity, elevated ozone levels can still cause moderate losses on cereal farms.

  pf it µ is the error term for the profit function. The subscripts i and t index farms and years respectively. By differentiating the profit function with respect to output and input prices, we obtain the following set of output supply and input demand equations.

	r o F ln 1 ln 2 r r r S p	7 r	1 =	ln	itr p	ln	it k	r it
	P
	e
	e r
	7 ln 1 r = p are wheat and barley prices, 3 0 7 2 1 ln ( , ) ln ln 1 ln ln 2 it r itr it it r itr it pf it r p k p k = = + + + + + µ p k k R e 1 2 + v i 7 1 r = e i where 1 p , 2 p , 4 p , 5 p , 6 7 1 1.....N, ln rd d = = p , 7 p are seed price, ln 1.....T itr itd p p t = (4) w

fertiliser price, crop protection inputs price, paid labour and land rent respectively, and k is tropospheric ozone. Since agricultural output and input price markets are competitive, exogeneity of prices is a reasonable assumption as made in several profit function studies of European Agriculture. Seed, fertiliser,

3

The translog specification is used as it is a interpretable as a second-order approximation to an arbitrary function at a given point. 'Flexible' functional forms such as the translog have become the forms of choice in applied production analysis. 8 crop protection inputs, paid labour and land are considered as variable inputs, and tropospheric ozone is considered a quasi-fixed input. &, ', (, ), * are parameters to be estimated.

Table 1 .

 1 scale. At an aggregate level, depending on the elasticities of cereal supply and demand, it is even possible that control of ozone may result in little or no economic gains, despite what is suggested by experimental evidence. Summary statistics for the variables used in the estimation after conditioning for outliers, negative and non-zero profits.

	Testing of farm-level outcomes of data using other European data may be a
	fruitful topic for further research. Ozone levels become elevated with
	temperature, and hence Southern Europe may be a particularly appropriate
	setting for such work.

Table 3 .

 3 Parameter estimates for the fixed effects model

	P wheat P barley P seed P fertiliser P labour P rent Ozone P wheat * P wheat P barley *P seed P barley * P fertiliser P barley *P labour P barley *P land P barley *P barley P seed *P seed P seed *P fertiliser P seed *P labour P seed *P land P fertiliser *P fertiliser P fertiliser *P labour P fertiliser *P land P labour *P labour P labour *P land P land *P land Ozone*Ozone	Coefficient 0.551336 *** 0.827126 *** -0.044557 *** -0.091751 *** 0.05488 *** -0.207915 *** 1.015608 *** 0.920322 *** 0.028964 *** 0.043336 *** 0.090885 *** 0.00677 0.341548 *** -0.098645 *** 0.040317 *** 0.050722 0.062232 *** -0.110577 *** 0.08301 * 0.052379 ** -0.230905 0.459642 *** -0.313523 *** 0.587347	Std. Error 0.011569 0.031144 0.003767 0.006901 0.014452 0.009066 0.096557 0.034907 0.003276 0.005982 0.012486 0.007879 0.027381 0.011466 0.009829 0.031379 0.017061 0.018143 0.037594 0.021443 0.177207 0.070313 0.047606 0.468568	t-Statistic 47.65673 26.55851 -11.828 -13.29474 3.797455 -22.93264 10.51825 26.36503 8.839945 7.243952 7.278989 0.859315 12.47385 -8.603178 4.102512 1.616401 3.647541 -6.094903 2.20806 2.442662 -1.303023 6.537115 -6.585762 1.253493
	P wheat *Ozone P barley *Ozone P seed *Ozone P fertiliser *Ozone P labour *Ozone P land *Ozone	0.035966 -0.441487 *** 0.087238 *** 0.143689 *** 0.173158 *** 0.233109 ***	0.043975 0.065576 0.007992 0.014182 0.02958 0.019897	0.817883 -6.732401 10.91552 10.13169 5.853968 11.71555
	Adjusted R 2 Notes: *** significant at 1%, ** significant at 5%, * significant at 10% 0.57

Table 4 .

 4 Log-likelihood ratios Null hypothesis D.F Log-likelihood ratio Critical value of 2

	0.05

Table 6 .

 6 Estimated price and cross price elasticities Price and cross price elasticities Elasticities are computed at the mean of the actual profit shares Standard errors are in parentheses *** significant at 1%, ** significant at 5%, * significant at 10%, ++ significant at 15%, + significant at 20% : Elasticities are computed at the mean of the actual profit shares Standard errors are in parentheses *** significant at 1%, ** significant at 5%, * significant at 10%

				Price
		Wheat	Barley	Seed	Fertiliser	Crop	Labour Land
						protection
	Quantity Wheat	0.9207 *	0.0859	0.9739 ++	0.5441	-3.0026 **	0.1587	0.3193 *
		(0.488)	(0.0759)	(0.654)	(0.499)	(1.364)	(0.354)	(0.169)
	Barley	-0.036	0.7557 +	0.2053	0.1323	0.4215	-1.795	0.3166
	Seed	(0.0331) -0.0695 (0.0985)	(0.568) -0.0346 (0.0543)	(0.369) -0.213 * (0.123)	(0.189) -0.3409 (0.446)	(0.562) 1.517 (2.025)	(4.401) 0.5995 * *	(0.845) 0.2595 (0.367)
							(0.268)
	Fertiliser	-0.120 (0.215)	-0.039 *** (0.015)	0.6092 (0.498)	-0.337 ** (0.169)	0.7219 ++ (0.487)	-1.028 ***	0.1949 (0.265)
							(0.369)
	Crop	0.019	-0.806 ***	-0.4947 *	0.0568	-1.698 +	2.6618	0.2627
	protection	(0.0235)	(0.236)	(0.264)	(0.0481)	(1.221)	(2.351)	(0.415)
	Labour	0.0013	0.1861	-0.3687	-0.354 +	1.5187 ***	-2.66 **	1.679
		(0.0147)	(0.663)	(0.441)	(0.264)	(0.569)	(1.357)	(2.025)
	Land	-0.712 ***	-0.146 ***	-0.712 **	0.2992 **	0.5222	3.262	-2.513
		(0.239)	(0.015)	(0.368)	(0.152)	(0.41)	(2.985)	(2.651)

Notes:

Notes

Page 29 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

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

Note however that these studies did not estimate multi-output profit functions and instead aggregated data from multiple crops into scalar indices.

Acknowledgements

The authors are grateful to Xavier Irz and Alastair Bailey for comments on a previous version of the material presented in this paper. We are also thankful to two anonymous referees for perceptive comments that have improved the paper.

Any remaining errors are our own.

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


Mikael ; Bask
email: mikael.bask@hanken.…

Jens Lundgren
email: jens.lundgren@econ.umu.se

Niklas Rudholm

Market Power in the Expanding Nordic Power Market

Keywords: C32 -Time-Series Models < C3 Bresnahan-Lau method, conjectural variation elasticity, electricity market, market power, Nord Pool JEL classi…cation: C32, D43, L13 Bresnahan-Lau Method, Conjectural Variation, Electricity Market, Market Power, Nord Pool

HAL is

Introduction

Denmark, Finland, Norway and Sweden have cooperated during several years to provide their citizens with an e¢ cient and reliable electricity source. In fact, all of them have reformed their electricity sectors and have today access to a common power market consisting of two parts: (i) bilateral trade of contracts between operators; and (ii) the non-mandatory power exchange, Nord Pool.

Because of these reforms, it is natural to ask whether they have been successful: has the common power market been competitive or have electricity suppliers had market power? Moreover, since there was a stepwise evolution from national markets to a multi-national and largely deregulated power market, we also ask how the degree of market power has evolved during this integration process?

A straightforward measure of a market's competitiveness is the price-marginal cost markup since it is zero at a perfectly competitive market, meaning that the electricity price should equal the production cost of the marginal unit of electricity. However, even though market prices are easily accessible in the Nordic power market, this is not the case with marginal costs and some other method must be used to measure the degree of market power. One such method is a conjectural variation method named the Bresnahan [START_REF] Bresnahan | The oligopoly solution concept is identi…ed[END_REF]-Lau [START_REF] Lau | On identifying the degree of competitiveness from industry price and output data[END_REF] method. 1The conjectural variation elasticity at the industry level is the average of the individual …rms'conjectural variation elasticities, which measure the …rms' output response to the single …rm's output change as conjectured by this …rm. Thus, if there is perfect competition, there is no output response since a single …rm cannot a¤ect output at the industry level, whereas the response is one-toone if there is no competition since the industry behaves as a single …rm.

The conjectural variation elasticity is estimated from a two-equation system, where the …rst equation is electricity demand as a function of electricity price and at least one exogenous variable, whereas the second equation is electricity supply, derived from pro…t maximization, which is electricity price as a function of industry output, the same exogenous variables as in electricity demand and maybe some other exogenous variables.

The exogenous variables are introduced to solve an identi…cation problem. Bresnahan [START_REF] Bresnahan | The oligopoly solution concept is identi…ed[END_REF] solved this problem by using a rotation variable in the demand equation, whereas Lau [START_REF] Lau | On identifying the degree of competitiveness from industry price and output data[END_REF] showed that the identi…cation of market power is possible as long as demand is non-separable in at least one exogenous variable. Thus, if at least one exogenous variable is part of an interaction term in the demand equation, the identi…cation problem is solved since the interaction term acts as a rotation variable and it is also non-separable in the exogenous variable. 2Hjalmarsson [START_REF] Hjalmarsson | Nord Pool: A power market without market power[END_REF] and Vassilopoulos [START_REF] Vassilopoulos | Models for the identi…cation of market power in wholesale electricity markets[END_REF] are the only studies that we are aware of that measure the degree of market power in the Nord Pool area, and they …nd that the power market has been competitive. However, none of them studies the e¤ect of market expansion on the degree of market power, meaning that the present paper …lls a gap in the literature. The rest of this paper is outlined as follows: The Bresnahan-Lau method or model is presented in Section 2, Section 3 contains the empirical analysis, and Section 4 concludes the paper with a discussion.

2 The Bresnahan-Lau model

The static model

The Bresnahan-Lau model is a static model since there are no lagged or lead values of the variables included. Speci…cally, the electricity demand function is

Q = D (P; Z; ) + "; (1)
where Q is quantity demanded, P is price of power, Z is a vector of exogenous variables, is a vector of parameters to be estimated, and " is a random term. Moreover, the electricity supply relation is

P = c (Q; W ; ) h (Q; Z; ) + ; ( 2
)
where W is a vector of exogenous variables, is a vector of parameters to be estimated, is the degree of market power, and is a random term. c ( ) in ( 2) is the marginal cost of producing electricity, meaning that when = 0, the price of power is equal to the marginal cost and we have a perfectly competitive power market since all suppliers of electricity are price-takers. However, when suppliers are price-setters, the marginal revenue as perceived by the single supplier is equal to the marginal cost, and this is because P + h ( ) is the marginal revenue at the industry level and is the perceived percentage of this revenue. Thus, when = 1, we have a perfect cartel in the power market.

Then, by assuming a linear demand function for electricity,

Q = 0 + P P + Z Z + P Z P Z + "; (3)
including an interaction term between P and Z that acts as a rotation variable, and a linear marginal cost function,

c ( ) = 0 + Q Q + W W; (4)
the electricity supply relation is

P = 0 + Q Q + W W Q P + P Z Z | {z } =Q + : (5)
Thus, if we …rst estimate (3), meaning that we can calculate Q , we can identify the degree of market power, , after having estimated (5).

The dynamic model

Steen and Salvanes [START_REF] Steen | Testing for market power using a dynamic oligopoly model[END_REF]

P Z;0 P Z t + P Z;1

P Z t 1 + Q;1 Q t 1 + " t ;
and continue by writing the electricity supply relation as an autoregressive distributed lag model:

P t = Q;0 Q t + Q;1 Q t 1 + W;0 W t + W;1 W t 1 + (7)
0 Q t + 1 Q t 1 + P;1 P t 1 + t ;
where the long-run stationary equilibrium is found by setting

Q t = Q t 1 , P t = P t 1 , Z t = Z t 1 , P Z t = P Z t 1 , W t = W t 1 and Q t = Q t 1 .
Thereafter, if we relax the restriction of one lag and include an intercept term, ( 6)-( 7) can be written in error-correcting forms:

Q t = 0 + k 1 X i=1 Q;i Q t i + k 1 X i=0 P;i P t i + (8) k 1 X i=0 Z;i Z t i + k 1 X i=0 P Z;i P Z t i + Q t k P P t k Z Z t k P Z P Z t k + " t ;
and

P t = 0 + k 1 X i=1 P;i P t i + k 1 X i=0 Q;i Q t i + (9) k 1 X i=0 W;i W t i + k 1 X i=0 i Q t i + P t k Q Q t k W W t k Q t k + t :
See Steen and Salvanes [START_REF] Steen | Testing for market power using a dynamic oligopoly model[END_REF] for a derivation and a discussion of the relationship between the distributed lag model and its error-correcting form.

3 Empirical analysis

Data set

The data set consists of weekly data from all Nord Pool participants, covering the period from week 1 in 1996 to week 16 in 2004. See Table 1 for the dates in the integration process, and Table 2 for the variables used, their de…nitions and data sources.

[Tables 1-2 about here.] The price variable is Nord Pool's spot price at the system level (P ). Further, since the industry sector is the largest consumer of electricity, we include industrial production (Prod ) when studying electricity demand. A problem, however, is that data are available only on a monthly basis, whereas all other variables are available on a weekly basis. There are two options at hand: (i) to exclude this variable (Vassilopoulos [24]); or (ii) to interpolate data into weekly estimates (Hjalmarsson [15]). We choose to interpolate since the variation of this important variable within each month is expected to be small. Two other variables a¤ecting electricity demand are the temperature (Temp), which is a proxy for the amount of electricity needed for heating, and the length of a day (Daylength), which is a proxy for the amount of electricity needed for lightning. We also need at least one interaction variable to be able to identify the degree of market power. For this reason, we let the spot price at the system level to interact with the temperature as well as the length of a day in the Nord Pool area (P*Temp and P*Daylength).

To determine electricity supply, we need to approximate the marginal cost function and also …nd variables that shift this function. For this reason, we look at the opportunity cost of hydro generation, and two factors that a¤ect this cost are in ‡ow of water to reservoirs (In ‡ow ) and how full they already are. We choose the in ‡ow variable as a shift variable.

The Nordic power market consists of a relatively large amount of hydro generation, which is a cheap electricity source and has almost no variable costs (Andersson and Bergman [START_REF] Andersson | Market structure and the price of electricity: An ex ante analysis of deregulated Swedish markets[END_REF]), meaning that hydro power is a base load electricity. When more energy is needed, more expensive sources such as thermal power are used, and this residual electricity is produced with a number of inputs such as bio fuel, coal, gas, and oil.

Contrary to hydro power, the technology of residual electricity has higher and more variable costs (Green and Newbery [START_REF] Green | Competition in the British electricity spot market[END_REF]). Therefore, we incorporate the coal price (Coal ) and the Brent crude oil price (Oil ) into electricity supply to account for the thermal part of electricity generation. Moreover, to account for the residual electricity trend, we include residual electricity in relation to total electricity production (Resel ) as a variable in the analysis.

Finally, the increase in electricity traded at Nord Pool's spot market is an exogenous trend that need to be taken into consideration when building the empirical model. Following Hjalmarsson [START_REF] Hjalmarsson | Nord Pool: A power market without market power[END_REF], this is accomplished by regressing the system turnover (Turnover ) on the market share (Market share) and, thereafter, use the residual as a detrended quantity variable (Q).

See Table 3 for descriptive statistics of the variables used in the empirical analysis in the di¤erent subperiods in the integration process.

[Table 3 about here.]

Statistical tests

Before specifying the two-equation regression model, we need to test if the variables are stationary. If this is not the case, we also need to test for cointegration to ensure the existence of a long-run equilibrium in data. Finally, a separability test is preformed on the interaction variables to make sure that the degree of market power is identi…able (Lao [START_REF] Lau | On identifying the degree of competitiveness from industry price and output data[END_REF]). Dickey-Fuller's augmented unit root test is used in companion with the AIC to test if the variables are stationary. However, a potential problem is that the variables are highly seasonal, meaning that we have to deseasonalize data before using the test. This is accomplished by introducing weekly dummy variables and estimate the following equation:

y t = 0 + 52 X i=2 i W eek i + ŷt ; ( 10
)
where ŷt is the regression residual, which is the deseasonalized value of y t . See Table A.1 in the Appendix for results. Thereafter, we use the Johansen [START_REF] Johansen | Statistical analysis of cointegration vectors[END_REF] approach to search for cointegrated relations between the variables. Speci…cally, we use the Johansen and Juselius [START_REF] Johansen | Maximum likelihood estimation and inference on cointegration: With applications to the demand for money[END_REF] multivariate cointegration test, which is a maximum likelihood test on the results from a vector autoregression. As above, a potential problem is that the variables are highly seasonal, meaning that deseasonalized data are used in the tests. See Tables A.2-A.3 in the Appendix for results, which show that we have cointegrated relationships among the integrated variables, both at the demand and supply sides of the power market.

Finally, electricity demand must be non-separable in at least one of the interaction variables, and the appropriate test is an extension of the cointegration test by introducing restrictions that the interaction variables are zero. The restricted model is, thereafter, compared to the unrestricted model using a likelihood ratio test. See Table A.2 in the Appendix for results, which show that the interaction variables should be included in the regression model.

Estimation results

The demand function and the supply relation for electricity are

Q tj = 0 + k X i=1 Q;i Q t i + k X i=0 P rod;i P rod t i + (11) k X i=0 T emp;i T emp t i + k X i=0 Daylength;i Daylength t i + l X j=1 k X i=0 CVj ;i CV j;t 1 + " t ;
and where fCV g l j=1 are cointegrated vectors. Because of a simultaneity problem that arises in demand and supply models, two-stage least squares is used in the analysis. In [START_REF] Edin | Marknadsmakt i vattenkraft-värmekraftsystem[END_REF], the …rst lag of the system price, the temperature, and the in- ‡ow of water to reservoirs are used as instruments, and in [START_REF] Fuller | Introduction to statistical time series[END_REF], the temperature and the length of a day are used as instruments. Both equations are estimated using autocorrelation and heteroscedasticity consistent standard errors. First, ( 11) is estimated for the whole period using …ve lags. Insigni…cant variables are, thereafter, removed from the regression equation and a parsimonious model is derived. See Table A.4 in the Appendix for results for the whole period and for each subperiod in the integration process, which show that lagged quantities have a positive impact on electricity demand. The estimates for the cointegrating vectors show that the current price has a negative impact on electricity demand. Moreover, increased temperature and longer days cause electricity demand to fall.

4P tmj = 0 + q X m=1 k X i=1 Pm;i 4P m;t i + k X i=0 Q;i Q t i + (12) k X i=0 Q 2 ;i Q 2 t i + k X i=0 i Q t i + k X i=0 Inf low;i Inf low t i + k X i=0 Coal;i Coal t 1 + k X i=0 Oil;i Oil t 1 + k X i=0
Second, ( 12) is estimated including Q = Q Q= P in the regression equation. Since the price variables are non-stationary, an error-correction model is used to estimate electricity supply, and as the error-correction term, we use the …rst lag of the cointegrating vector. Electricity supply is estimated for the whole period, and a parsimonious model is derived as above, which is estimated for each subperiod in the integration process. See Table A.5 in the Appendix for results, which show that the in ‡ow of water to reservoirs has a negative impact on electricity price, while the use of residual electricity has a positive impact on this price. The error-correction term indicates a slow error-correction in line with previous literature (Hjalmarsson [START_REF] Hjalmarsson | Nord Pool: A power market without market power[END_REF] and Vassilopoulos [START_REF] Vassilopoulos | Models for the identi…cation of market power in wholesale electricity markets[END_REF]).

Finally, estimates of the degree of market power, , are found in Table 4. 3 [Table 4 about here.]

The results show that electricity suppliers have had a small, but statistically signi…cant, degree of market power during the whole period, even though it has been reduced as the market has expanded. In the last subperiod, there was no market power in the Nordic power market. In economic terms, the estimated market powers indicate small markups over marginal costs. In fact, the implied Lerner index gives a markup of less than one percent in the di¤erent subperiods and an even smaller markup for the whole period. 4

Discussion

The aim of this paper has been to examine how the degree of market power has changed as the Nordic power market has evolved from national markets to a multi-national market. While previous studies have not found any evidence of market power in the Nord Pool area (Hjalmarsson [15] and Vassilopoulos [START_REF] Vassilopoulos | Models for the identi…cation of market power in wholesale electricity markets[END_REF]), our study, which use a more comprehensive data set, indicate that there has been a small, but statistically signi…cant, degree of market power during almost the whole period. More importantly, our results show that the degree of market power has been reduced as the market has expanded. 4. However, since no minus sign is included in the regression equation, changes sign. Therefore, in Table A.5, 2 [ 1; 0]. 4 The implied Lerner index is de…ned as P M C P = " , where " is the demand elasticity (Steen [START_REF] Steen | Do bottlenecks generate market power? An empirical study of the Norwegian electricity market[END_REF]). However, the implied Lerner index gives a markup of less than one percent over marginal cost, meaning that the impact of market power on the electricity price has not been that severe. Steen [START_REF] Steen | Do bottlenecks generate market power? An empirical study of the Norwegian electricity market[END_REF] examined the Norwegian market with results similar to ours and concluded that "the results are probably more a word of warning that we should be careful to allow more concentration in this market". Most likely, there are several reasons why the markup has been low, one of them being the threat of entry.

Wolfram [START_REF] Wolfram | Measuring duopoly power in the British electricity spot market[END_REF] argues that there are two reasons why …rms in the UK have not utilized all potential market power: (i) the threat of market interventions from the authorities; and (ii) the threat of entry into the market. Although her results may not be directly transferable to the Nordic power market, Edin [START_REF] Edin | Marknadsmakt i vattenkraft-värmekraftsystem[END_REF] argues that it is possible that the threat of entry has kept the price close to marginal cost also in the Nordic market.

Moreover, Amundsen and Bergman [START_REF] Amundsen | Will cross-ownership re-establish market power in the Nordic power market[END_REF] analyze the e¤ect of cross-ownerships in the electricity market and how mergers will a¤ect this market. They conclude that mergers and cross-ownerships may re-establish at least part of the market power that the deregulation has removed.

Finally, Amundsen and Bergman [START_REF] Amundsen | Why has the Nordic electricity market worked so well?[END_REF] compare the Nordic power market to the Californian power market and …nd that the Nordic market has worked well. This is because the Nordic market is characterized by a simple but sound market design, successful dilution of market power, strong political support for a market-based electricity system, and voluntary informal commitment to public service by the power industry.

5

 5

3 2 [0; 1 ]

 31 in Table

Table 1 :

 1 Integration process at the Nordic power market Country Date for a¢ liation Date for complete integration

	Norway	January 1, 1993	January 1, 1993
	Sweden	January 1, 1996	January 1, 1996
	Finland	December 29, 1997 March 1, 1999
	Western Denmark July 1, 1999	March 1, 2002
	Eastern Denmark	October 1, 2000	March 1, 2002

Table 2 :

 2 Variables, de…nitions and data sources Variable De…nition and data source P Nord Pool's spot price at the system level, NOK/MWh. The cities in Denmark are Copenhagen and Billund; the cities in Finland are Helsinki and Ivalo; the cities in Norway are Oslo, Bergen, Trondheim and Tromsø; and the cities in Sweden are Stockholm, Gothenburg, Luleå and Östersund.

		Source: Nord Pool ASA
	Prod	Weighted average of the countries'industrial production
		indexes using the countries'GDP shares as weights.
	Daylength	Number of hours the sun is above the horizon in Gothenburg,
		Sweden. Source: www.stjarnhimlen.se
	In ‡ow	In ‡ow to water reservoirs, recalculated from water in ‡ow to
		the water's energy content in MWh.
		Sources: Nord Pool ASA and SYKE
	Coal	Price of coal used to generate electricity, USD/MWh.
		Source: The McCloskey Group
	Oil	Price of Brent crude oil used to generate electricity,
		USD/MWh.
		Source: tonto.eia.doe.gov/oog/ftparea/wogirs/xls/psw14.xls
	Resel	Residual electricity traded at Nord Pool's spot market in
		relation to total electricity production. Source: Nord Pool ASA
	Turnover	Number of MWh traded at Nord Pool's spot market.
		Source: Nord Pool ASA
	Market share The market share of Nord Pool's spot market measured as
		the turnover at the spot market in relation to total electricity
		production. Source: Nord Pool ASA
	Q	Detrended turnover at Nord Pool's spot market measured by
		regressing the turnover at the spot market on its market
		share, where the residuals are used as detrended turnover.
		Source: Nord Pool ASA
	Note: a

Sources: Statistics Denmark, Statistics Finland, Statistics Norway, Statistics Sweden and OECD Temp Weighted average of the participating countries average temperatures, where the weights are the countries'GDP shares, and the participating countries'average temperatures, in turn, are weighted averages of the average temperatures in selected cities, where the weights are the cities' populations. a Sources: Nord Pool ASA and SMHI 10 Page

10 of 15 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
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Table 3 :

 3 Descriptive statistics

	Variable	9601 0416	9601 9908	9909 0209	0210 0416
	P	178:17	181:06	135:08	234:85
		(85:45)	(79:09)	(44:50)	(103:07)
	Prod	96:21	90:96	98:51	100:72
		(8:09)	(6:68)	(7:48)	(6:46)
	Temp	6:83	5:95	7:61	7:05
		(7:46)	(7:56)	(6:96)	(7:91)
	Daylength	86:06	85:25	86:41	86:76
		(26:99)	(27:23)	(27:23)	(26:51)
	In ‡ow	3:66E + 06	3:43E + 06	4:24E + 06	3:20E + 06
		(2:98E + 06) (2:92E + 06) (3:02E + 06) (2:92E + 06)
	Coal	37:91	39:93	34:73	39:43
		(8:17)	(5:60)	(4:40)	(12:85)
	Oil	90:31	74:55	95:44	106:35
		(21:85)	(18:70)	(20:25)	(10:23)
	Resel	0:11	0:08	0:11	0:16
		(0:05)	(0:04)	(0:02)	(0:04)
	Turnover	1:66E + 06	9:31E + 05	1:86E + 06	2:43E + 06
		(7:43E + 05) (2:44E + 05) (4:56E + 05) (5:73E + 05)
	Market share	0:25	0:17	0:26	0:34
		(0:07)	(0:03)	(0:03)	(0:04)
	Q	0:00	3:63E + 05	8:37E + 05	6:47E + 05
		(3:22E + 05) (2:79E + 05) (3:25E + 05) (3:52E + 05)
	P*Temp	1:00E + 04	984:86	901:88	1:16E + 04
		(1:49E + 04) (1:62E + 04)	(985:65) (1:85E + 04)
	P*Daylength	1:46E + 05	1:51E + 05	1:13E + 05	1:86E + 05
		(7:25E + 04) (8:63E + 04) (4:82E + 04) (5:44E + 04)
	Number of	432	164	157	111
	observations
	Note: 9601-0416 refers to the period week 1, 1996, to week 16, 2004, etc.

Table 4 :

 4 Degree of market power

	Variable	9601 0416	9601 9908	9909 0209	0210 0416
	Q*	6:97E 05	5:56E 04	2:02E 04	7:58E 04
		(1:47E 05) (2:38E 04) (5:26E 05) (2:06E 03)
	Note: 9601-0416 refers to the period week 1, 1996, to week 16, 2004, etc. * Signi…cant at the
	1% level, ** signi…cant at the 5% level.
			11

Note: * Signi…cant at the 1% level. The critical values are from Fuller

[START_REF] Fuller | Introduction to statistical time series[END_REF]

.

Table A . 2 :

 A2 Multivariate cointegration test of the demand function Demand function b 95% critical valueTable A.3: Multivariate cointegration test of the supply relation Supply relation c 95% critical value Note: c k=2 number of lags, n=430 number of observations. * Signi…cant at the 1% level, ** signi…cant at the 5% level. The critical values are from Osterwald-Lenum [20].Table A.4: Estimation results of the demand function Note: 9601-0416 refers to the period week 1, 1996, to week 16, 2004, etc. * Signi…cant at the 1% level, ** signi…cant at the 5% level, *** signi…cant at the 10% level.Table A.5: Estimation results of the supply relation

				Submitted Manuscript Submitted Manuscript
	Variable Variable	9601 0416 9601 0416	9601 9908 9601 9908	9909 0209 9909 0209	0210 0416 0210 0416
	0 cointegration vector Constant 4:60E + 05	31:30 3:43E + 05	7:25E + 05	29:70 4:95E + 05
		r = 0	(9:41E + 05)	(1:28E + 05)	(1:53E + 05)	(2:36E + 05)
	Q(-1)	1 cointegration vectors 16:23 0:78	0:90	0:52	15:40	0:67
		r 1		(0:04)			(0:03)	(0:05)	(0:11)
	Temp	2 cointegration vectors 4:65E + 04		6:21	962:25	1:17E + 05	3:76 5:29E + 04
		r 2	(1:85E + 04)	(1:41E + 04)	(2:51E + 04)	(4:09E + 04)
	Daylength	3:21E + 04		1:58E + 04	4:97E + 04	4:67E + 04
		Standardized eigenvectors (495:68)	(443:86)	(788:63)	(1:21E + 04)
	CV1	Variable	712:57		P 291:97	Oil	Resel 1:01E + 04	889:17
	F o r CV1 CV2 F o r (189:48) 151:34 (73:48) 0:91 Long-run parameters CV2 R 2 F o r		1:00 1:00 (174:23) 51:07 1:69 208:56 (100:24) 0:96	110:93 2:36E + 05 (417:72) 211:05 (103:96) 0:95	(188:69) 46:80 (183:89) 0:81
	0 cointegration vector P e 71:69 e r P e e r Constant 2:10E + 06 (5:24E + 05) Temp P 2:12E + 05 (6:53E + 04) Daylength e 1:46E + 05 (3:40E + 04) CV1 3:25E + 04 e r (1:20E + 04) r = 0 1 cointegration vectors 30:04 r 1 R R CV2 689:73 (352:57) R	29:70 15:40
	2 cointegration vectors r 2 Standardized eigenvectors Variable CV1 CV2 Estimates of the individual components in CV1 and CV2 5:93 P Prod 1:00 0 1:00 853:46 e v i P*Daylength 3:76 0:01 e e v i e P1 e 3:25E + 04 P2 689:73 PD 325:00 Prod 5:89E + 05 v i e 0 Separability tests w w w
	H 0 : 1;P = 2;P = 0	28:17
	H 0 : 2;P rod = 0	30:18
	H 0 : 1;P Daylength = 0 26:32
	Note: b k=4 number of lags, n=428 number of observations. * Signi…cant at the 1% level,
	** signi…cant at the 5% level, *** signi…cant at the 10% level. The critical values are from
	Osterwald-Lenum [20].
						13

12 Page 12 of 15 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK 14 Page 14 of 15 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Examples of studies that use this method, or some variant of it, include Aiginger et al.[START_REF] Aiginger | Measuring market power for some industrial sectors in Austria[END_REF], Alexander[START_REF] Alexander | An empirical test of monopoly behaviour: An application to the Hardwood case[END_REF], Azzam and Park[START_REF] Azzam | Testing for switching market conduct[END_REF], Böckem[START_REF] Böckem | Cartel formation and oligopoly structure: A new assessment of the crude oil market[END_REF], Hyde and Perlo¤[START_REF] Hyde | Multimarket market power estimation: The Australian retail meat sector[END_REF], and Sha¤er[START_REF] Sha¤er | Ownership structure and market conduct among Swiss banks[END_REF].

The Bresnahan-Lau method has been criticized by Corts[START_REF] Corts | Conduct parameters and the measurement of market power[END_REF], who shows that the estimated conjectural variation elasticity measures the marginal, and not the average, collusive behavior in an industry. However, by using direct measures of marginal costs to calculate the 'true' value of the conduct parameter, Clay and Troesken [9] and Genesove and Mullin[START_REF] Genesove | Testing static oligopoly models: Conduct and cost in the sugar industry, 1890-1914[END_REF] show that the method preforms well when the degree of market power is not too high. Thus, since Nord Pool consists of over 100 …rms, the method is appropriate to use.

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