Heterogeneous Returns to Scale of Wind Farms in Northern Europe.

• Author: Benini, Giacomo

1. INTRODUCTION

   In order to achieve the Paris Agreement's goals, reducing greenhouse emissions from the power sector has become a priority of the global energy agenda (Stern, 2007). Among different renewable technologies, wind seems to be the most competitive (IEA et al., 2015). Therefore, it might become the primary option to achieve ambitious climate policy targets (Lantz et al., 2012).

   The industry learning processes and economies-of-scale are the main factors which allowed wind to become competitive over the years (Junginger et al., 2005a). The link between the gains in efficiency and the investment's efort has been studied in detail (Ibenholt, 2002; Neij et al., 2004; Junginger et al., 2005b; Neij, 2008). Less attention has been given to the relation between the average costs and the number of installations. Among the few notable exceptions, (Berry, 2009a) highlighted the existence of two types of returns. The first ones are the economies-of-scale of a single turbine. Here, the per-unit cost declines till three Mega Watts (MW) are installed, then it increases (Wiser and Bolinger, 2011). The second ones are the economies-of-scale of an entire wind farm.

   For nearly a century, it has been a widespread conjecture that large-scale power generation installations can deliver lower cost electricity. This idea is indeed right for fossil fuel and nuclear power stations where: 1) larger volume components add more usable space than the related materials costs; and 2) the fixed costs associated with the generation of power tend to be extremely high. However, the coexistence of two contrasting effects makes the analogy inappropriate for wind. On the one hand, taller turbines can support bigger rotors, which generate more electricity. On the other, each turbine generates a wake effect directly proportional to the size of the rotor's arm, preventing the installation of tall turbines close to one another (Gonzalez-Longatt et al., 2012; Kim et al., 2012). Furthermore, off-shore farms tend to produce more electricity than on-shore ones, as they often use bigger turbines which usually are more productive than the on land ones. However, they need to be connected with the grid increasing the capital expenditures of this type of projects (Wustemeyer et al., 2015).

   Traditionally, studies which try to explore the economies-of-scale of an entire wind farm, either concentrate on the existence of different economies-of-scale for different cost components (Blanco, 2009), or on the returns of one particular type of installation (Morgan et al., 2003; Dismukes and Upton Jr, 2015). The present paper aims to overcome these limitations introducing a production function able to calculate the amount of per-turbine installed capacity both for on-shore and off-shore farms using a unique econometric specification. The key to analyse different projects using a single regression model is to allow for high degrees of cross-farm heterogeneity.

   Varying Coefficient Models (VCM) are a generalization of traditional parametric regressions specifically designed to include diversity across economic units (Hastie and Tibshirani, 1993). In the case of the wind energy sector, the number of turbines is the factor which changes the impact of the site on the amount of installed capacity. This means that a VCM can quantify how a delta in the number of installed turbines impacts the competitiveness of off-shore and on-shore platforms shading light on the trade-of between the size of the rotors and the total number of installed turbines.

   Different regions have instituted market support policies for wind. While several jurisdictions support on-shore wind, fewer sponsor off-shore projects. According to the Bloomberg New Energy Finance's database, among the few areas which sustain both technologies, the North of Europe is the one with the biggest number of installations. The widespread use of on-shore and ofshore farms combined with a rather homogeneous market design makes this region an interesting case study to analyse the economies-of-scale of the wind industry.

2. ECONOMETRIC ANALYSIS

   2.1 Returns to Scale in Wind Farms

   A production plan is a bundle of m non-negative inputs ([X.sub.1], [X.sub.2],..., [X.sub.m]) which delivers a single output Y. In the case of a wind farm, the factors of production include labour, capital and turbines' technology. The outcome is the amount of installed capacity. The resulting technological set (TS),

   [mathematical expression not reproducible] (1)

   links the quantity of installed MWs to the different inputs via the production function v(.) (Mas-Colell et al., 1995). In order to empirically estimate the shape of v(.), we analyse the Bloomberg New Energy Finance's database. This collection of farm-level data provides information about 1307 investment projects realized during the decade 2004-2014 in 61 countries. For each of them, we know the installed capacity, the number of turbines, the site (on-shore or off-shore), the height of the wind turbines, the time required to complete the installation, the country of destination, the manufacturer, the status of the signed contract and the final buyer. The dataset contains only one region where both on-shore and off-shore projects are widespread, and the set of public incentives is comparable, the North of Europe. The high amounts of wind in the North Sea, the Baltic Sea, the North European Plain and the Scandinavian Peninsula, combined with the willingness of the European Union to promote renewable energy markets, makes this part of the world an interesting area where to compare the performances of off-shore and on-shore turbines. Table 1 reports the selected subset of the data.

   Once the area of interest is selected the study proceeds with an increasingly more sophisticated econometric analysis of the data. First, economies-of-scale are assumed to be homogeneous across the two technologies. Under this paradigm two enquiries are made. The first one is a fully parametric regression which connects the estimated coefficients to the economic theory. The second one is a fully nonparametric model which, while failing to deliver a unique elasticity of the inputs' demand, captures the non-linear nature of the relation Y [left right arrow] ([X.sub.1],..., [X.sub.m]) .

   Then a more elaborate analysis of the data, combined with the statistical difficulty to manage a homogeneous interaction between a factor and a continuous variable in a nonparametric context, suggests introducing heterogeneity between off-shore and on-shore farms. A first attempt to model the difference between cross-sectional units, which are displaced in different sites, is done using a semiparametric Random Coefficient Model (RCM). Once the RCM assumptions are discarded by the specificities of the wind industry, a semiparametric Varying Coefficient Model (VCM) is introduced. This last model can quantify the impact of the number of turbines on the installed capacity, shedding light on how the sites' characteristics determine the competitiveness of adding an additional turbine, see Figure 1.

   2.2 Intermediate Homogeneous Returns to Scale

   Assuming that all firms are profit-maximizing units, which operate at Y = v([X.sub.1],..., [X.sub.m]), it is possible to overcome the lack of data about the canonical factors of production postulating that all the unobserved inputs deliver an observed 'intermediate' good: the number of turbines. This 'final' factor of production can be seen as the only capital good of the installed capacity. Hence, the production function v(*) becomes an univariate relation between the nominal power Y and the total number of turbines X,

   [mathematical expression not reproducible] (2)

   where n is the dimension of the sample (Aigner and Chu, 1968). The first step needed to estimate the shape of v(.) is to replace the theoretical unobserved variables with the collected sample. When (Y = y,X = x), it is possible to redefine both theoretical and observed variables as stochastic objects and make the acceptance-rejection region function of the stochastic nature of the sample. This second step allows us to transform equation (2) into [y.sub.i] = v([x.sub.i],[[epsilon].sub.i]), where ei is a random error with finite variance (Haavelmo, 1943, 1944). Equations like [y.sub.i] = v([x.sub.i],[[epsilon].sub.i]) present a lot of statistical shortcomings (Imbens, 2007; Imbens and Newey, 2009). Therefore, it is common to impose v([x.sub.i],[[epsilon].sub.i]) = f([x.sub.i]) + [[epsilon].sub.i] and work with the simplified relation [y.sub.i] = f([x.sub.i]) + [[epsilon].sub.i] Once the error term has been transformed into an additive disturbance it is possible to assume an a priori functional form for f(.) and describe the relation Y [left right arrow] X using a finite number of parameters [[beta].sup.T] , such that [mathematical expression not reproducible] Given that the aim of the study is to estimate the elasticity of the installed capacity to the number of turbines, and...