Performance of dairy farms in Finland and Norway from 1991 to 2008

1. Introduction

Agriculture and agricultural policy in Finland and Norway have shared many common features in the past. Both have quite a few similarities in natural conditions, as well as in their pre-1995 agricultural policy and institutional conditions. Each country negotiated over European Union (EU) membership in the early 1990s along with some other countries (e.g. Sweden). However, these two countries have taken different paths after 1995. Finland, unlike Norway, joined the EU and started to follow the rules, which were in line with the Common Agricultural Policy (CAP). Finland's accession to the EU required significant strategic adjustments at the farm level and in the behaviour of its farmers. In contrast, Norway, for the most part, created its own agricultural policy outside the EU, although it is still subject to the influence of prevailing external agreements on the European Economic Area and especially with the World Trade Organization. While changes in agriculture have proceeded in both countries, Finland's introduction to the EU likely represents a more rapid form of adjustment, whereas the changes in Norway have been more gradual.

One of the main arguments against EU membership in Norway and Finland was that the agricultural sector in both countries could not survive if the CAP was implemented because of unfavourable natural conditions faced by the farmers. Indeed, at the time of EU accession, we observed declining land prices, shrinking investments and decreasing production in Finland due to this uncertainty. However, after the EU's administrative and subsidy system were established, the activities and renewal desires at farm level started to revive again. This change in trend could be partly explained by the adjustment supporting actions agreed in the EU accession treaty.

It is not possible to work out a reliable counterfactual analysis for Norwegian and Finnish dairy farming in the case that the countries had made an opposite decision about the EU accession. Therefore, we have chosen a different route to shed light on this question. Our approach is comparative, with focus on profitability and productivity dynamics of dairy farms in Norway and Finland. This approach builds on the fact that profitability is essential for the long-term survival of farms and productivity growth is one of the main factors contributing profitability in addition to price changes. More specifically, our objective is to examine whether there are differences in the development of agricultural profitability in Finnish and Norwegian dairy farms over the last 20 years, and which factors are driving these dynamics. We hypothesise that the accession of Finland to the EU in 1995 is one of the main factors that could have influenced dairy farm performances. Clearly, it is not possible to separate the effects of accession from all other changes in the economic environment. Thus, we cannot establish the causal link between the differences in development and the EU accession, especially when the time period under investigation is limited to only a few years before the accession. However, we can examine and compare the dynamics of productivity and profitability under different regimes, as discussed in the following section. The extent and speed of the changes, along with access to the long-term farm-level data, provide a unique opportunity for such comparison.

The remainder of the paper is structured as follows. In Section 2, we detail key features of Finnish and Norwegian dairy farming and agricultural policy. Section 3 provides an outline of the analytical framework of profitability change. In Section 4, we discuss derivation of the components of profitability change from the input distance function (IDF) parameters, the observed prices and quantities. In the IDF, we employ a model that accommodates unobserved farm-level heterogeneity and time-varying technical inefficiency. Section 5 describes the data used in the analysis in detail, while Section 6 discusses the estimation and decomposition of the empirical results. The final section provides some concluding remarks.

2. Key features of dairy farming and agricultural policy in Finland and Norway

In both Finland and Norway, the climate largely determines the crops that can be grown and their yields, with the main limiting factors being the (short) length and (low) average temperature of the growing season. In addition, the long and cold winter necessitates proper shelters for animals and large storage facilities for roughage and manure. For these reasons, productivity in both Finland and Norway is in general lower than in most other European countries.

The average farm size is also relatively small in both Finland and Norway for historical reasons and due to natural conditions. Therefore, Finnish farmers received access to a relatively generous investment support programme with direct investment aid and subsidised credits at the time of their accession to the EU. The motivation for this was to speed up structural change and to support the growth of individual production units and reduce their unit costs through exploitation of scale economies. The change has been fairly rapid in Finland: in 1991, there were approximately 40,000 dairy farms compared with only about 10,000 in 2011 (Kettunen, 1995; Niemi and Ahlstedt, 2011). A similar but slower trend is found in Norway, with the number of dairy farms falling from about 27,800 in 1990 to some 10,900 in 2011 (NILF, 2010). However, while the number of dairy farms in both countries has declined, the remaining farms have increased in both size and in the specialisation of their milk production. The speed of structural change (relative decline in the number of dairy farms) in Denmark and Sweden has been approximately similar to that in Finland but the average farm size in Finland is still small compared with those countries.

Relatively harsh natural conditions and small farm size are not the only common features of dairy farming in Finland and Norway. In both countries, a milk quota system has been effective since the mid-1980s. By the end of the 1980s, the total Finnish milk production diminished by 14 per cent to 2,750 million litres. In addition to the introduction of milk quotas, contracts for reduction of milk production were also provided. Since 1992, total production of milk has remained relatively stable, around 2,500 million litres. While the binding of quotas in Finland has been relieved since 1993 through administrative reallocation and by permitting the trade and leasing of quotas, the system still effectively restricts production quantities, especially in the central and northern parts of the country. Additional regulation has been linked to increased investments. A specific minimum quota per cow has also been a prerequisite for eligibility to receive investment support (Kettunen, 1995; Niemi and Ahlstedt, 2011).

In comparison, milk quotas were progressively reduced in Norway from about 1992 to 2002, and the total milk delivered decreased from about 1,800 million litres in 1992 to 1,500 million litres in 2002. A system of quota reallocation was introduced in 1997, but, for some years, only small amounts of milk quota were reallocated because of the reduction in total quota. From 2002, a farmer interested in selling quota had to sell a portion to the government; the remainder could be sold freely within Norway. Since 2002, all quotas sold to the government have been reallocated. The possibility of establishing joint operations has probably made the quota system more flexible than what it would have been otherwise. Another consequence of the quota restrictions was that average milk yield per farm stayed almost constant from the 1990s up until 2002. Since 2002, the average milk yield per cow has increased by nearly 1,000 litres, while at the same time the total number of dairy cows has decreased and total deliveries have been stable (NILF, 2010).

Although milk quota systems were introduced approximately at the same time in Finland and Norway, the reduction in total production and effectiveness/tightness of milk quotas have been realised at different time-periods. In Finland, this was in the early 1990s, but in Norway it lasted until 2002. This implementation timeline is another main driver of the differences in productivity and profitability dynamics in these two countries.

Agriculture in both EU/Finland and Norway is highly regulated and subsidised, and farmers face extensive farm policies with significant effects on their production choices. The cornerstones of the policy have been the border protection (import tariffs and export subsidies), which have affected the domestic price level of agricultural products, and the support from EU/state budgets. In Norway, national farm policy has been implemented in negotiations between the farmers' unions and the government on prices and other financial support measures to agriculture. In contrast, Finland follows the CAP and thus no price negotiations take place. Instead, there is a closer link between product prices and the supply and demand in the EU and the world market. All support measures are required to be in line with the agreements within the CAP.

The budgetary support in Norway includes price support, area payments, headage (livestock) support, investment grants, support for farm relief and grants for research and extension services. In 2000, a special tax deduction was introduced to compensate for a reduction in producer prices. In Norway, the support policy elements are mainly similar to those of the EU/Finland, although the import tariffs, and thus border protection, may be considerably higher in most products. The magnitude and specification of different support measures naturally vary (e.g. regionalisation, crop/animal species specificity) (NILF, 2010; Niemi and Ahlstedt, 2011).

During the past 20 years, both EU and Norwegian agricultural policies have been gradually directed to reducing price support and increasing the level of non-product-specific support (depending on area and herd size, but not on the volume of produced output) and decoupled payments (not depending on the production at all). However, decoupling in EU/Finland has been carried out further than in Norway. One important exception from the general trend in the EU is that the price support for milk has been allowed in Finland since the EU accession. All other subsidies (except investment aid) in Finland are paid on a per-hectare or per-animal basis.

In Norway, there is also a law regulating transfer of ownership of farms. This law has ensured that farms, with few exceptions, stay within the same families for generations. This legislation has been an obstacle to the merger of farms for the purpose of large-scale production. Combined with the farm support payments favouring small farms and rural policy, these laws have helped to keep smaller farms in business. In Finland, one of the central aims of the policy has been to encourage farm growth.

3. Analytical framework

The measurement and changes of performance are often examined by physical measures such as partial or total factor productivity (TFP). Examples of TFP change studies applying a multi-input multi-output technology include those of Brümmer, Glauben and Thijssen (2002), Karagiannis, Midmore and Tzouvelekas (2004), Newman and Matthews (2006) and Sipiläinen (2007). TFP change in macro-applications is often associated with economic prosperity. However, in a micro-study, this analogy might not be true. Maximisation of productivity might not maximise profit, and therefore, it might not be the objective of an individual producer. Here we measure performance of individual producers in terms of profitability and decompose profitability change into components such as output growth, output and input price changes, technical change (TC), returns to scale, mark-ups and efficiency. We also relate profitability with TFP change, which is widely used in the literature, even in micro-panels.

• is the output growth component;

• is the output price change component;

• is the input price change component;

• TC is the technical change component;

• is the scale component;

• is the mark-up component;

• is the technical efficiency change component.

As pointed out by Kumbhakar and Lien (2009), the last four components (iv–vii) in equation (1) are typical TFP growth components. In other words, we obtain TFP change as a component of profitability change, although recovering profitability change from TFP change is not possible.

4. Implementation of the framework

Computation of the TC component (iv), the scale component (v), the mark-up component (vi) and technical efficiency change component (vii) can be made from the estimated cost function. Because estimation of the cost function relies, among other things, on variation in the input prices, and there is almost no price variation across farms in any given year in our data, we cannot estimate the cost function parameters with reasonable precision. In this case, the solution is to estimate the transformation function or the IDF (Shephard, 1953, 1970) and use the duality results to estimate the components in (iv)–(vii). The estimation of IDF does not require price data. The IDF representation of production technology seems more realistic than an output DF for the quota-regulated Norwegian and Finnish dairy farming.³

Since the only change with the introduction of inefficiency is the addition of the inefficiency term, which in equation (8) appears additively, there is no change in the formula for RTS and TC.

In other words, we can use equation (13) to directly estimate the TC component (iv). As for the first three components (i–iii), we compute TC in this analysis by taking the averages of the consecutive periods (t – 1) and (t). Equation (14) is used in the estimation of and RTS, which are used in computing the scale (v) and mark-up (vi) components. Thus, if we estimate the IDF with multiple outputs and use the above results in equations (13) and (14), the components (iv), (v) and (vi) in equation (1) can easily be computed because they are functions of the parameters of the estimated IDF and data. Note also that the expressions in equation (11) reflect the relative importance of output to the farm.

5. Description of the data

The Finnish dairy farm-level data are from the Finnish Farm Accountancy Survey database collated by MTT Economic Research. The data are unbalanced and include 6,341 observations from 804 different dairy farms over the period 1991–2008. The source of the Norwegian data is the Norwegian Farm Accountancy Survey. The Norwegian Agricultural Economics Research Institute (NILF) collects these farm-level data. The Norwegian data also comprise an unbalanced panel with 5,926 observations on 791 dairy farms over the period 1991–2008. These accountancy surveys include information on farm production and economic data collected annually from about 1,000 Norwegian farms (approximately 900 in Finland) from different regions, farm size classes and types of farms. Participation in the survey is voluntary. There is no limit on the number of years a farm may be included in the survey. In both data sets, approximately 10 per cent of the farms surveyed are replaced each year. In this study, we use only the sample of specialised dairy farms. Further, only those farms for which there are at least two years of data available are included in the analysis.

Dairy farms are often involved in other farm production activities, such as beef production, grain production, machinery contracting work, etc. We specify two outputs: milk yield (in litres) and other output Common examples of other farm products include livestock products (such as beef, pork, mutton or lamb and planted crop products). We convert the other output variables from nominal monetary values to real 2000 values – Norwegian Kroner (NOK) in Norway and Euros (EUR) in Finland – using a combined (weighted) price index for cattle and crops. Finally, we convert monetary values originally expressed in NOK to EUR using the same average exchange rate from 1991 to 2008.

Subsidies are excluded from the distance function analysis, although subsidies may influence production in several ways. Some of these are (i) by changing the relative prices of inputs and outputs; (ii) by affecting income and thus changing the on- and off-farm labour supply; (iii) by affecting income and thereby investment decisions; and (iv) by influencing farm growth and exit (e.g. Kumbhakar and Lien, 2010; Zhu and Oude Lansink, 2010). Several articles have also concluded that subsidies distort technical efficiency of farms (e.g. Karagiannis and Sarris, 2005; Hadley, 2006; Kleinhanss et al., 2007; Zhu and Oude Lansink, 2010), and we followed this approach here.

We use the following inputs in this study: land (in hectares) purchased feed own and hired labour hours other materials and capital We convert the variables for purchased feed, other materials and capital that are originally in 2000 NOK (for the Norwegian data) to EUR in the same manner as the monetary output variables. Other adjustments include: deflating the cost of purchased feed by the purchased feed index, converting other materials to their 2000 values using the price index for other variable costs, deflating cattle capital by the price index for cattle (in Finland, by the average value of the livestock unit), deflating other capital by a weighted index (0.7 for machinery and 0.3 for buildings). We obtained the quantity index for capital flow by merging the interest on cattle capital and the interest and depreciation of other capital into a single variable. The price index for capital is the cost share weighted average of cattle and machinery/building price indices.

Output prices, and input prices, correspond to the output and input variables. The price information is obtained from the farm survey when available – price support is included in the milk price, the price of land follows the regional average rents, the price of labour is the wage of hired labour (derived from the value of paid labour and actually paid costs) – or from the agricultural sector of the national accounts.

Table 1 presents descriptive statistics of the variables for the Finnish and Norwegian sample data. During the sample period, Finnish dairy farms, on average, produced twice as much milk as their Norwegian counterparts. As shown, the share of other products is higher in Norway. Thus, Finnish dairy farms were more specialised in milk production during the sample period than Norwegian dairy farms. This is also, in part, because the prices of other outputs (such as cereals in Finland) are relatively lower than the subsidised milk price. This tends to lower share of other outputs in Finland compared with Norway. While the Finnish farms produced more milk, they also used more inputs. However, the input shares are unequal. These differences are smallest for purchased feed and capital (about 15 per cent). Regarding purchased feed, this may imply that the Finnish dairy farmers have produced more feed themselves as they produced twice the amount of milk as dairy farmers in Norway. This is supported by the fact that Finnish farms (41 ha) have almost double the arable land as Norwegian farms (20 ha). The price of the labour input also appears to be considerably higher in Norway than in Finland, while the ‘Z-variables’ characterising the production, subsidy/return ratio and debt/asset ratio, are also on average higher in Norway.

The mean values discussed above potentially obscure some significant changes over time. Figure 1 illustrates the outputs per farm (sample means per year) over the period 1992–2008. The most striking observation is that structural development has been faster in Finland than in Norway. For example, while milk production per farm has increased by about 80 per cent in Norway during the period 1992–2008, it has increased by some 200 per cent in Finland. Other outputs followed more or less similar patterns. As for the inputs, the land area per farm in Finland has increased by about 130 per cent, while the corresponding growth in Norway has been about 85 per cent. Note that the changes in labour use have been relatively similar in both Finland and Norway. However, this suggests that labour productivity has increased more rapidly in Finland than in Norway.

When comparing prices and quantities, one must bear in mind that despite our best efforts in maintaining uniformity in the definition of variables, some differences are likely to remain. We also note that the data are not exactly a representative sample of all dairy farm data. In addition, voluntary participation may make the sample biased towards farms that perform better than average. Unfortunately, we cannot correct this easily even with weighting schemes based on the observed criteria (region, size, age, etc.). In fact, the Norwegian and Finnish sample data are somewhat overrepresented with respect to larger farms, but this bias has (to some degree) been present during the entire period analysed. Based on this, we argue that, although biases from these factors might be present in both samples, they can still provide a meaningful comparison.

6. Results and discussion

We begin our empirical analysis by testing whether the parameters for both Finland and Norway are the same using the pooled data over the entire sample period. The Chow (1960) test shows that the parameters for Finland and Norway are statistically different, and therefore we decide to proceed with separate estimates for each country. We also noted that the intra-class correlation coefficient or intra-farm correlation coefficient for Finnish and Norwegian samples were 0.56 and 0.65, respectively. These high coefficients indicate the importance of separating the farm effects in a random farm effect and a farm-specific technical inefficiency effect.

Since there is no direct interpretation of parameter estimates, in Table 2 we report input and output elasticities and heteroscedasticity coefficients in the pre-truncated inefficiency function. In Table 3, we report average values (along with standard deviations and quartiles) of profitability change, overall TFP and profitability change components, technical efficiency levels and RTS.⁵ In Figures 2–6, we depict the temporal behaviour for selected components.

In Finland, the input distance elasticities (cost elasticities), which can be interpreted as shadow value shares, are highest for labour (0.32 at the mean of the sample) and land (Table 2). The input share of capital is the lowest. For Norway, the input elasticities are highest for labour (0.27 at the mean of the sample), closely followed by land and purchased feed. In both countries, the elasticity of milk yield is at about 0.52–0.53 and higher than the elasticity of other output (0.05 in Finland, 0.15 in Norway).

A significant negative association between technical efficiency and subsidies is found in both countries. As shown in Table 2, the subsidy/return ratio increased the variance of the inefficiency function, which means increased inefficiency. This result supports the findings of, e.g. tobacco farms in Greece by Karagiannis and Sarris (2005), husbandry and crop farms in England and Wales by Hadley (2006) and crop farms in Germany, the Netherlands and Sweden studied by Zhu and Oude Lansink (2008). The debt/asset ratio affected also significantly negatively on technical efficiency of Norwegian and Finnish dairy farms. This finding supports earlier results obtained by Karagiannis and Sarris (2005) as well as Kumbhakar and Lien (2010).

According to Table 3, the yearly average profitability change in Finland was −0.68 per cent, while in Norway it was −1.95 per cent. Additionally, we find larger variations in profitability change in Finland compared with Norway. Figure 2 (lower panel) shows a drop in profitability (profit/cost ratio) at the time of EU accession in 1995. Another period of falling profitability in Finland was around 2004–2005. Profitability changes in the last couple of years of the sample period were again fairly favourable for Finnish farmers when milk prices increased worldwide. Profitability level in Norway during the whole period stayed at about the same. Profitability change has been positive only in a few years (and for small groups of farms). We also observe (Figure 2, upper panel) that Finland, on average, had a higher TFP growth (2.8 per cent per year) than Norway (0.8 per cent per year) during the sample period, but neither country had a clear increasing or decreasing trend in TFP change over time. However, since 1999 the trend has been decreasing in Finland and increasing in Norway.

As detailed in Table 3, the output growth components average –0.84 and –0.52 per cent for Finland and Norway. The driving force behind this result is that most farm production is unprofitable, and increasing the size of operation caused an increase in losses. In spite of this, many owner-operated farms are able to continue production because family workers are not fully paid. As shown in Figure 3, we can see that there was no effect on the output growth component when Finland joined the EU in 1995. However, the trend in the output growth component was weakly decreasing up until 2001; after 2001, output growth trend increased slightly, although the effect remains generally negative. In Norway, there has been a weak decreasing trend in the output growth effect during the entire sample period 1991–2008.

It can be seen from Table 3 that the average annual output price change component was weakly negative for Finland (–0.39 per cent) and Norway (–0.19 per cent). That is, the overall effect of the change in output prices on profit has been mostly negative for Finland and Norway. However, a close look at the middle panel of Figure 3 shows that Finnish dairy farmers faced an immediate decrease in product prices when they joined the EU. This figure also depicts an increasing trend in output prices during the last three years, unlike the situation in Norway. We observe a similar pattern in the changes in input prices in Table 3 and the lower panel of Figure 3. At the time of EU accession, input prices in Finland initially fell, but soon began to climb, rising rapidly at the end of the sample period. In contrast, the changes in input prices have been more stable in Norway, except at the end of 2007–2008. Nevertheless, in both Finland and Norway, the average annual input price changes are positive (2.25 and 2.06 per cent, respectively). Overall, these positive input price effects (price increases) have impacted negatively upon profitability change in both countries.

The scale component during the sample period averaged 0.75 per cent for Finland and 0.31 per cent for Norway, implying the positive effect of scale on the overall profit change (Table 3). On average, the RTS were 1.71 for Finland and 1.51 for Norway, thereby indicating the presence of increasing RTS at the sample mean. In other words, our results imply that Finnish and Norwegian dairy farms have not fully exploited the benefits of scale economies. The results also indicate that the greatest variation in the scale effect in both space and time is in Finland (upper panel in Figure 4). Figure 4 also provides evidence of the decreasing magnitude of increasing RTS in Finland (and to a lesser extent, Norway), thereby indicating that dairy farms in Finland were moving towards their efficient scale size.

As shown in Table 3, during the sample period, technical progress in Finland averaged about 0.4 per cent, but steadily accelerated during the period from 1997 to 2008 (lower panel of Figure 4). The introduction of the more flexible quota scheme and extensive investment subsidies are likely to be behind the rapid TC in Finland during this period. Conversely, in Norway, as shown in Table 3, the average rate of TC (−0.01) is almost zero, with a slightly accelerating trend over time (lower panel of Figure 4). TC turned positive at the time when Norway introduced less restrictive quota regulation. However, structural change, as discussed earlier, has been slower in Norway than in Finland, and this may partly account for the differences in the dynamics of their TC.

As shown in Table 3 and Figure 5, the mark-up component during the sample period is generally positive in both Finland and Norway. A non-zero mark-up component implies that output prices diverge from the marginal costs of production. This in turn means that output markets are non-competitive, which is also an indication of the effectiveness of the quota restriction. Unlike in Finland, there is no evidence of a decreasing mark-up in Norway. Note that the price variable specified includes the price support paid per litre of milk.

Figure 6 presents estimates of technical inefficiency for the Finnish and Norwegian sample farms. As detailed in Table 3, the mean technical efficiency score for Finland is 0.93, while that for Norway is 0.95. From Figure 6, we can see that the spread in efficiency is greater in Finland than in Norway. One reason for the difference between Finland and Norway might be the faster pace of structural change in Finland. In general, this makes it difficult for inefficient farms to catch up to the technical frontier over time. This is in line with the increasing spread of technical efficiencies towards the end of the study period in Norway.

7. Concluding remarks

Unlike neighbouring Norway, Finland joined the EU in 1995. This study examined how profitability, productivity and their components in Finnish and Norwegian dairy farms have developed in the period between 1991 and 2008. Many factors, which have been described in Section 2, might have affected the dynamics of the profitability of milk production in Norway and Finland, of which the entry into the EU is only one. Nevertheless, our findings do not support the oft-stated observation that EU membership would have deteriorated profitability of dairy farmers in Finland, and that it would have been more favourable for Finland to stay outside the EU as Norway did. Instead, our results show that Finnish milk producers have higher productivity growth and more favourable, although still negative, profitability change than their Norwegian counterparts. The changes in prices were unfavourable in both countries during the period under investigation, thereby having a negative effect on profitability. The unfavourable effect was stronger in Finland. Thus, from farmers' perspective, Norwegian policy and negotiation system guaranteed favourable prices in comparison with Finland.

The unfavourable price effect in Finland has been compensated by higher TFP growth. One reason for this difference is the faster rate of growth of Finnish dairy farms. This is associated with differences in the exploitation of scale economies and the rate of TC, which affected Finnish farms favourably. In Finland, agricultural policy and extensive investment subsidies have probably encouraged more rapid growth and TC during the EU membership. In Norway, the contraction of quotas until 2002 slowed down TC of dairy farms. A slowdown of TC could also be observed in Finland before the EU accession, likely because of the uncertainties related to the EU membership. Mark-up, the difference between actual price and marginal cost price of output, is possibly easier to exploit in smaller than larger market. The (slightly) decreasing mark-up trend in Finland, as opposed to in Norway, might be partly explained by the fact that the Finnish milk market was transformed from more or less domestic market to a part of larger EU/international market.

There are some indications that rapid changes may have made it more difficult for individual dairy farmers to catch up the technical frontier. Technical efficiency scores are slightly lower and more diverse in the Finnish sample compared with the Norwegian sample. The variation is also increasing towards the end of the period. The inefficiency increasing effect of indebtedness also suggests that rapid growth may be difficult to control. We also found some evidence that increasing share of subsidies in total return is linked to increasing inefficiency. This may indicate some adverse effects of the increasing share of direct payments with respect to productivity of inputs.

The findings of this study provide support for the argument that profitability and productivity in Finnish and Norwegian farms have developed differently to some extent during the past two decades, primarily in favour of Finland. We suggest that more liberalised agricultural policy with respect to farm growth and investment support in Finland may have given greater flexibility to dairy farmers, which has led to a more favourable development in dairy farm productivity and profitability. We should also note that at least until 2008 the CAP has provided sufficient flexibility in order to guarantee reasonable development also in less favourable agricultural areas in Finland. However, we should be careful when interpreting these results. We have not identified a clear causal effect in this paper, and further study is, therefore, required to focus more particularly on the dynamics underlying the trends.

Acknowledgements

The authors thank Agnar Hegrenes for valuable comments and suggestions on an earlier version of this paper. The authors are grateful to the editor of this journal and anonymous reviewers for their contribution to our work. The authors also gratefully acknowledge the financial assistance of the Research Council of Norway.

References