Abandonment of milk production under uncertainty and inefficiency: the case of western German Farms

1. Introduction

The decision of whether to suspend production or exit a market are among the most impactful decisions a manager can ever make. Firms’ exit decisions are dynamic by nature, must be made in an uncertain economic environment, and their reversal is costly. Thus, firms carefully deliberate their exit decisions and usually do not re-enter the market once production has been suspended. Firms’ exit decisions are intrinsically connected to the evolution of the firms’ characteristics in the market. This changing evolution is, in turn, an integral part of the definition of structural change in a market. Given the importance of such decisions in defining market structure, many authors have attempted to explain why and when firms quit, the economic factors that may influence this decision, as well as their timing (see, e.g. Kazukauskas et al., 2013; Musshoff et al., 2013, and the literature cited therein).

This article focuses on the role of efficiency and uncertainty for exit decisions. Two strands of literature are particularly interesting for understanding firms’ exit decisions. The first strand encompasses the real options approach, which provides a convenient framework for analysing firms’ decisions under uncertainty and irreversibility (Dixit and Pindyck, 1994). By exploiting the analogy between financial options and (dis)investments, real options theory asserts that deferring an exit decision may increase a firm's profit, even if the expected present value of cash flows falls below its liquidation value. This finding has been used to rationalise sluggish disinvestment and exit behaviour. For example, O'Brien and Folta (2009) consider the impact of uncertainty and sunk costs on exit behaviour, and confirm that uncertainty dissuades firms from exiting only when sunk costs are large. Further, Tauer (2006) studies the exit and entry decision of dairy farms in the US State of New York by estimating the entry and exit trigger prices for different types of farm cost structures, but without considering production efficiency. Lastly, Luong and Tauer (2006) examine the entry and exit decisions of Vietnamese coffee growers with various degrees of cost efficiency using real options theory.

The second relevant strand of literature emphasises the impact of efficiency on firm exit. For example, Goddard et al. (1993) argue that more efficient firms show superior performance and are more viable in a competitive environment since they earn higher profits and increase their market shares at the expense of less efficient firms, thereby increasing industry concentration. This view is often labelled as the ‘efficient structure hypothesis’ and can be traced back to Demsetz (1973). An implication of this hypothesis is that efficient and inefficient firms cannot coexist in the long run. The hypothesis that technical inefficiency increases the probability of firm exit has been empirically tested. Among others, Tsionas and Papadogonas (2006), Kumbhakar, Tsionas and Sipiläinen (2009), and Wheelock and Wilson (2000) find a positive correlation between inefficiency and exit. At the same time, one can observe that inefficient firms persist in the market, at least in the short run (Emvalomatis, Stefanou and Oude Lansink, 2011). One explanation is that the costs of adjusting quasi-fixed inputs reduce firms’ ability to improve efficiency in the short run (e.g. Ahn, Good and Sickles, 2000; Tsionas, 2006). To sum up, it is widely acknowledged that efficiency constitutes an important driver of adjustment processes in the agricultural sector. Accordingly, the body of literature relating efficiency and structural characteristics of farms such as size, specialisation, organisation or financial structure is large (e.g. Lambert and Bayda, 2005; Mosheim and Lovell, 2009; Sauer and Latacz-Lohmann, 2015). However, the direct relation of efficiency as a driver for adjustment decisions is rarely analysed. Though we focus on efficiency and uncertainty in this paper, it should be acknowledged that many other determinants of exit decisions have been discussed in the literature. Breustedt and Glauben (2007) examine the impact of farm characteristics, macroeconomic conditions and policy intervention on farm exits of western European farms. These authors report that higher exit rates go along with smaller size and lower off-farm income. Weiss (1999), Pietola, Väre and Oude Lansink (2003) or Glauben et al. (2009) find that apart from farm size also socio-economic factors, such as the existence of a farm-successor, are important determinants of exit decisions. More recently, Kazukauskas et al. (2013) study the impact of European policies on farm exit. They find mixed effects of policy interventions depending on the type of farming for EU-15 member states.

The purpose of this article is to bridge the two aforementioned strands of literature by considering exit under output price uncertainty while allowing for technical inefficiency. We begin from a standard real options model and use a generic production function with an efficiency term. We then derive the properties inherited from the original production function to the instantaneous profit function by using a dual Legendre transformation. To obtain a closed-form solution of the real options model, we assume a homogeneous production function, and show that efficiency increases the reluctance to exit the market. Very efficient farms that have higher returns to scale are found to be more reluctant to exit the market than less efficient farms. Our model allows us to rationalise the co-existence of farms with varying degrees of efficiency in the market by interacting uncertain output price and real options effects. In other words, we explain the sluggishness of exit decisions by sunk costs, uncertainty, and managerial flexibility while accounting for efficiency. The work most similar to ours is Lambarraa, Stefanou and Gil (2015), which studies the effect of persistent inefficiency on the investment decisions of Spanish olive farms using a real options approach.

We apply our real options model to farm-level data from western Germany (1997–2011) to analyse the impact of inefficiency and uncertainty on abandonment in the dairy branch. The dairy sub-sector seems well-suited to test the hypotheses derived from the theoretical model for several reasons. First, the high degree of capital specificity for dairy equipment and livestock implies a strong irreversibility of invested capital. Second, the European dairy sub-sector was subject to several policy reforms during recent decades. The process of deregulation and market liberalisation was accompanied by an increase in commodity price volatility in the EU, and in Germany over time and by region (Keane and O'Connor, 2009; Ledebur and Schmitz, 2012). This change of milk price volatility allows us to study the impact of uncertainty on exit decisions. Third, milk quota prices varied during the study period, reflecting the aforementioned policy reforms. This variation enables the empirical analysis of the role of liquidation values as a further component of real options models. Also, the end point of the quota scheme has been repeatedly revised during the reforms, which introduced additional uncertainty to the value of quota prices.

Against this background, our analysis contributes to understanding the relationship between efficiency, milk price uncertainty and farm-level decisions of ceasing milk production. We account for the effect of persistent inefficiency potentially arising from the adjustment costs of dairy capital under the milk quota scheme.

The subsequent section introduces the theoretical modelling framework, followed by the data description. The third section includes the empirical strategy. We measure efficiency via a directional output distance function and then estimate the effect of efficiency and price volatility on dairy-exit decisions. In the fourth section we discuss our results, and in the last section we conclude.

2. A model of farm exit under uncertainty and inefficiency

In this section, we first present the general model without making functional assumptions about the way inputs combine to produce output. As a simple exemplifying case, we consider a Cobb–Douglas production function and derive explicit exit conditions.

To link efficiency and exit decision, we model the production technology by deriving a general form of the stochastic profit flow. Except for simple functional forms of the production function, an explicit solution for the profit function is difficult to attain. We thus use the dual Legendre transformation to derive the structural properties of the profit function implicitly (Jorgenson and Lau, 1974).

The optimality condition (6) states that the instantaneous profit on the left-hand side must equal the appropriately discounted liquidation value $(δ′L)$⁠, times a multiple $(β2β2−11−k )$⁠, which is lower than unity. Equation (6) shows that the exit trigger price decreases in efficiency a. That is, more efficient farms have a comparatively lower exit trigger price than less efficient farms. Thus, the reluctance to irreversibly leave the market increases for more efficient farms.

The degree of homogeneity of the production function (k) has an impact on the level of exit trigger prices $h1(p*)$⁠. In particular, an increase in k in equation (6) decreases both the multiplier of liquidation value L and $δ′$⁠, implying a higher reluctance of farms that have a higher degree of homogeneity in inputs. However, the effect of k on the level of exit trigger prices can differ depending on the properties of the explicit production functional form considered.

Volatility decreases exit trigger prices (cf. Appendix  A2). This finding is a manifestation of the well-known (dis)investment reluctance that is emphasised in real options models. The intuitive explanation is that if a firm faces unfavourable economic conditions there is a chance for profits to recover if prices are volatile. Otherwise one should immediately stop production if revenues fall below variable costs, that is, if operating profits are zero. Note that the impact of volatility on exit trigger prices depends on the level of efficiency. The lower the efficiency, the higher is the marginal effect of volatility on the exit trigger prices. The exit trigger prices decrease when drift rate α increases for the relevant range of parameters.

Because efficiency only affects the net worth, it shifts exit trigger prices down as in equation (6) for the general homogeneous case. The derivative of the trigger price with respect to efficiency is negative. Efficient farms are more reluctant to exit the market. This finding is in line with the efficient structure hypothesis. For $ϕ=0$⁠, equation (12) reduces to the standard real options exit trigger price with variable output (Dixit and Pindyck, 1994). Moreover, as in the general homogeneous case, the derivative of the trigger price with respect to volatility is negative. Finally, the exit trigger price decreases when the drift rate increases for the relevant range of parameters, as in the general homogeneous case.

Note that the optimal exit trigger price has been derived for a farm with a single output, though in reality most farms produce more than one output. Switching from a single- to a multi-output context may affect the efficiency measurement as well as the exit decision. In principle, one could extend the real options model to more than one output and consider a situation where the farm faces multiple abandonment and investment options, each related to a different product. The complexity of such a model would increase considerably since the options effects are, in general, not separable (cf. Triantis and Hodder, 1990;,Brekke and Schieldrop, 2000). As a result, the continuation region would no longer be characterised by a simple exit trigger price. Since the objective of our paper is to analyse the impact of technical efficiency on the optimal exit timing by means of a parsimonious model, we do not pursue this approach. Referring to Trigeorgis (1993), we argue that the qualitative results of our single-output model remain valid in a multi-output farm, as interacting real options usually preserve familiar option properties. Our empirical model, however, accommodates a multi-output setting. Further simplifying assumptions of our theoretical model relates to the choice of the stochastic process, as well as the existence of a perfect capital market. While violations of these assumptions affect the size of the optimal (dis)investment trigger, they usually do not change the qualitative impact of model variables.³ Thus, we are confident that the derived hypotheses about the influence of efficiency and uncertainty are robust against violations of the underlying assumptions and will be pertinent in more complex real world decision problems.

3. Empirical strategy

3.1. Empirical approach

Moreover, we take into account additional determinants for exit decisions of milk-producing farms, which are not explicitly considered in the theoretical framework. That is, we control for additional covariates such as dairy operation size, efficiency of other branches and regional off-farm working possibilities. Overall, we employ a two-stage procedure: in the first stage, we measure efficiency in milk production and in other outputs via a directional output distance function. In the second stage, we model the decision to abandon the dairy branch using a panel data mixed effects logit model where efficiency scores are included as explanatory variables.⁴ In what follows, we detail the two stages, starting with a description of the used data set.

3.2. Data

We use an unbalanced panel data set from the Farm Accountancy Data Network (FADN) for western German milk-producing farms observed between 1997 and 2011. The data from the FADN contain accountancy data for representative farms from a stratified, rotating sample. These data, however, do not allow us to disentangle whether a farm ceases to exist or stops participating in the sample but continues to exist. Nonetheless, we are able to study the abandonment of milk production by considering farms that remain in the sample at least one year after ceasing milk production. That is, we investigate the abandonment of the dairy branch instead of complete farm exit. This is the reason we analyse all milk-producing farms and do not focus on specialised dairy farms. The predictions of our theoretical model apply to this case rather well. An advantage of this narrow exit definition is that otherwise relevant factors, such as the personal circumstances of the farmer and their family (e.g. illness, divorces, no successor), are less important in this situation.

A farm is considered to have abandoned milk production if one period shows milk output and milk revenues to be zero, but these amounts were positive in at least four preceding periods. This implies that the exiting farm actively produced milk during some periods and we observe the first period after exiting.

To ensure reliable consideration of farm characteristics (e.g. volatility of milk revenues) in the empirical modelling, we consider only farms with a minimum of four years of milk production. We exclude as outliers farms that are below the 1 per cent quantile and above the 99 per cent quantile of the distributions for volatility and drift rate of milk returns. The resulting sample consists of 3,192 milk-producing farms with an average length of presence in the sample of 9.2 years. Thereof, 1,608 are specialised dairy farms according to the FADN classification based on the proportion of dairy contained in the value of standard output of production, which marks a share of more than 50 per cent of our farm observations.⁵ In the observation period 2000–2011, a total of 267 farms abandoned milk production, which corresponds to a share of 8.36 per cent on the total number of farms in the sample.

Our sample is a subset of the number of farms that actually gave up milk production: according to the agricultural census, the total number of farms with dairy cows declined from 152,653 in 1999 to 89,763 in 2010 (a 41 per cent decrease). This overall development, however, differs between herd size classes. According to census data, the number of farms with less than 20 cows decreased from 68,475 in 1999 to 28,117 in 2010 (a 59 per cent decrease). In contrast, the number of farms with more than 100 dairy cows increased from 3,892 to 6,920 over the same period (a 77 per cent increase). Given this development, we control for a farm's mean herd size in the second-stage model and analyse the probability of exit by herd size classes.⁶

3.3. Production technology and efficiency measurement

We face the challenge of estimating the effect that inefficiency has on the probability of abandoning the milk production sub-sector in the context of multi-product farms. Thus, we calculate inefficiency in a non-radial manner in two directions: milk and other outputs. To this end we apply a directional distance function approach rather than studying a residual of the entire technology in a Solowian sense (cf. van Beveren, 2012). This procedure allows us to measure farm-level inefficiency in the direction of milk output, which is considered to be a crucial determinant of the decision to cease operating in the dairy branch (cf. Färe et al., 2005). Furthermore, we can disentangle effects of both efficiency measures on the decision to cease milk production. We postulate that efficiency of milk production has a negative effect on the abandonment decision, while the opposite is true for efficiency in other outputs.

We represent the technology of the farms by two outputs and four inputs. The outputs are milk (in tons) and other output as a residual category in which we include an aggregated implicit quantity index of all other outputs produced by the farm. That is, we divide the other outputs’ monetary value by an aggregated output price index, weighted by the respective revenue shares. We use four aggregated inputs: land, capital, labour, and intermediate inputs. Land includes arable land and grassland, but excludes woodland, other areas, and fallow land. Capital is defined as the sum of the total capital assets’ opening values deflated with a price index, which is obtained by aggregating corresponding price indices at the national level, weighted with input value shares.⁷ Labour input is the amount of family and paid labour measured in working units. Intermediate inputs are considered through an implicit quantity index obtained by aggregating feed, crop inputs, energy and other inputs. Feed includes costs for purchased and home-grown marketable farm products. Crop inputs are a similar aggregate implicit quantity index composed of seed inputs, fertilisers, and chemicals. The descriptive statistics of the variables characterising the production technology are presented in Table 1.

For estimation purposes we rely on the approach suggested by Guarda, Rouabah and Vardanyan (2013). This approach exploits the translation property of the directional distance function. By expanding only one output at a time, we avoid the simultaneity bias that plagues econometric estimations of radial distance functions (cf. Grosskopf et al., 1997). A similar method has recently been applied by Sauer and Latacz-Lohmann (2015) to estimate the efficiency and technological change of German dairy farms.

We parameterise the directional output distance function with a second-order flexible quadratic functional form. The choice of the functional form follows Färe, Martins-Filho and Vardanyan (2010), who show that the quadratic functional form has global approximation properties when used to estimate parametric directional distance function models.

where $κq⁎i$ denotes the output-specific part of the long-run farm inefficiency possibly due to farm i’s poor management. Parameter $γq⁎1$ denotes an estimated coefficient attached to a time trend. The modified production function results in a dynamic version of equation (14), similar to Ahn, Good and Sickles (2000: equation 7). In the following we refer to these two measures as long-run dynamic inefficiency for milk and other output.

Since we cannot rule out endogenous input choices or heteroskedastic and serially autocorrelated errors, and given the high estimate for the autoregressive parameter, we opted for a System Generalized Method of Moments (GMM) estimator.⁸ We obtain relative measures of long-run inefficiency $aˆq⁎i$ from each $vˆq⁎i$ as follows: $aˆq⁎i=vˆq⁎max−vˆq⁎i$⁠, where $vˆq⁎max=maxivˆq⁎i$⁠.

3.4. Exit

Starting with the variables directly motivated by the real options model, we include the farm-gate milk price (p_it), which is hypothesised to be negatively related to the likelihood of ceasing milk production. We also introduce an index of variable input cost that approximates the input cost (⁠$wit$⁠) and is supposed to increase the probability of exit.⁹ The drift rate (⁠$αi$⁠) and output price volatility (⁠$σi$⁠) are calculated as mean and standard deviation of relative milk price changes (log returns) among consecutive years of presence in the sample, by farm. Both variables are expected to reduce the probability of exiting.

We proxy liquidation value (L) by two variables: the price of sellable dairy cows at the farm level and the milk quota prices at the NUTS 1 regional level.¹⁰ According to the theoretical model, both variables are hypothesised to be an incentive to cease milk production. Since the milk quota scheme limits expansion possibilities, especially at a regional level, adding the regional milk quota price as an explanatory variable has a double meaning in the empirical model. On the one hand, it accounts for a substantial part of the liquidation value that a farm might obtain after ceasing the milk branch. On the other hand, the quota value is a market price and thus reflects the interplay of supply and demand. That is, the higher the value of the quota, the higher the competition, which might be because of expected future profits in a certain region. Thus, higher quota prices could potentially be negatively associated with the probability of ceasing milk production (cf. Hüttel and Jongeneel, 2011).

The theoretical model cannot capture all factors that in reality have an influence on the abandonment decision for milk production. For this reason, we include additional covariates in the second-stage regression that do not directly result from the theoretical model and describe the context of this application. We control for dairy operation size (mean herd size) to directly test whether small milk producers are more prone to cease milk production, which is suggested by the observed characteristics of exiting farms (cf. Table 2) and by the literature (e.g. Zimmermann and Heckelei, 2012). We account for specialisation by a dummy variable equal to 1 if a farm has specialised in dairy according to the FADN classification. Including this variable allows us to test whether specialised farms have other characteristics that cause a lower probability of ceasing milk production beyond the technical efficiency measure, e.g. managerial skills or income diversification. Finally, the decision to abandon might depend on alternative income streams, including off-farm working opportunities (D'Antoni and Mishra, 2012). Favourable outside options might facilitate farmers’ decisions to exit when considering future potential income streams. As a proxy, we use the regional unemployment rate (municipality level, LAU 1) to capture such effects.

Moreover, we control for the self-financing capability of the farm and add the cash flow to assets ratio. In previous studies on disinvestments in agriculture, the financing structure of the farm turned out to be important (e.g. Hinrichs, Musshoff and Odening, 2008, 2010). Expansion or rationalisation investments are more difficult to finance if farms have limited internal financing capabilities. As a result, terminating milk production may turn out to be the only feasible alternative. Thus, we hypothesise a higher probability of exiting for farms with lower cash flow to assets ratios.

Policy measures in general and the CAP reform in particular were important drivers for the adjustment process of the German dairy sub-sector in the last two decades. Many of the factors that are influenced by agricultural policy instruments like the current level of the milk price, its drift rate and volatility, and the liquidation value, which is affected by the milk quota price, are already part of the model. Acknowledging the considerable role of farm payments as part of the income flow (e.g. Mishra, Fannin and Joo, 2014), and to single out the effect of the fundamental 2003 reform of the CAP, we include the level of the single farm payments. These payments start in 2005, that is, the first year in which the reform was implemented with the beginning of the decoupling of the direct payments from production, the deregulation of the EU milk market, and the introduction of the dairy premium. Prior to that, dairy farms might have expected falling milk prices in the nearer future, together with a devaluation of the milk quotas. Thus, this variable implicitly captures time effects as well.

Finally, we include a regional dummy variable to control for unobserved regional-specific effects. Within western Germany, the milk production structure follows a north–south divide, thus the dummy variable equals 1 if the farm is located in the southern federal states of Bavaria or Baden-Wurttemberg. This subdivision accounts for possible different regional developments, different expansion possibilities, and off-farm working possibilities in these areas: larger farms are more concentrated on dairying, but fewer possibilities for off-farm activities exist in the north, while smaller farms are possibly less specialised on dairying, but more alternatives to milk production exist in the south.

Due to the panel structure of our data, non-captured farm-specific unobserved heterogeneity may also be correlated with exit in the second-stage exit model. We control for such confounding factors through a mixed effects estimation approach with fixed parameters and farm-specific random intercepts.

The summary statistics of all explanatory and some additional informative variables are depicted in Table 2 for all farms and by group (i.e. persisting and exiting farms). On average, farms that abandon milk production are typically smaller in their dairy operation size (22 dairy cows versus 43 dairy cows) than continuing farms, though not significantly different in utilised agricultural area (60 utilised agricultural area (UAA) versus 64 UAA) or size units (68 economic size units [ESU] versus 85 ESU). While the variable input cost index seems rather similar across groups, it is statistically different. The milk quota price is lower, on average, among persisting farms than among exiting farms. Additionally, average milk yield is lower among exiting farms than in continuing farms—5.7 tons per cow against 6.4 tons per cow. For persisting farms we find a positive drift but for farms ceasing the dairy branch we find a negative one. The latter group might not benefit from price mark-ups for larger output quantities paid by dairies, might not be able to deliver high-quality standards, or even suffer from a downward trend in milk quality and contents such as fat or protein, all of which might lead to a downward drift in milk revenues.

4. Empirical results

In Table 3 we present the results of the first-stage model (14) to estimate efficiency in the direction of milk and other outputs. Monotonicity of the directional distance function requires the estimated potential milk (other) output to be increasing in the inputs and decreasing in other (milk) outputs. On average, input elasticities are, as expected, positive and output elasticities are negative, with the only exception of labour in both models (negative) and land in the milk model (slightly negative). Moreover, the directional output distance function should be concave in the outputs. This is not true in either model, on average. This result may hint at synergies between milk output and livestock production, which is part of the other output. In fact, more than 56 per cent of the other output produced in our sample is from livestock products.

The inefficiency is composed of a fixed effect (⁠$κq⁎i$⁠) estimated using a dynamic version of equation (14), which we interpret as the average of inefficiency over time (cf. Ahn, Good and Sickles, 2000). The second part of the inefficiency measure as shown in equation (16) corrects the output-specific effect for the persistence of farm inefficiency (⁠$1−φq⁎$⁠) and the speed of technological progress adaptation in the long run, $γq⁎1$⁠, attached to the time trend. This term penalises farmers exhibiting a lower capacity to adapt to technological changes with higher long-run inefficiency. Given the positive time trend estimate that captures technological progress (the estimate is 16.3, with standard error 7.125, with milk as an output and 1.6, with a standard error of 0.175 in the direction of other output), the penalisation effect is amplified because the estimated parameter (⁠$1−φˆq⁎$⁠) is 95 per cent in the milk model and 55 per cent in the other output model. That is, on average, farmers adapt sluggishly to a positive productivity trend in the sub-sector, both in the production of milk and of the other output. Even though we cannot directly compare the technological trend measures in the two outputs because they are expressed in the different output units, both reveal a positive technological progress, on average.

The average level of technical efficiency (as in formula 17) in the direction of milk output with 0.436 is lower than values reported in other studies of the dairy sub-sector, for example, Emvalomatis, Stefanou and Oude Lansink (2011). The farms in our sample, however, show higher heterogeneity in their production structure since we do not confine our analysis to specialised farms. Moreover, the estimated efficiency scores in milk production show rather similar values among the size classes: larger farms with more than 75 cows operate at an average level of efficiency equal to 0.441 (with a standard deviation of 0.095), while smaller farms with less than 20 cows operate at an average efficiency level equal to 0.438, but with a lower dispersion (standard deviation is 0.029). It is interesting that farms with smaller herds seem to be, on average, as efficient as farms with larger herds in the long run. Given that the persistency parameter $φq⁎$ is the same for all farms, the variation by size is purely based on the farm effect $κq⁎i$ representing farms’ inefficiency accounting for input adjustment in the long run. This result indicates that some inefficiency, due to limited possibilities to adjust efficiently inputs in the long run (quasi-fixed factors), might be rooted in the milk quota scheme and its limited trading flexibility in Germany. Transferring production rights from less efficient to more efficient milk producers is known to be crucial for an efficient allocation of production (see Colman, 2000). This process, however, started slowly in western Germany in 2000, with gradual adjustments resulting in quota transfer possibilities in the eastern and western part of the country only from 2007 onwards. The results obtained for the efficiency in the other output are peculiar: larger farms with more than 75 cows present an average level of efficiency equal to 0.368, (standard deviation is 0.087), only slightly lower than the average efficiency of farms with less than 20 cows, which is equal to 0.373 with a dispersion of 0.037. These numbers hint at a higher degree of diversification among small farms.

Maximum likelihood estimates of the second-stage mixed effects logit model (18), their standard errors, as well as the marginal effects are reported in Table 4. Given the unbalanced nature of our panel data, the overall fit of the model appears satisfactory (McFadden Pseudo R² = 0.342). Joint significance of the variables in the model is confirmed by the Wald test. To assess the relative contribution of those variables that are motivated by the real options model compared with the additional context-specific variables, in the last column we provide partially standardised coefficients. These values facilitate a ranking of the regressors according to their importance. Dairy operation size and specialisation are the most crucial contextual variables, followed by the technical milk efficiency, the milk quota price as a proxy for the liquidation value, and the volatility measure. Furthermore, comparing the Pseudo R² measure of the full model (0.342) to a model where only variables motivated by the real options model were considered (0.165) reveals that the real options variables and the additional variables share the explanatory power of the model rather equally.

Most parameter estimates are significant and in line with the predictions from real options theory. First of all, the empirical results confirm our hypothesis on the impact of both technical efficiency scores on farm exits from milk production: the coefficient of milk efficiency is negative and highly significant while other output efficiency is positive and also strongly significant. This confirms that farms that are more efficient in milk production are more reluctant to exit milk production than inefficient ones: a 1 per cent increase in milk efficiency decreases the probability of exit from dairy by 1.5 per cent. This also shows that farmers more efficient in the other output are more prone to abandon the dairy branch: a 1 per cent increase in other output efficiency increases the probability to exit from milk production by only 0.5 per cent. Comparing the standardised coefficients again reveals the stronger effect of the technical efficiency in the direction of milk production (−0.8 for milk efficiency and 0.3 for efficiency in other outputs).

While variable cost¹¹ significantly matters, as expected (higher costs lead to a higher probability of ceasing milk production), the level of the farm-gate milk price turns out to be insignificant. Its drift rate and volatility, however, show a negative significant impact. That is, an increase of these variables reduces the probability of abandoning milk production.

The liquidation value consists of two components. Whereas results show a positive significant impact of the price of sellable cows on the probability of exiting, the regional milk quota price reveals a significantly negative effect. According to the real options model, we expect a positive impact of both variables representing the liquidation value. The different interaction of these variables with the exit probability might express the uncertain effect of the milk quota in the context of milk production. Higher regional milk quota prices also represent higher competition in the region, and thus reflect the positive expectation of farms regarding potentially higher future profits.

The results also confirm that larger farms in terms of average herd size, as well as specialised farms, are more reluctant to exit the market, as also found by Breustedt and Glauben (2007).

The off-farming options in the different German regions, proxied by the regional unemployment rate, are significantly negatively correlated to the probability of exiting. In other words, it is more likely that a farmer would dismiss the dairy branch if the farm resides in a region with a lower local unemployment rate. The better the local outside option is, the higher the probability of deciding to exit the dairy branch. Further, significant differences by region exist: farms in Bavaria and Baden-Wurttemberg have a lower probability of exit. The single farm payment is also found to have a positive impact. That is, farms with a higher (at least partially decoupled) single farm payment have a higher chance of abandoning dairying. Since the single farm payment starts in 2005, this covariate might also capture some positive time effects. At the time of the reform, dairy farmers might have expected falling milk prices in the nearer future, together with a devaluation of the milk quotas (Deutscher Bauernverband, 2009). Hence, farmers contemplating abandoning production might have taken the opportunity to sell their quotas before the high rates dropped below acceptable levels. This points to the considerable importance of the income stream coming from the diversification of on-farm activities compared to direct payments and the potential off-farm working possibilities. The estimated coefficient of the cash flow to assets ratio has, as hypothesised, a negative sign, though it is insignificant.

Two aspects are noteworthy. First, a change in efficiency has a different impact on the probability of exiting depending on the efficiency level. Apparently, a mild deviation from optimality does not trigger immediate abandonment. In fact, the probability of ceasing milk production is close to zero above an efficiency level of 0.4. To put this in perspective, recall that the average value of the efficiency score amounts to 0.436. In other words, a large fraction of the farms produce at efficiency levels where the probability of exiting is insensitive to marginal changes of technical efficiency in the milk direction. Second, increasing price volatility leads to a downward shift of the marginal effect of efficiency on exit probability. This downward shift is more distinct at low efficiency levels. Indeed, the aggregate German milk sub-sector experienced an increase in price volatility from 5 to 21 per cent between 2002 and 2007. This increase in volatility led to a considerable reduction of the predicted exit probability for different farm efficiency levels. Taken together, Figure 1 rationalises the observed heterogeneity of efficiency levels among the farms under current high-volatility market conditions.

5. Conclusions

The purpose of this article is to scrutinise the impact of price uncertainty and efficiency on market exit decisions and thus analyse the dynamics of structural change. To this end we develop a model that explicitly accounts for production efficiency in a stochastic dynamic decision framework. Starting from a standard real options approach we model the technological structure of a farm and derive a dual profit function through a Legendre transformation without assuming a specific functional form for the production function. Based on the theoretical model, we find that efficient farms are more reluctant to exit the market under the assumption that the production function is homogeneous in the production inputs. Moreover, higher output price volatility decreases the optimal exit trigger prices. Combining efficiency estimates with the exit decision can explain why there is a farm exit continuum over a price range.

We test the hypotheses of the theoretical model with a sample of dairy farms in western Germany. Two efficiency measures are calculated in a directional distance function framework in the direction of milk and other output. The empirical analysis confirms most hypotheses derived from the real options model. In particular, we find that a higher level of milk price volatility and drift both reduce the probability of exiting the dairy branch. Moreover, our empirical model is able to replicate stylised facts of structural change in the German dairy sub-sector, for example, the persistence of large and specialised farms.

Most important for our research question is the finding that abandoning dairy production goes along with low technical efficiency in the direction of milk output and goes along with high technical efficiency in the other output. In other words, we find empirical support for the efficient structure hypothesis. Further, our results also provide an explanation of the observed heterogeneity of existing dairy farms’ efficiency scores. The first reason is that the exit-fostering effect of inefficiency is only effective at lower levels of efficiency. That is, a mild deviation from optimal production does not lead to an immediate exit decision. Second, poor efficiency can be partially compensated by other factors that determine the optimal exit trigger. Since price volatility in the EU milk market increased in recent years, the propensity of inefficient farms to exit the milk market attenuated under these more volatile market conditions. This implies that variability of farms’ efficiency might increase as a result of increasing price volatility. This conclusion, however, relies on the equivalence of time-varying volatility under varying market conditions and farm-specific risk that we capture in our empirical model.

Even though we found empirical evidence for our theoretical hypotheses, a critical reflection of the chosen real options framework seems advisable. Clearly, this approach cannot accommodate all aspects that come into play when farmers consider ceasing dairy production. Since real options models are rooted in financial economics, less emphasis is given to factors that are suggested by household theory, such as opportunity costs of family labour. Moreover, socio-economic variables (e.g. age, education and gender) or nonpecuniary benefits from holding cows, which certainly affect abandonment decisions (Peerlings and Oomes, 2008; Howley, 2015), are not accentuated by this approach. One may even question the basic assumption of fully rational behaviour of farmers and instead refer to behavioural economics as an explanatory approach for observed (dis)investment reluctance (Sandri et al., 2010). Several directions of further research are possible. An example of refining the theoretical model could involve an endogenous stochastic milk price process. Finally, with regard to the empirical estimation, the analysis of specialised farms that entirely quit agriculture would be clearly desirable.

Acknowledgements

The authors would like to thank two anonymous reviewers and the editor for their helpful comments. Financial support from the German Research Foundation (DFG) through Research Unit 986 ‘Structural Change in Agriculture’ is gratefully acknowledged. We also thank the Directorate-General for Agriculture and Rural Development of the European Commission (in particular DG AGRI C.3) for providing the FADN data. The data are confidential and can be obtained via personalised agreement from DG AGRI C.3.

Footnotes