Structural change in agriculture – an equilibrium approach

Structural change is a fundamental phenomenon that accompanies the development of market-based economies. Structural change in agriculture can be understood in a broad sense as adjustments of economic entities in the agricultural sector in response to various driving forces. Depending on the perspective and the aggregation level of the analysis these entities are single farms, value chains, markets, or institutions. Decisions that affect structural change are, for example, market entries and exits of farms, growth and shrinkage, change of the production structure or the adoption of new technologies (Chavas, 2001). These decisions not only have an impact on business goals, such as profitability and competitiveness, but also on public goals, such as employment, sustainability, and food security. Understanding causal relationships between entrepreneurial decisions, political instruments, and exogenous factors is an indispensable requirement for assessing and predicting structural change as well as for governing structural change in terms of economic, environmental, and social objectives. Due to the complexity of the involved causal relationships modelling structural change is usually carried out on a very abstract level using restrictive assumptions. This paper suggests an equilibrium modelling framework that supports the analysis of structural change in an economy considering three important characteristics: First, entry and exist decisions of farms as well as prices and production output are determined endogenously. Second, decisions are made in a dynamic framework. This allows to track changes in the composition of the sector. Third, the model is driven by a stochastic component. Thus our model resembles a Dynamic Stochastic General Equilibrium Model (DSGE). To our best knowledge, this is the first time that this model class has been applied in an agricultural context. The DSGE modelling framework is used explore a long-lasting puzzle in agricultural economics: What is the impact of production quota on the dynamics of structural change? It is frequently hypothesized that the introduction of a production quota slows down structural change and hinders efficient adjustment processes (Colman, 2000). But is this also true if quotas are traded (Barichello, 1995)? Clearly, a sectoral production quota causes a strong interdependence of farms within this sector. Farms can only grow if free capacities are available and thus exits of other farms are crucial for any further industry development. From a more general perspective, this kind of interdependency can be generated by the existence of any production factor which is limited on a sectoral level, as for example agricultural land. Production capacity is thus a valuable asset and determines a farm’s liquidation value. As a consequence, the price for investing in additional capacity depends also on the exit and shrinking rate of the other firms determining free capacity (e.g. Weiss, 1999 or Zepeda, 1995). If firms benefit from economies of size investing in production capacity is an option to increase profitability and competitiveness. However, under capacity constraints like production quotas this is more expensive (e.g. Richards and Jeffrey 1997). Against this background we conjecture that profit maximizing firms do not base their investment/disinvestment decision on an isolated view, it is rather that regional structure and its expected evolution is taken into consideration. The literature offers different theoretic approaches to investigate the impact of capacity constraints on entry/exit of firms in an industry. However, considering the interaction among the firms and the consequence on structural development are not well elaborated. Generally, game theoretic models are capable to model growth and shrinkage of firms in a given market with endogenous supply, but they are difficult to handle, in particular if there are more than two firms within the market (e.g. Besanko and Doraszelski, 2004). The real options approach primarily focusses on the optimal timing of investment and neglects the mentioned interdependency of farms’ decisions and the relation between exit and investment (cf. among others Dixit and Pindyck, 1994, or Leahy, 1993). Authors like Jovanovic (1982) and Hopenhayn (1992) model entry and exit of firms into an industry endogenously, however, without modelling of capacity constraints. In view of the relevance of capacity constraints in general and particularly for the agricultural sector, it is somehow surprising that the literature has little to offer with regard to a formalized theoretical analysis of the impact of capacity constraints like production quotas or land constraints on structural change. Against this background, our objective is to investigate how farms’ exit decisions are affected by the uncertain ability to invest in production capacity, and vice versa. We aim to show the implications for the structural change of the agricultural industry when firms take prospective entry/exit of other firms into consideration for their own optimal investment/disinvestment behaviour. Our analysis will improve the understanding of the interdependency between entry and exit of farms and shed light on the question whether the inability to expand production capacity increases the likelihood that inefficient firms leave the market. For this reason, we incorporate capacity constraints into the model as proposed by Hopenhayn (1992) and derive a dynamic stochastic equilibrium for a finite time horizon. We further apply this model to different market structures – structure is here defined as firm size distribution – and show how the industry dynamics depend on the underlying distribution of firms and are affected by the capacity constraint. We employ the stochastic dynamic framework proposed by Hopenhayn (1992), to analyse entry and exit in an industry over a finite time horizon. A continuum of firms is considered, to model a perfectly competitive output market. The firms are assumed to be identical and to produce a homogeneous good. They differ just with respect to their firm specific productivity shock which is stochastic and follows a Markov process. The structure of the industry at a given point in time is described by the distribution of productivity shocks among all firms. In each period, all active firms choose their optimal amount of output according to their own productivity and a given market price. Production incurs a fixed cost which is the same for all firms and total market demand is described by an inverse demand function. At the end of each period all incumbents decide whether to leave or stay in the industry. If they cease production they receive a positive premium depending on the total mass of the industry. This takes into account, that the firm’s production capacity as a liquidation value is more valuable when there are more firms in the industry looking for additional production capacity. Continuing firms are hit with a new productivity shock and start production in the next period. A firm stays in the industry if its expected discounted future profits offset the exit premium. The expected profits depend on a firm’s current productivity as well as on the future price sequence. The exit-point describes the critical threshold for being indifferent between staying in or leaving the market. All firms with a productivity above the exit-point stay in the industry while all firms with a lower productivity take the exit premium and quit. New firms can enter the industry in each period, but they have to pay entry costs which are affected by the mass of the industry. If there are more firms willing to enter the market, the entry is more expensive. Each new firm gets a productivity shock drawn from the same distribution function and there will be firms entering the industry as long as their expected future profits cover the entry costs. In this regard, the term “new firms” also refers to active firms who invest the entry costs and expect to improve their productivity this way. The mass of new entering firms together with the exit-point and the stochastic process for productivity shocks fully describe the change of industry structure from one period to the next. We make some explicit assumptions on the stochastic process and other functions to show that a dynamic stochastic equilibrium exists. In such an equilibrium the firms base their exit/entry decision on the evolution of output prices, exit premium and entry costs in future periods. We compute equilibria for different scenarios to show the influence of capacity constraints on industry dynamics. Furthermore, we check how changes of the underlying starting distribution of firm productivity affect the equilibrium outcome and which implications this has for the structural change of highly or weakly concentrated regions in the agricultural sector. We find that both, the underlying starting distribution and the imposed capacity constraints, have an impact on firms’ investment and disinvestment decision in a dynamic equilibrium. In a scenario without capacity constraints we observe almost all new firms enter the industry in the first period. If we incorporate capacity constraints, however, entry occurs also in higher time periods. This is due to the varying entry costs which would be too high if all firms entered the industry at the same time. Thus, some firms wait for others to leave the market first and postpone their investment to a later date. In addition to this, we find that less productive firms tend to stay longer in the industry if the entry of new firms is restricted by capacity constraints. Another interesting finding is that the equilibrium outcome and the structure of the industry in subsequent periods are sensitive to the assumed starting distribution. This could be an instrument to make explicit statements about the prospective structure of the agricultural sector. By fitting the starting distribution to the firm size concentration in a selected region and calibrating crucial parameters of the model, we could be able to simulate changes of this industry structure for a number of time periods.