Modeling farm households' price responses in the presence of transaction costs and heterogeneity in labor markets.

The agricultural development literature has long recognized that rural markets are often underdeveloped or absent. These market imperfections create transaction costs and, if transaction costs are sufficiently high, households find it unprofitable to either buy or sell a good in the market, i.e., remain autarkic (de Janvry, Fafchamps, and Sadoulet 1991). In this case, production and consumption decisions are no longer separable and conventional microeconomic theory is no longer suitable to model farm household behavior. As a result, farm household models (FHMs) have been developed that explicitly incorporate the interdependency of production and consumption decisions.

Early FHM studies use nonseparable FHMs to explain sometimes paradoxical--and even perverse--microeconomic responses of peasants to changes in relative prices (Strauss 1986; Lopez 1984; de Janvry, Fafchamps, and Sadoulet 1991; de Janvry et al. 1992). Several theoretical and empirical studies have used the FHM approach to analyze farm household responses under imperfect labor (Lopez 1986; Thijssen 1988; Benjamin 1992; Jacoby 1993; Sadoulet; de Janvry, and Benjamin 1998), capital (de Janvry et al. 1992), or food markets (de Janvry, Fafchamps, and Sadoulet 1991; Goetz 1992; Omamo 1998; Skoufias 1994; Abdulai and Delgado 1999). However, nonseparability makes theoretical and, in particular, empirical analyses more difficult. Therefore, most empirical analyses assume separable FHMs or use reduced forms of a nonseparable FHM.

In contrast to early FHM work, recent studies emphasize transaction costs and institutions in determining households' decisions on market participation (Goetz 1992; Key, Sadoulet, and de Janvry 2000; Vakis, Sadoulet, and de Janvry 2003; Vance and Geoghegan 2004; Carter and Yao 2002; Carter and Olinto 2003). For instance, Key, Sadoulet, and de Janvry (2000) develop a model of supply response when transaction costs cause some producers to buy, others to sell, and others not to participate in markets (Key, Sadoulet, and de Janvry 2000, p. 245). They consider fixed transaction costs (FTC) and proportional transaction costs (PTC) only. Fixed transaction costs are invariant to the quantity of the good traded, whereas proportional transaction costs increase proportionally in quantity. Thus, PTC correspond to constant marginal transaction costs.

An aspect that is conceivable, but has not yet received attention in the FHM literature is the role of nonproportional variable transaction costs (NTC) on production and consumption decisions or market participation. We fill this gap by examining how NTC affect farm household decisions.

We also show that not only transaction costs, which are partly implied by unobserved heterogeneity, but also observed heterogeneity of labor can result in a nonseparable FHM. To this end, we construct an FHM, taking into account labor market imperfections via FTC, PTC, NTC, and observed labor heterogeneity. Based on this generalized FHM approach, we derive the following theoretical results: (a) nonseparability of production and consumption decisions can occur even if households participate in markets, (b) imperfect labor markets take a middle ground, with respect to price responses, between standard nonseparable FHMs assuming absent labor markets and standard separable FHMs assuming perfect labor markets, and (c) a test of the joint significance of NTC and heterogeneity for farm household's behavior is possible.

We estimate our generalized FHM approach econometrically using farm household data from Poland. The estimation procedure utilized allows us to consider both potential selectivity and endogeneity problems.

Furthermore, we explicitly test for the significance of NTC and heterogeneity in rural labor markets as well as for the differences between price elasticities calculated for different degrees of labor market imperfection.

Theoretical Model

In this section we construct a static model of the price responses of farm households in imperfect and perfect labor markets (see also Glauben, Henning, and Henningsen 2003). To concentrate on the role of labor market constraints, our model ignores some aspects of farmers' decisions, notably (price) risk (Finkelshtain and Chalfant 1991: Fafchamps 1992) and credit constraints (Chambers and Lopez 1987). The farm household is assumed to maximize utility subject to a technology, time, and budget constraint. Therefore, farm households solve the following maximization problem:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to

(2) G(x,r) = 0 (production function)

(3) TL--[absolute value of [X.sub.L]] + [X.sup.h.sub.L] - [X.sup.S.sub.L] - [C.sub.L] [greater than or equal to] 0 (time constraint)

(4) [P.sub.m][C.sub.m] [less than or equal to] [P.sub.c][X.sub.c] + [P.sub.a] ([X.sub.a]-[C.sub.a]) - [P.sub.v] [absolute value of [X.sub.v]]- g([X.sup.h.sub.L]) + f([X.sup.s.sub.L] + E (budget constraint)

where U(c) is the farm household's utility function, which is monotonically increasing and strictly quasi-concave, and c is a vector of consumption goods consisting of market commodities ([C.sub.m]), self-produced agricultural goods ([C.sub.a]), and leisure ([C.sub.L]).

Production technology is represented by a well-behaved multi-input multi-output production function (2) (Lau 1978a), where x is a vector of production goods, expressed as netputs, and r is a vector of quasi-fixed factors. The farm household produces pure market goods ([X.sub.c] > 0) and goods that are partly consumed by the household ([X.sub.a] > 0). It uses variable intermediate inputs ([X.sub.v] < 0), labor ([X.sub.L] < 0), and the quasi-fixed factors land ([R.sub.g]) and capital ([R.sub.k]).

The farm household faces a time constraint (3), where [T.sub.L] denotes total time available. [absolute value of.[X.sup.h.sub.L] = [X.sup.f.sub.L] + [X.sup.h.sub.L] is the total of on-farm labor time subdivided into family labor ([X.sup.f.sub.L]) and hired labor ([X.sup.h.sub.L]), and [X.sup.s.sub.L] denotes off-farm family labor. There are four possible regimes of labor market participation. First, the household simultaneously sells family labor and hires labor. Second, farmers neither sell nor hire labor (autarky). Third, households only sell off-farm labor and fourth, they only hire on-farm labor. Earlier studies have neglected the regime in which households simultaneously hire and supply labor. For instance, Sadoulet, de Janvry, and Benjamin (1998) argue that this labor market regime is rarely observed and that their theoretical model cannot explain this specific labor strategy. However, in our data set this regime is rather frequent, with 29% of households falling into that category (table 1).(1)

The budget constraint (4) states that a household's consumption expenditures (left-hand side) must not exceed its monetary income (right-hand side). The household may receive income from farming and off-farm employment. In addition, it receives (E > 0) or pays (E < 0) transfers, which are determined exogenously. Here, [P.sub.i], i [member of] {m, a, c, v}, denote the exogenous consumer and producer prices.

Rural labor markets are often plagued by incomplete formal institutions, which implies transaction costs (Benjamin 1992; Sadoulet, de Janvry, and Benjamin 1998; Key, Sadoulet, and de Janvry 2000). Transaction costs are normally considered as FTC and PTC in existing studies (Key, Sadoulet, and de Janvry 2000; Vakis, Sadoulet, and de Janvry 2003). In particular, PTC correspond to transportation and marketing costs, while search, information, negotiation, and bargaining costs as well as screening, enforcement, and supervision costs are generally considered as FTC (Key, Sadoulet, and de Janvry 2000). Although the concept of FTC and PTC appears intuitive, there is apparently no theoretical justification for excluding NTC ex ante. Empirically there might be some transaction costs that vary nonproportionally with the quantity traded, implying NTC for both onfarm labor demand and off-farm labor supply. Theoretically, it is unclear how the marginal costs vary, i.e., if they are increasing, decreasing, or constant. (2) In this paper we present a theoretical framework that considers the impact of NTC on both on-farm labor demand and off-farm labor supply, and also provide an empirical test of their significance.

To formally include NTC as well as FTC and PTC in our model, we denote total variable transaction costs (PTC + NTC) of off-farm employment by [TC.sup.s.sub.v]([X.sup.s.sub.L], [z.sup.s.sub.v]) and total variable transaction costs of on-farm labor demand by [TC.sup.h.sub.v]([X.sup.h.sub.L], [z.sup.h.sub.v]), where [z.sup.s.sub.v] and [z.sup.h.sub.v] denote factors explaining variable transaction costs of the farm household for selling and buying labor, respectively (see Key, Sadoulet, and de Janvry 2000). For the special case of only PTC these functions are linear in [X.sup.s.sub.L] and [X.sup.h.sub.L], respectively.

Transaction costs are partly implied by unobserved heterogeneity of labor (Spence 1976; Eswaran and Kotwal 1986; Frisvold 1994; Sadoulet, de Janvry, and Benjamin 1998). However, heterogeneity of labor quality might also have an impact, although it can be observed by employers. For example, family members might have heterogeneous skills to work off-farm, which are generally observable by firms. In such cases, family members would receive different off-farm wage rates corresponding to their observable skills.