SUBSISTENCE RESPONSE TO SHOCKS

GEORGE A. DYER,STEVE BOUCHER, AND J. EDWARD TAYLOR

Microeconomic models posit that transaction costs isolate subsistence producers from output mar- ket shocks. We integrate microeconomic models of many heterogeneous households into a general equilibrium model and show that supply on subsistence farms may respond, in apparently perverse ways, to changes in output market prices. Price shocks in markets for staple goods are transmitted to subsistence producers through interactions in factor markets. In the case presented, a decrease in the market price of maize reduces wages and land rents, stimulating maize production by subsistence households; however, real incomes of subsistence households fall.

Key words: agricultural households, agricultural supply, general equilibrium models, immiserized growth, Mexico, transaction costs, village economies.

No [one] is an island, entire of itself ... is guided not by exogenous market prices, but —John Donne rather, by shadow prices endogenous to the household. It is received wisdom that subsistence pro- The premise of this article is that even ducers are isolated from output markets in subsistence producers are likely to adjust which they do not participate; that is, their their supply—possibly in perverse ways—to supply response is inelastic with respect to changes in output market prices. While sub- price shocks in those markets. Stiglitz (1989) sistence households are not affected directly notes the pervasiveness of market failures in by price shocks in markets in which they do developing economies. De Janvry, Fafchamps, not participate, the shadow prices that guide and Sadoulet (1991, p. 1401) argue that selec- their behavior are affected by the market. tive market failures “severely constrain peas- Market prices affect shadow prices through ants’ abilities to respond to price incentives other markets—in particular those for factors and other external shocks.” Omamo (1998a,b) of production—in which subsistence house- and Kurosaki (1995) highlight the effects of holds and commercial producers interact. As market failures on diversification on farms. a result, a change in the market price of sta- Access to markets is not uniform across ru- ples produced by commercial farms may in- ral households, because some households face directly alter the shadow price of staples in lower transaction costs than others (De Janvry, subsistence households as it is transmitted via Sadoulet, and Gordillo de Anda, 1995; Key, general equilibrium effects in land and labor Sadoulet, and de Janvry, 2000; Omamo, 1998b; markets. The sign as well as magnitude of the Kurosaki, 1995). The result is a heterogeneous market-price effect on subsistence-household rural economy in which commercial producers shadow prices depends upon the nature of the may coexist with subsistence farmers who are other markets. In some cases, the indirect re- shielded from selected markets by high trans- lationship between market and shadow prices action costs. Production of subsistence goods may dampen or even reverse the aggregate supply response. We illustrate this argument with a simple an- George A. Dyer is UC-CONACYT postdoctoral fellow in the alytical model that shows how a price shock Center of Economic Studies at El Colegio de Mexico, and Steve in an output market in which a single class Boucher and J. Edward Taylor are, respectively, Professor and As- sistant Professor of Agricultural and Resource at the of actors participates can be transmitted to University of California, Davis. Boucher and Taylor are members other actors via a labor market, resulting in the of the Giannini Foundation of . The authors are grateful to an editor and three referees of this seemingly paradoxical combination of produc- journal and to participants in the UC Davis Development Work- tion gain and welfare loss. The simple model shop for their valuable comments. Critical financial support was highlights the importance of capturing het- provided at various stages of this research by the William and Flora Hewlett Foundation, the University of California Institute erogeneity among rural households when es- on Mexico (UC Mexus), and the McKnight Foundation. timating production and welfare effects of

Amer. J. Agr. Econ. 88(2) (May 2006): 279–291 Copyright 2006 American Agricultural Economics Association 280 May 2006 Amer. J. Agr. Econ. market shocks. We then propose an empiri- tion and welfare in small-farm economies. cal methodology designed to capture multiple Barrett (1998) presents a model in which agri- factor-market linkages across heterogeneous cultural liberalization policies that increase households in a rural economy. The empirical both the mean and variance of food prices model incorporates the highest degree of het- exacerbate food insecurity, reducing welfare erogeneity possible by integrating a series of while stimulating farm effort and output in net- individual agricultural household models into buyer households. In our model, a decrease a general-equilibrium model of a village econ- rather than an increase in the market price omy. It is estimated with data from surveys car- triggers a positive output response on subsis- ried out in a Mexican village. tence farms. The market-price shock increases Mexico is an ideal site to test our hypoth- labor effort on subsistence farms via factor- esis that subsistence households are not iso- market linkages, which transmit the influence lated from the market. Heterogeneity among of the shock from commercial to subsistence producers is a trademark of Mexican agri- producers. culture, where a majority of land-poor, sub- Shively (forthcoming) proposes a model in sistence households coexist in more or less which labor-market and environmental link- isolated markets with a small number of ages may lead to immiserized growth. In land-rich commercial (i.e., surplus) growers Shively’s model, upland farm households en- (Hewitt de Alcantara, 1976; Esteva, 1982; gage in crop production that creates nega- Appendini, 1993). The extent of their inter- tive for lowland farms. They also action is such that social scientists often ex- supply labor to lowland farms. If the exter- plain each group’s actions in relation to those nalities reduce productivity and the wage, a of the other group (see Bartra, 1982; Fox, 1992; downward spiral can result, in which highland Wilk, 1997). In recent years, Mexico has been households reduce their labor supply to low- the site of major agricultural policy and mar- land farms and intensify production on their ket reforms that significantly increased maize own farms. This, in turn, increases the exter- imports and reduced prices but, contrary to nality and further lowers lowland farm produc- predictions of economic models, not aggre- tivity and the wage. The result is an increase gate output or cultivated area on rain-fed in production accompanied by a decrease in farms.1 Despite this, the Mexican government welfare of upland households. An endogenous has faced pressure from farmer and peasant feedback between upland and lowland produc- organizations who argue that increasing maize tions creates the possibility of mutually rein- imports have adversely affected small-farmer forcing declines in income and environmental incomes.2 quality. This is similar to our model, in that a We show that the presence of even a small shock perceived by one group or class of pro- number of commercial producers is sufficient ducers is transmitted to the other group via to generate a supply response by subsistence factor markets. Both studies attempt to explain households to a change in the market price of puzzling production and welfare outcomes in a staple. Under plausible market assumptions, the presence of a market imperfection; how- when the market price falls, subsistence pro- ever, the nature of the imperfection is differ- duction increases and welfare decreases. This ent. In Shively’s model, it is an endogenous significantly dampens the aggregate supply re- environmental , whereas in our sponse to the market price shock. model it is an exogenous market failure that The combination of increased staple out- buffers subsistence households from market put and welfare loss is reminiscent of the pre- shocks. dictions of models of “immiserized” growth, i.e., the negative correlation between produc- A Simple Analytical Model of Subsistence Supply Response 1 For example, see Levy and van Wijnbergen (1994). According to the FAO and Mexican Ministry of Agriculture (SAGAR and SIACON databases and “Anuario estad´ıstico de la produccion ´ De Janvry, Fafchamps, and Sadoulet (1991), agr´ıcola 1999–2002”), average annual maize production on rain- building upon Singh, Squire, and Strauss fed lands was 40% higher in 2001–03 than in 1983–90, despite lower maize prices. This change was due to an increase in planted area (1986), argue that many producers are iso- and, to a lesser extent, in yields. lated from changes in the market prices of 2 The National Accord for the Countryside (ANC), signed in goods they produce. Production and consump- April 2003, increases subsidies (PROCAMPO payments) to pro- ducers with fewer than five hectares and expands several programs tion decisions on subsistence farms are shaped benefiting the poorest sectors of the rural society. by unobservable “shadow prices,” which are Dyer, Boucher, and Taylor Subsistence Response to Market Shocks 281 household-specific. Because of this, they are yields the following labor supply rule for each unresponsive to the market price.3 subsistence household: This is not the case, however, when subsis- 1 tence and commercial households interact in w −1 S w = − local economies. In theory, the presence of a (6) L ( ) 1 single commercial household is sufficient to s transmit a market-price shock in a village com- S w prised primarily of subsistence households. To and an aggregate labor supply equal to nL ( ). illustrate this, consider a simple model in which Setting aggregate labor supply equal to labor there are two types of agents, a single commer- demand yields the equilibrium wage: cial farmer and n subsistence households. The − profit maximizing commercial farm produces (p, Z) 1 (7) w ∗ (p, Z) = ¯ a staple, Qc, using Cobb–Douglas production ¯ n technology with variable inputs of labor, Lc, and fixed land, T¯c (where the subscript “c” de- where Z = [, c, s , , , n] is a vector of notes “commercial”): technology¯ and preference parameters, and

1− (1) Q = AT¯ L = L . 1 c c c − 1 1 − s (8) (p, Z) = (pc) 1 + n . For simplicity, assume that all labor utilized ¯ on the commercial farm is supplied by subsis- tence households. For a given wage, w, and out- Since ∂/∂p > 0, an increase in the staple put price, p, profit maximization yields the fol- price will lead to an increase in the village lowing labor demand by the commercial farm: wage. Substituting w ∗ (p, Z) into (6) yields the reduced-form labor supply:¯ 1 − pc 1 D w = . 1 (2) Lc ( ) n 1− w (9) L S(p, Z) = 1 − () ¯ (p, Z) Subsistence households maximize utility from consuming the home-produced staple, which is an increasing function of the staple Qs, and market goods, Ms, according to a sim- market price. Finally, substituting (9) into (4), ple linear utility function: it is evident that subsistence production is a decreasing function of the staple price: (3) U(Q, M) = Q + M (10) ⎡ ⎤ 1 subject to the same staple-production technol- 1− ¯ < ¯ ⎣ n s ⎦ ogy but with a smaller fixed land input Ts Tc: Qs (p, Z) = s , ¯ (p, Z) ¯ = ¯ 1− = (4) Qs ATs L s L dQs (p, Z) ¯ < 0. and a cash-income and time constraint (assum- dp ing each subsistence household has a labor en- dowment equal to 1): While the model is simplistic, it highlights a basic insight that can easily be overlooked in M = wL S partial equilibrium analyses of market imper- (5) fections: subsistence households are indirectly + S = L L 1 connected to markets via factor market linkages with commercial producers. LS is the labor supplied by a subsistence house- In our stylized model, the supply of labor to hold to the commercial farm. The solution subsistence production, and thus subsistence of the constrained utility maximization model production itself, are functions of the market price of the staple good as well as household- specific production and consumption parame- 3 The exception is when the market-price change is of sufficient ters. Subsistence households do not participate magnitude to nudge the household out of the “price band” that is created by transaction costs; see Key, Sadoulet, and de Janvry in the staple market, yet subsistence produc- (2000). tion increases when the market price falls, due 282 May 2006 Amer. J. Agr. Econ. to the labor market linkage. The same argu- within the village or that land transactions are ment holds, ceteris paribus, for other factors illegal or associated with high transaction costs (i.e., rented land). for other reasons, so that no land market ex- ists. This provides us with the following four Empirical Modeling of Subsistence– scenarios: (A) Endogenous wage with local Commercial Interactions land market; (B) Exogenous wage with lo- cal land market; (C) Endogenous wage with- In our empirical model, as in real life, subsis- out land market; and (D) Exogenous wage tence producers are heterogeneous and may without land market. interact with commercial producers in more The optimization problem facing a given than one factor market.4 An analytical model household depends upon whether or not the quickly becomes intractable under these con- household is a subsistence or a commercial ditions. Our empirical model integrates many maize producer and on the existence (or not) individual agricultural households into a re- of a local land market. Consider first the prob- gional general-equilibrium model, calibrated lem facing household h in scenarios A and B with survey data and solved using Grants Ap- (i.e., with a local land market): plication and Management System (GAMS). Thus, in our model, households share the same max U(M, X, c; h) M,X,c,L,T ¯ general form of preferences and technologies, ¯ ¯ ¯ ¯ but the parameters in the utility and produc- Subject to : tion functions may vary across households. I This sets it apart from conventional village (C1) pi ci = pM (Q M − M) Social Accounting Matrix (SAM) and Com- i=1 putable General Equilibrium (CGE) mod- v − w − + els (Taylor and Adelman, 1996; Lewis and L M rTM pi Qi Thorbecke, 1992; Subramanian and Sadoulet, i =1 1990; Adelman, Taylor, and Vogel, 1988), in v − w − h which households are aggregated into groups Li F and all households share the same prices, pref- i=1 erences, and technologies. v h Our objective is to trace out the impact − r Ti − T¯ + I = of a shock to the market price of a staple i 1  good—maize—on household resource alloca- (C2) Q = Q L , T ; k¯ h , h tion and welfare. We hypothesize that market M M M M M  M = , ¯ h, h price shocks are transmitted via interactions Qi Qi Li Ti ; ki i across households in factor markets; thus, we i = 1,...,v explore the sensitivity of the results to differ- ent assumptions regarding the integration of (C3) X + F = L¯ the village into regional labor markets and the (C4) M ≤ Q functioning of local land markets. We exam- M ine four scenarios based on combinations of two polar assumptions regarding factor mar- In the above optimization program, U is a kets. On the labor market side, we assume that standard, quasi-concave utility function, M is either the village wage is exogenously deter- consumption of home-produced maize, X is leisure, and c = (c1, c2, ..., cI) is a vector of mined, institutionally or in markets outside the ¯ village, or that high transaction costs prevent consumption of other goods which may be pro- labor contracting across villages so that the lo- duced by the household or purchased in the lo- cal wage is instead determined endogenously cal market. Li and Ti are the amount of labor and land used¯ in the¯ production of each good. within the village. On the land side, we assume h that either a perfect land rental market exists is a vector of household-specific preference parameters¯ and I is exogenous transfer income from remittances and government programs. 4 This article’s focus is on interactions between subsistence and commercial households in local markets. We therefore assume Equation (C1) is the household’s cash-income throughout that subsistence households exist. Our treatment of constraint in which goods are ordered such that subsistence production is analogous to Becker’s (1965) treatment the first v goods are produced by the house- of “Z goods,” produced by households for home consumption us- ing purchased and family inputs. These goods implicitly have en- hold, Qi is the output of the ith good produced dogenous, shadow prices. by the household, w is the local wage rate, F is Dyer, Boucher, and Taylor Subsistence Response to Market Shocks 283 the household’s total labor supply (to both own a function of the prices of good i as well as farm and off-farm), r is the rental rate of land the price of all other goods produced by the and T¯ h is the household’s land endowment. household. Equation (C2) gives the household’s technol- For subsistence households, home-produced ogy constraints, where output of each good is maize is a nontradable good. Subsistence assumed to exhibit constant returns in labor, households face a binding subsistence con- land, and capital, k¯i , which is assumed fixed. straint and therefore must strike an inter- Equation (C3) is the time constraint, with L¯ h nal equilibrium of supply and demand for the household’s time endowment. Finally, (C4) home grown maize. The relevant maize price is the subsistence constraint which restricts for subsistence households is not the exoge- consumption of home-produced maize to the nous market price—as it is for commercial household’s production. households—but instead the household’s en- Commercial households are defined dogenous shadow price of maize, h = /, by a nonbinding subsistence constraint. where is the shadow value of the subsis- Equivalently, as characterized by de Janvry, tence constraint (C4) and is the marginal Fafchamps, and Sadoulet (1991), the home- utility of income (de Janvry, Fafchamps, and produced staple is a tradable good for these Sadoulet, 1991). To explicitly acknowledge the households. Thus, the optimization problem dependence of this shadow price on household is recursive and commercial households will preferences, we write h = h(h). Given the allocate resources to maximize profit. Profit missing market for maize, the optimization maximization, in turn, implies factor demands problem for subsistence households is not re- h h in the production of maize—L M and TM —and cursive. Under the assumption of nonjoint pro- h h duction and some fixity of capital, subsistence in the production of other goods—Li and Ti — that are functions only of exogenous (to the households will behave as profit maximizers household) prices of goods and factors, with respect to goods other than maize that the household’s capital endowment, and they produce. Thus, their factor demands in the household-specific technology parameters: production of these goods have the same form  as those of commercial households, as given by h h h h equation (11). Factor demands in the produc- L = L pM ,w,r, k¯ , M M M M tion of maize as well as the demand for con- h = h ,w, , h , h T T pM r k¯ sumption goods will be functions of household (11) M M M M Lh = Lh p ,w,r, k¯ h, h i = 1,...,v preferences: i i i i i  h = h ,w, , ¯ h, h = ,...,v.  Ti Ti pi r ki i i 1 h = h h , ,w, , ¯ h , h , h L M L M ( ) p r kM M ¯  h h = h h , ,w, , ¯ h, h, h The household’s full income Y includes Li Li ( ) p r ki i ¯ profit plus the value of household endow- i = 1,...,v ments. Utility maximization subject to the full  h = h h , ,w, , ¯ h , h , h income constraint yields commercial house- TM TM ( ) p r kM M ¯  holds’ demand for consumption goods and h = h h , ,w, , ¯ h, h, h Ti Ti ( ) p r ki i leisure: (13) ¯ i = 1,...,v h = h , ,w, h, h  M M (pM p Y ) Mh = Mh (h), p,w,r, Y h, h ¯ ¯ h = h , ,w, , h, h ¯  (12) ci ci (pM p r Y ) ch = ch((h), p,w,r, Y h, h ¯ ¯ ¯ ¯ i i h = h , ,w, , h, h . ¯ X X (pM p r Y ) i = 1,...,I ¯ ¯  h = h h , ,w, , h, h . In scenarios C and D, where land markets X X ( ) p r Y ¯ are absent, the final term on the right-hand side of the cash income constraint (net rental To operationalize our model, a household payments) is dropped and a household land version of a SAM (Stone, 1986; Pyatt and constraint is added. In these two scenarios, Round, 1979) was constructed from survey commercial households are again profit max- data for each household in the sample (the imizers with land being treated as a fixed fac- data are described in the next section). Data tor. In addition, as households must allocate in the household SAMs were used to cali- a fixed land area across alternative uses, fac- brate the individual household models. Each tor demands in production of good i will be household model is in effect a CGE for a very 284 May 2006 Amer. J. Agr. Econ. small economy. The precise form of the factor put and thus implicitly has a shadow price that and consumption demands in (11), (12), and varies across households. This may be a rea- (13) depend on technology and preferences. sonable assumption when policies or customs On the technology side, we assume Cobb– impede the functioning of local land markets Douglas production functions for each good. (e.g., the Mexican ejido or reform-sector lands Exponents in the household-specific produc- prior to liberalization of land markets in 1992). tion functions were set equal to measured fac- However, it is not reasonable when there is sig- tor shares in value added, as implied by profit nificant activity in local land rental markets, maximization. Thus, for example, the expo- which work toward equalizing the marginal nent on labor in the maize production func- value product of land across farms. This is tion for a subsistence household was set equal increasingly the case in post-reform Mexico to the local wage times total labor used (in- (World Bank, 2001). cluding the household’s own labor) divided by With regard to wages, it might be argued the value of output which, in turn, equals the that there is an active labor market in rural household’s shadow value of maize times the Mexico that is linked to internal and interna- quantity of output.5 This parameter for a com- tional migration. However, there is a striking mercial household was computed in the same geographic variation in the agricultural wage.8 way, except that output was valued at the mar- This suggests the existence of market imper- ket price. Consumption demands were mod- fections generating local wages or at least wage eled using a linear expenditure system (LES) rigidities. If all households had access to a mi- with no minimum required quantities (Deaton grant labor market, one might expect rural and Muellbauer, 1980). This LES specification wages to tend toward equalizing. However, ac- implies that preferences are described by a cess to migrant labor markets is not uniform; it Cobb–Douglas utility function. The parame- is geographically concentrated and shaped by ters in the demand equations were set equal to networks of family contacts at migrant desti- measured budget shares for each household nations and other local and household-specific and each good.6 These simple specifications variables (Munshi, 2003; Taylor, 1987).9 are sufficient to demonstrate the transmission We believe that the endogenous-wage and of market prices into subsistence economies.7 land rent specification (Scenario A) is realis- The individual household models were then tic, but alternative market specifications are linked together into a village CGE model. The not likely to change the basic argument of this general equilibrium closure equations depend article. The existence of any good or service upon which goods are tradable versus nontrad- whose price is determined in the local econ- able at the village level as well as the nature omy, in theory, can transmit changes in market of factor markets. As discussed above, we ex- prices to shadow prices in subsistence house- amine four different scenarios with respect to holds. As discussed above, Scenarios B–D are factor markets. added to explore the sensitivity of our empir- In the textbook model (Singh, Squire, and ical findings to the endogenous-wage assump- Strauss, 1986), land is treated as a fixed in- tion as well as to the existence of land rental markets. Endogenous village factor prices are in- 5 To provide an idea of the distribution of a given parameter corporated into the model through general- across sample households, the exponent on land in the production equilibrium constraints equating total village function for maize ranged from 0.04 to 0.67 with a median value of 0.12. The budget share of maize ranged from 0 to 0.5 with a median demand for land and labor to total village en- of 0.18. dowments of these factors. 6 The budget and factor shares for the subsistence good were ob- Comparative statics in the village model tained by valuing this good at a shadow price equal to its observed per-unit cost of production; see Becker (1965). are complex because of the large number of 7 We have found the results of policy experiments using similar models to be robust to the specification of functional forms, in- cluding more complex production and expenditure functions with assumed elasticities. This is not surprising, inasmuch as the model 8 According to data from the 2003 Mexico National Rural is always estimated at the same point given by the survey data, Household Survey (Encuesta a Hogares Rurales de Mexico— and policy experiments involve marginal changes in exogenous ENHRUM), daily agricultural wages in Mexico ranged from 50 variables. Simple functional forms permit estimation of a sepa- to 300 pesos in summer 2003 (estimates by authors). rate model for each agricultural household in the sample and lend 9 Among the eighty villages surveyed in the ENHRUM, the per- transparency to results. Despite linearity of individual household centage of village populations working as international migrants responses, aggregate outcomes of market shocks are highly non- in 2002 ranged from 0% to 49.7%, with a mean of 14.0%. The per- linear, shaped by specific households’ production and demand pa- centage working as internal migrants ranged from 0.0% to 53.0%, rameters and the endogenous prices of nontradables. with a mean of 15.2%. Dyer, Boucher, and Taylor Subsistence Response to Market Shocks 285

Table 1. Technology, Preferences, and General Equilibrium Conditions Production Technology h h − h − h h = h h L,i h T,i ¯ h 1 L,i T,i = ,...,v Goods produced by Qi ai (Li ) (Ti ) (ki ) i 1 household h: h = = v + ,..., Goods not produced by Qi 0 i 1 I household h:   H = h − w h − h + w ¯ h + ¯ h + h = Budget constraint Y i (pi Qi Li rTi ) L rT I i pi chi Factor demands: Nonmaize Maize-commercial Maize-subsistence h · · h h · · h h ·h h · h h = L,i pi Qi h = L,M pM Q M h = L,M ( ) Q M Labor Li w L M w L M w h · · h h · · h h ·h h · h h = T,i pi Qi h = T,M pM Q M h = T,M ( ) Q M Land (Scenarios A and B) Ti r Ti r TM r h Y h h h h h h = i h = M Y h = M Y Consumption demands (based c c c h h i pi M pM M ( ) on LES) General-equilibrium conditions for factors   ¯ h − h = Labor market clearing h i (Li Li ) 0 (Scenarios A and C)   ¯ h − h = Land market clearing h i (Ti Ti ) 0 (Scenarios A and B) ∂ h h ¯ h , ¯ h  = Qi (Li ;ki Ti ) , ¯ h − h = ∀ No land market (Scenarios rh pi ∂T T i Ti 0 i C and D; implicit household-specific rental rates) General-equilibrium conditions for  h − h = Village tradables (possibility h (Qi ci ) MSi of nonzero village- marketed surplus, MSi )  h − h = Village nontradables h (Qi ci ) 0

agricultural households, each with its own 2000), and a diversity of crops and services production technology and consumption de- associated with maize are typically nontrad- mands, interacting in multiple markets. They able (Clawson, 1985; Mart´ınez et al., 1995; involve direct effects (e.g., Slutsky effects Evangelista, 1998).10 However, enormous geo- of exogenous price changes on house- graphical heterogeneity suggests that the par- hold demands) as well as indirect effects ticular combination of market imperfections (household-farm profit effects and influences affecting this sector varies widely. acting through endogenous village prices and Our village model was calibrated using data household-specific shadow prices). Signing as from a survey of households in Zoatecp´an, an well as quantifying the total impacts of policy indigenous community in the rugged Sierra shocks requires a programming approach. Norte region in the state of Puebla, Mexico. Technology and preference specifications as Household income and expenditure data were well as the general equilibrium closure equa- gathered over the 1999/2000 crop cycle by sur- tions are summarized in table 1. The GAMS veying a random sample of forty-eight house- program including the model and data is avail- holds representing slightly more than 10% able from the authors on request. of the village household population. To in- crease reliability, each household in the sam- Study Site and Data ple was interviewed four times (three months apart), and data were collected on the previous month’s consumption. Income and production Mexican maize agriculture is marked by a panoply of market imperfections. Transaction costs have been described in relation to maize 10 Nonmarket benefits of maize cited include economic, social, markets (de Janvry, Sadoulet, and Gordillo and ritual services; e.g., food security, income diversification, and de Anda, 1995; Key, Sadoulet, and de Janvry, social standing. 286 May 2006 Amer. J. Agr. Econ. data were gathered for the entire quarter dur- tor markets (e.g., credit interlinked with labor ing each visit. The four seasonal observations and output markets), which have been found were combined to produce a single annual ob- to be important in other countries (Bardhan, servation per household. 1980). Maize is overwhelmingly the main agricul- tural output in this village. Most (94%) of Empirical Findings the households in the village are subsistence maize growers; only two households in the Results of the market-price simulations are re- sample can be considered commercial growers ported in tables 2 and 3. Table 2 presents im- of maize (i.e., households that grow maize for pacts of a 10% decrease in the market price the market). Nearly all households own land, of staples, both on village aggregates and sep- but endowments vary widely: 2% of house- arately for commercial and subsistence house- holds own 50% of the land, and the average holds. Table 3 summarizes welfare effects of land holding is 0.4 hectares. There is an active the price change. land rental market in which nearly half of all households participated at the time of the sur- Local Land and Labor Markets (Scenario A) vey. Forty-six percent of households rented in land (all to produce maize), and 5% of house- In this first scenario, we allow for a village holds rented out land. (No land was rented to land rental market and assume that transac- individuals outside the village.) The few house- tion costs of transacting in extra-village labor holds that rented out land are the largest land- markets are sufficiently high that the wage is holders in the village, a pattern widespread in determined locally. Commercial production of this region. The rental market fosters a more maize contracts sharply (by 28.5%) in response egalitarian distribution of arable land among to the decrease in output price. This implies local households. No household in this village a higher supply elasticity than most estimates had a migrant in the United States, while just from agricultural household models. For exam- under half (47%) had a migrant at an inter- ple, staple output price elasticities in models nal destination. Agricultural wages averaged reviewed by Singh, Squire, and Strauss (1986) 450 pesos—just under $5 US—per day, putting ranged from 0.11 (in Sierra Leone) to 1.56 (in this village at the bottom end of the distribu- the Republic of Korea). They are also higher tion of agricultural wages in Mexico. No farm- than in most village models, where general- ers in the sample had credit to grow maize, equilibrium effects influence response elastic- and there was no evidence of interlocking fac- ities (Taylor and Adelman, 1996). In all of the

Table 2. Percentage Effects of a 10% Decrease in the Market Price of Maize, Zoatecpan´ Village, Mexico Scenarioa ABCD Production activities Maize: aggregate −4.89 −14.22 −2.52 −10.12 Commercial households −28.52 −47.65 −14.57 −31.15 Subsistence households 4.77 −0.56 2.40 −1.53 Other agriculture 4.45 0.00 2.89 0.00 Livestock −0.64 0.64 0.32 1.01 Nonagricultural activities −18.98 −9.49 −12.50 −7.11 Commerce −36.19 −18.45 −23.82 −13.81 Wage −9.60 — −6.46 — Rental rate −14.05 −14.25 — — Village GDP −7.26 −3.77 −4.78 −2.82 Household real income −1.69 −0.87 −0.77 −0.45 Commercial households −3.97 −3.04 −1.30 0.39 Subsistence households −1.57 −0.75 −0.74 −0.50 aThe scenarios are as follows: (A) Local land market (endogenous rental rate)/local labor market (endogenous wage); (B) Local land market/open labor market (exogenous wage); (C) No land market/local labor market; (D) No land market/open labor market. Dyer, Boucher, and Taylor Subsistence Response to Market Shocks 287

Table 3. Welfare Effects of a 10% Decrease in the Market Price of Maize Scenarioa Indicator Base A B C D Gini coefficient Real income 0.36 0.35 0.35 0.35 0.35 Cultivated land 0.56 0.52 0.51 0.56 0.56 Percentage change in poverty Poverty gap ( = 1) 0.90% 0.47% 0.14% 0.06% Squared poverty gap ( = 2) 1.70% 0.67% 0.48% 0.24% aThe scenarios are as follows: (A) Local land market (endogenous rental rate)/local labor market (endogenous wage); (B) Local land market/open labor market (exogenous wage); (C) No land market/local labor market; (D) No land market/open labor market. above-mentioned studies, land was assumed to mercial to subsistence farmers, the less effi- be a fixed input in production. In our highly cient use of inputs by the latter results in a 4.9% disaggregated model, commercial staple pro- decrease in the village’s total (commercial plus ducers respond to the price decrease by sharply subsistence) maize output. curtailing production and renting land to other Impacts of lower maize prices are trans- (subsistence) households in the village. The im- mitted to other sectors of the village econ- pact of a local land market can be seen by com- omy, producing secondary income effects. The paring column A to column C and column B to consumption demand for nonmaize goods and column D. Under each wage scenario, the com- services decreases. Lower village demand pro- mercial supply response is considerably lower vokes a contraction in activities that supply lo- when there is assumed to be no local land mar- cal demand but that do not make intensive use ket (i.e., −28.52 versus −14.57 and −47.65 ver- of land or labor, such as nonagricultural ac- sus −31.14). Aggregate supply elasticities for tivities and, in some households, livestock.12 the village, in which total land area is fixed, are The price of village nontradables drops, coun- lower, and they are similar to those found in teracting the drop in demand, but demand other village models.11 for fixed-priced imports decreases even more In scenario A, the market-price shock is sharply, spurring the decline of the formal- transmitted to subsistence households via ad- commerce sector. As a result, the village’s justments in the equilibrium prices of land and GDP decreases by 7.3%. labor. The exogenous decline in the market price of maize causes a contraction of demand Impacts under Alternative Village Market by commercial farmers for both factors, result- Scenarios (B–D) ing in a decrease in the local land rent and wage rate of 14% and 9.6%, respectively (table 2, Outcomes are sensitive to factor market as- column A). Lower rents and wages reduce the sumptions. A missing land market (Column C) incomes of households supplying these factors, forces commercial farmers to cultivate land, causing an inward shift in the demand for nor- which they otherwise would rent out. This mal goods, including maize. However, because cushions the negative impact of the price land and labor are inputs into subsistence pro- shock on commercial production, wages, and duction, the lower factor prices also cause an subsistence-household incomes, and it damp- outward shift in the maize supply curves of ens adverse demand effects on other sectors subsistence households. Total maize produced in the village. Paradoxically, perhaps, income by subsistence households increases by 4.8%, falls less sharply when the land market is con- while the largest increase on an individual sub- strained; indirect income effects on the lo- sistence farm is 12.5%. That is, in spite of in- cal economy diminish. When households are come losses in subsistence households, output deprived of the ability to enter into rental increases. As land cultivation shifts from com- contracts, the shadow price of land is lower for surplus growers but higher for subsistence

11 Taylor and Adelman (1996) estimate staple-price elasticities of 12 These activities are geared entirely to satisfy local demands; 0.38 to 1.4 in village models for Senegal, India, Mexico, Kenya, and they are not connected with outside markets. Thus, they are treated Java. as village nontradables with endogenous local prices. 288 May 2006 Amer. J. Agr. Econ. households. Subsistence output increases by where n is the total number of adult equiva- less than in the perfect land-market scenario. lents in the village and y is a vector of per- If wages are fixed (Columns B and D), pro- capita incomes, q = q(y; z) is the number of duction does not benefit from the general equi- adult equivalents living in poor households, librium wage feedback when the price of maize z–yi is the income shortfall (the gap between falls. The staple sector’s overall contraction is the individual’s income and the poverty line) larger than before, and subsistence production of the ith (poor) individual, and is a param- no longer expands. Nevertheless, fixed wages eter. The poverty line we use is the per-capita and fixed land cushion subsistence-household income required to purchase a basic basket incomes from the collapse in commercial pro- of food items in rural areas, estimated by the duction (Column D). This partially mitigates Mexican government at 15.4 pesos (approx- the contraction of nonagricultural activities imately US$1.50) per day in 2000.14 Impov- and commerce. The livestock sector grows, erished individuals are those who were living stimulated by lower feed costs. Other (com- in households in which the per-capita income mercial) agriculture is completely unaffected, per day was less than 15.4 pesos. Using this inasmuch as its output price and labor costs are poverty line, 90% of households in the vil- unchanged. lage were poor. Because of this, sensitivity of the poverty index to the depth and severity of Welfare poverty is critical when measuring poverty im- pacts of market shocks. In each of the four scenarios, every house- As increases, greater weight is placed on hold experiences a decrease in nominal in- the poorest households. Using a simple head- come. Changes in real income range from a count poverty measure ( = 0), there is no 2.7% increase to a 12.4% decrease; seven out change in poverty under any of the market sce- of ten households experience a real-income narios (table 3). Using the poverty gap mea- loss. sure ( = 1), poverty increases. The poverty Table 3 summarizes distributional and impact of the staple-price shock is far and away poverty outcomes of the 10% decrease in sta- greatest using the squared poverty gap mea- ple price. These are calculated from house- sure. This indicates that the price shock in- hold-level impacts, which are not obtainable creases inequality among the poor, adversely from village or aggregate general equilibrium affecting the poorest households in the vil- models that do not model households individ- lage. Factor-market linkages shape poverty ually. As household real income falls, income outcomes. Under both the poverty gap and is redistributed, but only in a marginally pro- squared poverty gap measures, poverty in- gressive fashion: in each scenario, the Gini co- 13 creases most when land markets exist and efficient for income drops from 0.36 to 0.35. wages are endogenous. It increases least when The redistribution of operated land is pro- wages do not adjust to the price shock and land gressive in the two scenarios with local rental inputs are fixed, so farmers cannot use the land markets: the Gini coefficient for operated land market to adjust to the price shock. decreases from 0.56 to 0.51 in Scenario A (0.52 These findings indicate the vulnerability of in Scenario B). Nearly 15% of households rent very poor households, who rely primarily on in land previously cultivated by commercial their endowment of labor, to the general growers. equilibrium effects of market price shocks. Concerns about welfare changes in rural The poorest households receive a large share economies are concentrated largely on the of their income from local wage work, and lower tail of the income distribution. To ex- they suffer disproportionately via general- plore the poverty impacts of the staple-price equilibrium effects operating through labor change, we compare poverty estimates under markets. Households engaged in formal com- each of the four factor-market scenarios to the merce experience the greatest percentage de- base poverty level, using the Foster–Greer– creases in income, even greater than those of Thorbecke poverty index: commercial maize growers. However, they are q not poor. Poor households whose chief income = 1 − P(y; z) (z yi ) source is public or private transfers experi- nz i=1 ence increases in real income. They benefit as

13 See Deaton (1997) for the formula to estimate the Gini coeffi- 14 See http://www.sedesol.gob.mx/subsecretarias/prospectiva/me cient. dicion pobreza. Dyer, Boucher, and Taylor Subsistence Response to Market Shocks 289 consumers from the lower staple prices, with- Findings using data from a single village out being adversely affected by the decrease in cannot be generalized; the mix of commer- wages. However, they are not among the poor- cial and subsistence households in one vil- est in the village. lage do not reflect the overall rural economy. Nevertheless, they are sufficient to demon- Conclusions strate that interactions in local markets can transmit changes in market prices to shadow The presence of a single commercial producer prices in subsistence households, affecting sup- theoretically is sufficient to transmit the im- ply response in surprising ways. The outcomes pacts of price and other policy shocks through- of our experiments would almost certainly out a largely subsistence economy, with be different in villages that are more closely potentially surprising results. Commercial pro- integrated with outside markets, particularly ducers transmit shocks from national and for labor, and in regions with commercial al- international commodity markets through ternatives to staple production. Commercial their interactions with subsistence producers farmers in Puebla did not benefit from input in local factor markets. As a result, no one is subsidies that supported Mexico’s commercial production of maize in the wake of falling out- truly isolated from market shocks; “shadow 16 prices” in subsistence households ultimately put prices. are linked with outside market prices. A basic tenet of our modeling approach is Our analytical and empirical findings sug- that heterogeneous local conditions can gen- gest a previously unrecognized explanation for erate a variety of policy and market outcomes. immiserized growth, or a negative association Disaggregated models that allow for hetero- between output and welfare changes, in small- geneous micro responses as well as interac- farm economies. General equilibrium linkages, tions among actors in a general-equilibrium via local factor markets, can result in conflict- context can help explain unexpected micro re- ing welfare and output effects of market price sponses and aggregate effects of policy and shocks in subsistence households. Our results market shocks. Micro agricultural household also suggest a local explanation for the sluggish models, with or without missing markets, are (and apparently perverse) response of pro- special cases of general-equilibrium models, duction on rain-fed lands to changes in mar- because they rule out the transmission of in- ket prices of maize in the wake of Mexico’s fluences among households. This limitation is agricultural reforms. Most farmers in Mexico likely to be increasingly serious as market lib- are subsistence producers on rainfed lands.15 eralization enables diverse agents to respond Like consumers in a Becker (1965) household to policy changes in new ways. model, they combine land, labor, and other inputs to produce a utility-generating output. [Received September 2004; As structural adjustments lower the oppor- accepted July 2005.] tunity cost of land and labor, production of homegrown maize expands. The result, iron- References ically, may be a movement toward a more inward looking, subsistence economy in the Adelman, I., J.E. Taylor, and S. Vogel. 1988. “Life in wake of market liberalization. Development a Mexican Village: A SAM Perspective.” Jour- of land markets may exacerbate this appar- nal of Development Studies 25:5–24. ently perverse supply response by encourag- Appendini, K. 1993. De la Milpa a los Tortibonos: ing land rental. While the existence of local La Restructuracion´ de la Pol´ıtica Alimentaria en land markets increases the supply elasticity on Mexico´ . Mexico: El Colegio de M´exico, Insti- commercial farms, our experiments show that tuto de Investigaciones de las Naciones Unidas it also can reinforce a positive supply elasticity para el Desarrollo Social. on subsistence farms. Integration with outside Bardhan, P.1980. “Interlocking Factor Markets and labor markets, via migration or expansion of Agrarian Development: A Review of Issues.” rural nonfarm employment, may dampen the Oxford Economic Papers 32(1):82–98. subsistence response (while exacerbating the commercial response) by limiting local wage adjustment. 16 ASERCA marketing supports to commercial producers of ba- sic crops reached 6,406 million pesos (US$613 million) in 2003. Around 30% of ASERCA payments are to commercial produc- ers of corn; however, they are concentrated in the northwestern 15 De Janvry, Sadoulet, and Gordillo de Anda (1995). regions, primarily the state of Sinaloa (de Ita, 2003). 290 May 2006 Amer. J. Agr. Econ.

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