TESTING HOUSEHOLD-SPECIFIC EXPLANATIONS FOR

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1 TESTING HOUSEHOLD-SPECIFIC EXPLANATIONS FOR THE INVERSE PRODUCTIVITY RELATIONSHIP JULIANO J. ASSUNÇÃO AND LUIS H. B. BRAIDO The nverse relatonshp between land productvty and farm sze s an old and puzzlng emprcal regularty. Most explanatons for ths relatonshp rely on market mperfectons that jontly determne the farm sze and the household s shadow prce of some productve nputs. We use plot-level data from the ICRISAT/VLS to assess whether these household-specfc theores can explan the puzzle. The data exhbt plots of dfferent szes beng smultaneously cropped by the same household. The nverse relatonshp s shown to hold true wth the same magntude across the plots of each household, thus cross-household heterogenety does not suffce to explan the puzzle. Key words: development, farm sze, nverse, IP relatonshp, productvty. The nverse relatonshp between land productvty and farm sze has puzzled economsts for a long tme. 1 Chayanov (1926) frst documented that small farms produced more output per unt of land n Russa. The same result was found n Inda by Sen (1962), Bardhan (1973), and Rosenzweg and Bnswanger (1993); and n Brazl, Pakstan, and Malaysa by Berry and Clne (1979). Ths nverse relatonshp s ntrgung as there s a large body of lterature that estmates constant returns to scale for agrcultural producton n dfferent countres (e.g., Hayam and Ruttan 1970; Bardhan 1973; Berry and Clne 1979; Fulgnt and Perrn 1993). Moreover, n the absence of market falures, farmers would voluntarly subdvde ther lands n order to ncrease productvty thereby elmnatng the nverse relatonshp. Understandng ths emprcal regularty has mportant polcy mplcatons. Land redstrbuton would ncrease the agrcultural productvty f small plots were ntrnscally more productve than large peces of land. However, ths would not be effectve f the puzzle was just a spurous statstcal result; and Julano J. Assunção s wth the Department of Economcs, Pontfcal Catholc Unversty of Ro de Janero PUC-Ro and Lus H. B. Brado s wth the Graduate School of Economcs, Getulo Vargas Foundaton. The authors are especally ndebted to the edtor, Chrstopher Barrett, and three anonymous referees for nsghtful remarks that consderably mproved the paper. They are also thankful for comments from Steven Helfand and Rodrgo Soares. Fnancal support from CNPq s gratefully acknowledged. 1 As s usual n ths lterature, the term productvty refers to the value of the output per unt of land. alternatve polces would be requred f the nverse relaton were caused by market falures n the labor and credt markets. Feder (1985) noted that a sngle market falure s typcally nsuffcent to generate the nverse relatonshp. Under constant returns to scale, the explanatons for the puzzle are lkely to depend on market falures that smultaneously prevent land subdvson and dstort the shadow prce of some productve factors. Chayanov (1926), Sen (1962), Carter (1984), and Carter and Webe (1990) argue that peasant households apply famly labor more ntensvely because the opportunty cost of ther tme s low. If mperfectons n the labor market cause the peasant s shadow prce of tme to dffer from the market wages, and f falures n the land rental market prevent them from managng lands owned by others, then the peasant mode of producton would generate an nverse relatonshp. In an alternatve ven, Bardhan (1973), Feder (1985), Eswaran and Kotwal (1986), and Taslm (1989) theorze that labor s subject to ncreasng margnal cost of supervson, thus the optmal land-to-labor rato s hgher for large landowners. Ths argument generates the nverse relaton when the land market s mperfect. Moreover, as noted by Srnvasan (1972), Rosenzweg and Bnswanger (1993), and Barrett (1996), rsk concerns could also generate the nverse relatonshp. Consder, for nstance, a scenaro n whch ncomplete nsurance markets hnder full hedgng aganst agraran rsks and falures n the land market Amer. J. Agr. Econ. 89(4) (November 2007): Copyrght 2007 Amercan Agrcultural Economcs Assocaton DOI: /j x

2 Assunção and Brado Household-Specfc Explanatons for the Inverse Productvty Relatonshp 981 prevent small farmers from ncreasng the cropped area. In ths case, small farmers experence food-securty stress and then overapply productve nputs on ther lands. Assunção and Ghatak (2003) state that the heterogenety of farmers sklls, coupled wth credt-market mperfectons n an envronment wth constant returns to scale and no labor-market mperfecton, s another explanaton for the puzzle. In equlbrum, the occupatonal choce s such that hgh-sklled peasants end up croppng small farms because they have hgher opportunty costs to become wage workers. In ths context, there s a range n whch small farms are proftable for sklled peasants and not proftable for unsklled peasants. Farmer self-selecton would then generate the nverse relatonshp. In ths artcle, we emprcally assess these theoretcal explanatons. Our man contrbuton s notcng that all of these theores depend on cross-household heterogenety, and ths should equally affect the lands cropped by the same household. We analyze a very specal data set from the Internatonal Crops Research Insttute for Sem-Ard Tropcs (ICRISAT) whch contans households croppng multple plots n each season. Ths allows us to nvestgate the nverse relatonshp across dfferent plots cropped smultaneously by the same household. If the nverse relatonshp were due to ether the peasant mode of producton or ncreasng supervson costs, then the plot-level productvty should be related to the total area managed by the household n each perod, rather than the area of each partcular plot. Contrary to ths predcton, we show that plot productvty s nversely related to plot area and unrelated to the total area managed by the household. Furthermore, accordng to all prevous explanatons, the nverse relatonshp s due to unobserved features n the household. We assess the mportance of those explanatons by usng regresson models wth fxed effects to estmate the nverse relatonshp. We frst use household fxed effects n order to account for household characterstcs that are fxed over tme. We then explore the fact that households harvest multple plots n each season and ntroduce dummy varables for households n each perod (season of the year), whch accounts for unobserved household characterstcs that are not fxed over tme. The results show that the magntude of the nverse relatonshp remans statstcally unchanged. Ths evdence does not make the case for explanatons based on crosshousehold heterogenety. Naturally, some of those explanatons could be coupled wth ntrahousehold ssues to generate the nverse relaton. For nstance, members wth dfferent characterstcs could be allocated to supervse croppng actvtes n dfferent plots of each household. We show, however, that the nverse relatonshp holds wth the same magntude when we restrct the analyss to plots cropped by households wth one sngle adult member. Other ntrahousehold ssues such as heterogeneous supervson costs due to geographcal dstance and dfferences n the croppng pattern across plots of each household are also analyzed n a secton of robustness checkng. The results do not support those possbltes. Our artcle s related to the work by Lamb (2003), whch explores the ICRISAT/VLS sample at the aggregate farm level. In contrast, we explore the plot-level data to nvestgate the nverse relaton across plots smultaneously cropped by the same household. Ths strategy leads us to obtan more conclusve results on the lack of mportance of householdbased explanatons for the puzzle. By rejectng household-based explanatons for the nverse productvty relatonshp, our fndngs favor the lterature that explans the puzzle by unobserved heterogenety across plots and lands (e.g., Bhalla 1988; Bhalla and Roy 1988; Benjamn 1995; Chen, Huffman, and Rozelle 2003; Lamb 2003; and Kmh 2006). In our vew, future attempts to understand the economc content of the nverse relatonshp should focus on plot-specfc unobservables as opposed to market falures affectng productvty at the household level. The polcy mplcatons of ths research agenda depend crucally on understandng whch are the specfc unobservables assocated wth sze at the plot level and whch are the market forces behnd ths assocaton. Data We use data from the longtudnal Vllage- Level Studes (VLS) conducted by the Internatonal Crops Research Insttute for Sem-Ard Tropcs (ICRISAT), n Inda, from 1975 to Sx vllages were ntally selected from dfferent agroclmatc zones, namely Aurapalle and Dokur (n the state of Andhra Pradesh); Kanzara, Knkheda, Shrapur, and Kalman (n the state of Maharashtra). In 1980,

3 982 November 2007 Amer. J. Agr. Econ. the vllages of Borya Becharj and Rampura (n the state of Gujarat) were also ncluded n the study. Farmers were randomly selected n each of these vllages and resdent nvestgators recorded nformaton about all plots cultvated by them n each season of the year. Note that although the database s collected at the plot level, the household s the prmary samplng unt. Farmers who moved out of the vllage durng the perod of data collecton were randomly replaced. Further detals about the data collecton method can be found n Jodha, Asokan, and Ryan (1977) and Sngh, Bnswanger, and Jodha (1985). The man data source s the ICRISAT s PS fles, whch contan plot-level nformaton on croppng actvtes such as output value, cropped area, value of dfferent nonlabor and labor nputs, estmated per acre value of the plot, rrgaton, sol type, croppng pattern, vllage, year, and season. An auxlary schedule, the C fles, whch contan nformaton on household characterstc, s also used to measure the number of adult members n each household. The ownershp status s vared among the surveyed plots. We focus on plots cropped by ther owners n order to avod concerns about ncentve problems sometmes assocated wth farms managed by tenants. The qualtatve results, however, reman unchanged when we nclude these plots n the analyss. 2 Farmers typcally manage many dfferent plots smultaneously. On average, each household harvests 5.6 plots per perod. In order to study the mportance of montorng actvtes, we construct a varable descrbng the total area managed by the household n that perod.e., for each plot, ths varable sums the area of all plots cropped under the responsblty of the same household n that partcular year and season. When constructng ths varable, we nclude the plots rented by each household because, even f farmers faced ncentve problems n rented farms, they would stll expend part of ther tme wth these plots. All results reman dentcal f we exclude the rented area from ths varable. Fnally, some households have plots that produce no output n some seasons the reported output s zero for about 6% of the plot observatons. These are lkely to be plots under rotaton or temporarly abandoned after extreme shocks and are gnored n our analyss. 3 Table 1 descrbes the varables used throughout the artcle, and table 2 presents a few summary statstcs. The Inverse Relatonshp Theoretcal Framework Consder a Cobb Douglas producton functon. For each plot n, managed by household h, n perod t (namely, the season of each year), one has (1) Y = A T t K k L l exp(ε ) where = (n, h, t) ndexes the observatons (plots, households, and perods); Y represents the total output; T s the cropped area; K and L represent the amount of nonlabor and labor nput used; A s a technologcal factor that accounts for observable household and land characterstcs as well as specfc effects assocated wth dfferent vllages, years, seasons, and crops grown; and ε s an error term accountng for unobserved and dosyncratc determnants of the output such as clmatc shocks and nfestatons. By multplyng Y,K, and L by ther respectve prces (namely, p, r, and w), we can represent the producton functon n monetary unts, as follows: (2) y = a T t k k l l exp(ε ) where y = py represents the value of the output; k = rk and l = wl are the value of nonlabor and labor nputs (respectvely); and a = A p s a prce-adjusted technologcal (r) k (w) l term. Consder now a compettve envronment wth no externalty and constant return to scale,.e., t = (1 k l ). For any arbtrary plot sze, farmers would maxmze the expected proft, such that plot s nput choces would solve (3) max k,l E ( a T t k k l ) l exp(ε ) k l. The optmal amount of nonlabor and labor nputs would be then gven by 2 Table A2 n the techncal appendx (Assunção and Brado 2007) shows that our analyss s robust to the ncluson of plots managed under sharecroppng and fxed rent. 3 The ICRISAT/VLS documentaton does not menton what could potentally explan the zero reported values. We elaborate on ths topc n the techncal appendx (Assunção and Brado 2007).

4 Assunção and Brado Household-Specfc Explanatons for the Inverse Productvty Relatonshp 983 Table 1. Data Descrpton Varable Descrpton Output Nomnal value of man output and by-products, measured n Indan rupees Plot Cropped Area Area of the plot actually cultvated (measured n acres) Total Cropped Area Area of all plots managed by the farmer n each season (nclude plots managed under ownershp, fxed rent, and sharecroppng) Per Acre Land Value Per acre value of the plot estmated by ICRISAT s nvestgators usng nformaton from vllage specalsts about the potental sale value, topography, and locaton (nomnal values expressed n 100 rupees per acre) Irrgaton Dummy Dummy for rrgated plots Sol Dummes 7.1% deep black; 33.9% medum black; 22.1% shallow black; 10.6% shallow red; 2.7% gravelly; 0.5% problem sol (salne, etc.); 10% sandy sol; 1.2% other sols; 11.9% undefned Croppng Pattern Qualtatve varable (wth 1,031 dfferent codes) descrbng all products cropped n each plot Man-Crop Dummes Dummy varables constructed from the frst letter of the croppng pattern code (whch descrbes a general category for the domnant croppng product): 16.4% olseeds; 52.4% cereals; 8.8% fber crops; 0.5% garden crops; 15.1% pulses; 1% sugar cane; 4.4% vegetables and spces; 1.2% fodder crops; 0.2% mssng nformaton Vllage Dummes 14% Aurepalle; 5.2% Dokur; 21.1% Shrapur; 15.9% Kalman; 14% Kanzara; 5.4% Knkheda; 9.1% Borya; 15.3% Rampura Year Dummes 1975 (11%); 1976 (11.2%); 1977 (10.8%); 1978 (9.5%); 1979 (9.2%); 1980 (9.6%); 1981 (10.5%); 1982 (9.7%); 1983 (9.3%); 1984 (9.2%) Season Dummes 35.19% planted from June to October; 59.22% from November to February; 5.34% from March to May; 0.21% perennal crops; 0.04% mssng nformaton Adult Members Number of members aged 18 years or more (n each partcular year) Note: Data from the ICRISAT/VLS. The prmary samplng unt s the household, but the observatons refer to plots managed by each household n each season of the year. Plots managed under fxed rent and sharecroppng are not ncluded n the analyss. Table 2. Summary Statstcs Varable Obs. Mean Std. Dev. Mn. Max. Per Acre Output 8, , ,964 Plot Cropped Area 8, Total Cropped Area 8, Adult Members 7, Per Acre Land Value 8, Irrgaton Dummy 8, Note: Data from the ICRISAT/VLS. (4) (5) (6) k ( (1 = T l ) k l l a E(exp(ε )) ) 1 1 k l l ( (1 = T k ) l k k a E(exp(ε )) ) 1 1 k l. Equaton (2) can be wrtten as y 1 = ( a ) k l exp(ε ) T 1 where = ( k ) k ( l ) l [E(exp(ε ))] ( k+ l ). Equaton (6) plays a central role n our emprcal analyss. In prncple, the technologcal term a and the producton shocks ε should both be ndependent of the cropped area T. Under ths assumpton, the per acre value of the output should also be ndependent of the cropped area that s, y T T. Ths uncondtonal ndependence should be verfed at the plot level as well as at the household aggregated level. To emphasze ths pont, assume that the technologcal factor a and shocks ε are common across all plots (n) cropped by each household (h) n a certan perod (t); that s, a = a h,t and ε = ε h,t, = (n, h, t). Ths assumpton s natural, for nstance, f all those plots belong to a contguous and homogenous farm. In ths scenaro, equaton (6) could be aggregated as follows: (7) y h,t 1 = ( a h,t ) k l exp(ε h,t ) T h,t 1

5 984 November 2007 Amer. J. Agr. Econ. where y h,t I h,t y ; T h,t I h,t T ; and I h,t represents the set of plots cropped by household h n perod t. The farm-level model (7) has been predomnantly used n the lterature because aggregate data are more frequently avalable. Agan, the per acre productvty y h,t T h,t should (n prncple) be unrelated to the cropped area T h,t. We show, however, that, for the ICRISAT/VLS data, the nverse relatonshp s present n both econometrc specfcatons. The dsaggregated plotlevel specfcaton wll be used n ths artcle snce t allows us to test for household-specfc explanatons. Emprcal Characterzaton We start the emprcal analyss by showng the nonparametrc relatonshp between the logarthm of the per acre output and the logarthm of the cropped area. Smlar to Barrett (1996), we show n fgure 1 the curves obtaned by the Nadaraya Watson estmator wth an Epanechnkov kernel of bandwdth They show the exstence of an nverse relatonshp between per acre output and cropped area, both at the plot level and at the aggregated household level. In both cases, the relatonshp s approxmately log-lnear. The exstence of the nverse relatonshp as depcted n fgure 1 can potentally be explaned by a negatve correlaton between the technologcal factor (A ) and the cropped area. In ths case, regressons controllng for observed regressors (such as land value, sol type, rrgaton, vllage, year, season, and crop grown) are needed. Furthermore, as noted before, the cropped area could be negatvely correlated to household-specfc features that affect land productvty (such as farmng sklls, montorng capablty, stress-nduced effort, etc.). In the remander of the artcle, we examne these dfferent possbltes n detal. Testng for Household-Specfc Explanatons Throughout the artcle, we consder the plotlevel model of producton and use the loglnear verson of (6), namely, ( ) y (8) ln = ln(a ) + ε T ln( ) 1 1 k l. where 0 = 1 k l and 1 = Table 3 presents OLS regressons for (8), where dfferent varables are sequentally ntroduced to control for a = A p r k w. All l ln(output per acre) ln(sze n acres) Plot regresson Farm regresson 95% Conf. nterval Note: Curves from Nadaraya Watson regressons usng the Epanechnkov kernel wth bandwdth Confdence ntervals obtaned from 200 bootstrap samples. Fgure 1. Inverse relatonshp

6 Assunção and Brado Household-Specfc Explanatons for the Inverse Productvty Relatonshp 985 Table 3. Household-Based Explanatons OLS Dependent Varable: Log per Acre Output Wthout Wth Fxed Fxed Sol Sol Total Effects I Effects II Qualty Qualty Area (Household) (Household & Perod) (1) (2) (3) (4) (5) Log plot cropped area (0.030) (0.023) (0.024) (0.025) (0.026) Log total cropped area (0.017) (0.018) Log per acre land value (0.048) (0.048) (0.052) (0.069) Dummes for rrgaton and No Yes Yes Yes Yes sol type Constant and dummes for Yes Yes Yes Vllage Vllage, year, and the man-crop, vllage, dropped season dropped year, and season Number of observatons 8,908 8,906 8,906 8,906 8,906 Number of groups 268 2,633 R Note: Robust standard devaton (n parenthess) account for the fact that farmers, rather than plots, are the prmary samplng unt ( sgnfcant at 10%; sgnfcant at 5%; sgnfcant at 1%). Fxed effects I refer to 268 household dummes; whle fxed effects II refer to 2,633 dummy varables generated through the teraton of the household and perod codes (household-vllage, year, and season). regressons nclude a constant term and dummes for the man crop, vllage, year, and season. These varables account for dfferences n A as well as for dfferences n prces across vllages and perods (.e., seasons of each year). 4 The frst regresson does not control for plot attrbutes, whereas the second one controls for land value, rrgaton, and sol type. In both cases, the per acre output s negatvely correlated wth the plot cropped area. One must notce that the nverse productvty relaton s consderably smoothed when one controls for observed plot attrbutes the pont estmates drop from 30% to 16%. Ths suggests that larger plots have worse productve attrbutes. Next, we note that the explanatons lsted n the Introducton are all based on household-specfc features (namely, the peasant mode of producton, mperfect labor supervson, food-securty stress, or unobserved farmng sklls). The frst two theores are drectly lnked to the total area managed by the household (nstead of the area of each plot). The other theores are also ndrectly lnked to the total area cropped by the household. We then ntroduce ths varable nto the regresson n column (3) and notce that the coeffcent assocated wth the total cropped area 4 Snce we consder nomnal values throughout the artcle, the year dummes also account for nflaton. s postve (rather than negatve), whle the coeffcent assocated wth the plot area remans unchanged (.e., negatve and wth the same statstcal magntude). In the fourth regresson of table 3, we estmate equaton (8) wth household fxed effects (based on the household codes), explorng the varaton n the area cropped across all plots cultvated by each household n all perods. 5 Observed and unobserved effects that are specfc to the household and constant over tme are consdered n ths regresson. The coeffcent of the total cropped area turns out to be nonsgnfcant, but there s vrtually no change n the nverse relatonshp wth respect to the plot sze. However, t could stll be possble that the nverse relatonshp s drven by the unobserved household characterstcs that are not fxed over tme. The ICRISAT/VLS data provde a strkng means of control for ths possblty, snce there are many farmers cultvatng multple plots wth dfferent szes n each perod (year and season). The estmates of the regresson wth household-perod fxed effects (based on codes for the household, year, and season) are reported n the last column and renforce the results of the prevous regres- 5 Household fxed effects account for 23% of the varaton of the logarthm of the per acre output. See the techncal appendx (Assunção and Brado 2007) for detaled varance decomposton of the man varables.

7 986 November 2007 Amer. J. Agr. Econ. son. 6 The effect of the total cropped area on y T s not sgnfcant, whle the nverse productvty relaton stll holds steady wth the same magntude. 7 These results show that theoretcal explanatons focusng exclusvely on household-specfc features do not account for the nverse productvty puzzle. Intrahousehold Issues Table 3 suggests that the nverse relatonshp between productvty and farm sze s not explaned by household-specfc theores such as those based on the peasant mode of producton, mperfect labor supervson, food-securty stress, and skll bas. Condtonal on land value and other plot attrbutes (namely, sol type and presence of rrgaton), household-specfc features have vrtually no mpact on the estmated magntude of the nverse relatonshp. However, our emprcal strategy depends on some dentfcaton hypotheses about how resources are allocated nsde each household. Intrahousehold ssues are now submtted to falsfcaton tests. Intrahousehold Allocaton of Manageral Resources We have mplctly assumed that a sngle manager controls all plots of each household. If so, household-perod fxed effects could account for all unobservable characterstcs of the manager. However, dfferent members could be systematcally assgned to plots of dfferent szes, based on a combnaton of manageral sklls and sol characterstcs or as a result of ntrahousehold barganng. Ths possblty s studed, for nstance, by Carter (1984) and Udry (1996). If ths s vald here, our nterpretaton for the results of table 3 needs to be revsed. The ICRISAT/VLS survey has no nformaton about the actual manager of each plot. However, we can check the robustness of our results by restrctng the prevous analyss to households wth the same numbers of adult members. For example, ntrahousehold barganng or manageral heterogenety should not arse n households wth a sngle adult member. Table 4 presents the regressons for subsamples of households wth 1, 2, 3, and 4 adult members. The econometrc specfcaton s the same that s used n the last regresson of table 3 that s, t controls for sol attrbutes and household-perod fxed effects. The nverse relatonshp s present n all four subsamples. Moreover, ts magntude does not change (when compared to the last regresson of table 3). The p-values for the hypothess test that the estmated coeffcent for the log area cropped s statstcally equal to 0.16 (our best estmate from table 3) are reported n table 4. In all subsamples, these estmated coeffcents are ether statstcally equal to ths value or sgnfcantly more negatve. Ths does not support the hypothess that the nverse relatonshp estmated n table 3 s due to dfferentated ntrahousehold allocaton of manageral resources. 8 Supervson Costs across Plots of Each Household A key aspect of our emprcal analyss s the fact that we observe farmers cultvatng multple plots n each gven perod (season of the year). Ths provdes a powerful means of controllng for unobserved household characterstcs. However, the possblty of havng heterogenety among the dstances to each plot s another potental source of bas f these dfferences are systematcally related wth sze. The ICRISAT/VLS database does not contan nformaton about the geographcal dsperson of the plots cultvated by each household. Plots mght be contguous or not. If the largest plots avalable to each household are solated and harder to be montored, the results presented n table 3 would not necessarly be rejectng the labor supervson explanaton. In ths case, the plot sze could be correlated wth unobserved montorng capablty through the geographcal dsperson of the plots. We are not able to drectly address ths ssue. We are restrcted to an ndrect assessment 6 As s shown n the techncal appendx (Assunção and Brado 2007), household-perod fxed effects explan 57% of the varaton n the logarthm of the per acre output. 7 Our estmates for the nverse relatonshp are robust to the specfcatons wth random effects. The Hausman s specfcaton tests favor the models wth fxed effects, thus we left these estmates n the techncal appendx (Assunção and Brado 2007). 8 When comparng the results across households wth dfferent numbers of adults, t s mportant to note that the gender composton s systematcally related to the number of adult members. For nstance, 61% of the sngle-adult households are headed by females, whle 99% of the two-adult households are couples. For further detals on gender composton, see the techncal appendx (Assunção and Brado 2007).

8 Assunção and Brado Household-Specfc Explanatons for the Inverse Productvty Relatonshp 987 Table 4. Intrahousehold Manageral Resources OLS Dependent Varable: Log per Acre Output 1 Adult 2 Adults 3 Adults 4 Adults Log plot cropped area (0.077) (0.042) (0.059) (0.059) Log per acre land value (0.360) (0.122) (0.152) (0.199) Dummes for rrgaton, Yes Yes Yes Yes sol type, and man crop Constant and fxed effects Yes Yes Yes Yes (household & perod) Hypothess test: = (p-value) (0.689) (0.020) (0.560) (0.882) Number of observatons 399 2,689 1,854 1,173 Number of groups R Note: Robust standard devaton (n parenthess) account for the fact that farmers, rather than plots, are the prmary samplng unt ( sgnfcant at 10%; sgnfcant at 5%; sgnfcant at 1%). All regressons nclude a constant term, and fxed effects generated through the teraton of the household and perod codes (household-vllage, year, and season). Table 5. Number of Plots and Crop Mx OLS Dependent Varable: Log per Acre Output Number of Man Plots Crop Mx (Cereals) 2 plots 3 plots Jowar Sorghum Paddy Log plot cropped area (0.039) (0.065) (0.068) (0.074) Log per acre land value (0.111) (0.132) (0.238) (0.084) Dummes for rrgaton, sol type, Yes Yes Yes Yes and man crop Constant and fxed effects Yes Yes Yes Yes (household & perod) Hypothess test: = 0.16 (p-value) (0.732) (0.608) (0.135) (0.902) Number of observatons 1,829 1,325 1, Number of groups R Note: Robust standard devaton (n parenthess) account for the fact that farmers, rather than plots, are the prmary samplng unt ( sgnfcant at 10%; sgnfcant at 5%; sgnfcant at 1%). All regressons nclude a constant term, and fxed effects generated through the teraton of the household and perod codes (household-vllage, year, and season). of ths possblty. Our test s based on the assumpton that the possblty of havng sgnfcant dfferences n the supervson costs due to geographcal dsperson of the plots depends on the number of man plots cultvated by the household (where the man plot s characterzed by the frst letter of the plot dentfcaton code). The underlyng hypothess s that the transportaton costs of supervson are smlar to farmers harvestng the same number of plots. The frst two columns of table 5 show the estmates of the log-lnear model wth household-perod fxed effects, restrcted to the subsamples of farmers cultvatng two and three plots, respectvely. We also test whether the coeffcent of the logarthm of the cropped area s statstcally equal to 0.16 (our best estmate from table 3). The p-values for these tests are dsplayed n table 5. The nverse relatonshp and ts magntude are robust to the possblty of heterogenety n supervson costs due to the geographcal dsperson of plots. Intrahousehold Crop Mx We also consder the possblty of aggregaton bas caused by heterogenety n the crop mx across plots of each household.

9 988 November 2007 Amer. J. Agr. Econ. 3 7 Number of crops Condtonal varance log(sze n acres) Number of crops Condtonal varance 95% Conf. nterval 0 Note: Curves from Nadaraya Watson regressons, usng the Epanechnkov kernel wth bandwdth Confdence ntervals obtaned from 200 bootstrap samples. Fgure 2. Plot sze, crop mx, and output rsk Bharadwaj (1974) frst documented that plots wth dfferent szes are typcally used to produce dfferent crops. The dfferences n the croppng patterns could also be related to nsurance motves, as noted by Barrett (1996). Facng a rsky envronment, small and net buyer farmers mght change the crop mx n order to avod food-securty stress. In ths case, the nverse relatonshp could be generated by an aggregaton bas determned by a systematc assocaton between crop mx and sze. Fgure 2 shows that the number of products cropped n each plot ncreases wth the cropped area, whle the plot rsk decreases wth the area cropped. When constructng fgure 2, we used a qualtatve varable (wth 1,031 dfferent codes) descrbng all products cropped n each plot; and our rsk measure was constructed by computng the squared error of the regresson of the logarthm of the per acre output aganst vllage dummes. The expected value of ths varable gves the plot varance of the log per acre output, condtonal on the vllage were the plot s located. Fgure 2 suggests that the largest plots mght have been used for rsk dversfcaton. Hence, f there s a trade-off between crop rsk and return, t s possble to observe small plots wth hgher (although rsker) returns than large plots. We then analyze subsamples of plots croppng the same product. We beneft from the exstence of the large number of plots growng two types of cereals namely, jowar/sorghum (1,079 observatons) and paddy (680 observatons). Columns (3) and (4) n table 5 show that the nverse relatonshp s statstcally the same n the subsample of plots croppng only paddy or only jowar/sorghum. In both cases, the estmated coeffcents are not statstcally dfferent from 0.16 (our best estmate from table 3) at the conventonal levels of sgnfcance. Concluson Ths artcle tests household-based theores for the nverse productvty puzzle usng the ICRISAT/VLS data. Consderng multple plots cultvated by a sngle household n a gven season, our evdence does not support explanatons that hnge on household level characterstcs such as the peasant mode of producton or ncreasng supervson costs. In our frst estmaton, a doublng of the plot area s assocated wth a 30% decrease n the output per acre. When we control for observed

10 Assunção and Brado Household-Specfc Explanatons for the Inverse Productvty Relatonshp 989 plot attrbutes, ths coeffcent s reduced to 16%. As suggested n the lterature, observed plot attrbutes play an mportant role n explanng the nverse relatonshp, although t does not account for the entre effect. A second set of regressons assesses explanatons based on household-specfc effects. Our results show that household-specfc theores do not explan the puzzle. The nverse relatonshp remans vrtually unchanged when we ntroduce household fxed effects and household-perod fxed effects nto the model. Ths latter result explores the presence of farmers cultvatng multple plots n the same year and season, whch allows us to account for tme-varyng unobserved characterstcs of the households, gong beyond the tradtonal fxedeffect estmates. In a robustness exercse, the nverse relatonshp s shown to hold wth the same magntude n subsamples contanng: (a) plots cropped by households wth one sngle adult member; (b) plots cropped by households croppng only two or three man plots; and (c) plots croppng the same man product. A consequence of these results s that the content of the nverse relatonshp s related to unobserved characterstcs of the plot rather than the household. Further analyses should then focus on the economc forces that assocate the area cropped wth plot-specfc productve features. [Receved November 2005; accepted February 2007.] References Assunção, J.J., and L.H.B. Brado AJAE Appendx: Testng Household-Specfc Explanatons for the Inverse Productvty Relatonshp. Unpublshed manuscrpt. Avalable at Assunção, J.J., and M. Ghatak Can Unobserved Heterogenety n Farmer Ablty Explan the Inverse Relatonshp between Farm Sze and Productvty? Economcs Letters 80: Bardhan, P.K Sze, Productvty and Returns to Scale: An Analyss of Farm-Level Data n Indan Agrculture. Journal of Poltcal Economy 81: Barrett, C.B On Prce Rsk and the Inverse Farm Sze-Productvty Relatonshp. Journal of Development Economcs 51: Benjamn, D Can Unobserved Land Qualty Explan the Inverse Productvty Relatonshp? Journal of Development Economcs 46: Berry, R.A., and W.R. Clne Agraran Structure and Productvty n Developng Countres. Baltmore: Johns Hopkns Unversty Press. Bhalla, S.S Does Land Qualty Matter? Theory and Measurement. Journal of Development Economcs 29: Bhalla, S.S., and P. Roy Msspecfcaton n Farm Productvty Analyss: The Role of Land Qualty. Oxford Economc Papers 40: Bharadwaj, K Producton Condtons n Indan Agrculture. Cambrdge, UK: Cambrdge Unversty Press. Carter, M Identfcaton of the Inverse Relatonshp between Farm Sze and Productvty: An Emprcal Analyss of Peasant Agrcultural Producton. Oxford Economc Papers 36: Carter, M., and K. Webe Access to Captal and Its Impact on Agraran Structure and Productvty n Kenya. Amercan Journal of Agrcultural Economcs 72: Chayanov, A.V The Theory of Peasant Economy, In D. Thorner, B. Kerblay, and R.E.F. Smth, eds. Irwn: Homewood. Chen, Z., W.E. Huffman, and S. Rozelle The Relatonshp between Farm Sze and Productvty n Chnese Agrculture. Workng paper, Dept. of Agr. Econ., Iowa State Unversty. Eswaran, M., and A. Kotwal Access to Captal and Agraran Producton Organzaton. Economc Journal 96: Feder, G The Relaton between Farm Sze and Farm Productvty: The Role of Famly Labor, Supervson and Credt Constrants. Journal of Development Economcs 18: Fulgnt, L.E., and R.K. Perrn Prces and Productvty n Agrculture. Revew of Economcs and Statstcs 75: Hayam, Y., and V.W. Ruttan Agrcultural Productvty Dfferences among Countres. Amercan Economc Revew 60: Jodha, N.S., M. Asokan, and J.C. Ryan Vllage Study Methodology and Resource Endowment of the Selected Vllages n ICRISAT s Vllage Level Studes. Economcs Program Occasonal Paper no. 16. Hyderabad: Internatonal Crops Research Insttute for Sem-Ard Tropcs. Kmh, A Plot Sze and Maze Productvty n Zamba: Is There an Inverse Relatonshp? Agrcultural Economcs 35:1 10. Lamb, R.L Inverse Productvty: Land Qualty, Labor Markets, and Measurement Error.

11 990 November 2007 Amer. J. Agr. Econ. Journal of Development Economcs 71: Rosenzweg, M.R., and H.P. Bnswanger Wealth, Weather Rsk and the Composton and Proftablty of Agrcultural Investments. Economc Journal 103: Sen, A.K An Aspect of Indan Agrculture. Economcs Weekly Annual Number: Sngh, R.P., H.P. Bnswanger, and N.S. Jodha Manual of Instructons for Economc Investgators n ICRISAT s Vllage Level Studes. Techncal Report, Internatonal Crops Research Insttute for Sem-Ard Tropcs. Srnvasan, T.N Farm Sze and Productvty: Implcatons of Choce under Uncertanty. Sankhya The Indan Journal of Statstcs 34: Taslm, M Supervson Problems and the Sze-Productvty Relaton n Bangladesh Agrculture. Oxford Bulletn of Economcs and Statstcs 51: Udry, C Gender Agrcultural Producton, and the Theory of the Household. Journal of Poltcal Economy 104: