Testing for separability in household models with heterogeneous behavior: A mixture model approach

Transcription

1 Testng for separablty n household models wth heterogeneous behavor: A mxture model approach by Renos Vaks 1, Elsabeth Sadoulet 2, Alan de Janvry 2, and Carlo Cafero 3 August 2004 Abstract Knowng whether a household behaves accordng to separablty or non-separablty s needed for the correct modelng of producton decsons. We propose a superor test to those found n the lterature on separablty by usng a mxture dstrbuton approach to estmate the probablty that a farm household behaves accordng to non-separablty, and test that the determnants of consumpton affect producton decsons for households categorzed as non-separable. Wth non-separablty attrbuted to labor market constrants, the swtcher equaton shows that Peruvan farm households that are ndgenous and young, wth low levels of educaton, and lack of local employment opportuntes are more lkely to be constraned on the labor market. Keywords: Labor, separablty, mxture dstrbutons, Peru. JEL classfcaton number: J43, C16, Q12 1 The World Bank: rvaks@worldbank.org 2 Unversty of Calforna at Berkeley: sadoulet@are.berkeley.edu, alan@are.berkeley.edu 3 Unverstà degl Stud d Napol Federco II : cafero@unna.t 1 August 04

2 I. Introducton Market falures affect household behavor. Indeed, an mportant aspect of the analyss of household behavor conssts n observng and explanng the strateges they devse to mtgate the welfare costs market falures mpose on them. Wth market falures pervasve for rural households n developng countres, there are many patterns of behavor that would be ncomprehensble were t not for takng nto account the effect of these falures. For example, Eswaran and Kotwal (1986) show how labor and credt market falures mply that households wth dfferent asset postons relatve to labor endowments follow dfferent strateges of labor deployment, and use ths n turn to establsh socal classes. These same market falures mply exstence of an nverse relaton between land productvty and farm sze that establshes the potental gans of redstrbutve land reforms. Behavor under perfect markets mples separablty between producton and consumpton decsons (Sngh, Squre, and Strauss, 1986): the household can solve recursvely frst ts producton problem, and then allocate the full ncome obtaned to consumpton choces. By contrast, producton and consumpton decsons are non-separable when there are market falures: n ths case, varables that affect consumpton decsons (such as wealth, the household s total famly labor endowment, consumer goods prces, and household characterstcs affectng consumpton) also affect producton decsons. Correct modelng of household producton decsons thus requres knowledge of whether a specfc household s lkely to behave accordng to separablty or non-separablty decson rules. For ths reason, numerous tests of the separablty hypothess have been made. These tests have been done followng varous approaches and assumptons, such as whether to use the reduced form or the structural form of a household model, to confnr the test to behavor on one specfc market or not, to recognze or not heterogenety across households, and to clam or not that sample separaton nto separable and nonseparable behavor can be observed. We revew these tests below, usng these four categores n order to dentfy the dstngushng features of the approach proposed here. We show that a desrable approach combnes the followng four features: () use a reduced form approach, () do not confne test to behavor on one specfc market, () recognze heterogenety across households, and (v) use unknown sample separaton. (1) Global tests that do not recognze heterogenety across households ) A reduced form approach can be used to test whether varables that affect consumpton decsons also affect producton decsons, wthout concern for heterogenety n the sample of households observed. The test s not specfc to falure on one partcular market, as falure on any market wll nduce non-separable behavor. Usng ths approach, Benjamn (1992) and Bowlus and Scular (2003) cannot reject separablty for households n Java and Chna, respectvely, whle Lopez (1984) and Grmard (2000) reject t for households n Canada and Côte d Ivore, respectvely. 2 August 04

3 ) A structural form can be used, where estmaton of a producton or cost functon allows to estmate the margnal productvty (.e., the shadow prce) of an nput whch can then be compared to the market prce. Jacoby (1993) for Peru and Skoufas (1994) for Inda use ths approach to reject separablty n labor decsons across the sample of households, wth no concern for heterogenety. The test s not specfc to a specfc market falure snce t does not presume that the constrant s necessarly n the market for the factor analyzed. Nonetheless, global tests that do not take heterogenety nto account have lmted usefulness snce t s well known that market falures are largely dosyncratc. (2) Idosyncratc tests that recognze heterogenety across households These tests have been pursued through four dfferent approaches. The frst two are confned to market falures on specfc markets. The latter two tests dagnose falures on any market. ) Whether a household s constraned or not on a specfc market can be asked drectly. Ths has been used by Feder, Lau, Ln, and Luo (1990) to partton Chnese rural households nto constraned and un-constraned on the credt market, and to test at the reduced form level that producton decsons are affected by lqudty avalable at the begnnng of the season for constraned households, but not for the others. However, tests that account for heterogenety on the bass of self-declared exposure to a constrant on a specfc market may hde unrecognzed constrants on other markets. ) Structural form tests can be done usng a dsequlbrum model to estmate the probablty of beng constraned on a specfc market (Maddala, 1983). In ths case, there s unknown sample separaton nto separable and non-separable behavor, and separaton s derved from revealed determnants of behavor. Carter and Olnto (2003) thus specfy a credt demand and supply functon and estmate an dosyncratc probablty of beng lqudty constraned. Ths allows assgnng to each household a probablty of makng nvestment decsons accordng to separable or non-separable rules. Dffcultes wth the approach are: (a) specfyng and estmatng supply and demand functons for transactons on a specfc factor market, and (b) confnng the cause of non-separablty to beng constraned on that specfc market, credt n ths case. The probablty of beng constraned on that market s used as the probablty of behavng n a non-separable way n all producton decsons, whch may be erroneous f households that are unconstraned on the credt market happen to be constraned on other markets. ) If observed non-partcpaton n a partcular market can be used to nfer market falure, and ths not only n that but possbly also n other markets, then market partcpaton can be used to nfer separablty. Reduced form tests wth regme specfc parttons based on observed market partcpaton have been done by Sadoulet, de Janvry, and Benjamn (1998) for Mexco, Carter and Yao (2002) for Chna, and Dutlly-Dane, Sadoulet, and de Janvry (2004) for Burkna Faso. They verfy ex-post that the group of market-partcpatng households ndeed behaves accordng to decson rules n a separable model. Selfsuffcent households are, by contrast, verfed to behave n a non-separable fashon. Dffculty wth the 3 August 04

4 approach s that tests that account for heterogenety on the bass of observed market partcpaton may hde non-separable behavor due to constrants on that market. v) Fnally, structural form tests have been used wth unknown sample separaton and wthout market falure beng specfc to one market. Ths has been done by Lambert and Magnac (1994) for Côte d Ivore and by Bhattacharyya and Kumbhakar (1997) for Bengal. They estmate a producton functon and, from ths, an expected factor margnal productvty and ts standard error for each household. Ths allows comparng an estmated dosyncratc shadow prce wth an assocated confdence nterval to an observed effectve market prce for each household, classfyng them ex-post nto separable and nonseparable groups, where separablty s rejected f prces dffer. Lambert and Magnac thus fnd that separablty s rejected for 90% of men but only for 50% of women. Dffcultes wth the approach are n: (a) specfyng and estmatng a producton functon for agrculture, a dffcult task both conceptually and emprcally. The proposed test s hghly senstve to correct specfcaton and estmaton of ths functon; (b) specfyng effectve prces aganst whch to compare the estmated margnal productvtes. (3) Tests that reveal dosyncratc non-separablty on the bass of observed behavor should consequently be done at the reduced form level. Ths s what we propose n ths paper. Specfcally, the test nvolves assgnng to each household a probablty of beng exposed to market falure and of behavng accordng to non-separablty rules, before testng for the contrasted behavor of the two groups. In the Peruvan case analyzed here, the test conssts n analyzng on-farm labor decsons of farm households that partcpate n the off-farm labor market, as follows: ) Unknown sample separaton estmaton s used to attach probabltes to households n the sample as to whether they make producton decsons accordng to separable or non-separable rules. Whle ths s revealed n labor allocaton decsons n producton, the cause of non-separablty s not confned to exstence of a constrant on the labor market. ) Verfy that households that are ex-post classfed n the separable category make producton decsons that are not affected by varables that affect consumpton decsons. ) The swtcher equaton helps reveal the causes of market segmentaton between constraned and un-constraned labor market partcpants among farm households n Peru. Results show that dfferental sklls, youth, ethncty, as well as lack of regonal opportuntes are mportant mpedments to unconstraned market partcpaton. The paper s organzed as follows. Secton II develops a household model wth a labor market constrant and derves a testable hypothess for separablty among market partcpants. The econometrc approach s presented n secton III. The Peruvan data and fndngs are presented n secton IV. Secton V concludes. 4 August 04

5 II. Theory Buldng on tradtonal farm household models (see Sngh et al., 1986), we consder a farm household whose objectve s to maxmze utlty. Utlty s derved from ncome y and lesure tme l l. 1 The household s endowed wth a total amount of tme E to be allocated among on-farm work l, off-farm work l o whch wll be pad a salary w o, and lesure. 2 Fnally, there exsts an unknown upper lmt L to the amount of labor that can be sold on the market. The household s problem can be represented as follows: subject to: max Uyl,, z o l l, l, l l h ( ) q o o l o y = pq( l, A, z ) + w l ; l = E -l - l ; l, l 0; and 0 l L, l where: U s the household's utlty functon, y s total household ncome, l l s lesure, z h s a vector of household characterstcs relevant n consumpton decsons, p s the output prce, q s the quantty produced, z q s a vector of farm characterstcs relevant n producton decsons, l and l o are the amounts of famly labor employed on and off-farm, respectvely, w o s the effectve wage receved by famly labor outsde the farm, A s exogenous farm sze (for smplfcaton, we assume no land market), E s total famly labor endowment, and L s the maxmum amount of famly labor that can fnd work off-farm. The utlty functon U() s assumed to be ncreasng and quas-concave; the producton functon q() s assumed to be ncreasng and concave. Snce the focus of ths study s to explan labor allocaton decsons and unobserved heterogenety of small farmers that partcpate n the market as net sellers, we concentrate the rest of the analyss on them. Dervaton of how regmes emerge s avalable n Sadoulet et al. (1998). In absence of other constrants (lke, for example, consumpton cash constrants or food market constrants) for households that partcpate n the labor market as net sellers, whether there s separablty between producton and consumpton decsons wll depend on whether the maxmum off-farm labor constrant s bndng or not. The smple observaton that a household s sellng labor wll not be suffcent to nfer separablty. One can show that, for net sellers of labor for whom the off-farm labor constrant s not bndng, producton and consumpton decsons are separable. The reduced form equaton for l s expressed as a functon of only producton sde characterstcs and not of consumpton sde characterstcs : o q l f p, w, A, z. (1) = ( ) o 1 For smplcty, we are assumng no mperfectons on the commodty markets, whch allows to nclude ncome drectly n the utlty functon rather than other consumpton goods. 2 Hred labor could be also ntroduced n ths settng. We nonetheless gnore t snce our ultmate focus s on net sellers of labor. 5 August 04

6 In ths case, the household wll sell n the labor market all the excess labor and the decson prce wll be the market prce w o. For net sellers of labor for whom the off-farm labor constrant s bndng,.e., l o = L, separablty between producton and consumpton decsons breaks down. The household wll sell L on the labor market and supply labor on-farm up to the pont where the margnal product of labor equates the margnal utlty from lesure. The decson prce becomes a shadow prce lower than w o. The reduced form equaton for l s: ( ) o q h o l = f p, w, A, z, Ez,, l = L. (2) As can be seen, the constraned optmal allocaton for on-farm labor l also depends on consumpton sde varables E and z h, and on the off-farm labor quota L. Therefore, the separablty hypothess breaks down. At ths pont, a bref dscusson about the nature of the off-farm labor constrant s warranted. It can be verfed that the off-farm labor allocaton rule s gven by: l o Ï o* o q h o* l p, w, A, z, E, z f l L Ì, o* ÓÔ L f l L = ( ) < where l o* s the unconstraned level of off-farm labor. Denotng by l the probablty that a household s constraned, we have: o* o q h [ ] l = l l ( p, w, A, z, E, z ) - L 0 whch n reduced form becomes: o q h l = l( pw,, Az,, Ez,, L). (3) To conclude, we show that under the assumpton of no other market mperfectons that mght ntroduce non separablty (for example, presence of credt constrants or food market mperfectons), a labor sellng farm-household wll determne the amount of labor employed on farm l accordng to one of two alternatve regmes, defned by equatons (1) and (2), respectvely. One emprcal mplcaton of ths s that, f the researcher had nformaton on households' classfcatons, a testable hypothess on the separablty assumpton could be drectly mplemented. However, n most cases, ths nformaton s unobserved. The next secton addresses ths ssue of unknown sample separaton. 6 August 04

7 III. Econometrcs The precedng secton establshed that t s concevable for farm-households to partcpate n the market as net sellers, and yet to be constraned by unobservable quantty lmtatons or by transactons costs n ther ablty to respond to prce changes. When the sample dvson s unknown, the farm labor supply response functon of a group of market partcpatng households can be econometrcally represented by a swtchng regresson model wth unobserved sample separaton (Maddala, 1983). Formally, we can characterze the sample behavor n a three-equaton model: 1 l = x b + u l = x g + u 2 2 l * = x x + u l l where, usng results from the household model, o q 1 = { } x p, w, A, z 2 = { o q h } x p, w, A, z, E, z, L l = { o q h } x p, w, A, z, E, z, L b, g, and x are coeffcents to be estmated, and u j s are normal d dsturbances wth zero means and varances s j 2 (wth s l = 1 for dentfcaton purposes). 1 2 l defned by: l, l, and l * are latent unobserved varables. Instead, for each observaton, we observe varable l = Ïl Ì Ól 1 2 * f l < 0 * f l 0. { } from the sample of N observatons on The problem s that of estmatng the parameters b, g, x, s1, s 2 { lk, xk1, xk2, xkl }, k = 1,..., N. Gven that we cannot dentfy a pror the regme partcpaton, a randomly selected observaton l k ( ) (household k's on-farm labor supply) wll have probablty 1 - l = F -x k x of belongng to the frst regme, and probablty l of belongng to the second. The probablty densty functon of observaton l k s thus: ( ) = - ( ) - ( ) + ( - ) f l l j l x b lj l x g (4) k 1 1 k k 1 2 k k 2 where j 1 and j 2 are the probablty densty functons of u and u, that s, the mxture of two dstrbutons. The lkelhood functon for a sample of N observatons s then: 1 2 N L( b, g, x, s1, s 2) = f ( l k ), (5) k = 1 l 7 August 04

8 A natural way of estmatng the parameters would be to maxmze (5) wth respect to { b, g, x, s1, s 2}. Estmaton of the maxmum lkelhood s obtaned va the E-M method (see Hartley (1978) and Dempster, Lard, and Rubn (1977)), after havng used other pre-estmaton technques to decde on the ntal values of the parameters (Kefer, 1978). The steps of the E-M algorthm are as follows: usng startng values for b, g, s1, s 2, we frst obtan estmates of the classfcaton vector l (the E step). The startng values for b, g, s1, s 2 can be set equal to the estmated values for the pooled sample regresson, the ratonal for whch s that, f the observatons were truly comng from the same populaton, those would be the values that maxmze the lkelhood functon. Usng the estmate for l to weght the probablty densty functons of each observaton n the two regmes, we obtan estmates for b, g, s1, s 2 (the M step). Ths teratve procedure s repeated untl t converges. IV. Data and results Data The data come from the 1997 Peruvan LSMS (World Bank, 2004). The survey was conducted on 4,500 households. From these, 1,131 allocate work to both on and off-farm actvtes and are used n the analyss. We postpone a dscusson on descrptve statstcs for now as t wll be more relevant to present them after the estmaton. We offer nstead Fgure 1, whch plots the frequency dstrbuton of ndvdual off-farm hours worked and seems to suggest the exstence of two dstnct subpopulatons, one n whch ndvduals work less off-farm and another where they work more. What the econometrc procedure attempts to do s to explore, among other thngs, ths heterogenety and characterze the two regmes. We supermpose a normal dstrbuton to hnt on the mplcatons of assumng one homogeneous populaton. Separablty Accordng to a fully separable model, the decson about on-farm labor allocaton should be purely a producton decson, and thus household characterstcs (such as Ez,, L) should not affect t. Our theoretcal model postulates the possblty of two dfferent regmes among farm-households n the sample. It also predcts that household characterstcs should only affect the constraned regme. We, therefore, specfy one of the two regmes by ncludng the total famly labor endowment (E, the number of adults), household characterstcs n consumpton z h such as ethncty and the number of boys and grls, and the constraned famly off-farm employment l o. We specfy the second regme by only ncludng producton sde characterstcs z q among household characterstcs. We also nclude any varables z qh, that can be argued to affect both producton and consumpton decsons. Apart from ths restrcton that comes drectly from the theoretcal model, we do not mpose any other restrctons on the parameters of the two models n the belef that, f a dchotomy actually exsts, t h 8 August 04

9 should be strong enough to let the econometrc technque separate the two regmes. We apply the maxmum lkelhood procedure descrbed n the prevous secton to determne the best way of dvdng the observatons nto two groups. The dependent varable s the amount of hours allocated by the household to farm actvtes. 3 Table 1 presents the results. The frst column contans the results of an OLS estmaton of the model on the pooled sample. 4 As expected, producton characterstcs such as human captal assets (farmng experence) and land assets sgnfcantly affect on-farm labor allocaton. In addton, these pooled estmates show a sgnfcant effect of household characterstcs n consumpton (number of adults and of boys and grls) on the on-farm labor use decson. Ths alone provdes some ndcaton that the ssue of nonseparablty s mportant. Columns 2-4 present the results from the mxture model. On average, a household has a probablty of 0.51 of beng constraned n ts labor market partcpaton. As expected, for those households n the constraned regme, we fnd that not only producton characterstcs affect ther on-farm labor allocaton but consumpton ones as well, thus rejectng the separablty hypothess. In partcular, we fnd that the numbers of chldren and of adults sgnfcantly ncrease on-farm labor allocaton. Other varables that can be consdered as household characterstcs n both producton and consumpton also affect on-farm labor allocaton. For example, educaton of the household head ncreases on-farm work. In addton, regonal dummes that capture dosyncratc effects and shocks of specfc geographc areas affect on-farm labor decsons. Households that lve n the Coast, Serra, and Ranforest regons work more on-farm compared to those n Lma. Ths s expected as off-farm employment opportuntes are much more abundant n Lma than n rural areas. 5 For the second group of households allocated by the mxture model to the unconstraned regme, we fnd that producton characterstcs such as land and cattle ownershp postvely affect on-farm labor allocaton. In addton, transacton cost n the form of tme to get to the man market, negatvely affects work on-farm. Robustness The analyss above would not be correct f any of the consumpton sde characterstcs affect the on-farm labor decson for what we specfy as the unconstraned regme. For ths, we mplement a counterfactual estmaton ncludng n the specfcaton of the unconstraned regme all of the consumpton characterstcs used n the constraned one. The am s to test whether any of these consumpton varables have a sgnfcant mpact on on-farm labor allocatons for the unconstraned. The sample s dvded nto 3 Remember that we do not consder hred labor n ths analyss snce we are only lookng at households that are net sellers of labor. 4 The coeffcents of ths OLS estmaton were also used as startng values for the lkelhood maxmzaton routne. 5 We also estmated these models usng dstrct dummes and obtaned smlar results. 9 August 04

10 constraned and unconstraned households. Followng Hartley (1978), we assgn observaton lk, xk, xk, * { 1 2 xkl } to regme 1 f E l lk, xk1, xk2, xkl 0, and to regme 2 otherwse. Note that ths [ ] < assgnaton uses all the nformaton that s ex-post observed on the households, ncludng ther behavor on the labor market, rather than smply the predctors x kl of the choce of regme. Ths condtonal expectaton s computed as: * [ 1 2 l ] = l + [ l 1 2 l ] E l l, x, x, x x x E u l, x, x, x = xlx + E[ ulregme1] Pr [ regme1l, x1, x2, xl ] + E[ ulregme 2] Pr [ regme 2l, x1, x2, xl ] = xlx + E[ ul ul < -xlx] w1( l ) + E[ ul ul -xlx] w2 ( l ) ( ) j -xl x j xl x = xl x - w ( l ) w l (-x x) ( ) F 1 - F( -x x) l ( ) l where w 1 ( l ) and w 2 ( l ) are the weghts: ( 1 - l) j1 l x 1b k k w1( l ) ( - ) = and w f ( lk ) 2 lj ( l ) = ( b ) ( ) 2 lk - xk2 f lk. Ths classfes 527 households, or almost half of the sample, as constraned. In Table 2, we estmate the ex-post on-farm labor regressons for the two groups, assumng that ex-ante knowledge of the regmes was known. The results support the separablty hypothess for the unconstraned regme. Specfcally, none of the consumpton characterstcs Ez,, l h o ( ) have a sgnfcant mpact on the on-farm labor decsons of unconstraned households. By contrast, productve assets (land and cattle owned and years of farmng experence) ncrease the level of on-farm work. To summarze, applyng the mxture model approach allowed us to separate the sample nto two sub-populatons of labor market partcpants. We fnd strong evdence that, n one of them, the separablty hypothess between producton and consumpton decsons s rejected, whle for the other t s not. A counterfactual test strengthens our fndngs by showng that the households n the unconstraned regme behave n a separable fashon. Understandng the labor constrant The results above sgnal the presence of a group of farm households that, albet partcpatng n the labor market, are makng ther decsons on farm actvty accordng to a non-separable model of behavor. Ths s, of course, not enough to conclude that the cause of non separablty s the presence of a quantty constrant on the labor market of the knd we descrbed n presentng the theoretcal model. The last column of Table 1 contans the estmated coeffcents for the equaton that determnes group separaton. Gven specfcaton of the two regmes, we can nterpret ths swtcher equaton as representng the probablty of 10 August 04

11 beng n the constraned regme. We use equaton (3) from the theoretcal model to specfy the determnants of group separaton. Interestng patterns emerge regardng market ntegraton and partcpaton. A larger farm lowers the probablty of beng constraned as t ncreases labor demand for on-farm labor. In terms of household characterstcs, larger numbers of adult members (E) and of grls n the household ncrease the probablty of beng constraned. Households wth hgher levels of educaton, wth less years of farmng experence, and wth an older head are less lkely to be constraned. Fnally, ndgenous households are more lkely to be constraned, whch could be reflectng greater dffcultes for them n partcpatng to labor markets. At the regonal level, households lvng n all the regons, as opposed to Lma, have a hgher probablty of beng constraned as ther off-farm opportuntes are more lmted. Greater avalablty of prvate jobs n the communty s also effectve n reducng the probablty of beng constraned n off-farm employment. We can use the ex-post predcted groups of constraned and unconstraned households to get nsghts on the structure of the labor market constrant. From the theoretcal framework, we know that the constraned households off-farm labor supply l o s also ther bndng off-farm labor allocaton L. Ths dstrbuton s plotted n Fgure 2. We would expect that, f there were a common market-based barrer on the amount of labor to be allocated, t would show up as a very narrow dstrbuton for l o = L for those households n the constraned regme. The fact that ths s not true suggests that household dosyncraces may be more mportant n terms of accessng the labor market. Fgure 2 also plots the dstrbuton of ndvdual off-farm hours for the unconstraned. These ndvduals work more overall than constraned ones, as seen by the fact that the off-farm hours dstrbuton s shfted to the rght. Ths s consstent wth our fndngs above. Fnally, a descrptve comparson between constraned and unconstraned households s presented n Table 3. Overall, constraned households are qute dfferent from unconstraned households. They work almost three tmes as much on ther own farm, although they have almost three tmes less land. They have lower levels of educaton, the key asset to gan access to off farm work. They are more often ndgenous, they are poorer n terms of per capta consumpton, ncome, and wealth (land owned), and have larger households to support wth more adults and grls. They are located more n the Serra, and defntely less n Lma. They are also more dedcated to farmng, wth more cattle owned and more years of farmng experence. These observatons suggest that beng constraned on the labor market s closely related to lack of employment opportuntes and to lack of control over the essental human and physcal assets needed to successfully partcpate n the labor market. 11 August 04

12 V. Concludng remarks We use mxture dstrbuton technques to develop a more accurate test of the separablty hypothess n household models than prevously avalable. The approach has the advantage of usng a reduced form estmate, detectng non-separablty on all markets at once, and allowng for heterogenety n separablty behavor across households. It avods relance on labor market partcpaton to conclude separablty between producton and consumpton decsons of farm-households. Fndngs clearly show the exstence of two dstnct types of households among net-sellers of labor: those behavng as f unconstraned and hence n a separable way, and those that behave as f constraned and hence n a non-separable fashon. In addton, the econometrc technque helps understand the orgns of market segmentaton. In dong ths, we look at the role of both demand and supply sde effects on labor constrants. In the case of Peru, low educatonal attanments, youth, ethncty, lower avalablty of job opportuntes n the communty, and handcaps assocated wth resdence especally n the Serra are mportant constrants on labor market partcpaton. 12 August 04

13 References Benjamn, Dwayne Household Composton, Labor Markets, and Labor Demand: Testng for Separaton n Agrcultural Household Models. Econometrca, 60(2): Bhattacharyya, Anjana, and Subal Kumbhakar Market Imperfectons and Output Loss n the Presence of Expendture Constrant: A Generalzed Shadow Prce Approach. Amercan Journal of Agrcultural Economcs, 79(3): Bowlus, Audra, and Terry Scular Movng Toward Markets? Labor Allocaton n Rural Chna, Journal of Development Economcs, 71(2): Carter, Mchael, and Pedro Olnto Gettng Insttutons Rght for Whom? Credt Constrants and the Impact of Property Rghts on the Quantty and Composton of Investment. Amercan Journal of Agrcultural Economcs 85(1): Carter, Mchael, and Yang Yao Local versus Global Separablty n Agrcultural Household Models: The Factor Prce equalzaton Effect of Land Transfer Rghts. Amercan Journal of Agrcultural Economcs 84(3): Dempster, A., Nan Lard, and D. Rubn Maxmum Lkelhood from Incomplete Data Va the E-M Algorthm. Journal of the Royal Statstcal Socety 39: Dutlly-Dane, Célne, Sadoulet, Elsabeth, and Alan de Janvry "Household Behavor under Market Falures: How Improved Natural Resource Management n Agrculture Promotes the Lvestock Economy n the Sahel". Forthcomng n Journal of Afrcan Economes. Eswaran, M., and Kotwal, A "Access to Captal and Agraran Producton Organzaton." Economc Journal, 96: Feder, G., Lau, L. J., Ln, J. Y., and Luo, X "The Relatonshp between Credt and Productvty n Chnese Agrculture: A Mcroeconomc Model of Dsequlbrum." Amercan Journal of Agrcultural Economcs, 72(4): Grmard, Franque "Rural Labor Markets, Household Composton, and Ranfall n Côte d'ivore." Revew of Development Economcs, 4(1): Hartley, Mchael Estmatng Mxtures of Normal Dstrbutons and Swtchng Regressons. Journal of the Amercan Statstcal Assocaton 73(364): Jacoby, Hanan "Shadow Wages and Peasant Famly Labour Supply: An Econometrc Applcaton to the Peruvan Serra." Revew of Economc Studes, 60: Kefer, Ncholas Dscrete Parameter Varaton: Effcent Estmaton of a Swtchng Regresson Model. Econometrca 46(2): Lambert, Sylve, and Therry Magnac "Measurement of Implct Prces of Famly Labour n Agrculture: An Applcaton to Côte d'ivore." In Callavet, Gyomard, and Lfran (eds.), Agrcultural Household Modelng and Famly Economcs. Amsterdam: Elsever. 13 August 04

14 Lopez, Ramón Estmatng Labour Supply and Producton Decsons of Self-Employed Farm Producers. European Economc Revew, 24: Maddala, G.S Lmted-Dependent and Qualtatve Varables n Econometrcs. Cambrdge: Cambrdge Unversty Press. Sadoulet, Elsabeth, Alan de Janvry, and Catherne Benjamn Household Behavor wth Imperfect Labor Market. Industral Relatons, 37(1): Sngh, I., Lynn Squre, and John Strauss, (eds.) Agrcultural Household Models. Baltmore. MD: The Johns Hopkns Unversty Press. Skoufas, Emmanuel Usng Shadow Wages to Estmate Labor Supply of Agrcultural Households. Amercan Journal of Agrcultural Economcs, 76(2): World Bank Lvng Standards Measurement Study of the World Bank August 04

15 Table 1. On-farm labor allocaton: Pooled versus mxture model Pooled Mxture Constraned Unconstraned Swtcher Market wage (soles) w o *** ** Tme to market (mn.) p ** -9.1 Land owned (ha.) A 0.14** *** -10.8*** Cattle owned (number) z q *** Farmng experence (years) z q 2.1*** 1.36*** 0.18** 28.5*** Coast (dummy) z q 17.8** 19.9* *** Serra (dummy) z q,h 17.1** 21.9** *** Ranforest (dummy) z q,h 18.4** *** Household head educaton (years) z q,h ** 0.55* -31.2*** Household head sex (male=1) z q,h Household head age (years) z q,h *** *** Household head age squared z q,h *** *** Adults (number) E 18.9*** 16.1*** 254*** Boys (number) z h 9.7*** 21.8*** -46** Grls (number) z h 23.2*** 38.8*** 53*** Ethncty (ndgenous=1) z h *** Avalablty of prvate jobs n communty (proporton of employed) z lo -1428*** Hours worked off-farm l o -0.13*** -0.19*** Constant *** 1564*** Sample sze: 1131 Sample proporton ˆl R 2 (pooled) 0.28 Log lkelhood (mxture) All coeffcents of the swtcher regresson are multpled by Dependent varable: household's on-farm work (hours). Swtcher: probablty of beng constraned. The mssng dummy for regons s Lma. Sgnfcance level: * 10%; ** 5%; *** 1% 15 August 04

16 Table 2. Counterfactual test wth ex-ante separaton OLS wth sample separaton known (predcted ex-post): Constraned Unconstraned Market wage (soles) w o -0.12*** Tme to market (mn.) p * Land owned (ha.) A *** Cattle owned (number) z q *** Farmng experence (years) z q 1.03*** 0.23** Coast (dummy) z q Serra (dummy) z q,h Ranforest (dummy) z q,h * Household head educaton (years) z q,h Household head sex (male=1) z q,h ** Household head age (years) z q,h 6.02*** Household head age squared z q,h -0.07*** Adults (number) E 9.84** Boys (number) z h 21.4*** Grls (number) z h 38.3*** Ethncty (ndgenous=1) z h Hours worked off-farm l o -0.16*** 0.01 Constant *** Sample sze R Dependent varable: household's on-farm work (hours). The mssng dummy for regons s Lma.. Sgnfcance levels:* 10%; ** 5%; *** 1%. 16 August 04

17 Table 3. Selected household descrptve statstcs by predcted constraned regme Constraned Unconstraned Market wage (soles) w o * Tme to market (mn.) p Land owned (ha.) A Cattle owned (number) z q * Farmng experence (years) z q * Coast (%) z q,h Serra (%) z q,h * Ranforest (%) z q,h Lma (%) z q,h * Household head educaton (years) z q,h * Household head sex (male=1) z q,h Household head age (years) z q,h * Adults (number) E * Boys (number) z h Grls (number) z h * Ethncty (ndgenous %) z h * Avalablty of prvate jobs n communty (%) z lo * Total hours worked on-farm (last week) l * Total hours worked off-farm (last week) l o Income per capta (soles) y * Consumpton per capta (soles) C * Sample sze: Note: * means that there s a sgnfcant dfference between the unconstraned and constraned groups at the 10% level or less. 17 August 04

18 Fgure 2: Kernel denstes of off-farm hours worked per ndvdual Constraned Unconstraned Densty August 04