Fafchamp DyadicReg Risk

8/2/2019 Fafchamp DyadicReg Risk

1/6

American Economic Association

Risk Sharing and Network FormationAuthor(s): Marcel Fafchamps and Flore GubertReviewed work(s):Source: The American Economic Review, Vol. 97, No. 2 (May, 2007), pp. 75-79Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/30034424 .

Accessed: 09/03/2012 14:16

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The

American Economic Review.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=aeahttp://www.jstor.org/stable/30034424?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/30034424?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=aea


2/6


3/6

76 AEAPAPERSAND PROCEEDINGS MAY2007TABLE1-LINKS ANDINCOME ORRELATION

Coefficient Dyadicestimate t-valueIncome correlation

Correlationof i and 's incomesa 1.083 1.44Geographic proximitySame sitio = lb 2.647 8.84Difference in distanceto road if same sitio -0.121 -3.90Difference in:Dummy = 1 if primaryoccupationof head is farming 0.028 0.23Number of workingmembersX numberof activities 0.003 0.06Age of household head -0.010 -2.52Health index 1-4 (1 = good health,4 = disabled) 0.027 0.46Years of educationof household head -0.010 -0.59Total wealtha -0.113 -2.37

Villagedummies Includedbut not shownIntercept -5.995 -15.41Number of observations 10,264Notes: The dependentvariable= 1 if i citesj as the source of mutual nsurance,0 otherwise.Estimator is logit. All t-values based on standarderrors correctedfor dyadic correlation oferrors.a Instrumentedvariables-see text for details.bSmall clusterof 15-20 households.

Dyadic regressorscome in two forms: attri-butesw1iof the link between i andj, such as thegeographicaldistance between them;and attri-buteszi andzjof individuals i andj. Regressorsmust enter a dyadic regressionin a symmetricfashion so that the effect of (zi,zj) on YIis thesame as the effect of (zj,zi) on Yji.Therefore,dyadicregressionsmust be written n a waythatpreserves this symmetry. How this is accom-plished dependson whether he dyadicrelation-shipis directionalor not.A dyadic elationships undirectionalf Yji = Yijfor all i, j. In this case, symmetryrequiresthatregressors atisfy

pXu= pXji.One easy way

of satisfying this requirement s to specify theregressionas(2) Yij= a + Pl zi - zj

+ B2(Zi Zj)+ Ylwijl+ uij,wherezi andzj are characteristicsof individuali andj thought to influence the likelihood ofa link Yjibetween them. Coefficient 01 mea-sures the effect of differences in attributesonYi, while ,2 captures he effect of the combinedlevel of zi and zjon Yij. f a dyadicrelationshipis directional,Yjineed notequalYji. n this case,

the symmetry equirementanbe satisfiedbyspecifyinghe modelas(3) Yij= a + P1(zi - zj)

+ 32(zi+ zj) + Ywij+ Uij.For 32 o be identified, ndividualsmust not havethe same number of links (see FafchampsandGubert2006 fordetails).Dyadic observations are not independentsince E[uij,uik]# 0 for all i and E[uij,uij # 0for all j. We also have E[u1i,ujk]# 0 and E[uij,uik]# 0. Provided that regressors are exog-enous, applyingOLS to (2) and (3) yields con-sistent coefficientestimates,but standard rrorsare inconsistent. To obtain consistent standarderrors,we extend the method that TimothyG.Conley (1999) developed to deal with spatialcorrelationof errors:

(4) AVar(3)= (X'X)-1N-K( N N NnmjklX ijkIlI=Ik=ll-Xi'uijUklXkl

X (X'X)-1,


4/6

VOL.97 NO. 2 RISKSHARINGAND NETWORK ORMATION 77

TABLE -GIFTS, LOANSAND NETWORKSGifts receiveda Loans receiveda

Coefficient Dyadic Coefficient Dyadicestimate t-value estimate t-valueGeographical proximitySame sitio = 1 0.052 6.56 0.038 4.31Difference in distance to road if same sitio -0.002 -5.27 -0.001 -2.62NetworkdummyX differencein:Dummy = 1 if primaryoccupationof head is farming -0.234 -1.25 -0.256 -2.32Numberof workingmembersx numberof activities -0.080 -0.72 -0.004 -0.08Age of householdhead 0.005 0.61 0.001 0.18Health index 1-4 (1 = good health,4 = disabled) 0.281 2.62 0.011 0.12Years of educationof household head -0.018 -0.66 -0.009 -0.48Total wealthb -0.035 -0.28 0.019 0.26Difference in:

Dummy= 1 if primaryoccupationof head is farming 0.001 0.51 -0.009 -2.36Numberof workingmembersx numberof activities 0.000 1.36 0.002 1.09Age of household head 0.000 -0.44 0.000 -0.52Health index 1-4 (1 = good health,4 = disabled) 0.001 2.04 0.000 -0.21Years of educationof householdhead 0.000 -0.81 0.000 -0.74Totalwealthb 0.000 0.51 -0.002 -0.71Village X time dummies Includedbut not shownIntercept -0.003 -0.59 -0.007 -1.48Numberof observations 21,184 21,184Notes: Estimator s least squares.All t-values based on standarderrorscorrected for dyadiccorrelationof errors.a Dependentvariable n log(valueof gift or loan +1).b nstrumented-see text for details.

where/3denotes the vector of coefficients,N isthe numberof dyadicobservations,K is thenum-ber of regressors,X is the matrix of all regres-sors, Xijis the vector of regressorsfor dyadicobservationij, andmijkl 1 if i = k,j = l,i = lor j = k, and 0 otherwise.' Formula(4) alsocorrectsforpossible heteroskedasticity.

II. EmpiricalResultsThe empirical analysis is based on a surveyconducted in the northernPhilippines specifi-cally to study risk-sharing networks (Lund1996). Sampledhouseholdsderive most of theirincome from nonfarmactivities(FafchampsandLund2003).

At the beginning of the survey,each house-hold was asked to identify four individuals onwhom it could rely in case of need. Most ofthese individuals are close family membersresidingin the samevillage. They constitute henetwork of insurance partnersof each house-hold. Approximately 939 network memberswere identifiedby respondents,of which 189arein households covered by the survey.In threesubsequentsurveyrounds,detailedinformationwas collected on income shocks and all loansand gifts between households. Loan repaymentinformationwas also gathered.Usingthesedata,Fafchampsand Lund(2003)haveshown that new loans andgifts play a risk-mitigatingrole. Fafchampsand Gubert (forth-coming) show that loan repayments contingenton shocks faced by the borrower.Here, weexamine the structureof risk-sharingnetworks.Webeginby estimatingequation(1).DependentvariableLij s 1 if householdi cites householdjas a source of assistance, 0 otherwise. Since ican citej withoutj citing i, Lij s directional.Regressors include income correlation andvarious measures of geographical and social

1By construction,all observationswherej = i ork = 1areidentically zero and hence are omitted. Dividing the innertermby two corrects for the doublecounting impliedby thesimple way we have writtenthe formula.


5/6

78 AEA PAPERSAND PROCEEDINGS MAY2007

distance. Tocontrolforpossible endogeneity,weinstrument income correlationusing the occu-pation status of various householdmembersasmeasured at the beginning of the survey (seeFafchampsand Gubert 2006 for details).2Geo-graphicaldistance is measuredbytwo variables:whether both households i andj reside in thesamehamlet orsitio, and thedifferencebetweeni's and 's distance to the nearestroad,providedthey reside in the same sitio. Other dimensionsof social distance are included as additionalcontrols, such as occupation, household size,age, health, education,and wealth.3Results are shown in Table 1.4 Income cor-relation has the wrong sign and is not statisti-cally significant.The same conclusion holds fordifferences in occupation,health,and householdcomposition.Therefore, urveyedhouseholdsdonot appearto establish risk-sharing inks withthose in the best positionto pool incomerisk. Incontrast,geographicalproximity s stronglysig-nificant. We also find thatrespondents ite, as asource of mutualinsurance,households that areon averageolderand richerthan themselves.These results could be misleading if Lijhaslittle or no relationshipwith actual risk sharing.To eliminate this possibility, we need to showthatreported inks play a role in the sharingofrisk. From the work of Fafchampsand Lund(2003),we knowthat, n thestudyarea,gifts andloans servea risk-sharingpurpose.Wethusesti-mate a model of the form(5) Ga "= a + io(zi - zj)Ltt

+ P (zi - zj) + ywij + uij,where G' denotes the value of all gifts (orloans) received by i from j in survey roundst = 2 and t = 3. Variableszi and wijare as in

TABLE 3-PROPENSITY TO REPAY

Hazard z-stat.Difference in distance to road if 0.933 -2.860

same sitio betweenresp.andpartnerLoan characteristicsLoan amount 0.718 -3.560Interest factor 0.026 -4.640Share still due 3.308 1.350ShocksShock to respondent 0.667 -1.790Household characteristicsof respondentAge of householdhead 1.017 1.300Last grade completed by head 1.095 1.510Craft skill dummy 2.080 1.970Permanentwage dummy 0.779 -0.680Household size 0.817 -2.950Wealth 1.052 0.750Household characteristicsof partnerAge of household head 1.006 0.500Income level 0.898 -0.470Villagedummies includedbutnot shownp-parameter 0.701 8.070Note: Estimator s a durationmodel.

Table1.Interaction erms(zi- zj)Ltiestwhetherreported inks areirrelevant.Results for gifts and informal loans arereported n Table2. Geographicproximityvari-ablesarestronglysignificant n bothregressions,confirming earlier results. The existence of alink is associated with gifts to unhealthyindi-viduals that are 200 times largerthanwithoutalink. Loans fromnonfarmers o farmers are 27times largerwith a link. These results demon-stratethatreported inks Lijare not irrelevant.So far, resultsemphasize the importanceofgeographic proximity.Could it be thatproxim-ity mitigatesmoral hazard?In the surveyarea,loans between friends and relativesaregrantedwithoutspecifying a due date. The borrower sexpectedto exertdiligence, but repaymentmaybe delayed in case of shock (FafchampsandGubert forthcoming). As distance increases,monitoringbecomes more difficult. This gen-eratesmoral hazard and may explain why risksharing takes place primarily among nearbyhouseholds.To investigatethis issue, we estimatea dura-tion model in which the dependentvariableisthe time elapsed until a loan is repaid,and wetest whether informal loans between nearbyhouseholds are repaidfaster.As in Fafchampsand Gubert (forthcoming), we control for

2 Income includes earnings from jobs held in the lastthree months, unearned income received in the last threemonths, and earnings from the sale of crops and livestockin the last three months.3Wealthis also instrumentedusing birthplace,numberof siblings, andinheritedwealth.4 Since each surveyedhousehold was asked to identifyfourlinks, it is notpossible to estimatef2 reliably.For thisreason,/2 terms are omittedfrom the regression.Includingthem does not affect the result (see Fafchampsand Gubert2006 for details).


6/6

VOL.97 NO. 2 RISKSHARINGAND NETWORK ORMATION 79

shocks, loan size, interestcharges, and partialrepayment.Household characteristicsand vil-lage dummies are included as well. Resultspresentedin Table 3 show that informal loansbetween distant households are paid less rap-idly. This is consistent with the existence ofmoral hazard and may in turn explain whyproximity plays such a paramountrole in theformationof risk-sharingnetworks.

III. ConclusionWe have examinedthe determinantsof risk-

sharing inks betweenhouseholds.We foundthatgeographic proximity s a majordeterminantofsuch links. In contrast,occupationand incomecorrelation are not significantdeterminantsofnetwork links. We also find that reportednet-work links have a strongeffect on subsequentgifts and loans, and that geographical proxim-ity is associated with fasterrepaymentof infor-mal loans. Takentogether,our findings suggestthat surveyed households do not form linksthat maximize potential gains from poolingincome risk, perhapsbecause of moral hazardconsiderations.

Two caveats must be made. First, we wereunable to control for family relationshipsbecause we do not have the necessary data.But from anthropologicalaccountsin the studyarea, we know that kinship is correlatedwithgeographical proximity. Results relative togeographic proximity should be interpreted nthis light. Second, network inks with individu-als outside the four surveyed villages were notincludedin the analysissince the focus was onintravillagerisk sharing.From the literatureonmigrations, we nevertheless know that linkswith migrantsplay an importantrole in diversi-fying income riskacrossspaceandoccupations.Close kinship with migrantsprobablyserves asa substitute or directmonitoring.This paperalso makes a methodologicalcon-tribution o the burgeoningempiricalliteratureon economic networks.First,we clarified iden-tification issues in dyadicdata, especially withrespect to directed networks and degree dis-tribution. Second, we facilitated inference on

networkprocesses by applyingthe well-knownconceptof robuststandard rrors o dyadicdata.REFERENCES

Coate, Stephen, and Martin Ravallion. 1993."Reciprocitywithout Commitment:Charac-terizationand Performance f InformalInsur-ance Arrangements."ournalof DevelopmentEconomics,40(1):1-24.Conley, Timothy G. 1999. "GMMEstimationwith CrossSectionalDependence." ournalofEconometrics,92(1):1-45.Fafchamps,Marcel.1992."SolidarityNetworks nPreindustrial ocieties:RationalPeasantswitha Moral Economy."Economic Developmentand CulturalChange,41(1):147-74.Fafchamps,Marcel, and Flore Gubert. Forth-coming. "ContingentLoan Repaymentn thePhilippines." Economic Development andCulturalChange,55(4).Fafchamps,Marcel, and Flore Gubert. Forth-coming."The Formation f Risk-SharingNet-works." ournalof DevelopmentEconomics.Fafchamps, Marcel, and Susan Lund. 2003."Risk-Sharing etworks n RuralPhilippines."Journal of Development Economics, 71(2):261-87.

Foster,AndrewD., and Mark R. Rosenzweig.2001. "ImperfectCommitment,Altruism,andthe Family:Evidence fromTransferBehaviorin Low-Income Rural Areas." Review ofEconomicsandStatistics,83(3):389-407.Ligon, Ethan, Jonathan P. Thomas, and TimWorrall.2002. "Informal nsuranceArrange-ments with Limited Commitment:Theoryand Evidence from Village Economies."Re-viewof EconomicStudies,69(1):209-44.Lund,SusanMarie. 1996. "InformalCreditandRisk-SharingNetworks:EmpiricalEvidencefrom the Philippines."PhD diss. StanfordUniversity.Mark R. Rosenzweig, 1988. "Risk, ImplicitContracts,and the Family in Rural Areas ofLow-IncomeCountries."Economic Journal,98(393):1148-70.Townsend,RobertM. 1994."RiskandInsurancein VillageIndia."Econometrica, 2(3):539-91.

Documents

Fafchamp DyadicReg Risk