Are Gifts and Loans between Households Voluntary? Margherita Comola Paris School of Economics

Marcel Fafchamps Oxford University

December 2010

Comola and Fafchamps ()

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Motivation

Research has shown that: many important economic phenomena take place within social networks the architecture of these networks can a¤ect the e¢ ciency and equity of the resulting allocation the architecture depends on whether links are unilateral or bilateral: if unilateral, equilibrium architecture is circle (if one-way bene…ts) (Bala and Goyal) if bilateral, equilibrium architecture is star (Jackson and Wolinsky)

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Risk sharing This is particularly important for risk sharing in poor economies: risk sharing takes place within social networks (Fafchamps and Lund, De Weerdt and Dercon) risk sharing is not e¢ cient (Townsend 1994) The formation of risk sharing links is not fully understood. Con‡icting claims in the literature as to whether households can abstract themselves from the obligation to assist others. This can ultimately be turned into a question on the nature of the link formation process: is it bilateral/driven by mutual agreement, as assumed by repeated game models of risk sharing? is it unilateral/driven by social norms, i.e., cannot refuse to help (certain people)? Comola and Fafchamps ()

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Research question

We have data from all 115 households in one Tanzanian village. During …ve rounds over a 15 months period, all respondents were asked: to whom they gave gifts, in cash or in kind from whom they received gifts to whom them lent money from whom they borrowed money It is very common for household i to report giving to j but j not reporting receiving from i – and vice versa.

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Research question

They were also asked to name those households to which they would turn in times of trouble. There are many cases in which household i names household j but j does not name i, and vice versa. Comola and Fafchamps (2009) show that responses are best regarded as willingness to link, not actual link.

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What we do

Building on Comola and Fafchamps (2009), we test: devise an original estimation method that allows for mis-reporting – either over-reporting or under-reporting test whether are gifts and loans correspond to a unilateral or bilateral link formation process

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Testing strategy

if lending and gift giving are a voluntary agreement between two households, then both households should want to rely on each other for help. if households cannot refuse to assist others, then gifts and loans are best seen as a unilateral process: only willingness by one is necessary

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Two maintained hypotheses:

answers to …rst-round question on who people would turn to for help are good proxies for willingness to link after controlling for covariates, reporting propensities are independent between giving and receiving households

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We …nd that

much mis-reporting evidence in agreement with unilateral link formation hypothesis This suggest that households …nd it di¢ cult to extricate themselves from social and familial obligations to assists others in need. This stands in contrast with much of the economic literature on risk sharing which emphasizes self-interest and reciprocal obligations.

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Bilateral versus unilateral link formation

τ ij = 1 if transfer from household i to household j wij = f0, 1g willingness of i to share risk with/link to j

wji = f0, 1g willingness of j to share risk with/link to i

if bilateral, Pr(τ ij ) increases only in wij wji : once we control for for wij wji , coe¢ cients of wij and wji = 0 if unilateral, Pr(τ ij ) increases with both wij and wji if pure unilateral, once we control for both wij and wji , coe¢ cient of wij wji = 0

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Testing strategy We estimate a regression model of the form: τ ij = λ(αwij + βwji + γwij wji + θXij )

(1)

Xij is a vector of controls λ is the logit function.

1

If risk sharing is unilateral, τ ij = 1 if fwij , wji g = f1, 0g, f0, 1g, or f1, 1g. Hence: α = β = α+β+γ > 0 which implies that γ =

2

β=

α.

If risk sharing is bilateral, τ ij = 1 if fwij , wji g = f1, 1g. Hence: α = β = 0 and γ > 0 Comola and Fafchamps ()

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Reverse model

hij = 1 if τ ij = 0 uij = 1

wij , i’s unwillingness to link with j.

Estimate a model of the form: hij = λ(α0 uij + β0 uji + γ0 uij uji + θ 0 Xij ) 1 2

(2)

If unilateral, hij = 1 if fuij , uji g = f1, 1g.

If bilateral model of link formation, hij = 1 if fuij , uji g = f1, 0g, f0, 1g, or f1, 1g.

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Discrepancies

Let τ be true transfer Discrepancies between reports on τ made by giver and receiver Let G = f0, 1g be report on τ made by giver

Let R = f0, 1g be report on τ made by receiver We only observe R and G

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Under-reporting Assume discrepancies are due to under-reporting only, i.e., if either i or j report τ, a transfer took place Given this assumption, the data generation process is:

Pr(G = 1, R = 0)

= = Pr(G = 0, R = 1) = = Pr(G = 1, R = 1) = = Pr(G = 0, R = 0) = Pr(G =

Pr(τ = 1, G = 1, R = 0) Pr(τ = 1) Pr(G = 1jτ = 1) Pr(τ = 1, G = 0, R = 1) Pr(τ = 1) Pr(G = 0jτ = 1) Pr(τ = 1, G = 1, R = 1) Pr(τ = 1) Pr(G = 1jτ = 1) 1 Pr(G = 1, R = 0) Pr(G 1, R = 1)

Comola and Fafchamps ()

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Pr(R = 0jG = 1, τ = 1) Pr(R = 1jG = 0, τ = 1) Pr(R = 1jG = 1, τ = 1) = 0, R = 1)

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Response bias Assume under-reporting by i is independent of under-reporting by j, Pr(R jG , τ ) = Pr(R jτ ). Reasonable if under-reporting results from reporting mistakes and omissions. We get: Pr(G Pr(G Pr(G Pr(G

= = = =

1, R 0, R 1, R 0, R

= 0) = 1) = 1) = 0) Pr(G

= = = = =

Pr(τ = 1) Pr(G = 1jτ Pr(τ = 1) Pr(G = 0jτ Pr(τ = 1) Pr(G = 1jτ 1 Pr(G = 1, R = 0) 1, R = 1)

= 1) = 1) = 1) Pr(G

Pr(R = 0jτ = 1) Pr(R = 1jτ = 1) Pr(R = 1jτ = 1) = 0, R = 1)

Three probabilities: P (τ = 1), P (G = 1jτ = 1) and P (R = 1j τ = 1). Comola and Fafchamps ()

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Response bias

We assume that these three probabilities can be represented by three distinct logit functions: Pr(τ = 1) = λT ( βτ Xτ )

(3)

Pr(G = 1jτ = 1) = λG ( βG XG )

(4)

Pr(R = 1jτ = 1) = λR ( βR XR )

(5)

The main equation of interest is λT ( βτ Xτ ) which corresponds to equation (1): it is on this equation that we wish to test the restrictions imposed by our testing strategy.

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Simulation analysis

We simulate the data generating process above Response bias can dramatically a¤ect inference regarding wij , wji and wij wji . Say we ignore reporting bias and estimate equation (1) by assuming that a transfer took place if either i or j reported it. if the reporting bias does not depend on willingness to link wij and wji , estimated coe¢ cients are …ne if the reporting bias depends on willingness to link wij and wji , they are severely biased in this case, the ML estimator above is consistent

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Reverse model We assumed there is no over-reporting. Do our results depend on this assumption? Assume now that discrepancies are due to over-reporting. A bit counter-intuitive, but perhaps respondents ashamed of not having given or received, and mis-report to enumerator. The data generation process is: Pr(G Pr(G Pr(G Pr(G

= = = =

1, R 0, R 0, R 1, R

= 0) = 1) = 0) = 1) Pr(G

Comola and Fafchamps ()

= = = = =

Pr(τ = 0) Pr(G = 1jτ Pr(τ = 0) Pr(G = 0jτ Pr(τ = 0) Pr(G = 0jτ 1 Pr(G = 1, R = 0) 0, R = 0)

Are Gifts Voluntary?

= 0) = 0) = 0) Pr(G

Pr(R = 0jτ = 0) Pr(R = 1jτ = 0) Pr(R = 0jτ = 0) = 0, R = 1)

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Reverse model

The DGP is expressed in terms of three probabilities: P (τ = 0), P (G = 1jτ = 0) and P (R = 1jτ = 0): Pr(τ = 0) = λT ( β0τ Xτ ) Pr(G = 1jτ = 0) = Pr(R = 1jτ = 0) =

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(6)

λG ( βG0 XG ) λR ( βR0 XR )

(7) (8)

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Standard errors

Dyadic observations are not independent. Standard errors must be adjusted, otherwise inference will be inconsistent. We apply the formula developed by Fafchamps and Gubert (2007), using the scores in lieu of X .

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The data village of Nyakatoke in the Buboka Rural District of Tanzania, at the west of Lake Victoria 600 inhabitants, 119 households interviewed during 2000-01 for 5 rounds at 3 month intervals in …rst round each adult respondent was asked: “Can you give a list of people from inside or outside of Nyakatoke, who you can personally rely on for help and/or that can rely on you for help in cash, kind or labor?". wij = 1 if an adult member of household i mentions an adult member of household j in their response each adult respondent i was then asked about all gifts and loans given to – and received from – household j these answers are the focus of our analysis Comola and Fafchamps ()

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Discrepancies 119 118 = 14042 possible dyads 1420 dyads (10%) for which i or j reports a gift in 42% of cases the report comes from the giver only in 30% from the receiver only in 27% from both in 73% of the cases one side reports something while the other reports nothing

545 dyads (4%) for which i or j reports a loan in 56% of these cases, the report comes from the giver only, in 36% from the receiver only, in 8% from both in 92% of the cases one side reports something while the other reports nothing

378 dyads for which both i and j report a gift only 22 report the same amount.

37 dyads for which both i and j report a loan only 5 report the same amount Comola and Fafchamps ()

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Reporting bias for gifts

We calculate a rough estimate of under-reporting We wish to estimate three unconditional probabilities: Pr(τ = 1), Pr(G = 1jτ = 1), and Pr(R = 0jτ = 1). We have three equations to do so: Pr(G = 1, R = 0)

= = Pr(G = 0, R = 1) = = Pr(G = 1, R = 1) = =

Comola and Fafchamps ()

Pr(τ = 1) Pr(G = 1jτ = 1) Pr(R = 0jτ = 1) 0.043 Pr(τ = 1) Pr(G = 0jτ = 1) Pr(R = 1jτ = 1) 0.031 Pr(τ = 1) Pr(G = 1jτ = 1) Pr(R = 1jτ = 1) 0.028

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Reporting bias for gifts

Simple algebra yields the following solution: Pr(τ = 1) = 15% Pr(G = 1jτ = 1) = 47%

Pr(R = 1jτ = 1) = 39%

There is considerable under-reporting of gifts: setting τ = 10.1% underestimates the frequency of gifts by almost 50%.

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Reporting bias for loans

A similar calculation for loans yields: Pr(τ = 1) = 14% Pr(G = 1jτ = 1) = 18%

Pr(R = 1jτ = 1) = 12%

Massive under-reporting of loans: setting τ uij = 3.9% only captures a quarter of the loans we suspect were made.

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Comola and Fafchamps ()

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The Data Table 1. Descriptive variable τ iij (gifts) τ jij (gifts) τ uij (gifts) τ oij (gifts) τ iij (loans) τ jij (loans) τ uij (loans) τ oij (loans) w ij and w ji w ij w ji weighted w ij and weighted w ji wealth i and wealth j same religion related distance hh membersi and hh membersj ni female dependentsj male dependentsj Comola and Fafchamps ()

statistics (N=14042) mean min max 0.071 0.059 0.101 0.028 0.025 0.017 0.039 0.003 0.045 0.020 0.023 0 0.933 4.546 0 27.970 0.354 0.016 0.522 0.014 1.738 2.555 1 9 5.294 0 19 1.101 0 6 0.437 0 3

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sd

0.117 4.815

0.303 1.314 3.063 0.864 0.729 December 2010

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Results for gifts

w ij w ji w ij w ji wealth i wealth j religion related distance

Pr (τ = 1 ) 2.563*** (0.371) 2.817*** (0.305) -0.196 (0.980) 0.081*** (0.016) 0.105 (0.066) 0.530** (0.251) 1.961** (0.762) -1.678** (0.660)

Comola and Fafchamps ()

Pr (G = 1 jτ = 1 ) 1.492*** (0.180)

Pr (R = 1 jτ = 1 ) 1.920*** (0.227)

-0.035** (0.016) -0.045*** (0.015) 0.025 0.012 (0.211) (0.196) 0.433 0.614 (0.505) (0.377) -0.585 -0.533 (0.536) (0.485) [to be continued]

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τ uij 1.401*** (0.107) 1.582*** (0.093) -0.417** (0.194) 0.029*** (0.007) 0.035** (0.018) 0.221*** (0.052) 0.942*** (0.173) -0.829*** (0.186)

τ oij 1.129*** (0.116) 1.521*** (0.109) -0.235 (0.165) 0.013* (0.008) 0.000 (0.012) 0.174** (0.068) 0.583*** (0.189) -0.892*** (0.317)

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Results for gifts (cont.)

membersi membersj

Pr (τ = 1 ) 0.110** (0.043) 0.262 (0.168)

ni

Pr (G = 1 jτ = 1 )

Pr (R = 1 jτ = 1 )

τ uij 0.047*** (0.018) 0.108** (0.054)

τ oij 0.038 (0.028) 0.082* (0.044)

-2.016*** (0.156)

-2.511*** (0.191)

0.026* (0.013)

female dep j male dep j constant

-3.525*** -0.277 (0.540) (0.590) Note: dyadic-robust standard errors in parentheses.

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-0.149 (0.143) -0.191 (0.133) -0.209 (0.359)

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Results for loans

w ij w ji w ij w ji wealth i wealth j religion related distance

Pr (τ = 1 ) 2.639 (5.599) 2.536 (6.437) -2.021 (8.388) 0.061* (0.036) 0.031 (0.051) 0.323 (2.717) 0.681 (18.080) -1.775 (1.282)

Comola and Fafchamps ()

Pr (G = 1 jτ = 1 ) 0.570 (0.624)

Pr (R = 1 jτ = 1 ) 1.206** (0.558)

-0.041 (0.051)

-0.058 (1.601) -0.079 (1.946) -0.083 (1.608) [to

-0.012 (0.031) -0.041 (1.048) 0.133 (1.760) 0.020 (1.191) be continued]

Are Gifts Voluntary?

τ uij 0.969*** (0.112) 1.006*** (0.106) -0.750*** (0.116) 0.010 (0.009) 0.008 (0.006) 0.080 (0.055) 0.107 (0.170) -0.576*** (0.125)

τ oij 0.464 (0.413) 1.169*** (0.191) -0.195 (0.421) -0.005 (0.013) 0.006 (0.006) -0.082 (0.219) -0.100 (0.376) -0.471** (0.231)

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Results for loans (cont.)

membersi membersj

Pr (τ = 1 ) 0.013 (0.270) 0.192 (0.635)

ni

Pr (G = 1 jτ = 1 )

Pr (R = 1 jτ = 1 )

τ uij 0.023 (0.040) 0.021 (0.026)

τ oij 0.028 (0.048) 0.018 (0.055)

-1.915*** (0.136)

-2.969*** (0.223)

0.113** (0.047)

female dep j male dep j constant

-1.991 -2.478 (2.032) (2.208) Note: dyadic-robust standard errors in parentheses.

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-0.047 (0.168) -0.222 (0.157) -2.442* (1.409)

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Results for total transfers

w ij w ji w ij w ji wealth i wealth j same religion related distance

τ uij 1.392*** (0.102) 1.565*** (0.093) -0.344* (0.188) 0.026*** (0.007) 0.031** (0.015) 0.198*** (0.052) 0.851*** (0.168) -0.839*** (0.160)

Comola and Fafchamps ()

τ oij Pr (τ = 1 ) Pr (G = 1 jτ = 1 ) 1.122*** 2.414*** 1.605*** (0.107) (0.377) (0.212) 1.564*** 2.793*** (0.100) (0.311) -0.320* 0.510 (0.164) (2.297) 0.011 0.076*** -0.039*** (0.007) (0.016) (0.012) 0.006 0.092* (0.010) (0.052) 0.170*** 0.430* 0.058 (0.062) (0.256) (0.212) 0.558*** 1.657** 0.527 (0.187) (0.680) (0.434) -0.937*** -1.593*** -0.667 (0.292) (0.607) (0.488) [to be continued]

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Pr (R = 1 jτ = 1 ) 1.994*** (0.202)

-0.035*** (0.012) 0.078 (0.182) 0.708** (0.346) -0.601 (0.463)

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Results for total transfers (cont.)

hh membersi hh membersj

τ uij 0.045* (0.024) 0.109*** (0.040)

τ oij 0.043* (0.023) 0.066** (0.032)

Pr (τ = 1 ) 0.100** (0.049) 0.272** (0.113)

ni

Pr (G = 1 jτ = 1 )

Pr (R = 1 jτ = 1

0.053*** (0.016)

female dependentsj

-0.139 (0.125) -0.207* (0.123) -0.357 (0.333)

male dependentsj constant

-1.796*** -2.363*** -3.022*** (0.143) (0.162) (0.505) Note: dyadic-robust standard errors in parentheses.

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-0.350 (0.533)

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Summary for gifts Results reject the bilateral link formation model: both α and β are strongly signi…cant, while γ is never signi…cantly positive. Results at least partly consistent with unilateral link formation: α and β are both signi…cant and of the same order of magnitude. A Wald test cannot reject the hypothesis that α = β in column (3), with a p-value of 0.3652. coe¢ cient γ of wij wji is negative in all three columns (1), (2) and (3) – but only signi…cantly so in column (1).

Contrary to unilateral model, γ 6=

β and γ 6=

α:

a Wald test rejects the joint hypotheses γ + α = 0 and γ + β = 0 with p-value=0.002. means that if wij = 1 and also wji = 1 the probability of transfer is larger than if either of them alone is equal to 1. This suggests that some bilateral dimension is present

Respondents more likely to report a transfer when wij = 1 Comola and Fafchamps ()

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Summary for loans

Results more or less satisfy α = β = model.

γ , consistent with unilateral

A Wald test of the joint hypothesis that α = β = γ has p-value of 0.9303, implying that we cannot reject the hypothesis of unilateral link formation. But these coe¢ cients are only statistically signi…cant in column (1) Fewer reported loans, hence less power

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Reverse model

Results less conclusive but more consistent with unilateral model For gifts, α0 and β0 are signi…cantly positive in all three regressions For loans, α0 and β0 are positive in all three regressions, but only signi…cant in the logit regressions.

But γ0 , the coe¢ cient of (1 wij )(1 wji ), is also positive and signi…cant in several of the regressions This is consistent with some bilateral link formation e¤ect

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Estimate of the underestimation bias

Table 5. The estimate of the bias gifts loans average …tted Pr(τ ij = 1) 0.1568 0.1942 in data: declared by i 0.0709 0.0249 in data: declared by j 0.0587 0.0169 in data: declared by i or j 0.1011 0.0388 average …tted Pr(G = 1jτ = 1) 0.3742 0.1138 average …tted Pr(R = 1jτ = 1) 0.3110 0.0729

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Estimate of the underestimation bias

Table 6. No wij and wij in response equations gifts loans average …tted Pr(τ ij = 1) 0.1473 0.1763 average …tted Pr(G = 1jτ = 1) 0.4608 0.1346 average …tted Pr(R = 1jτ = 1) 0.4130 0.0943

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Discussion Do Nyakatoke villagers unilaterally decide: to whom they wish to give? from whom they can demand assistance?

Suppose we had separate information: wijg denotes i’s desire to help j wjir denote j’s willingness to solicit help from i.

Estimate: τ ij = λ(αwijg + βwjir + θXij ) If unilateral willingness to give determines transfers (altruism, moral norms on charitable giving), then α > 0 and β = 0 If unilateral willingness to receive determines τ ij (social norms of redistribution), then α = 0 and β > 0.

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Discussion Now imagine that wij = wijg . Hence the model we estimate is: τ ij = λ(αwijg + βwjig + θXij ) If transfers unilaterally driven by willingness to give, we should observe α > 0 and β = 0. NOT Alternatively, imagine that wij = wijr . Hence the estimated model is: τ ij = λ(αwijr + βwjir + θXij ) If transfers unilaterally driven by willingness to request assistance, we should observe α = 0 and β > 0. NOT This suggests wij captures both willingness to give and willingness to receive, i.e., willingness to enter in a reciprocal relationship.

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Conclusion

We test whether gifts and informal loans result from unilateral or bilateral link formation: we …nd no evidence to support bilateral link formation. we …nd evidence to support the unilateral link formation hypothesis. these results are robust to di¤erent choices of model speci…cation.

What could account for these results? social norms probably play an important role in determining mutual assistance in Nyakatoke these norms state that individuals in need can convince others to enter in a reciprocal relationship

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