Non-Linearities in Returns to Participation in Grameen Bank Programs

Transcription

1 Journal of Development Studies, Vol. 42, No. 8, , November 2006 Non-Linearities in Returns to Participation in Grameen Bank Programs NIDHIYA MENON Brandeis University, Waltham, MA, USA Final version received July 2005 ABSTRACT This paper studies the benefits of participation in micro-finance programs, where benefits are measured in terms of the ability to smooth the effect of seasonal shocks that cause consumption fluctuations. It is shown that although membership in these programs is an effective instrument in combating inter-seasonal consumption differences, there is a threshold level of length of participation beyond which benefits begin to diminish. Returns from membership are modelled using an Euler equation approach. Fixed effects non-linear least squares estimation of parameters using data from 24 villages of the Grameen Bank suggests that returns to participation, as measured by the ability to smooth seasonal shocks, begin to decline after approximately two years of membership. This implies that membership alone no longer has a mitigating marginal effect on seasonal shocks to per capita consumption after four years of participation. Such patterns suggest that the ability to smooth consumption as a function of length of membership, need not accrue indefinitely in a linear fashion. JEL Classification: 012, 016, D12 I. Introduction Micro-credit programs such as the Grameen Bank s in Bangladesh have innovatively tackled a major problem associated with poverty alleviation in less developed countries. In these countries, vast sections of the population are caught in a poverty trap because their lack of collateralisable assets precludes them from using formal credit mechanisms, which, in turn, ensures continued poverty. By targeting credit to those who have no collateral, and by utilising innovative schemes to deliver that credit, micro-finance has proven to be a means of deliverance (see Appendix for a description of these programs). Despite the vast amounts of research on micro-finance organisations, few studies have attempted to evaluate the long-run benefits of participation, or sought to understand how behavior of participants evolves over time. Although development programs provide aid in the immediate short run, their main objective is to ensure Correspondence Address: Nidhiya Menon, Department of Economics and International Business School, MS 021, Brandeis University, Waltham, MA 02454, USA. nmenon@brandeis.edu ISSN Print/ Online/06/ ª 2006 Taylor & Francis DOI: /

2 1380 N. Menon that benefits are self-sustaining, and that the participants are able to stand on their own in the future. Programs such as the Grameen Bank meet these objectives more effectively than others in two ways. First, the interest charged on loans is at market rates, and thus local banks have a chance to become self-reliant within a couple of years of operation. Second, Grameen teaches its members how to administer their resources more effectively, and how to obtain and manage working capital. By doing so, micro-finance programs assist the poor in achieving the objectives of consumption smoothing and asset accumulation. Since loans are stipulated for use in non-agricultural self-employment activities, participating households are better able to smooth seasonal shocks to consumption. Additionally, through forced savings, these programs increase the assets of poor households. The hypothesis in this paper is that experienced members are better able to withstand seasonal shocks to household per capita consumption. This enhanced ability to buffer consumption against shocks captures the household s long run capacity to survive independently without aid. There are two facets to consumption smoothing that are of interest. The insurance aspect emphasises the ability to buffer consumption against exogenous shocks that are not perfectly foreseen. By stressing the importance of savings, micro-credit programs develop the means of withstanding unexpected negative shocks. Furthermore, given the lack of storage and the low levels of income, poor households are unable to smooth consumption even in response to anticipated seasonality. By diversifying sources of income within the household (these programs target women) and by requiring that loans be used for non-agricultural activities, lending programs help to insulate the consumption of poor households against anticipated seasonal shocks. Specific reasons for why participation might reduce the household s cost of borrowing (and thus facilitate consumption smoothing) are as follows: (1) Precautionary experienced members would have accumulated assets over time, which, may be used in a precautionary role to smooth consumption. (2) Accumulated assets may also be used as collateral for loans from other sources. (3) Membership leads to the formation of a reputation for more experienced clients. By demonstrating their ability to meet regular installment payments, experienced members signal their ability to be good credit risks for other lenders. (4) Since experienced members have assets that may be used as collateral, their demand for credit conditional on a particular source is more elastic. This implies that they are charged a lower interest rate (Iqbal, l988). Parameter estimates of the model analysed here indicate the presence of declining returns to consumption smoothing benefits, after a certain number of years of participation. The theoretical model formulates a time varying household specific interest rate, where the deviation of this interest rate from the average interest rate for households in the village captures the higher cost of borrowing faced by a poor household. Poor households may face a higher cost of borrowing due to a host of reasons, the most prominent being the lack of collateral. The household specific interest rate reflects the implicit price of intertemporal resource transfer and may be affected by social and monetary costs, as well as the household s reputation in the village. It thus captures both the physical cost of borrowing as embodied in the actual interest rate faced by the household, and other social considerations that might affect how much this household can borrow in that village. Participation in

3 Grameen Bank Programs 1381 micro-finance programs is hypothesized to reduce the deviation of the household specific interest rate from the average village interest rate. A natural method to test this hypothesis is to examine the ability of participants to smooth per capita consumption across seasons. Following Zeldes (1989) and Foster (1995), an Euler equation incorporating the cost of borrowing faced by the household, is adopted to study inter-seasonal consumption differentials. The deviation of the household interest rate from the average village interest rate is a function of the length of membership in a credit program. If the change in per capita household consumption between seasons is negatively correlated to the length of membership, it follows that experienced members are better able to smooth seasonal shocks. To allow for non-linear effects in the returns to participation, a quadratic approximation is used to model the length of membership in a credit program. A fixed effects non-linear least squares estimation of an equation that relates changes across seasons in household per capita consumption expenditure to length of membership, changes in prices, preferences, and the cost of borrowing, demonstrates that membership length is inversely related to the change in seasonal per capita food consumption. Data from 24 villages of the Grameen Bank indicate that although participation does have a mitigating effect on seasonal shocks to consumption, the magnitude of such effects begins to diminish over time. Estimates from the model suggest that the effects reach a maximum at two years of membership, and begin to decline thereafter. This does not imply that consumption volatility increases for experienced members, merely that participation no longer has the same mitigating influences as before. The layout of the paper is as follows. Section II provides details on the model that is estimated. Section III summarises the data, and Section IV discusses issues involved in the estimation. Results are reported in Section V and Section VI provides various robustness checks of the estimates obtained. Section VII concludes with policy implications. II. Model The presence of credit constraints is tested by deriving an Euler equation from a dynamic utility maximisation model. This Euler equation relates consumption changes to changes in prices and the interest rate, under the assumption that no borrowing constraints exist. Consider a household that maximizes the expected value of a time separable lifetime utility function. In each time (season) period t, household i in village j chooses the quantity of per capita consumption C ijt to solve the following: X T 1 Max E t b k UðC ijt þ kþ subject to an asset update: k¼0 A ijtþk ¼ð1 þ r ijt ÞðA ijtþk 1 ÞþY ijtþk P jtþk C ijtþk 8k where b is the discount rate, E t is the expectations operator conditional on information available as of time t, T is the end of the household s horizon, r ijt is the

4 1382 N. Menon interest rate faced by the household, A ijt are household assets, Y ijt is household income, and P jt are prices in village j at time t. The first order conditions for the above problem are Euler equations of the following form: U 0 ðc ijtþ1 Þ E t U 0 ðc ijt Þ ¼ 1 P jtþ1 bð1 þ r ijt Þ P jt ð1þ Assuming a CRRA utility function: UðC t Þ¼ C1 a t 1 a and substituting its first derivative into Equation (1) yields: C a ijtþ1 bð1 þ r P jt ijtþ ¼ 1 þ e 0 ijtþ1 C ijt P jtþ1 where e 0 ijtþ1 is the expectational error. Defining R ijt ¼ (1 þ r ijt ) and substituting into the above implies: ln C ijtþ1 ¼ 1 C ijt a lnðbr P jt ijtþþln lnð1 þ e 0 ijtþ1 P Þ ð2þ jtþ1 Following Zeldes (1989), it can be shown that lnð1 þ e 0 ijtþ1 Þ¼lnð1 þ e ijtþ1þþ 1 2 s2 e ijt þ1. Substituting in Equation (2), we obtain: ln C ijtþ1 C ijt ¼ 1 a lnðbr ijtþþln P jt P jtþ1 þ e ijtþ1 where e ijtþ1 ¼ lnð1 þ e ijtþ1 Þþ 1 2 s2 e ijt þ1. In order to analyse the cost of borrowing faced by a household, the term that captures the difference between the household interest rate and the average interest rate in the village needs to be incorporated. Approximating 1 a lnðbr ijtþ to its first order Taylor series expansion about the village average interest rate R jt gives: ln C ijtþ1 C ijt ¼ 1 a lnðbr jtþþðr ijt r jt Þ 1 ln P jtþ1 R jt P jt þ e ijtþ1 where r jt is the average interest rate in village j at time t, andr ijt is the interest rate faced by household i in village j at time t, Simplifying, we obtain: ð3þ Dln C ijtþ1 ¼ g 0 þ g 1 ðr ijt r jt Þþg 2 Dln P jtþ1 þ n ijtþ1 ð4þ where D denotes changes over time, that is, Dln C ijtþ1 ¼ (ln C ijtþ1 ln C ijt ) and Dln P jtþ1 ¼ (ln P jtþ1 ln P jt ). Furthermore, g 0 ¼ 1 a ln br jt; g 1 ¼ 1 ar jt ; g 2 ¼ 1 a ; and

5 Grameen Bank Programs 1383 n ijtþ1 ¼ 1 a e ijtþ1. Those households that are better able to engage in credit based consumption smoothing (that is, with small (r ijt 7 r jt )) do not experience large deviations in their cost of borrowing (relative to the rest of the village). Thus for them, changes in per capita consumption are primarily governed by changes in prices, preferences, and the average village interest rate. We hypothesise that the deviation between the average village interest rate and the household interest rate depends on the length of time the household has been a member of a credit program. Membership reduces the cost of borrowing since those who have been participants for longer periods of time would have accumulated the means to minimise the effect of seasonal shocks. 1 The (r ijt 7 r jt ) term captures the extent to which the household specific interest rate differs from the average village interest rate, where the latter reflects the effect of average village and time (season) shocks. For those who do not participate, (r ijt 7 r jt ) picks up the full effect of average village and time (season) shocks. For those who do participate, the effect of the average village time (village season) shock is dampened by the length of membership variable. This is captured in the following specification: g 0 þ g 1 ðr ijt r jt Þ¼FðD ijt Þm jt ð5þ F(D ijt ) denotes that the household s cost of borrowing is a function of D ijt where D ijt represents the duration of membership (of household i in village j at time t) ina credit program, and m jt is a village time (season) dummy that captures average interest rate change. Where 2 FðD ijt Þm jt ¼ðe d td ijt Þm jt ; g 0 þ g 1 ðr ijt r jt Þ¼ðe d td ijt Þm jt. Adjusting the time subscript appropriately and substituting into Equation (4): Dln C ijtþ1 ¼ðe d tþ1d ijtþ1 Þm jtþ1 þ g 2 Dln P jtþ1 þ n ijtþ1 ð6þ Variables such as characteristics of the household head as well as the quantity of land owned by the household also play a role in reducing the cost of borrowing. These are represented by X C ijtþ1 (the C superscript denotes that these are the X ijtþ1 in the equation where change in consumption is the dependent variable (Equation (6))), and may be included in (6) in a similar manner to the inclusion of D ijtþ1. Non-Linear Returns to Participation The measure of returns to program participation in this paper is the household s ability to minimise fluctuations in per capita consumption expenditure across seasons. In order to ascertain whether these returns become smaller over time, we estimate a quadratic counterpart of Equation (6): Dln C ijtþ1 ¼ e d 1tþ1D ijtþ1 þd 2tþ1 D 2 ijtþ1 þb cx C ijtþ1 fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} A m C jtþ1 þ g 2Dln P jtþ1 þ n ijtþ1 This quadratic approximation allows consumption-smoothing benefits to decline over time (a cubic functional form was initially estimated, but the quadratic model is used since the effect of the cubic term in the cubic functional form was insignificant). ð7þ

6 1384 N. Menon Equation (7) is estimated using a non-linear least squares technique with villagetime fixed effects. Since the data has information on 24 Grameen villages over three seasons, more than one village season fixed effect parameter ðm C jtþ1þ is estimated. The coefficients d 1tþ1 and d 2tþ1 are the marginal effects of interest. A negative value for d 1tþ1 would confirm the idea that experienced participants are better able to smooth consumption. The declining returns hypothesis is supported if d 2tþ Consider the term denoted by A in Equation (7). Intuitively, A denotes the parameters that dampen the effect of seasonal shocks m C jtþ1. For those households that do not participate, D ijtþ1 ¼ 0. Therefore for such households, A ¼ðe b CX C ijtþ1 Þ. For those households that do participate, A is as shown in (7). As long as d 1tþ1 is negative and larger than d 2tþ1 (in absolute terms), participants are better able to buffer consumption against seasonal shocks. The ability to dampen the effect of seasonal shocks becomes stronger with length of participation (large value for D ijtþ1 ). III. Data The data used in this analysis were collected from rural Bangladesh during The estimation sample was drawn from eight Grameen thanas (Grameen is the only program that operates in these thanas), and participants from three villages in each of these eight thanas were interviewed. These villages were selected on the basis of their having had a Grameen program in operation for three or more years. Since Grameen does not lend to households that own more than half an acre of cultivable land, this rule is used to classify households in each of the 24 villages as target or non-target. Participants and non-participants among the target households are then separately identified, and target non-participants as well as participants are over sampled in the data. The data has information on a total of 479 Grameen households, of which 420 are target households (own less than half an acre of cultivable land). Of the 420 target households, 297 are participants. Each household is surveyed for three rounds, corresponding to the three major rice crop seasons in Bangladesh. Data in the first round were collected in December/ January 1991 the post harvest time of the Aman rice crop. The second round corresponds to the post harvest time of the Boro crop (April May 1992), and the third round corresponds to the post harvest time of the Aus rice crop (August September 1992). The Aman rice crop is the largest of the year, and the Aus harvest is the smallest. In this paper, Round 1 refers to the Aman season (Season 1), Round 2 to the Boro season (Season 2), and Round 3 to the Aus season (Season 3). Table 1 ( HH is a short-form for household in all tables) provides the weighted means and standard deviations of all the independent variables used in the analysis. In order to account for the choice based sampling of the data, the means of the variables are adjusted by weights that correct for the difference between the actual distribution of households in the villages surveyed, and the distribution of households in the sample. Length of membership is measured by the number of years the participant has been a member of Grameen s lending program. Two households had members belonging to a program other than the Grameen Bank,

7 Grameen Bank Programs 1385 Table 1. Weighted means and standard deviations of independent variables Independent variable Full sample Target participants Target non-participants Non-participants Log of decimals of land owned by HH { (3.3305) (3.1963) (2.5771) (3.3503) Years of education of HH head (3.2934) (2.6773) (3.1419) (3.5269) Gender of HH head: ¼1 if male (0.2464) (0.2446) (0.3079) (0.2474) Age of HH head ( ) ( ) ( ) ( ) Highest value of years of education for a female in HH Highest value of years of education for a male in HH Dummy for no adult (416 years) female in HH (2.8872) (2.1507) (2.4950) (3.1544) (3.5280) (3.0256) (3.4143) (3.7287) (0.1182) (0.0832) (0.1743) (0.1308) Dummy for season 3 (Aus) (0.4716) (0.4717) (0.4720) (0.4718) Price of coarse grain rice (1.0461) (1.0488) (1.0419) (1.0453) Difference in the log of price of rice (0.0846) (0.0836) (0.0903) (0.0851) between seasons 2 and 1 Difference in the log of price of rice (0.0757) (0.0764) (0.0735) (0.0754) between seasons 3 and 2 Difference in the log price of rice and (0.0665) (0.0669) (0.0677) (0.0664) wheat flour between season 2 and 1 HH maximum years member program* (2.4223) (2.1117) HH maximum years member program* (1.9828) (2.3986) for female participant HH maximum years member program* for male participant (1.6702) (2.7690) Observations { 1 decimal ¼ 1/100 th of an acre. *Denotes endogenous variable. Standard errors in parenthesis.

8 1386 N. Menon thus for each household, the maximum value for length of program membership is used in the estimations. 3 Table 2 reports the weighted means and standard deviations of the dependent variables. The second and third variables in Table 2 (the main dependent variables) consist of two sets of differences in per capita consumption Between Seasons 2 and 1, and between Seasons 3 and 2. Per capita consumption is measured by per capita food expenditure in the week previous to the survey. In these data, expenditure on food constitutes almost 80 per cent of total expenditure at the household level. Equation (7) shows that the difference in per capita consumption between Season 2 and Season 1 is a function of Round 2 data, and the difference in per capita consumption between Season 3 and Season 2 is a function of Round 3 data. The flowchart in Figure 1 depicts the structure of the data ( HH refers to household). IV. Estimation The main aim of micro lending programs is to alleviate poverty. If programs are deliberately placed in areas that are relatively poorer than others (non-random program placement), then estimates of the effects of program participation are necessarily biased. The use of village level fixed effects that capture systematic differences in attributes across villages, aids in removing this bias. The m C jtþ1 fixed effect parameters that we estimate in Equation (7) have both a village j and a time (season) t dimension. The village j dimension controls for non-random program placement. Individual heterogeneity also needs to be taken into account since those who choose to participate could be systematically different from non-participants. Once a credit program is established in a village, participants self-select into groups to become members of the program. If those who join are more able at managing selfemployment activities, or have higher than average entrepreneurial skill levels as compared to non-participants, then the estimation of participation effects is biased. Individual and household level heterogeneity of this type could confound results and incorrectly attribute to the program those effects that arise from differences in the nature of household unobservables. The presence of individual heterogeneity implies that the length of membership variable (D ijtþ1 ) in Equation (7) is endogenous. Given this, identification of the effect of membership length requires the use of instrumental variables. If a household is a target household (owns less than half an acre of land) in a village with the Grameen program, the household is considered to be eligible and to have the choice to participate. Where choice is a dummy variable, the interaction of choice and the exogenous variables ðx C ijtþ1þ of Equation (7) form the set of identifying instruments. It is important to note that the exogenous variables of themselves are not the instruments, the interactions of the exogenous variables with the choice dummy constitute the instrument set. This is because exogenous variables can have an effect on length of membership only if the household is eligible and has choice. For households without choice, length of membership is identically zero. That is: D ijtþ1 ¼ b D X D ijtþ1 þ md jtþ1 þ w ijtþ1 if choice ¼ 1 ¼ 0 if choice ¼ 0

9 Grameen Bank Programs 1387 Table 2. Weighted means and standard deviations of dependent variables Dependent variable Full sample Target participants Target non-participants Non-participants Log of per capita food expenditure last week (expenditure in takas per week) Difference in the log of per capita food expenditure last week between seasons 2 and 1 (expenditure in takas per week) Difference in the log of per capita food expenditure last week between seasons 3 and 2 (expenditure in takas per week) (0.3410) (0.3190) (0.3683) (0.3503) (0.3568) (0.3079) (0.3992) (0.3768) (0.2588) (0.2390) (0.2610) (0.2672) Observations Standard errors in parenthesis.

10 1388 N. Menon Figure 1. Structure of the data Since length of membership is identically zero for those who do not have choice and endogenous for participants, the interaction of choice and the exogenous variables (X D ijtþ1 ; the D superscript denotes that these are the X ijtþ1 in the duration of membership equation immediately above) form the set of instruments. These instruments affect membership length discontinuously since exogenous variables can have an effect only if the household owns less than half an acre of land and resides in a village with a program (that is, if the household has choice). In the following section, we test the validity of these instruments. V. Results Motivational Results Table 3 reports results of a linear village fixed-effects model where the log of per capita food expenditure is regressed on (instrumented) length of membership of all participants (in the interests of brevity, the estimated fixed-effect coefficients are not reported in Table 3). We acknowledge that this is a selected sample. The purpose of Table 3 is to provide a cursory check of the relationship between membership length and food consumption for households that participate in the Grameen program. Columns (1) and (3) show results for the cubic term of membership duration. Given the insignificance of the cubic term in Columns (1) and (3), the quadratic form of Columns (2) and (4) is appropriate. Columns (2) and (4) of Table 3 indicate that although the predicted length of membership has positive and significant effects on the log of per capita food expenditure, the square of this variable is negative (except in Column (4) where the square of length of membership of a female participant is measured imprecisely). Thus, although membership in the Grameen program increases food consumption, such returns do not accrue indefinitely in a linear fashion. There is preliminary evidence in these data that non-linearities in the returns to participation are present. Most of the other variables in Table (3) have predicted effects.

11 Grameen Bank Programs 1389 Table 3. Dependent variable: log of per capita food expenditure Explanatory variable Pooled (1) Pooled (2) Genderstratified (3) Genderstratified (4) Predicted length of ** ** membership (0.2087) (0.0789) Predicted length of { membership squared (0.0489) (0.0091) Predicted length of membership cubed (0.0031) Predicted length of { membership of male (0.0582) (0.0412) participant Predicted length of * membership of male (0.0251) (0.0075) participant squared Predicted length of membership of male (0.0021) participant cubed Predicted length of * ** membership of female (0.1439) (0.1171) participant Predicted length of membership of female (0.0264) (0.0085) participant squared Predicted length of membership of female (0.0025) participant cubed Log of decimals of ** ** ** ** land owned by HH (0.0039) (0.0037) (0.0090) (0.0083) Years of education of * * HH head (0.0062) (0.0061) (0.0117) (0.0112) Gender of HH ** ** ** ** head: ¼1 if male (0.0398) (0.0398) (0.1095) (0.1008) Age of HH head ** ** ** ** (0.0012) (0.0010) (0.0033) (0.0030) Highest value of years ** ** ** ** of education for a female in HH (0.0050) (0.0049) (0.0085) (0.0081) Highest value of years of education for a male in HH ** ** (0.0058) (0.0057) (0.0084) (0.0081) Dummy for no adult ** ** ** ** (416 years) female in HH (0.1706) (0.1445) (0.5684) (0.5200) Price of coarse grain rice ** ** ** ** (0.0120) (0.0117) (0.0145) (0.0140) Price of wheat flour * ** { { (0.0170) (0.0155) (0.0239) (0.0225) Observations R-squared Model includes village-time fixed effect parameters. Standard errors in parentheses. { significant at 10%; *significant at 5%; **significant at 1%.

12 1390 N. Menon Main Results Table 4 reports the results from the non-linear village fixed-effects estimation of Equation (7) in Round 2 (estimates in Round 3 were insignificant), for the pooled and gender-stratified models (in the latter, separate coefficients are allowed for the length of membership of male and female participants). Both the pooled and genderstratified models include village time fixed effect parameters, but these are not reported in order to conserve space. 4 The dependent variable in Table 4 is the difference in log per capita food expenditure between Season 2 and Season 1, and the main right hand side variable of interest is the predicted (instrumented) length of membership. An F-test that the identifying instruments (interactions of choice and the exogenous variables) are jointly zero is strongly rejected (F(30, 897) ¼ 8.33, Prob 4 F ¼ ). Thus our instruments are valid. Table 4. Dependent variable: difference in log food expenditure b/w seasons 2 and 1 Explanatory variable Pooled (1) Gender-stratified (2) Predicted length of membership ** (0.2563) Predicted length of membership squared ** (0.0598) Predicted length of membership of male participant * (0.2594) Predicted length of membership of male participant squared ** (0.0567) Predicted length of membership of female participant * (0.2994) Predicted length of membership of female participant squared * (0.1313) Log of decimals of land owned by HH (0.0407) (0.0343) Years of education of HH head { (0.4152) (0.3943) Gender of HH head: ¼1 if male ** (0.3582) (0.4361) Age of HH head ** { (0.0112) (0.0099) Highest value of years of education ** ** for a female in HH (0.0389) (0.0373) Highest value of years of education { { for a male in HH (0.4152) (0.3953) Dummy for no adult (416 years) female in HH Difference in the log of price of rice between seasons 2 and 1 (0.5828) (0.5911) { { (0.2722) (0.3301) Observations R-squared Model includes village-time fixed effect parameters. Standard errors in parentheses. { significant at 10%; *significant at 5%; **significant at 1%.

13 Grameen Bank Programs 1391 Columns (1) and (2) of Table 4 show that (instrumented) membership has a significant effect on smoothing inter-seasonal consumption changes. Note that although the coefficient on the linear term is negative (in keeping with the hypothesis that experienced members face smaller deviations in seasonal consumption), the coefficient on the squared term is significant and positive, indicating the presence of diminishing returns. Estimates from the gender-stratified and pooled models suggest that the maximum effect of participation is at about two years. After approximately four years, the length of membership variable has a substantially reduced mitigating effect on seasonal shocks in both models. Table 4 also reports that male-headed households experience smaller consumption fluctuations across seasons, as do households with older heads. As expected, households with educated males experience reduced deviations in inter-seasonal consumption. Unexpectedly, higher levels of female education increase consumption differences across seasons. This counter-intuitive result may be explained by the fact that households with highly educated females are also comparatively more rich. Such households may spend on luxury food items that are available on a seasonal basis. The price of rice variable has the expected effect in Table 4. It is important to note that although the length of membership variable produces little dampening effects on seasonal shocks after four years, the household s cost of borrowing need not increase since other exogenous variables (such as gender and age of household head) still play a mitigating role. In other words, it is not the case that after approximately four years of membership, participants (again) experience increased volatility in their consumption patterns. These data suggest that after a certain threshold, membership in the Grameen program (as measured by the length of participation variable) succeeds in reducing the vulnerability of the poor to seasonal shocks. VI. Support for Results Influence of Village Level Heterogeneity As opposed to village time (village season) shocks, patterns of inter-seasonal food consumption may be influenced by village level differences alone. This implies that in the context of the model, membership should be interacted with a village dummy instead of a village season dummy. As noted before, the m jt parameters of Equation (7) capture both village (j) and season (t) variations. Since the m jt parameters have a village and a time dimension, they already allow for village-level heterogeneity. However, it is possible to model a less general form by interacting membership with village dummies alone (m j ). This is relatively more restrictive, since the m j do not allow for seasonal effects. If the m C jtþ1 parameters of Equation (7) include the m j as a special case, then we expect few significant changes to the main results of Table 4. That is, length of membership should still have negative effects on inter-seasonal consumption changes, and these effects should decline over time. Table 5 shows that our main results hold when membership is interacted with only village dummies, as opposed to village-time dummies. The dependent variable in Table 5 is the difference in food consumption between Seasons 2 and 1 in Round 2, and the difference in food consumption between Seasons 3 and 2 in Round 3. Thus in

14 1392 N. Menon Table 5. Dependent variable: difference in log food expenditure b/w Seasons 2 and 1 in Round 2 and b/w Seasons 3 and 2 in Round 3 Explanatory variable Pooled (1) Gender-stratified (2) Predicted length of membership (0.1768) Predicted length of membership squared * (0.0436) Predicted length of membership of male participant Predicted length of membership of male participant squared Predicted length of membership of female participant Predicted length of membership of female ** (0.1863) * (0.0175) ( ) (0.1140) participant squared Log of decimals of landowned by HH (0.0276) (6.3779) Years of education of HH head { (0.1400) (0.6344) Gender of HH head: ¼1 if male * (0.2610) ( ) Age of HH head { (0.0069) (1.8245) Highest value of years of education for a female in HH Highest value of years of education for a male in HH Dummy for no adult (416 years) female in HH Difference in the log price of rice and wheat flour b/w seasons 2 and 1 in round 2 and b/w seasons 3 and 2 in round ** (0.0303) (1.8267) * (0.1405) (1.1305) (0.4720) ( ) ** ** (0.1489) (0.1388) Dummy for season 3 (Aus) (4.2593) (4.1308) Observations R-squared Model includes village fixed effect parameters. Standard errors in parentheses. { significant at 10%; *significant at 5%; **significant at 1%. Round 2, the dependent variable of Table 5 is the same as that in Table 4 (main results). As is clear from Column (1), length of membership has a negative effect (significant at the 11.8 per cent level) which becomes smaller over time. In the gender-stratified model of Column (2), estimates of the length of participation of male members are consistent with our main results. For female participants, length of membership has the correct sign although it is measured with error. Hence as expected, results of the pooled and gender-stratified models of Table 5 are broadly consistent with the hypothesis of this study. Other variables in Table 5 have predicted effects. 5

15 Grameen Bank Programs 1393 Functional Form of Length of Participation The theory in Section II derives from a model in which the length of participation variable is interacted with village season shocks. This allows us to gauge the extent to which membership in the Grameen program dampens the effect of seasonal shocks to per capita food consumption. The interaction of membership and village time shocks is an intuitive way to study consumption smoothing behavior among Grameen participants. However, it is possible to estimate the effect of membership separately from its interaction with village time shocks. Although it does not directly follow from the model of consumption smoothing derived in Section II, length of participation may be entered as a separate term in Equation (7). 6 Table 6 reports the results of the estimation where membership is entered separately in the model of Table 4. As is clear from both the pooled model of Column (1) and the gender-stratified model of Column (2), length of participation variables that are entered separately (that is, not interacted with village time shocks) have little effect on inter-seasonal consumption changes. That length of membership acts to smooth consumption by buffering seasonal shocks is evident from the first two terms of Column (1) and the first four terms of Column (2). In support of our hypothesis, these terms in Table 6 show that membership length (interacted with village season shocks) reduces inter-seasonal consumption variation. Again, there is strong evidence that such returns to participation decline with time in the program. Simultaneous Estimation of Both Sets of Consumption Changes The theoretical model of Section II indicates that the change in consumption between Seasons 2 and 1 is a function of Season 2 (Round 2) variables. Hence, the difference in consumption between Seasons 2 and 1 is a function of Village season 2 dummies (that is, dummies for the 24 Grameen villages in Season 2). Similarly, the difference in consumption between Seasons 3 and 2 is a function of village season 3 dummies (dummies for the 24 Grameen villages in Season 3). If we consider only one set of inter-seasonal consumption changes (as is done in the main results of Table 4), then the model includes village time dummies that are specific to only one season (Season 2 in Table 4, since the dependent variable is the change in consumption between Seasons 2 and 1). 7 It is possible to measure the effect of two dummies (since Bangladesh has three rice-based seasons) if both sets of consumption changes are estimated simultaneously, Table 7 reports the results of this estimation (although dummies for both Season 2 and Season 3 are included in the model, these are not reported in the interests of brevity). As evident, the pooled and the gender-stratified models in Season 2 have the same effects as before, with membership length reducing interseasonal consumption changes. Consistent with results obtained above, there is evidence that benefits from membership decline over time. With the simultaneous estimation of both sets of consumption changes, length of participation in Season 3 (in Column (1) of the pooled model) has the expected influence on changes in consumption between Season 3 and Season 2 (this was not the case before). There is also evidence that returns to participation decline over time. However, the effects of

16 1394 N. Menon Table 6. Dependent variable: difference in log food expenditure b/w Seasons 2 and 1 Explanatory variable Pooled (1) Gender-stratified (2) Predicted length of membership ** (0.2658) Predicted length of membership squared ** (0.0621) Predicted length of membership of male participant Predicted length of membership of male participant squared Predicted length of membership of female participant Predicted length of membership of female * (0.0241) * (0.0005) ** (0.0252) ** (0.0008) participant squared Log of decimals of land owned by HH (0.0421) (0.0353) Years of education of HH head { (0.3682) (0.4022) Gender of HH head: ¼1 if male ** (0.3618) (0.4520) Age of HH head ** { (0.0114) (0.0103) Highest value of years of education for a ** ** female in HH (0.0403) (0.0403) Highest value of years of education for a { * male in HH (0.3685) (0.4036) Dummy for no adult (416 years) female in HH (0.6012) (0.6075) Predicted length of (0.0273) Predicted length of membership (0.0083) Predicted length of membership of male (0.0043) Predicted length of membership of male participant (0.0001) Predicted length of membership of female (0.0035) Predicted length of membership of female participant (0.0001) Difference in the log of price of rice between { { seasons 2 and (0.2728) (0.3301) Observations R-squared Variable entered separately in model in additive form. Model includes village-time fixed effect parameters. Standard errors in parentheses. { significant at 10%; *significant at 5%; **significant at 1%. membership length in Season 3 are still measured imprecisely in the gender-stratified model (Column (2)). To summarise, the simultaneous estimation of both sets of dependent variables which allows for two seasonal dummies provides results that are consistent with the main findings of this study.

17 Grameen Bank Programs 1395 Table 7. Dependent variable: difference in log food expenditure between Seasons 2 and 1 in Round 2 and between Seasons 3 and 2 in Round 3 Explanatory variable Pooled (1) Gender-stratified (2) Predicted length of membership season ** (0.2207) Predicted length of membership squared season ** (0.0508) Predicted length of membership of male participant season ** (0.0185) Predicted length of membership of male participant squared season ** (0.0003) Predicted length of membership of female participant season ** (0.0210) Predicted length of membership of female participant squared season * (0.0007) Log of decimals of land owned by HH season 2 (0.0357) (0.0299) Years of education of { * HH head season 2 (0.3474) (0.3464) Gender of HH head: ¼1 if ** male season 2 (0.3120) (0.3826) Age of HH head season ** * (0.0097) (0.0086) Highest value of years of education ** ** for a female in HH season 2 (0.0339) (0.0324) Highest value of years of education * * for a male in HH season 2 (0.3474) (0.3473) Dummy for no adult (416 years) female in HH season 2 (0.5118) (0.5151) Difference in the log of price of { * rice between seasons 2 and 1 (0.2372) (0.2878) Predicted length of membership season ** (1.1814) Predicted length of membership squared season ** (0.1971) Predicted length of membership of male participant season (0.1946) Predicted length of membership of male participant squared season { (0.0038) Predicted length of membership of female participant season (0.1562) Predicted length of membership of female participant squared season (0.0347) Log of decimals of land owned ** by HH season 3 (0.1811) (0.2254) Years of education of HH head season (0.0962) (0.2090) Age of HH head season ** * (0.0164) (0.0344) Highest value of years of education ** * for a female in HH season 3 (0.1437) (0.3919) (continued)

18 1396 N. Menon Table 7. (Continued) Explanatory variable Pooled (1) Gender-stratified (2) Highest value of years of education for a male in HH season 3 Dummy for no adult (416 years) female in HH season 3 Difference in the log of price of rice between seasons 3 and ** (0.0998) (0.1920) (2.7828) ** ** (0.1014) (0.0952) Observations R-squared Model includes village-season 2 and village-season 3 dummies. Standard errors in parentheses. { significant at 10%; *significant at 5%; **significant at 1%. Dummy for no adult female in HH was not identified for the pooled model in season 3. Gender of HH head for both the pooled and gender-stratified models was not identified in season 3. Cohort Effects If the earlier cohort of participants was more able as compared to later cohorts, then the onset of diminishing returns for experienced members (which is indicative of easier capital access, greater assets, and so on) could be driven by this characteristic. Given the nature of the data used in Table 4, conventional tests for cohort effects cannot be conducted (note that endogeneity due to self-selection is already controlled for with the use of instrumental variables). But using the education of the household head as a proxy for ability, it is possible to study the relationship between ability and length of membership conditioning on village-level effects. A graph of the lag between program introduction and joining against the household head s schooling in Grameen villages that have had the program for more than 8.67 years (the upper 90 per cent of length of time a program has been present in a village) and those that have had the program for less than 3.5 years (the lower 10 per cent), provides evidence of ability bias if the distribution of participants who joined first in either case is higher than those who joined later. If the plot for the distribution of early participants is higher (as measured with respect to the household head s education), then this would suggest that regardless of when a program begins, able people are the first to join the program. Figure 2 controls for village-level fixed effects and shows a Lowess smoothed plot of log education of the household head (adjusted for differences in average schooling) and the lag between program availability and time of joining (separately for the two groups of villages mentioned above). The lag variable (plotted along the x-axis) is the gap between the time the program was set up in the village, and the time that a particular household in that village became a member. Figure 3 is a clearer view of Figure 2, and shows the data for participants who joined within the first three and a half years (lag 3.5) of the program s operation in the two groups of villages mentioned above. From Figures 2 and 3, it is evident that there is no consistent pattern in the data to support the claim that high ability people always join first. Thus diminishing returns to consumption smoothing

19 Grameen Bank Programs 1397 Figure 2. Lag between program availability and joining versus household head s schooling in Grameen Thanas Figure 3. Lag between program availability and joining versus household head s schooling in Grameen Thanas

20 1398 N. Menon benefits for experienced members are not being driven by the fact that earlier cohorts of participants were more able. Robustness Check for Length of Membership In order to ensure that results are being driven by length of membership as opposed to just participation, several tests were conducted. A dummy for participation was introduced into the model of Equation (7). With control for participation, both length of membership and the dummy for participation become insignificant. When the model is estimated with only the participation dummy, its effect is insignificant. Hence, results are being driven by the length of membership variable and not by participation alone. VII. Conclusion and Policy Implications This paper examines the presence of non-linearities in consumption smoothing benefits for experienced participants of micro-lending programs. A fixed effects nonlinear least squares estimation of data from 24 villages of the Grameen Bank suggests that returns to membership do vary by length of participation. Estimates from pooled and gender-stratified models indicate that the maximum dampening effect on seasonal shocks occurs at about two years of participation. This suggests that after approximately four years of participation, length of membership has a weak mitigating influence on per capita consumption fluctuations caused by seasonal shocks. A section of the paper is devoted to conducting various robustness checks. Our results remain unaltered. Although this study does not directly link repayment rates to length of membership and the ability to smooth seasonal shocks, declining consumptionsmoothing returns may provide a possible explanation for why more experienced members miss installments on outstanding loans (anecdotal evidence suggests that this is the case). If marginal returns to membership decline over time in the program, then experienced participants benefit (where benefits are solely measured in terms of the ability to smooth seasonal shocks) to a lower extent than those who have recently joined. If such returns drive self-selection into these programs (Pitt and Khandker (2002) show that consumption poverty in the lean season motivates self-selection into these programs), then missed payments may result when marginal returns begin to decline. Again, there could be several reasons for why experienced members choose to skip installments, and given the analysis here, we cannot say that declining returns are the only reason for this phenomenon. However, we suggest that smaller consumption smoothing benefits over time could provide one possible explanation. The results of this research have important implications for program structuring. In order to avoid strategic behavior over time, the lending and repayment terms for experienced members may need to be different (as compared to those for less experienced members). Eligibility to join these program (wealth status) and to remain a participant needs to be re-evaluated at regular intervals, instead of just once at the very beginning as is now the practice. Although smaller benefits over time may signal that micro-finance programs are succeeding in making their clients

21 Grameen Bank Programs 1399 self-sufficient, recognition of the fact that the nature of participants changes over time will help these programs become more cost-effective in the future. Acknowledgements I am indebted to Mark Pitt, Andrew Foster, Moshe Buchinsky, Shahid Khandker, Faruq Iqbal, Jonathan Morduch, Rachel McCulloch, Gary Jefferson, and Narayanan Subramanian. Thanks a1so to seminar participants at Brown, Georgetown, The World Bank, and Brandeis University. I am grateful to two anonymous referees whose comments have greatly improved the paper. Support from the Hewlett foundation is acknowledged. I am responsible for all errors that remain. Notes 1. As noted before, given a poor household s inability to cope with either kind of shock, the model does not differentiate between the effects of exogenous unforeseen shocks and anticipated shocks from seasonality. 2. Note that for those households that face a below average cost of borrowing, (r ijt r jt ) may be negative. This is not problematic here since there are practically no such households in these data. 3. Length of membership is not endogenous due to drop out rates. In these data, only two households are reported to have dropped out of the program between the first and third rounds. 4. We estimate fixed effect parameters for all 24 Grameen villages by excluding the constant term from the model. 5. The positive sign on the price variable indicates that the demand for rice and wheat are relatively inelastic. This is not unexpected since rice and wheat are staple food grains in Bangladesh. 6. The model thus becomes: Dln C ijtþ1 ¼ e ditþ1dijtþ1þd2tþ1d2 ijtþ1 þb CX C ijtþ1 m C jtþ1 þ d 3tþ1D ijtþ1 þ d 4tþ1 D 2 ijtþ1 þ g 2Dln P jtþ1 þ n ijtþ1 7. As noted above, when we estimate each set of inter-seasonal consumption changes separately, length of participation in Season 3 does not have significant effects in reducing consumption fluctuations between Seasons 3 and In the absence of land ownership, only those households whose assets are less than or equal to the value of one acre of medium quality land in that area are eligible to participate. References Chowdhury, O. H. (1992) Credit in rural Bangladesh, Asian Economic Review, 34(2). Copestake, J., Bhalotra, S. and Johnson, S. (200l) Assessing the impact of Microcredit: a Zambian case study, Journal of Development Studies, 37(4), pp Dadhich, C. L. (197l) Willful default of co-operative credit in Rajasthan, Indian Journal of Agricultural Economics, 26(4), pp Flavin, M. (1981) The adjustment of consumption to changing expectations about future income, Journal of Political Economy, 89(5), pp Foster, A. D. (1995) Prices, credit markets and child growth in low-income rural Areas, Economic Journal, 105(430), pp Iqbal, F. (1988) The determinants of moneylender interest rates: evidence from rural India, Journal of Development Studies, 24(3), pp Khandker, S., Samad, H. and Khan, Z. (1998) Income and employment effects of micro-credit programs: village-level evidence from Bangladesh, Journal of Development Studies, 35(2), pp Lawrance, E. (1991) Poverty and the rate of time preference: evidence from panel data, Journal of Political Economy, 99(1), pp