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Saving Patterns and Probability of … 12 In converting this theoretical relationship into an econometric equation, consider the conditional probability of Prob=1 to depend on a function of the above-mentioned explanatory variables as shown in equation 1: Pr( Prob = 1 I, M , N, L , P, βi ) = 1− F( −( I, M , N, L , P), βi) J J (1) where β s are unknown parameters and F is the functional form of the relationship (i.e., the type i of the binary model). One of the most commonly used functional forms in the specification of a binary equation is the Logit model, which is based upon a cumulative distribution model for logistic distribution. 11 Due to the popularity of this functional form, the Logit model was used to estimate the parameters in equation (1). Our main task, to recap, is to measure the probability of success in completing savings based on values of the explanatory variables. The results from estimation of this model are shown in Table 4. 12 Reviewing the numbers reported in this table shows that all parameters have the expected signs and are all statistically significant at the 0.01% level. The results suggest that the probability of participants’ success in completing savings is directly related to the number of months since opening account and average amount of deposit during each visit to the bank. 13 Further, type of the program (i.e., microenterprise or homeownership) has a significant impact on the probability of success with the microenterprise savers standing a better chance of success in light of their lower savings limit. Obviously, active savers, as measured by the (L/J) ratio, have a much higher chance of success in terms of reaching their savings limit. 12
Saving Patterns and Probability of … 13 Last but not least, the results from Table 4 suggest that, ceteris paribus, people with a higher deposit frequency have a higher probability of completing savings. This finding is significant. On the one hand, if we assume that effective case management helps establish a regular saving pattern for IDA savers, then it could be argued that by providing the proper structure, IDA programs will have a net positive impact on accumulation of savings for low-income households. On the other hand, controlling for all other variables, if there is a positive association between saving regularity and the probability of completing savings, then providing proper incentives to reward regularity, would help reduce attrition rates across IDA programs. The implications of this result for program cost analysis and scale considerations could be the subject of a future study. Since in a logit model the estimated parameter values do not represent the marginal impacts of their respective variables, graphical techniques are utilized to show how changes in one variable can impact the overall probability of success while other variables in the model are held at their average levels, or any other constant level, for that matter. 14 In this respect, Figure 1 shows the relationship between probability of success in homeownership IDAs and deposits ratio for all active participants who stay in the program for 24 months while their amount of deposit per bank visit is measured at the average level for the entire sample. Simple inspection of the graph suggests that there is a 90% chance for participants to complete savings in 24 months if they visit the bank (i.e., make a deposit) on average more than 2 times per quarter (or at a deposit ratio of 0.8). Similarly, there is an 80% chance of success for people who visit the bank only 7 times in a year. The implications of this relationship for a study of attrition rates are noteworthy. For example, in Table 3, the average deposit ratio for the UWGLA’s homeownership IDA program 13
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