Estimation and Identification

Identification of the impact of the February 2000 interest rate increase (from 2 percent per month to 3 percent per month) exploits the fact that the change occurred in Tikkapara and Kalyanpur branches, but not in Geneva Branch. Geneva had already started with an interest rate of 3 percent per month when it opened in March 1999.

Identification hinges on the presumed lack of correlation of the timing of the interest rate change with other events occurring in Tikkapara and Kalyanpur. Based on interviews with the bank, the timing of the switch seems to have been both arbitrary and unexpected.¹² Contemporaneous changes that occur in all three branches will be controlled for through the inclusion of data from Geneva branch and the estimation of baseline trends using those data.

This setup suggests a difference-in-difference estimator, although there is one feature that merits particular attention here. Unlike a situation in which customers move from one equilibrium to another with little else in the environment changing but the price, here customers are steadily building up savings and the capacity to borrow. New customers are also joining, and some older customers are beginning to depart. Because we have records for all customers, past and present, concern with attrition is limited here, but we pay close attention to the underlying upward trends in borrowing and saving. It is against those trends that we see a reduction of demand for borrowing. The net effect we will find is a slowing down in the rate of borrowing in the year following the interest rate increase.

The basic trends can be seen in Figure 4 [ PDF 161.4KB | 7 pages ], which gives average monthly loan balances in Geneva Branch versus Tikkapara and Kalyanpur combined. Since Geneva started only in March 1999, we find a steady rise from zero upward, whereas growth in the other two branches starts at a higher level and flattens in the middle of the period. The vertical line marks January 2000, the month prior to the interest rate increase. It is notable that in 1999 both groups have a similar, linear trend. This suggests that the differences-in-differences assumption is plausible. Hence, we begin with a simple difference-in-difference specification:

y_it = β₀ + β₁ Treated_i + β₂ Post_t + β₃ Treated_i*Post_t + ε_it  (1)

where: i indexes clients and t the month; y_it is the dependent variable (typically average monthly loan balances, but also an indicator for loans, amount loaned, and repayments); Treated_i takes on a value of 1 for individuals in Tikkapara and Kalyanpur and 0 for those in Geneva; and Postt refers to time periods after the interest rate increase. Hence, β₃ gives the impact of the interest rate increase: the change in borrowing before and after the interest rate increase in Tikkapara and Kalyanpur, relative to the contemporaneous change in Geneva.

We proceed to refine this estimation strategy along a number of dimensions. First, we control for borrower characteristics, including age and length of time in the program. Second, rather than simply controlling for time effects with a before-versusafter dummy, we include a full set of month-year dummies. Third, we include account fixed effects; this then controls for all non-time-varying differences among borrowers. Fourth, we allow for trend differences between the treated and comparison groups, in addition to a shift in the level of borrowing. Finally, the basic setup is expanded to consider the heterogeneity of responses (along dimensions such as gender, wealth, and age).

We extend these results with an alternative specification that uses knowledge of SafeSave’s product rules to control for credit supply. In particular, we use the exact formula used by SafeSave to determine and control for an individual’s maximum borrowing capacity. For example, in Tikkapara and Kalyanpur, borrowers are not allowed to borrow until they have been customers for at least two months and their savings have reached 500 taka (just under $10 in January 2000).¹³ At that point they can borrow their saving balance plus 1000 taka. The next time, they can increase the loan size by another 500 taka, and so on, without limit, adding another 500 taka to their credit limit with each successive cycle. (The exact rules are in the appendix.)

This is an important advantage of the data we are using because individuals might respond differently to changes in the interest rate based on their ability to borrow. For example, individuals with low (or zero) borrowing capacity cannot significantly respond to changes in interest rates. Since borrowing capacity hinges in part on savings behavior, and since savings behavior is likely to be jointly determined with borrowing, there is a fear that simultaneity and, possibly, omitted variables will bias the results. We thus instrument for capacity using the length of time the accountholder has been with the bank. Time in program is a valid instrument for capacity under three assumptions, all of which seem reasonable for our data: exogeneity (since time in program increases linearly it is unlikely to be correlated with simultaneous shocks to borrowing and saving), relevance (the longer individuals are in the program typically the more savings they accumulate), and exclusion (assuming we have correctly computed borrowing capacity, which is reasonable since we observe all the information that the bank does, then the only reason that time in program should affect borrowing is through savings and in turn capacity).

The views expressed in this paper are the views of the authors and do not necessarily reflect the views or policies of the Asian Development Bank Institute (ADBI), the Asian Development Bank (ADB), its Board of Directors, or the governments they represent. ADBI does not guarantee the accuracy of the data included in this paper and accepts no responsibility for any consequences of their use. Terminology used may not necessarily be consistent with ADB official terms..

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