Economic impact of a private sector micro-financing scheme in South Dakota

Please refer to the map of South Dakota (Fig. 1), which identifies both these counties.

The exponential intensity measure was divided by 10,000 to normalize the data and provide more accurate coefficients. Because the geometric intensity measure is, in essence, an interaction between logged loan values and the exponential intensity measure, it, too, was divided by 10,000 prior to the logarithmic transformation.

It assumes the geometric series form \( \sum_{n = i}^{k} {a_{n} \delta^{n} } \) where a _n represents the average loan in year n and within which δ ⁿ interacts with the impact of the programs intensity on the loan size progressively with time. We choose e for the δ ⁿ base and allow the exponent to assume increasing integer values with year n. Assuming a geometric form can yield certain advantages, one may derive under certain assumptions, for example, a mathematical relationship between the income over time (or perhaps income autocorrelation), loan values, and the program’s intensity measure. Assume that changes in average loan values can be absorbed by growth in the economy (e.g., more money finds a home on the reservation) and that the income response to a change in loan value is governed by a certain coefficient α, that the period of response is undefined, and that some degree of time-related correlation for income exists. For the above series, then, the sum as time period n approaches infinity is given simply by \( \frac{{a_{n} }}{1 - \delta } \), where \( a_{n} \) represents an average loan injection, and the impact of that summed effect on income over an undefined time period is \( \alpha \left( {\frac{{a_{n} }}{1 - \delta }} \right) \). In this form, δ becomes the ratio or rate at which the loan value a _n converges to its full effect. If one wishes to elicit the impact this ratio (or of the loan value given a certain base ratio) to income over time, one could equate income to the convergent sum and income of the previous period, ceteris paribus. This, then, takes the form \( y_{t + 1} = \alpha \left( {\frac{{a_{n} }}{1 - \delta }} \right) + y_{t} \). Moving y _t to the left side of the equation grants a regressive autocorrelation equation into which one could place a desired income level and thus derive criteria applicable for examining loan values and response rates. Solving separately for the loan value and for the convergence ratio provides equations for determining loan benchmarks necessary to achieve a targeted income over time and the required impulse response of the local economy to a given loan amount to achieve a desired income level, respectively: and

Please refer to the Data Appendix for complete description of the variables and respective sources. Also refer to footnote 3 for the specifics regarding computation of the variable PGMINT_GEO.