which selection is based. E.g. unobserved household characteristics such as entrepreneurial abilities, which may condition credit demand, may change over time depending on previous exposure to microfinance credit. Under these conditions, a more robust specification is required to remedy bias in the parameter estimates of interest. A more robust specification due to Heckman and Hotz (1989)- the individual-specific trend model- allows both household specific time-invariant unobservables and individual trends of time-varying unobservables to correlate with program participation (Wooldridge, 2002: 315). This model, also used by Papke (1994) to study the effect of nonrandom enterprise zone designation on unemployment and investment, is specified as: itiiitititutgMprogXC++++=αγβ(3)where gi is an individual trend parameter, which in addition to the level effect Mi,captures individual-specific growth rates over time. A consistent estimate for γ, viz. the treatment effect of borrowing, can be obtained by wiping out the time-varying unobservables and the trend in time-invariant unobservables that can potentially bias γ(Wooldridge, 2002: 315). First, eq. (3) is first-differenced to eliminate Mi, which gives a standard fixed-effects model: itiitititu~g~g~proX~C~+++=γβt=1,2,…,T (4) where 1itititCCC~−−=, 1itititXXX~−−=, 1ititituuu~−−=and )1t(gtgg~iii−−=. Second, eq. (4) is consistently estimated using a standard fixed-effects approach, i.e. using a within transformation or by differencing the equation (again) to eliminate gi and then estimate by OLS. The latter is preferred if uitafter the first differencing cannot be assumed white noise but at the cost of losing one period information in each transformation (Wooldridge, 2002: 316). Note that γcan be estimated consistently from this specification only if T > 3. In short panels
Evaluating the long-run impact of microfinance 80like ours, it may be reasonable to assume uitto be serially uncorrelated after first-differencing. However, using a second differencing transformation has an extra advantage of not assuming homoskedasticity of the first-difference of uit(Wooldridge, 2002:316). We therefore second-difference eq. (4) and estimate by pooled OLS. Although we only have four rounds of panel data, still our data covers a period of ten years. An advantage of panel data covering a longer period is that it enables to estimate the impact from long-term rather than one-shot program participation. Repeated participation may, in addition to shifting the levels in each borrowing year, affect the rate of change of the outcome variables relative to nonparticipation. Following Papke (1994) and Friedberg (1998), we account for this by including progit·tin eq. (4): itiiit2it1ititutgMtprogprogXC+++⋅++=αγγβ(5) This specification provides impact estimates robust to random periodical changes by allowing the individual-specific trend to vary on participation over time. Estimation follows the same procedures as in eq. (4).