However, it does not seem too early to theoretically investigate potential long-term effects of microcredit. Specifically, we study the long-term effects of microcredit on development, defined as output per capita, inequality and poverty. Nevertheless, we find that microcredit can increase or decrease long-term output per capita.
In summary, microcredit is modeled as a pure, if limited, improvement in the credit market.
Labor market equilibrium
All upper class agents take advantage of low wages to become entrepreneurs; all middle-class agents choose self-employment; and some of the lower class work in firms (nPtU) while the rest survive (PtL−nPtU). All upper-class agents become entrepreneurs, all lower-class agents and some middle-class agents become workers, and the rest of the middle class (1−(n+ 1)PtU) become self-employed.
3 Dynamics
Family dynamics
The graph depicts them as stuck in the lower class: given savings and interest rates, they can never accumulate enough to finance self-employment.22 The middle class are all self-employed. The graph depicts them remaining in the middle class if they earn normal returns, graduating to the upper class if they receive supernormal returns, and falling into the lower class if they receive below normal returns. Our assumptions about self-employment are flexible in allowing for transit in each class; the limitation is that normal (average) return guarantees staying in the middle class.
It limits "graduation" from the middle to upper class to those who achieve supernormal returns, ie. firstly, the underclass now earns wages equal to the expected payout from self-employment; we assume. Second, unlucky entrepreneurs face a high enough paycheck that they fall into the middle class.
There are wages so high that both lower and middle class families are transitioning into the upper class. The downside is that hapless entrepreneurs are now relegated to the lower class after paying the high wage bill. Our results would be equivalent if hapless entrepreneurs transitioned to the middle class - everyone earns the same high (expected) income regardless, and the dynamics would guarantee that the wage stays high if it ever gets high.
Aggregate dynamics
The wages of the middle class are unchanged, as they continue to choose self-employment or otherwise work for equivalent wages. In fact, the entire population runs or works in a business except for the self-employed middle class. Mobility also comes from active lower-class agents; at this wage they immediately move up to the middle class (hence the −PtL term in ˙PtL).
Active upper-class agents whose firms perform poorly now drop out of the upper class (hence the −πlEPtU term in ˙PtU). The first term in ˙PtU is because everyone who is not in the upper class goes there (1−PtU), because of the high wages. The second quarter reflects the fraction of unlucky entrepreneurs who fall to the lower class.
The first term in ˙PtL is because the lower class active agents are getting out; the second term includes the unfortunate entrepreneurs. The economy at any time t can be described by a point on the two-dimensional simplex (PtL, PtU); see Figure 3. This triangle is divided into three “regions” that correspond to the three equilibrium wages (see section 2.2).
4 Micro-Credit and long-run development
Dynamics with no graduation
Finally, economy SS clearly has higher poverty and inequality than the others, as the lower class earns v, the middle class earns ˆv, and the upper class earns ACCOUNT −nv. In particular, there is a critical line from the origin, with slope less than 1/n and thus lies in the v-region. Recall from section 2.1 that the introduction of microcredit is equivalent to a decrease in PtL reflected by an increase in PtM, with PtU unchanged.
First, microloans can affect few enough people to keep the economy in the v-region (pictured as a shift to SS). The only change in the economy is that the entities affected by microloans move from subsistence or wage labor to self-employment. However, the new and old Lorenz curves intersect, so the inequality is less clear; but the new generalized Lorenz curve dominates the old one.28 Second, microcredit can affect enough people, that is, improve the productive prospects of enough agents to raise the wage to ˆv (pictured as a shift to SS).
29Note that even ifπEl = 0, so that higher wages do not harm entrepreneurs' class transitions, development cannot be achieved. In summary, the introduction of microcredit reduces poverty and inequality (with exceptions under Lorenz dominance, but not under general Lorenz dominance, if it does not increase wages). However, microcredit may or may not increase overall income because it may reduce the use of the most productive, entrepreneurial technology if it is widespread enough.
Dynamics with winner graduation
- Dynamics with a large
- Dynamics with a small
Can microcredit bring an underdeveloped (low or medium wage) economy to full development. Although not a panacea, microcredit can have positive long-term effects.33 Economies that start in the shaded area of the thev region in Figure 4 will have their long-term outcomes altered. First, microcredit may affect few enough people that the economy remains in the shaded area of the v region (pictured as the shift from I to I).
Second, microcredit can influence enough people to move the economy out of the shadow zone (shift from I to I) and thus eventually into SS. On the positive side, micro-credit reduces the use of livelihood technology in favor of self-employment technology; on the negative side, it increases the wage and may decrease the use of entrepreneurial technology in the long run. Microcredit cannot bring about full development if it relies only on the graduation of the winner to move into the entrepreneurial class.
This means that it is not possible to raise the salary from v to ˆv without microcredit. Under these parameters, microcredit can leave an economy clearly disadvantaged in the long run. Thus, microcredit can worsen an economy in the long run if the autonomous technology it promotes generates supernormal returns much less often than subnormal returns (πhS πlS).
Dynamics with saver graduation
This allows the middle class to become so large relative to the lower class, while the upper class is still declining, that downward mobility from the middle class begins to dominate upward mobility into it from the lower class. At this point, the dynamics of the v region takes over and the steady state is in the upper right of the v region. The middle class is now divided into two subclasses, depending on whether one's wealth level is high enough to raise one's offspring into the upper class.
The upper class is growing due to the legacy of an active upper middle class, PtUM. The upper middle class grows due to the inheritance of the lower middle class (the term in parentheses) and declines due to the transition of its own members to the upper class. The lower class does not change, while the middle class gradually rises to the upper class.
The economy ends at the upper right arm of the v-region (if it starts in the shaded area of Figure 7) or passes into the ˆv-region.40. First, it is the exit of unfortunate entrepreneurs from the upper class due to higher wages. Second, it is not only the lower middle class that rises to the upper middle class, but also some from the lower class; see Figure 6.
5 Policy Implications and Conclusions
The assessment of microcredit in this case will involve comparing an economy in the ˆv region with one in the iv region, with results similar to those of the previous sections. One can show that the savings rate in the presence of a fixed rate tax τ on savings will be s = s/(1−τ). A microcredit institution can make use of its employee network, village organizational structures (e.g. groups) and geographical expansion to offer spare vehicles cost-effectively.
This model also supports a focus on graduation, which would ideally be incorporated into the incentives and evaluation of microcredit programs. At the institutional level, the programs could be evaluated in part by the number of their clients who have moved up from the microcredit sector. As an alternative to switching between credit institutions, microcredit institutions can commit themselves to their members for an indefinite period of time, provide ever-increasing loans and change the contractual terms if necessary.
However, the model suggests that graduation is not optional, and not simply an additional benefit of microcredit. Without significant graduation, microcredit can reduce overall income and even increase poverty in the long run. The model we analyze provides a rich basis for exploring different microcredit scenarios that differ in terms of initial conditions, amount of microcredit, and so on.
Endogenizing the capital and/or labor choices of the self-employed and entrepreneurs, and carrying out simulation with (even roughly) calibrated technology and preferred parameters,44 would be fruitful avenues.
A Proofs
This condition then guarantees that under ˆv- dynamics, PtU will reach the critical value 1/(n+ 1) in a finite time and v dynamics will take over. It remains to show that the trajectory through region ˆv never passes into region v; if it did, the dynamics would change and the above analysis would no longer apply. If PtL = 0, it is impossible to enter the region v, that is, to satisfy PtL> nPtU; we assume PtL>0.
Since PtL is decreasing, it requires that ˙PtU <0 and that|PP˙˙tUL to leave the ˆv region. Now consider a point in the ˆv region near the boundary of the v region, the line PtL = nPtU. This states that economies close to the frontier do not follow trajectories that allow exit from the ˆv region to the v region; that is, exit downwards is impossible.
