Their paper highlighted that the returns to capital “at the bottom of the Pyramid” could be very large indeed. In their favorite specification they find that these could be as high as 50 – 63 % per year (in real terms). This suggests that these investments pay-off on average. It was one of the first papers that used experimentally generated variation in capital stocks to estimate these returns. Thats why it became so influential and the authors have a set of papers on Mexico and Ghana, performing similar estimates.

They point out that there is a lot of heterogeneity in the estimated treatment effects. In particular, they observe that for female entrepreneurs, there is virtually no (average) treatment effect. This and the reasons that could be underlying this observation are explored in a second paper.

We had a look at the De Mel et al (2008) data, which is available here. We essentially ran their regressions of (reported) real profits on the treatment dummy. However, we did this iteratively for each individual treated person, using the whole group of non-treated individuals as counterfactual. This allow us to get an estimate of the treatment effect for each individual treated.

From this, we get a distribution of treatment effect estimates. The average of this should be the treatment effect that De Mel et al (2008) report in their paper. And indeed it comes quite close. However, what we are intrigued by is the significant heterogeneity in the point estimates for the treatment effect for different individuals.

A key observation is that the treatment effects are very heterogeneous – the mass of enterprises who saw a drop in profits is almost as large as the mass of enterprises that saw a rise, however, some saw a very significant and large rise in real profits. The vertical line is the average of the treatment effect, which here, as we lumped the cash treatments together, is around 900 rupees.  The median treatment effect however, is only  332 rupees. Thats some food for thought.

This map displays the intensity of microfinance institution headquarter distribution across India. The data comes from the MIX Market.

The fact that many MFIs are clustered around in the south is highlighted quite strongly. What this graph does not take into account however, is their variable size. This is problematic and I agree that this needs further refinement, i.e. that the intensity takes into account how big an MFI is. However, I would conjecture that this merely makes the contrasts in such a map just stronger.

Microfinance Institutions across India

I dont think anybody has produced such a map before. In fact, I can do this for all institutions reporting data around the world, which may be interesting to see. Also, I already tried to make the size of the dot proportional to e.g. measures of real yield or color-coding the nearest neighborhood (say the neigbhouring districts) by the average loan sizes reported. Lots of things to do. Maybe thats something for the guys at MIX Market or for David Roodman who, I think has finished his open book.

The key difficulty was actually not in plotting the map (though it took some time), but in obtaining geo-data on where the headquarters of the microfinance institutions are located. I managed to obtain this data – though its not perfect – by making calls to the Google MAP API via a PHP script., basically using the following two functions:

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function ResponseToArray($response) {
 
	return json_decode($response,true);
}
 
function findLocation($string) {
 
	$url = "http://maps.google.com/maps/geo?q=".$string."&output=json&sensor=true_or_false&key=your_api_key";
 
	$raw = file_get_contents($url);
 
	$geodata = ResponseToArray($raw);
 
	$point = $geodata["Placemark"][0]["Point"]["coordinates"];
 
return $point;
 
}

The first one transforms the JSON return into an array and the latter, actually does the call. The variable $string should contain the actual paramters, such as the city and the zip code of where the institution is located.

Intercontinental Ballistic Microfinance from Kiva Microfunds on Vimeo.

On another note, I am going to try to do some more work with R on mapping data, trying out several packages:

• http://crantastic.org/packages/RgoogleMaps
• http://cran.r-project.org/web/packages/maps/index.html
• http://crantastic.org/packages/RgoogleMaps

I found working with ArcGIS way too clumsy…

Of course, London greeted me with a Sunny morning but it would end up hitting me hard with rain later that day. And that was after bad news from our advisors and supervisors that our work ok Kiva is most likely in vain as we would never really get it published in a really good journal.

So we will see, the other projects are still up and running, but I need to get an idea for a joan Market paper sometime soon. I am down for 2013/2014 as the prospective year. Just two more years to go, exciting but a bit scary as well.

In recent years, more and more institutions started to disclose data on lending methodology. There are three categories. First “Solidarity lending”. It is not 100% clear, but from the glossary of terms on the MIX market website, I assume it means classical joint liability lending groups (JL). The other categories are “Individual lending” (IL) and “Village Banking”. A lot of early theoretical work has focused on the role that joint liability group lending had in context of classical problems  of adverse selection, moral hazard and ex-post moral hazard (enforcement problems).

Though in 2002 Grameen officially abandoned explicit joint liability and other institutions, such as BancoSol seemed to follow. So one interesting question is, whether institutions are shifting away from Joint Liability groups towards more Individual lending, or whether our perceptions are biased because two popular institutions have abolished explicit joint liability.

It turns out that in the MIX data for the year 2009, we observe that joint liability lending is still very much present. The following table tells us however, that a lot of institutions seem to offer both individual liability as well as joint liability loan products.

Number of Institutions by their Lending Method

The institutions recorded as “No JL” and “No IL” are falling into the category of “Villagebanks”.

I think it is interesting to try to understand the patterns, why so many institutions use both joint liability groups and individual liability lending methods at the same time. Are there clear patterns as to when which method is predominantly used? Are for-profits more likely to use individual lending? What are the effects of competition?

Some very simple questions, which need yet to be answered.

But what actually makes a lender a loan shark? The focus has been primarily on the interest rates charged. Yunus suggests a rule of thumb:

The maximum interest rate should not exceed the cost of the fund — meaning the cost that is incurred by the bank to procure the money to lend — plus 15 percent of the fund. That 15 percent goes to cover operational costs and contribute to profit. In the case of Grameen Bank, the cost of fund is 10 percent. So, the maximum interest rate could be 25 percent. However, we charge 20 percent to the borrowers. The ideal “spread” between the cost of the fund and the lending rate should be close to 10 percent.

This rule of thumb proves to be overly simplistic. It basically imposes a cost-target for lenders, suggesting that operational costs should be covered by a markup of 15% on the cost of raising funds. It has been noted that many institutions fall short of such a rule of thumb.

The Reserve Bank of India has suggested a whole range of regulations regarding lending practicies, in particular it suggested a interest rate caps and lending caps. And it clearly tried to push their interlinkage lending program through self-help groups.

• MFIs should lend to an individual borrower only as a member of a JLG and should have the responsibility of ensuring that the borrower is not a member of another JLG.
• a borrower cannot be a member of more than one SHG/JLG.
• not more than two MFIs should lend to the same borrower
• maximal loan size of Rs 25,000, that too from a maximum of two MFIs – this effectively introduces a cap on lending
• There should be a “margin cap” of 10 % in respect of MFIs which have an outstanding loan portfolio at the beginning of the year of `100 crores and a “margin cap” of 12 % in respect of MFIs which have an outstanding loan portfolio at the beginning of the year of an amount not exceeding `100 crores. There should also be a cap of 24% on individual loans.

See the whole report by the RBI.

Clearly, there are certain things that need to change in the microfinance industry, following the problems in India and especially in Andhra Pradesh. But regulators need to be very careful about the type of regulations they impose. We have to remind ourselves that microfinance institutions such as SKS and Compartamos came into existence only through initial subsidies and donations.

Profits are important in markets, as they signal to competitors that entry can be worthwhile. If regulation essentially imposes a margin cap, I think that this entry decision may be distorted. A margin cap essentially protects the interests of incumbent firms. If the margin cap is too low, then investors may be not willing to finance the fixed costs of entry. And here, institutions like SKS and Compartamos had a historical advantage, as their entry was basically financed by donors and through subsidies, which did not have to be refinanced.

Hence, a margin cap could stop the markets to evolve in the dynamic way it has done so far. Clearly, high interest rates are by no means desirable, but if we believe that these interest rates can be a signal to other players that entry may be worthwhile, we should not distort this signal.

So what should regulation be primarily focused on? Transparency!

Financial literacy is typically very low in developing countries and the interest rates charged by institutions tend to not include other types of fees or security deposits. Any deposit basically represents a reduction in the effective loan size and implies an increase in the effective interest rate that is charged.

This is something where the RBI has pushed quite strongly, increasing transparency is very important. Not only for the borrowers who have to pay the interest rates and hidden additional charges, but also to donors and social investors. I started to have a look at interest rate data from MFTransparency, which is an NGO that tries to increase transparency of pricing of microfinance loans. On their website, around 200 institutions report data on their loan products and on the interest rates charged for each of the loan products. Typically, these include all additional fees, taxes and security deposits.

I try to have a closer look at this data, as e.g. Scott Gaul and David Roodman have already done. What is really exciting is to see whether there are systematic interest rate differences between for-profits and non-profits.

Banerjee, A., Duflo, E. (2003), Journal of Economic Growth, Vol , pp. 267-299.

Abstract
This paper describes the correlations between inequality and the growth rates in cross-country data. Using non-parametric methods, we show that the growth rate is an inverted U-shaped function of net changes in inequality: changes in inequality (in any direction) are associated with reduced growth in the next period. The estimated relationship is robust to variations in control variables and estimation methods. This inverted U-curve is consistent with a simple political economy model but it could also reflect the nature of measurement errors, and, in general, efforts to interpret this evidence causally run into difficult identification problems. We show that this non-linearity is sufficient to explain why previous estimates of the relationship between the level of inequality and growth are so different from one another.

The relationship from Macroeconomic Data between inequality and growth is disputed. Relatively good data on inequality comesfrom Deininger and Squire (1996). They have a cross-country panel on inequality measures.  Results from previous OLS  cross-sectional work typically found negative relationship between growth and inequality. Benhabib and Spiegel (1998), Forbes (2000) work with the panel and use fixed effects estimatation. They argue that previously omitted country specific effects biases OLS. Their fixed effect approach yields positive relationship between inequality and growth.

Barro (2000) on the other hand uses a 3SLS approach treating country-specific error terms finds no relationship. However, after breaking up sample into more homogeneous, rich and poor subsamples, he finds negative relationship for poor and positive relationship in rich country sample. Clearly a
causal interpretation of evidence not clear, as variations of inequality correlated with a range of unobservable factors associated with growth; observation of data without imposition of linear relationship eye opening; changes in inequality in either direction associated with lower growth rates; same for relationship between growth rates and inequality lagged by one period 
non-linearity may explain why different variants of linear model (OLS; fixed effects, random effects) have generated very different conclusions.

Read the rest…Inequality and Growth: What Can the Data Say?

1. It is easy to see that…
2. Obviously…
3. Immediate. *
4. …and the result follows.
5. As a result, we find that…
6. One easily verifies that…
7.  The proof is left to the reader. *
8. The proof is left as an exercise.*
9. ….and the X theorem completes the proof.
10.  Clearly…
11. It can be shown that…
12. Trivially…
13. The proof is standard. 
14.  …the rest of the proof follows the same line.
15. …by a trivial argument…

Found on Urch.com.

Assume

so we have a simple Solow model with no depreciation.

The steady state is:

and finally, since

The process of convergence to the fixed point can be depicted in the folloing little graph. The green curve depicts the capital accumulation equation, the red arrows depict the convergence to the fixed point.

Convergence to steady state in Solow model with Cobb-Douglas production

With competitive markets, it has to hold that the marginal value product of capital equals the interest rate, so:

Notice that this is indexed by time, i.e. the interest rate evolves as well. In a small open economy, the domestic interest rate has to equal the World interest rate , this is what will speed up convergence. If the economy is below its steady state, then the maginal returns to capital exceed the level of the world interest rate. This will induce capital to flow in and will immediately lead to convergence towards the steady state.

This will also imply that the GDP will be smaller than the GNP for some time.  This is because GDP is the market value of everything produced within a country; GNP is the value of what’s produced by a country’s residents, no matter where they live.

Due to the flow of capital from abroad into the domestic economy, GDP will immediately reach its steady state level , yet the benefits from this income, i.e. the marginal returns due not entirely accrue to the domestic investors, but will partly flow to foreign investors.

This logic allows us to write the evolution of domestically owned capital as:

Note that capital per-se will immediately jump to . However, only part of this capital is owned by domestic investors.

If is the initial level of domestically owned capital, then one period later it is:

This is out of the GDP per capita y^*, the proceeds of size accrue to foreign investors; so domestically we are left with income per capita of size . Out of this, a constant amout is saved and invested in new domestic capital. So we see slowly, how foreign capital is driven out and we will observe an equalization of GNP and GDP in the long run.

But how do capital markets help here

One may be inclined to argue that access to capital markets do not help, as the capital income just accrues to the foreign capital owners and individuals still have to accumulate their own domestic capital out of “mere sweat”.

However, we can show that even with this, domestically owned capital grows faster with capital markets than without. Hence, there is still a positive effect.

To see this we compare the evolution of domestically owned capital in both cases. With access to capital markets we have:

We can rewrite this using our Cobb-Douglas production function by substituting out   from earlier we get:

Compare this with the equation of motion in case we do not have capital markets:
.

You can already see here, that the previous converges faster, as enters linearly, whereas it enters concave in the autarchy one. To see it even more formal, you can linearlize the non-linear autharchy equation of motion around the steady state. However, the essence is caputured in the following graph, where the yellow arrows indicate the faster convergence of domestically owned capital to the steady state value.

Convergence of domestically owned capital to steady state in Solow model with capital markets

 So things to note: with capital markets, we will reach immediately the steady state level of GDP per capita. However, GNP will be smaller than GDP as some of the income accrues to foreign capital stock owners. In the long run, domestically owned capital stock converges to the steady state level. This occurs at a rate which is faster than if we do not have capital markets.

What is the intuition for this?

Essentially the reason is, that due to capital markets we move instantaneously to , hence, also the factor labor receives a higher renumeration. So aggregate domestic savings are also higher and thus, total investment in domestic capital stock is period by period larger as compared to autarchy. This explains the faster speed of convergence.