Abhijit and Esther very graciously agreed to reply to Monday’s review  of their book. Here is their reply, followed by a couple of additional thoughts from me.
First of all, thanks for this thoughtful review of our book. We think you captured the spirit of the exercise quite well: our intent is to go beyond individual results from particular study to weave a coherent story of how the poor live their lives, and what this implies for policy. Further, we see this as the beginning of a conversation, so we don’t expect that everyone will agree with every bit of what we have to say. These kinds of comments are precisely where we should start from.
Still, it is interesting that we seem to slightly disagree on the interpretation of your own paper! But nevertheless, it is worth trying clarifying where our interpretation came from.
We insist on two key results in your fascinating study with De Mel and Woodruff. First of all, almost all the money was invested when people got the 10,000 rupees grant, and profit increased a lot in this treatment. The rate of returns to capital is very high for small injection of money, and people clearly take advantage of it.
Second, however, the increase in profit in the “20,000 cash rupees” treatment are actually LOWER than the profit under the “10,000 rupees treatment” (1421 vs 775). You cannot reject equality of the two treatments, but it is quite striking that the profits are not significantly higher when you give people twice the amount of capital. You can reject a point estimate of 2035 rupees (or a linear effect of amount given on profit). The reason why it is not rejected in the following table is that cash and kind are pooled: But are our point is that people may chose to invest differently small and large amount of money, and the cash treatment mixes that up.
It is correct that you cannot reject linearity in your IV estimate, but as you point out, you cannot reject much.
How does that square with the fact that there are many firms in the world with a capital stock of a million or even a billion rupees—if returns are already falling at 10000, wouldn’t they have fallen to unacceptably low levels by the time we get up to a million?
There are two possible resolutions to this conundrum and both probably have some truth to them. One is that the people who run the big firms are just different—no micro entrepreneur has the capacity to run one of those firms. The alternative, less pessimistic, view is that there are some micro entrepreneurs who have the capacity to run a large business, but to get there they would need to start by investing in a very different technology which would cost them many times what they can currently afford. Technological upgrading is a way to postpone the onset of diminishing returns but it is expensive and most people cannot get there.
This kind of “discreteness” in the technology is very hard to detect with the kind of data you mention for two reasons: you don’t observe many transitions from one technology to the other, for the simple reason that most people who can afford the better and more expensive technology go there directly, and most of the rest never managed to get up there. Second our guess is that it is simply outside the range of capital values that these studies consider.
However the idea of a minimum efficient scale for modern high-quality technologies is widely accepted in the IO literature based on studies of firm size distributions etc.
Here’s a couple of follow-up thoughts from me (David):
Here is the table that Abhijit and Esther refer to– the numbers they refer to are those from the cash treatment in column (3).
Note however that (i) the point estimates in column (3) are much higher from the 20,000 treatment than the 10,000 treatment when the capital is given in-kind – i.e. when we know it goes into the business to start with. So this is not so consistent with returns diminishing; and (ii) in column (4), when we use log profits rather than levels of profits, the cash treatment does have higher returns with 20,000 than 10,000. This was my first experiment, and we were over-optimistic on how much power we would have to distinguish between these four sub-treatments – this discussion points to the difficulty in interpreting too much on the sub-treatment level from this study – we get most of the results from pooling the different treatments together.
On their second point of whether discreteness of investment matters for whether to invest in really large businesses or not, I agree that the data from our studies or others like it are non-informative. But I don’t think this matters so much for discussions about poverty traps – we want to know whether people can get from under $1.25/day to above this, which is a different question than why don’t microenterprises often grow into giant firms. Banerjee and Duflo’s book certainly offers a lot of rich ideas for further research to explore these issues further.
Anyone else have comments on the book or on these issues?