Making people richer

by paulfchristiano

Many interventions seem to have the effect of “making people richer.” In addition to understanding the long-run impacts of prosperity, I am interested in looking in more detail at what happens when you make someone richer, and looking at a few examples to understand whether the intuitive model of a small across-the-board increase in real income is reasonable.

As a first example, I’ll look at cash transfers in the developing world. I think very similar ideas are needed for the analysis of many interventions in the developing world (e.g. health interventions) and also for many interventions in the developed world (e.g. supporting self-driving cars). But it seems useful to first go through the analysis with a particular case in mind.

There are a number of reasons we might be interested in cash transfers to the poorest people, but I’m going to focus on the possibility that poverty alleviation is actually an effective investment in human capital, which allows the poor to invest in basic necessities, health and education, and capital which is complementary with their otherwise underutilized labor. These investments may be otherwise inaccessible to the very poor because they have such tight financial constraints. Meanwhile, even if these investments are extremely profitable they may be inaccessible for rich investors, because making loans to poor people in the developing world is quite difficult.

When I transfer $1 to a poor person who is positioned to make such an investment, society foregoes resources worth $1 to it today (this happens whenever I spend $1 on anything) but receives resources worth $2 to it tomorrow—the fruits of the recipient’s labor. So our question is: what is the social value of those resources? How much better does that production make the world? (“$2” is not the answer we are looking for.)

Effects of production

When thinking about the impact of producing $1 of good X (e.g. eggs for sale in my hometown), I think it is useful to instead consider the effects of a big change and then to scale those effects down. This suggests it is best to focus on the effects in the long run even when considering a temporary shock to productivity.

When I produce X, others will produce slightly less X, and everyone will consume slightly more X. The resources that would have been used to produce X can now be used to produce other goods, and the consumers who consume X reduce their consumption of substitutes for X. These effects ripple through the economy in a complicated way. The result is that society gets more of the economically optimal uses of the average inputs to producing X. In the very long run many different types of resources are fungible, and the effect is not too sensitive to exactly what X was. Moreover, as the process becomes increasingly uncertain, the effects become increasingly diffuse.

The outcome is that we get roughly $1 more of whatever it was that society demanded on the margin, with the changes only very roughly concentrated in areas that are “near” X.

I think that geography is probably the main way in which these effects are concentrated. If I make some extra eggs in a village in Malawi, then the effects will be most pronounced in that village, to a lesser extent in Malawi, and so on.

Geography seems to be a special case because (1) two different people who could produce the same good are often from the same location, especially in poorer areas, (2) the people who consume a good are often from the same location as those who produce it, and (3) two different goods consumed by the same person tend to be from the same location. I’m not aware of other notions of locality which are nearly this robust, and so I expect the effects of increased productivity to be geographically localized but not well-localized in other senses. For example,  if I make food I would expect the effect to bleed over to manufacturing or health care much more quickly, because the same labor and to a lesser extent the same capital can be used for different projects.

That said, I still expect that the effects will eventually bleed out from one locality into nearby localities, and eventually to spread throughout the world. The question is just how quickly this process occurs. To estimate timescales, it is once again useful to think about large sustained changes and ask how long it would take those changes to spill over to other areas. The effect of a temporary change is then comparable to the average effect of such a large sustained change, neglecting non-linear effects such as arbitrageurs, and will spread out throughout the world over a similar timescale. My guess is that the effects spread out over one to a few decades. But this is just based on vague intuitions. I expect economists know much more about this, and I’m sure there have been many natural experiments, but they are hard to track down and so I’ll leave that to a future post.

Effects of income

A second important effect of me producing $1 of good X is that I am now a dollar richer. This essentially amounts to another cash transfer. If I’m a pretty representative member of the population then this transfer won’t have a big effect. But if I’m a particularly good person to give money to (e.g. if I am the recipient of a cash transfer, and if the transfer didn’t “use up” all of my great investment opportunities) then the effect of the original transfer might be multiplied. How much it is multiplied by depends on what returns I earn, how I spend my money, and so on.

A suitable way to estimate the total effect of a transfer, which takes into account both the earned returns and reinvestment, is to look at its total effect on the consumption of the recipient. Looking at the evidence on cash transfers, I would guess that a transfer of $1 leads to $2-$8 of increased consumption.