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How does migration affect development? Maybe the most obvious way is the money that migrants send home to poor countries: remittances. But for years, development researchers have faced a puzzle.

On one hand, our best estimates show soaring remittances to developing countries—over $400 billion last year, triple the value of all foreign aid. On the other hand, economists have a hard time detecting any effect of all that money on economic growth in the countries migrants come from.

How could that be? Remittances are more than 10% the size of the entire national economy in Nepal, Jordan, Nicaragua, Togo, and many other countries. That much money can’t just disappear.

In a new paper, David McKenzie of the World Bank and I propose three new reasons why economists can’t find a clear effect of remittances on economic growth. We believe they probably won’t be able to find it for a long time.

The first reason is explained in a companion post by David on the Development Impact blog. Suffice it to say that much of the growth in estimated remittances may be caused by changes in how official statistics record remittances, not by changes in how much money migrants are sending. It’s like trying to measure a child’s growth with a constantly shifting ruler.

We estimate that as much as 80% of recent sharp increases in remittance flows may arise from these accounting changes. Many of those changes relate to new regulations on the recording of international financial flows in the post-9/11 crackdown on terrorist finance. So an important reason that the huge growth in remittances seems to vanish in the mist is that real remittance flows didn’t actually change very much.

The second reason is about statistics. If you want to detect any effect in economic growth statistics, it’s a little like hearing a violin play during a windstorm: you have to separate the signal from the noise. It’s hard to do when the effect you seek is small (the violin plays softly) and the growth data are highly variable (the wind blows loudly). If you can’t detect the effect of remittances on growth, it’s too hasty to conclude there’s no effect at all. It could be that the effect is not large enough relative to the background statistical noise. In econ-speak, the test lacks power.

If one had infinite data one could detect an arbitrarily small effect. But macroeconomists have only a limited number of countries and years of data to work with. We show that the available number of countries and years is simply too limited to detect even substantial effects of remittances on growth that might exist, given the noise inherent in the growth data. It will be decades before enough additional data accumulate to make a big difference.

And the third reason is related to the second. We should expect the growth effects of remittances to be relatively small because increases in remittances are usually caused by something that has a negative effect on the size of the origin-country economy: increases in the departure of workers. When a worker departs country A to work in country B, that reduces country A’s GDP. The worker can in principle cause a countervailing rise in country A’s GDP if she sends enough money back, and if enough of that money is spent on domestically-produced goods and services. But the net effect need not always be positive—even when the gross flow of money back home is substantial.

In the paper we show this step-by-step in a numerical example. In that example, there is a rapid increase in a stock of migrants who each send home thousands of dollars a year. But that same increase in migrant stock means that those workers’ labor isn’t directly contributing to GDP in their home country. The straightforward net effect on incomes and expenditures at the home country may not raise GDP more than about a tenth of a percentage point each year. Changes that small get lost in the noise of cross-country statistics.

Nothing in the above suggests that remittances don’t have big, detectable effects of various kinds. They do have big effects—on things other than national GDP growth at the home country. For example, remittances do have important and easily measurable effects on poverty at the home country. David’s research has shown that they can affect recipient households more positively than most other development projects, and our colleague Dean Yang has rigorously measured substantial effects of remittances on households. Migration also has major and easily-measured economic effects on migrant workers themselves and on world GDP.

But any search for big effects of remittances on growth of the origin-country economy is likely to remain frustrating for a long time to come.