Quotas in General Equilibrium

David Baqaee and Kunal Sangani’s new working paper, “Quotas in General Equilibrium”, is one of the more exciting theory papers I have ever seen. The standard approach to modeling distortions is to treat it as a tax, which produces a “wedge” away from the optimal quantity. To take an example I am familiar with, in Hsieh and Klenow (2009) they model distortions as if companies faced different costs to borrow than each other, with this being equivalent to an increase or decrease in the price of capital. In this world, firms which are otherwise identical will be too small or too large, and there are gains possible from reallocating within the industry.

Distortions often come from quotas, however, rather than from taxes or things akin to taxes. With this, the allocation of resources within an industry is efficient, it just isn’t producing enough. What this allows us to do is greatly simplify the necessary facts to find in order to quantify the gains from changing the policy.

We can think about this in a simple monopoly model with a downward sloping demand curve. A monopolist, in order to get excess profits, has to reduce their output in order to price farther up the demand curve. Thus, if a quota leads to positive profits, it is because it reduced output below optimal. If profits are zero, then the quota is not actually binding anyone, and removing it has no impact on society. Note that the profits of a monopolist is a negative quadratic curve, so you do need total firm sales to be able to say how important the distortion is.

This is much simpler to estimate than a world of tax based wedges. Suppose that there is a productivity shock to one sector. In the world of tax distortions, we cannot actually know the net effect without knowing how it affects the whole system, and there is no guarantee the effects are positive. With quotas, you know that removing the distortion is always better than the alternative, no matter what, and you can even get the size of the effects

They then demonstrate how this method can be used in a variety of contexts, including zoning. Presented below is their estimate of the efficiency gains from one (1) unit of single family housing, including $350,000 in value just from unit of single family housing in San Francisco.

They’re also able to show that doubling the number of H-1B visas (a year where they have convenient data for estimating profits) would have increased world output by $1.07B, and US output by 2.7B.

Note that their estimates are bound to be underestimates of the true gains, because they assume away lobbying. The money spent advocating for a quota is pure waste, so getting rid of the possibility of setting a quota at all.

I’m extremely excited by the simplicity of their method. Previous estimates of the effects of distortions required extensive knowledge of input-output tables, which many places will not have and in any event can’t be trusted to stay the same over time. Boiling down the effects to profits over sales is incredibly easy to find.