Uses of the Heterogenous Firms Theory

Helpman, Melitz and Rubenstein (2007) use the HFT model to generalize standard Gravity models. General gravity models link country incomes and transport costs as critical determinants of trade flows. Add to that language, religion, membership in an FTA– all of those affect trade costs, which have an effect on trade flows.Now, there is this new ‘family’ of models — the HFT. Basically, it adds an additional wrinkle to monopolistic competition and trade. Each country has firms which are different based on differing productivities. To trade, firms need to pay a higher fixed cost, as well as a transport cost, compared to domestic production. So, only higher productivity (lower cost) firms are able to trade.They incorporate HFT by doing a two step estimation procedure. The first step is a probit to understand how the determinants of the decision to trade. From this, they calculate two additional regressors to include in the second stage gravity. One, an inverse mills ratio that controls for a selection effect/covariance between distance and the second stage error. This selection effect can be understood as a countries’ selection into exporting, so using gravity equations fall under sample selection mispecification. Two, a control function that incorporates heterogenous firms effect on productivity of a country’s export sector as firms decide to export. Only productive firms in each country export, so exporting raises average productivity in a country.  These two additional controls lead to a lower effect of distance on trade volumes, and it also makes religion, FTA and language insignificant to trade volumes (in the second stage). They discover asymmetry among country pairs in the effects of the unobserved selection and firm heterogeneity on trade volumes. The fact there is clear, of course, from a cursory examination of the data — some countries have one directional relationship, and of those that do trade, it isn’t balanced. Whats new is that they have managed to ‘explain’ these assymetries based on heterogenous firm theory.Whats striking is the assymetries in trade distance elasticities between possible combinations of North and South trading partners. When a trading relationship is between rich trading partners, the trade distance elasticities are lower (on average for all country pairs fitting the description) than South-south trading partners. [1.29 vs 1.69]. 

Competition Among Public Schools III

Hoxby uses the number of streams in a metro area, because it determines the number of natural school district boundaries. When these boundaries were first drawn, travel time was the main consideration. Travelling over streams significantly affect travel time, so a place with more streams would have more districts.

As the first stage regression, she regresses C over Streams(in educational market m) as a function of Y and Z [both at the market level].

Lets discuss the Results.

Competition Among Public Schools II

The main empirical challenge is to have a good measure of choice, and to discuss whether it is endogenous (i.e. Cov(Choice, error) /=0)

Let me discuss endogeneity.

Competition Among Public Schools

For my Cross Section Econometrics exam, we have to answer questions on Caroline Hoxby’s “Does Competition Among Public Schools Benefit Students and Taxpayers”

What follows is a summary of this paper about theory and estimation issues. Another post will analyse the results.