Timoshenko (2015) (Learning versus sunk costs explanations of export persistence)

This is a mostly empirical paper that tries to decompose exporter persistence into sunk cost and learning components.

Model

Let firms be indexed by i. Firms have two state variables: productivity z_i, t that follows an AR(1) process and export experience A_i, t. In A_i, t is the number of consecutive periods a firm has exported coming into period t.

Without microfoudations, Timoshenko assumes that per-period sales are the Melitz result, multiplied by a function g of export experience:

$S(z, A) = g(A) E P^{\sigma-1} \left( \frac{\sigma}{\sigma-1} \frac{\tau w}{\exp(z)} \right)^{1-\sigma}$

If a firm chooses to export, profits are given by π(z, A)=S(z, A)/σ less a sunk market-entry cost if A = 0. If a firm does not export, period profits are 0.

Timoshenko assumes that g(A) is increasing in A. She calls this the age-dependence (or learning) assumption and uses it to get empirical results later on.

Export decision problem has a policy rule characterized by a pair of cutoff productivities z_h > z_l: a exit threshold z_l(A) and an entry threshold z_h. Firms enter when they get a productivity draw above z_h. They continue to export until productivity falls below z_l(A). z_l(A) is a function of A because there is a hysteresis effect caused by $\frac{\partial g(A)}{\partial A} > 0$. z_h is not a function of A, because by definition of A we have A = 0 for all firms considering entry.

Empirics

Timoshenko then does some empirical work to try to tease out the importance of the g function on export sales and participation. Because there are sunk export costs in the model, she claims that considering both g and sunk costs isolates all learning effects into coefficients for g.

To do this she starts from her reduced form theoretical model to build an empirical model. She controls for firm characteristics like location, domestic sales, investment, labor and materials expenditures, capital stock, wage rate, productivity, etc. She also builds in plant specific random effects. The result is an system of estimable equations that effectively regress the export decision rule on firm characteristics, exporter age dummies, and other controls.

Aside

I don’t necessarily agree with her main claim. Without micro-foundations, g doesn’t say anything about learning specifically. As it is written g is a simply a mechanism that causes sales and profits to increase with exporter age. This could be learning, more efficient production, more efficient transporting of goods, exogenous rise in foreign demand, market penetration/firm reputation in foreign market, etc. You might make an argument that the efficiency angles are a subset of learning: firms are learning to be more efficient, but I believe separating different channels of learning is important.

Results

Using plant level data on Columbian firms in the 1980’s Timoshenko finds evidence that supports her age-dependence hypothesis. The findings are robust across industries. The punchline is that about ½ of the value of the state dependence parameter is attributed to sunk costs and about ½ is attributed to age-dependence. By state dependence I mean the impact of yesterday’s export status on today’s export decision.