Alessandria2014 (Trade adjustment dynamics and the welfare gains from trade)

Model

This is a general equilibrium trade model that focuses on producer export, entry, expansion, and exit. The structure of the model nests other standard models such as Krugman, Melitz and others.

In the model there are two symmetric countries. Within each country there are consumers, final goods producers, intermediate goods producers, and a government.

Consumers

• A unit mass of identical consumers live in each country and inelastically supple one unit of labor
• Choose sequences of capital, risk free one period bond holdings, and consumption to maximize expected present discounted value of CRRA utility over consumption.

Final Goods Producers

• The final goods producers combine home and foreign intermediate goods to produce a non-traded consumption good

Intermediate Goods Producers

Intermediate goods producers are the most interesting agents in the economy. Each producer is characterized by three state variables: technology level (z), iceberg costs (ξ), and fixed costs (f) and produces intermediate goods using capital, labor, and materials using a nested Cobb Douglass technology subject to TFP shocks.

The cost structure is discrete: fixed costs can be either low or high while iceberg costs can be one of three levels: low, high, or infinite.

A producer with infinite iceberg costs is a non-exporter. He can choose to pay no fixed cost and remain a non-exporter, or pay the high fixed cost and start the next period as an exporter with a high iceberg cost.

If a producer has either low or high iceberg costs, they can pay the low fixed cost to draw an iceberg cost for the next period. In the parameterization, the distribution is symmetric and places about 90% probability on staying with the same finite iceberg cost.

This structure nests other common models. If f_L < f_H, then there is a sunk cost to being an exporter. If f_L = f_H and ξ_L = ξ_H the export decision is static. If in addition the fixed costs are zero, then there is no export decision and the model is a generalized version of Krugman’s monopolistic competition.

Entry

Entrants pay a fixed cost to set up shop and cannot export in their first period. In equilibrium there is a free entry condition that determines the measure of entrants.

Aggregates

There is a government that collects export tariffs (calibrated to be 10%) and redistributes the proceeds lump sum to domestic consumers.

Equilibrium

Definition

An equilibrium is defined as allocations for consumers, intermediate good firms and final good firms in both countries as well as export decisions for intermediate good producers such that taking prices as given, the allocations are consistent with agent optimization, the free entry condition holds, market clearing and resource constraints hold.

Results

Two main calibrations:

1. Benchmark. Some features
   • Low fixed cost for becoming exporter relatively small (3.7% of the cost to enter as new firm)
   • Profits are back loaded: new exporters expect to run losses for at least the first 3 years
   • Iceberg transition matrix for exports is symmetric and the Markov process is very persistent.
   • Older exporters are typically more efficient (low iceberg cost). This provides an incentive to remain an exporter (don’t want to start over at high iceberg again)
2. Sunk cost model
   • Restricting the iceberg costs to be the same results in a sunk cost model
   • Entry cost vs continuation cost higher than in benchmark model
   • Profits are front loaded: exports pay a large cost up front, but expect to earn profits in their first period of exporting
   • Incentive to remain an exporter comes through a different channel: firms don’t want to pay large fixed cost again.

Experiments

The authors perform a number of experiments with different calibrations of the model.

Global Trade Liberalization: The first experiment is that tariffs are unexpectedly reduced to zero globally. The key features of the response to the new steady state are:

• Trade grows slowly and smoothly to a higher SS
• Consumption and output rise sharply and immediately, but follow a hump shaped path (overshoot new SS in early periods following policy change)
• Entry rate declines

They did the same experiment in the sunk cost model. Differing results were:

• Transition is much faster (after 3 periods trade growth 55% percent of long run value in benchmark model, but 90% in sunk cost model)
• Smaller welfare gain from policy change. Driven by stronger over shooting in consumption in benchmark model, which in turn is a driven by the fact that in sunk cost model new exporters export too large a share of aggregate exports. In the benchmark model new traders are less efficient, so they make up a smaller share of total trade

Also did a version where fixed costs are zero and iceberg costs constant (no export decision, no cost model). Differences in response to regime change are:

• Smaller welfare gain (relative to benchmark model) because consumption grows smoothly and doesn’t overshoot.
• This happens because The model without trade costs experiences smaller changes on the extensive margin than the model with costs.

References