Lee and Yi (2017) (Global Value Chains and Inequality with Endogenous Labor Supply)

The goal of this paper is to use the modeling concept of Global value chains to analyze the international impact of a lowering of trade costs.

Model

Most of the paper is about describing the model. It is too complicated to explain in full in just 5 minutes, so I will discuss some of the key features so we can understand the results.

The model is static.

There are N countries that are symmetric in technology, but will have different parameter values in the calibrated model.

Within each country there are a finite number of sectors.

Within each sector there is a continuum of final goods. Each final good is the output of a global value chain of length J. This means that each final good goes through J stages of production before becoming a final good. Stages can happen in any of the N countries.

Within each sector, the continuum of final goods within each sector is aggregated using a CES technology. Sector aggregates are combined via a Cobb Douglass technology. The output of Cobb-Douglass aggregator is used for household consumption or as an intermediate input in production.

The technology at each stage combines 4 inputs:

1. country-sector-stage idiosyncratic productivity
2. labor from O occupations,
3. the output of this good's previous stage,
4. the Cobb-Douglass aggregated good.

Labor is supplied by a continuum of workers that are of one of a finite number of types. Within each worker type, each worker has idiosyncratic productivity across occupations and sectors. Workers inelastically supply all their labor endowment to the sector and occupation that yields them the highest return.

The main outcome of the model is a nested system of comparative advantage. There is comparative advantage at the country level and the worker level.

At the country level, comparative advantage is driven by:

• Country-stage specific occupation weights in the production function
• Country-sector-stage distribution of productivity
• Country-stage weight on previous stage output
• Country-sector importance of the Cobb-Douglass aggregated good

At the worker level, comparative advantage is driven by:

• Type-sector-occupation distribution of productivity. This has two components:
  1. A type-sector-occupation component that captures between-worker-type comparative advantage
  2. A type specific component that captures within-worker-type variation in comparative advantage

My takeaway from the model section is that the model is very rich and if it can be estimated effectively, could shed some light on the structure of comparative advantage in the global economy as well as provide a laboratory through which we can study the network effects of changes in trade costs.

Calibration

... which brings me to the calibration.

They choose to calibrate a model with

• 5 worker types based on education
• 3 Countries: US, China, rest of world
• 5 occupations based on skill and routineness
• 2 production stages

They

• set some of the CES parameters exogenously
• Use the world input and output database to calibrate iceberg trade costs to match moments on aggregate trade flows by sector
• Estimate parameters of the worker productivity distribution using data from the American Consumer Survey for 2000
• Calibrate production parameters to match moments describing absorption of final and intermediate goods to similar moments in the data, computed from the world input output database for 200

In the end, their calibration suggests that China has a comparative advantage in manufacturing and stage two production, while the US has an advantage in high-skilled occupations in the services sector and stage one production.

Counter factual

With the calibrated model, they do a counter factual where trade costs between China and the US and between China and the rest of the world fall by 50%.

They report changes in the mass of sector-level aggregated goods that are entirely produced in one country. For China and the rest of the world, the mass of these goods falls sharply in all sectors. This indicates that lower trade costs allow for better sector-level specialization. On the other hand, for the US only manufacturing falls sharply while agriculture and mining fall by a small amount and services actually go up. The reason for these results is that the US already had a very strong comparative advantage in services, so it wasn't allocating many workers to agriculture or mining.

They also report changes in labor supply allocations across country, education level, and job type. They find in China, the movement for low educated workers is to move out of low skill jobs in services into low skill jobs in manufacturing. For highly educated workers the movement is from high skill jobs in services to high skill jobs in manufacturing. In the US the flows are a mirror: low education workers move from low skill jobs in manufacturing to low skill jobs in services and high education workers move from high skill jobs in manufacturing to high skill jobs in services.

In the end the results are quite predictable and in line with intuition. To me this is a positive as it helps me believe their very complicated model a little bit more.