The contribution of this paper is a model of how growth and wage inequality can be co-determined in equilibrium. The model is studied in both closed economy and international trade settings. We will focus on the closed economy description of the model and briefly mention the implications of having two copies of this economy interact in labor and product markets.

Model

Environment

Infinite horizon, discrete time. One country that operates two sectors: research (idea creation) and production (idea using). There is free entry into both sectors.

There is a mass of N individuals, indexed by their ability levels. Individuals have log preferences over consumption and share a common discount rate.

Consumption goods are constructed by using a CES aggregation technology over a set of differentiated intermediate goods.

Each intermediate good is produced by a single firm. Firms are distinguished by their productivity levels. Firms can hire labor of all types production technology where output is the integral over all worker types of labor hired of each type times a productivity that depends on worker type and firm productivity. The authors make assumptions on this join productivity terms so that there is positive assortative matching between firm productivity and the type of worker it chooses to hire. Higher productivity firms hire higher ability workers and pay a higher wage.

Intermediate goods are sold to the final goods producer in monopolistically competitive markets.

Intermediate goods are produced using differentiated blueprints. These blueprints are the output of research performed by entrepreneurs. When an entrepreneur considers a new project, they don’t know the quality of the project. They first rent capital, then observe the quality of their project, then hire workers to carry out the project and pays these workers the equilibrium wage for their ability level. In the economy, there is a stock of knowledge that is the mass of all variety types previously discovered multiplied by a parameter that indexes how effective the country is at using knowledge from other varieties. This parameter is important – we’ll come back to it soon.

The output of research firms is a mass of blueprints (new varieties) equal to the knowledge stock times an integral over all worker types of mass of labor hired of each type times a productivity that depends on worker type and project quality. There are assumptions on this productivity that ensure positive assortative matching in the research sector. Furthermore the productivity functions ensure that the highest quality workers optimally choose to work at a research lab instead of in production.

Manufacturing goods purchase the blueprints as an equilibrium price.

Equilibrium

Wages Each firm (in either sector) will optimally hire a single type of worker. The equilibrium wage will be determined by the productivity of the wage-firm match. The wage as a function of ability inherits the shape of the equilibriums productivity as a function fo ability (it is increasing).

Worker sorting The positive assortative matching within sectors and preference for higher ability types to choose research jobs introduces a cutoff ability level, above which all agents choose to do research. Once this cutoff level is determined, there is a system of coupled differential equations that gives the equilibrium mass of workers of each type hired by each production and research firm as well as the equilibrium wage function.

Wage inequality because higher ability agents choose research, and wage increases with worker ability – the ability for a country to utilize the knowledge stock is critical in determining wage inequality. All other things being equal, a country that is more effective at utilizing the knowledge stock will have higher growth rates (because more varieties can be discovered for the same level of inputs), but also have higher wage inequality.

Open economy

Let’s now turn to the open economy setting. Here the authors assume that there is a finite number of countries, each of which can differ in their research productivity, manufacturing technologies, and the ability to create and absorb international knowledge spillovers. Intermediate goods can be traded with no costs.

Labor for research and manufacturing is hired within each country. The knowledge stock in each country is a weighted sum of the mass of variety types in each country, where weights vary for each pair of countries. A weight of less than one means there is partial knowledge spillover between two countries.

When at least some of these weights are positive, each country is more effective at absorbing global knowledge than they were in closed economy model. This makes all researchers in the country more effective at producing new varieties, lowering the cutoff ability level for someone to be a researcher. From here the effect described above takes over and there is faster growth and more income inequality.

Consider an alternative setting where intermediate goods are still freely tradable, but now all cross-country knowledge spillover is eliminated (those weights zero for all countries except self). Here the result is that consumption, output, and wages grow faster than in the closed economy setting (because CES final goods means countries are variety loving and open trade allows more varieties). However, the innovation rate and wage inequality are exactly the same as in the closed economy model.

This shows a main result: in their setting increases wage inequality as the economy opens up is not driven by free trade of goods, but rather by knowledge spillovers.