Regional external economies and economic growth under asymmetry.

• Author: Holod, Dmytro

1. Introduction

   Much research in macroeconomics has studied the various factors responsible for promoting economic development. As has been emphasized by a number of economists, one of the most important sources of economic growth is the continued accumulation of knowledge. In particular, Lucas (1988) demonstrates that external effects of human capital may be responsible for accelerating a country's rate of growth. In addition, recent evidence finds that spillovers of knowledge flow across countries. (1) Consequently, it is important to consider the impact of both local and regional external economies on economic growth. However, despite their potentially significant influence, most models have failed to address how regional considerations affect the process of development. (2)

   Furthermore, because of the exogenous savings rate, the model has limited implications for policy coordination across locations. See also Tamura (1991).

   The objective of this article is to incorporate the impact of neighboring economic activity on a country's rate of development in an endogenous growth model. (3) This is accomplished by introducing spillovers of knowledge across locations into the Lucas (1988) model of economic growth. In contrast to Lucas, we consider an economy with two different countries. We allow for the extent of spillovers both within and across countries to vary between the home and foreign economies.

   There are a number of plausible reasons for such asymmetries. To begin, the transmission of information within a country is likely to be affected by the strength of intellectual property rights. For example, Matutes, Regibeau, and Rockett (1996) explain that patent policies promote the diffusion of knowledge but also protect innovative activity. Hopenhayn and Mitchell (2001) study optimal patent design through the breadth of patent protection, along with the length of time that innovators are protected. (4) In contrast, Lee and Mansfield (1996) discuss how differences in intellectual property rights across countries affect their ability to attract foreign direct investment.

   Furthermore, the diffusion of knowledge within a country is related to the extent of labor mobility. In particular, Franco and Filson (2006) point out that many new firms are established by hiring employees from existing firms. These employees transfer their human capital to new employers. As a result, labor market policies that promote labor mobility within a country, such as unemployment insurance, enhance the transmission of ideas.

   Finally, the transmission of information across borders is affected by a country's degree of openness to international markets. Notably, Coe, Helpman, and Hoffmaister (1997) find that developing countries experience more productivity growth by trading with countries that have a large amount of research-and-development activity. In contrast, Miller and Upadhyay (2000) emphasize that export activity is the key to raising productivity they conclude that countries that are more export oriented (a higher ratio of exports to gross domestic product) have higher levels of total factor productivity. Along these lines, Ederington and McCalman (2008) demonstrate that exporting countries are more productive because they have higher rates of technological adoption. In addition, Miyagiwa and Ohno (1995) contend that countries with more trade protection are slower to adopt new technologies.

   Our benchmark model consists of a world in which there are two countries: home and foreign. The framework includes both local and regional external economies in the production of final output. We show that knowledge spillovers from the foreign country unambiguously raise productivity in the home country and therefore contribute to higher rates of progress. In contrast, spillovers within the home country may adversely affect growth in the presence of substantial knowledge flows from the foreign country. (5) Although the transmission of ideas across borders to the home country raises domestic productivity, it also discourages the accumulation of knowledge at home because individuals can free-ride on foreign ideas.

   The framework also allows us to examine the impact of an increase in spillovers within the foreign economy on growth at home. As expected, an increase in the diffusion of knowledge within the borders of the foreign country weakens the incentives of foreign individuals to acquire human capital. Because agents at home rely on foreign knowledge, the domestic rate of growth suffers.

   Moreover, there are interesting insights if there are cross-country spillovers in both directions. In particular, if spillovers from home to the foreign country increase, the domestic growth rate will be lower. That is, the home country is worse off if it promotes the diffusion of knowledge to foreign agents. The mechanism is similar to the impact of spillovers within the foreign country--as knowledge to the foreign country is transferred more easily, the incentives to accumulate human capital in the foreign country decline. Since individuals in the home country utilize foreign knowledge, domestic productivity falls.

   The analysis from our benchmark structure yields novel insights for policies designed to affect the diffusion of knowledge. According to the standard, closed-economy Lucas (1988) model, an increase in domestic spillovers would unambiguously contribute to economic growth. From this perspective, strong protection of intellectual property rights would adversely affect development. In contrast, in our framework, protecting home property rights may stimulate productivity if the country is sufficiently open to inflows of knowledge from abroad. This is necessary in order to continue to provide individuals with incentives to develop new ideas. Furthermore, the home country benefits the most from trading with countries that also have strong intellectual property rights. Notably, this prediction mirrors the evidence from Coe, Helpman, and Hoffmaister (1997).

   We further recognize that spillovers may also occur in the production of human capital. Consequently, we extend the benchmark model to include spillovers in the human capital accumulation process. However, the results reinforce our previous insights--external economies that weaken the incentives to develop knowledge adversely affect an economy's rate of progress. Interestingly, externalities in human capital accumulation may not affect the stability properties of the economy's balanced growth path (BGP).

   Our analysis concludes by extending the benchmark model to look at migration decisions across countries. In the presence of asymmetries, growth in one country (the leader) will be higher than in the other. Although immigration restrictions could preclude individuals from taking advantage of differences in productivity across countries, limited amounts of natural resources, such as land, are also likely to affect location decisions. As a result, many individuals may decide to migrate to the country with a lower growth rate to take advantage of lower land prices and other forms of congestion costs.

   The article is organized as follows. Section 2 describes the benchmark model in which there are regional external economies in the production of final output. Section 3 extends the analysis to study the implications of external economies in the production of human capital. Section 4 investigates the stability properties of the BGP. Section 5 looks at the possibility of migration between the two countries. Section 6 concludes and provides additional extensions for future research. Proofs of major results are included in the Appendix.

2. The Benchmark Model

   We begin our investigation by incorporating regional external economies within the Lucas (1988) model of human capital and economic growth. That is, we initially consider that human capital spillovers affect productivity. In order to study the spatial aspects of knowledge transfers, there are two different locations in the economy. We refer to these locations as "country 1" and "country 2." Alternatively, country 1 may be viewed as the "home" country, while country 2 is the "foreign" country. In each location, individuals are endowed with some positive amount of country-specific knowledge. Agents in country 1 have an initial endowment of type 1 human capital but are born without any type 2 knowledge. As a result, we write [h.sub.1](O) > O, [h.sub.2](O) = 0. Similarly, for agents in the second country, we have [h.sub.2](O) > O, [h.sub.1](O) = 0. [H.sub.1](t)([H.sub.2](t)) represents the average stock of knowledge among agents in country 1(2).

   Production depends on labor input and physical capital. In particular, final output by type 1 agents is

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

   in which [u.sub.1](t) represents the fraction of time that individuals in country 1 devote to production. With the remaining amount of time, agents acquire additional human capital. In considering the effects of uncompensated knowledge spillovers, [[gamma].sub.1] represents the external effects of knowledge that take place within country 1, while [[gamma].sup.*.sub.1] describes the extent to which spillovers flow across borders from country 2. The same details apply to production in location 2:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   Interestingly, we allow for the degree of spillovers to vary across countries--external economies occur both within and across countries. That is, we study economies in which [[gamma].sub.1] [not equal to] [[gamma].sub.2] and [[gamma].sup.*.sub.1] and [[gamma].sup.*.sub.2] . There are a number of plausible reasons for such asymmetries. Notably, differences between [[gamma].sub.1] and [[gamma].sub.2] can represent institutional differences that affect the transmission of knowledge within each country. In particular, they may reflect different levels of intellectual property rights protection. Moreover, it is...