Trade and Growth with Heterogeneous Firms and Asymmetric Countries

By Takumi Naito (Vanderbilt University and Waseda University)

Trade liberalization encourages more productive firms to start exporting, while it forces more unproductive firms to exit from their domestic markets. The increase in the average productivity because of tougher selection contributes to higher welfare of countries. This idea, captured by the Melitz model of heterogeneous firms, has now become one of the standard principles of international economics.[1] However, the implications of liberalization-induced selection for countries’ growth was not explored until Richard Baldwin and Frédéric Robert-Nicoud (henceforth BRN) set up a two-country R&D-based endogenous growth model that embodies this underlying feature.[2] In the BRN model, trade liberalization has mixed effects on long-run growth: on the one hand, it allows knowledge to flow across borders more freely through trade in goods, which is good for growth; on the other hand, it makes it more difficult for a potential entrant to survive, which is bad for growth. The total growth effect of liberalization depends on the specification of R&D technologies.

Since BRN, many researchers have developed models of trade and growth with heterogeneous firms based on a common assumption: symmetric countries.[3] This is clearly unrealistic in the context of developing and developed countries: they are totally different in terms of endowments, preferences, and technologies. Not only that, the assumption also prevents us from studying the effects of policy shocks that are necessarily asymmetric across countries such as unilateral trade liberalization, regional trade agreements, and so on. To enlarge the scope of heterogeneous firm models of trade and growth for policy analysis, we have to extend them to allow for asymmetric countries.

In spite of the demand, there has been no successful attempt to deal with asymmetric countries in heterogeneous firms and endogenous growth settings. The problem is to evaluate an entrant’s future profits possibly growing at different rates across markets and over time, which makes it almost impossible for us to determine the entrant’s entry decision. How can we resolve the technical difficulty?

In a recent research project, which so far consists of two papers, I have provided two possible solutions to resolve this difficulty.  In the first paper, the solution I provide involves giving up the assumption that firms have an infinite horizon.[4] In my framework, each firm’s product life ends in each period, and they have to pay the initial and market entry costs every time they reenter their markets. By embedding the static Melitz framework in a two-country AK model (i.e., an endogenous growth model with constant returns to capital), I show that unilateral trade liberalization increases the numbers and revenue shares of exported varieties and the growth rates of all countries for all periods, and welfare of all countries, compared with the old balanced growth path (BGP), where all variables grow at constant rates. Intuitively, a country’s import liberalization directly encourages exports and domestic selection in the partner country, while it indirectly promotes exports and domestic selection in the liberalizing country through the decreased relative rental rate clearing its trade deficit.[5] More domestic selection implies the higher return to, and hence the growth rate of, capital. The greatest advantage of the model is the ability to describe the transitional dynamics caused by policy changes, distinguishing between the short- and long-run effects.

In the second paper of this project, the solution I provide involves giving up transitional dynamics in order to focus on a BGP in an asymmetric BRN model where firms do have infinite horizons.[6] Then we can still determine the relative number of varieties from the balanced growth condition, and also the relative wage from the balanced trade condition. It turns out that unilateral trade liberalization has similar selection effects to the first paper described above, and the symmetric BRN model: a country’s import liberalization encourages exports and domestic selection in both the partner and liberalizing countries. As a result, even unilateral trade liberalization can speed up global growth if it sufficiently facilitates international knowledge spillovers.

With the two solutions in hand, we are no longer restricted by the assumption of symmetric countries in endogenous growth models with heterogeneous firms. Our models are so flexible that they can be extended to study the effects of trade policies, domestic policies, or combinations thereof. For example, for governments of developing countries who depend heavily on import tariffs as a revenue source, it has been a serious concern how to design a domestic tax structure which recovers the revenue lost from trade liberalization. It will be interesting to see how such tariff and tax reform affects growth and welfare of developing and developed countries in a Melitz world. It should also be noted that the above two-country models can be extended to more than two countries, although the analysis will be much harder. This allows us to examine the effects of a regional trade agreement on member and nonmember countries. It is hoped that the papers will trigger applications of asymmetric heterogeneous firm models of trade and growth to more relevant policy issues.


Baldwin, R. E., and F. Robert-Nicoud (2008) “Trade and growth with heterogeneous firms,” Journal of International Economics 74(1), 21-34

Demidova, S., and A. Rodríguez-Clare (2013) “The simple analytics of the Melitz model in a small economy,” Journal of International Economics 90(2), 266-272

Felbermayr, G., B. Jung, and M. Larch (2013) “Optimal tariffs, retaliation, and the welfare loss from tariff wars in the Melitz model,” Journal of International Economics 89(1), 13-25

Gustafsson, P., and P. Segerstrom (2010) “Trade liberalization and productivity growth,” Review of International Economics 18(2), 207-228

Melitz, M. J. (2003) “The impact of trade on intra-industry reallocations and aggregate industry productivity,” Econometrica 71(6), 1695-725

Naito, T. (2017a) “An asymmetric Melitz model of trade and growth,” Economics Letters 158, 80-83

Naito, T. (2017b) “Growth and welfare effects of unilateral trade liberalization with heterogeneous firms and asymmetric countries,” Journal of International Economics 109, 167-173

Sampson, T. (2016) “Dynamic selection: an idea flows theory of entry, trade, and growth,” Quarterly Journal of Economics 131(1), 315-380


[1] Melitz (2003).

[2] Baldwin and Robert-Nicoud (2008)

[3] See, for example, Gustafsson and Segerstrom (2010) and Sampson (2016).

[4] Naito (2017a)

[5] The reallocation mechanism induced by unilateral trade liberalization described here is the same as that in the static asymmetric Melitz models of Felbermayr et al. (2013) and Demidova and Rodríguez-Clare (2013), except that they consider labor as the only factor.

[6] Naito (2017b)