The impact of trade on aggregate productivity and welfare with heterogeneous firms and business cycle uncertainty

Abstract

This paper presents a model with monopolistic competition, productively heterogeneous firms, and business cycle aggregate shocks. With firm-specific productive heterogeneity, weaker firms quit when faced with a negative aggregate shock. Consequently, trade does not always increase firm-level aggregate productivity as negative shocks on the home market can be compensated for by positive shocks elsewhere. Weaker firms, which would otherwise quit in autarky, can continue to operate by exporting. Despite this, trade can still improve welfare for the risk-averse consumer by reducing aggregate price fluctuations.

Keywords:

• firm heterogeneity
• globalisation
• business cycles

JEL Classifications:

• F4
• F12

Acknowledgements

The author wishes to thank Stephen Redding, Anthony Venables, Gianmarco Ottaviano, Paula Bustos, Daniel Sturm, Frederic Robert-Nicoud, Alejandro Cunat, Rachel Ngai, David Greenaway and Davin Chor for their comments. The author would also like to acknowledge the PhD scholarships from the Ministry of Trade and Industry (Singapore).

Notes

 1. On the other hand, business cycle shocks with homogeneous monopolistically competitive firms do not yield much meaningful analysis. For example, suppose a Krugman-type firm has to decide on market entry by making a fixed asset investment without knowing the level of demand, entry under uncertainty will occur until ex-ante profit becomes zero for all firms. If demand turns out to be high, there will be insufficient entry and all firms will make a profit. Conversely, there will be too many entry firms if demand is low and all firms will be unable to recover fixed costs and thereby make losses. Depending on the realisation of the aggregate demand shock, either all firms make profits or all firms make losses since firms are homogeneous. The equilibrium does not provide any richness in describing the reallocation effect that would occur with heterogeneous firms.

 2. In Ghironi and Melitz (2005), the aggregate shock in that model is introduced via firms' uncertainty over their future productivity. As there are no fixed production cost, production decisions are not affected by shocks – only exporting decisions are affected. The departure in this paper is the presence of a fixed production cost, which then affects a firm's decision whether to continue through adverse shocks.

 3. Melitz and Ottaviano (2005) provide a model with quasi-linear preferences with firm heterogeneity that delivers reallocation of market shares through competition in the goods market. However in that model, any changes to income affect only the consumption of the competitive sector and have no impact on the monopolistic sector. The model is therefore less suitable in the context of modelling demand shocks to the monopolistic sector.

 4. This is a different result from Mundell (1957) that shows that free trade in factors is equivalent to free trade in goods in a neoclassical setting.

 5. For example, it will not be possible to generate variable moments to fit the data, greatly reducing the testable implications on parameters.

 6. The minimum support of the pareto distribution is given as, while the shape is given by parameter k.

 7. In the Melitz (2003), there is constant steady state entry to replace the exogenous steady state exit (subject to paying sunk cost f_e and drawing a productivity level above the cut-off). This paper has elected to keep the number of firms fixed to simplify the exposition. This can be motivated by the fact that the economy has a long-run size of LH, despite period to period γ shocks. To be explicit, the paper is making the assumption that the γ shocks are small enough relative to a large sunk cost f_e such that no firms will find it profitable ex-ante to enter on the basis of business cycle shocks alone. Coupled with the assumption of no exogenous destruction, the number of firms becomes fixed.

 8. See the Appendix for a detailed derivation of the Euler equations.

 9. The price of the homogeneous good is normalised to 1, and therefore does not appear in the indirect utility equation.

10. For example, if today is a good state while the previous state is bad, the indirect utility is in fact given as , where P_G  < P_B . Although today's income is high, welfare is lower due to the higher CES aggregate price. therefore gives the highest indirect utility and the lowest.

11. In other words, the distribution of market shares across firms does not affect the aggregate resource constraints.

12. Note that by putting ϕ in the X-axis raised to the power of σ−1, the profit conditions become straight lines. The level of capital costs becomes the Y-axis intercepts (see Helpman et al. 2004).

13. This could be due to incentives issues such as moral hazard, or costly monitoring and high transaction costs. Because of these reasons, income insurance between countries is not widely observed. Therefore, the trading of international bonds is ruled out.

14. Note that from equation (17), since there is no insurance across consumers in the different countries, their levels of expenditures are affected by their domestic shocks only.