from the infant industry literature (Succar, 1987; Young, 1991). Such models feature industries experiencing learning externalities, at rates that may vary across industries. Our paper embeds such a framework into an otherwise standard open economy endogenous growth model. The conditions characterizing our _trade-dependent_ economies can be seen as the analogous of the Mill-Bastable test that determines whether government intervention in support of infant industries is welfare-improving.<sup>9</sup> More recently, Rodrik (2008) has presented empirical evidence and has developed a model of growth through exchange rate undervaluation similar to ours. Our theoretical analysis differs in two main aspects: First, Rodrik does not investigate how undervaluation can help to internalize the learning-by-investing spillovers. Instead, he assumes that the returns to capital in developing countries are artificially depressed because of difficulties in appropriability in the tradable sector, and he proposes that real exchange rate undervaluation can reduce this distortion. In other words, Rodrik assumes the tradable sector is special because it suffers more from distortions; we assume the tradable sector is special because of its learning-by-investing spillover effects. Secondly, our paper contributes a welfare analysis of the static losses versus dynamic gains that arise from exchange rate undervaluation in economies with endogenous growth. We express both in a tractable analytical formula and in an intuitive graphical diagram.

Aizenman and Lee (2008) investigate the policy implications of learning-by-doing externalities in two/three-period models. The focus of their paper is on how different forms of learning-by-doing externalities call for different first-best policy interventions. We focus instead on the benchmark Romer (1989) learning-by-investing externality and focus on second-best policy interventions in the presence of a targeting problem. We also derive quantitative welfare and policy implications.

In the empirical literature, the question whether higher exports can lead to higher growth has not been conclusively settled. Though several more recent empirical studies are available, the perhaps most telling summary of this literature is given in a survey by Giles and Williams (2000), which concludes that “it is difficult to decide for or against [the export-led growth hypothesis], as the results are conflicting.” Evidence on learning-by-doing externalities associated with exporting is likewise inconclusive, owing in large part to the difficulty in disentangling productivity-based selection into exporting from true learning-by-exporting effects (Harrison and Rodriguez-Clare, 2009).<sup>10</sup> Given the inconclusive results in the empirical literature, our paper aims to theoretically clarify the channels through which undervaluation can increase growth and welfare so as to better guide future empirical research.

> 9The Mill-Bastable test essentially states that the discounted stream of productivity gains generated through learning should exceed the discounted cost of the government intervention required to achive the learning; see e.g. Melitz (2005) for some specific applications.

> 10Rodrik (2009), however, finds that a large (tradable) manufacturing sector leads to positive growth externalities.

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