The discussion on functional form and identification, coupled with the empirical evidence of non-linearities even in very simple exercises, suggests that cross-country regressions are unlikely to be able to shed any meaningful light on the empirical relevance of models that integrate credit constraints and other imperfections of the credit markets. This is made worse by the poor quality of the aggregate data, despite the considerable efforts to produce consistent and reliable data sets. This contrasts with the increased availability of large, good quality, micro-economic data sets, which allow for testing specific hypotheses and derive credible identifying restrictions from theory and exogenous sources of variation. Throughout this chapter, we quoted many studies using micro-economic data which tested the micro-foundations for the models we discussed in this section.
Even a series of convincing micro-empirical studies will not be enough to give us an overall sense of how, together, they generate aggregate growth, the dynamics of income distribution, and the complex relationships between the two. The lessons of development economics will be lost to growth if they are not brought together in an aggregate context. In other words, it is not enough to use them to loosely motivate cross-sectional growth regression exercises—the discussion in this section is but an example of the misleading conclusions to which this can lead.
An alternative that seems likely to be much more fruitful is to try to build macroeconomic models that incorporate the features we discussed, and to use the results from the microeconomic studies as parameters in calibration exercises. The exercise we performed in section 5 of this chapter is an illustration of the kind of work that we can hope to do. There are a number of recent papers that in some ways go further in this direction than we have gone. In particular, Quadrini (1999) and Cagetti and Nardi (2003), for the U.S., and Paulson and Townsend (2004), for Thailand, try to calibrate a model with credit constraints to understand the correlation between wealth and the probability of becoming an entrepreneur. The paper by Buera (2003) mentioned above, emphasizes the fact that the long run correlation between wealth and entrepreneurship is weaker than the short run correlation, because as noted by Skiba (1978), Deaton (1992), Aiyagari (1994) and Carroll (1997), those who are credit constrained now but want to invest in
the future have a very strong incentive to save. This, Buera points out, reduces the ultimate efficiency cost of imperfect credit markets, though in spite of this, the person with the median ability level and the median starting wealth loses about 18% of lifetime welfare because of the credit constraints. Caselli and Gennaioli (2002) offer a slightly different calibration: Like Buera, they are worried about the fact that with credit constraints the biggest firms may not be run by the best entrepreneurs. This can be a source of very large productivity losses in the short run. However, since the best entrepreneurs will make the most money, in the long run their firms would necessarily become the largest, unless they died young. They show that even with this limiting factor, reasonable death rates would imply a 20% loss of productivity when we compare an economy without credit constraints with one that has them.
The calibrations so far have not attempted to see if the path of wealth distribution that results from calibrating this type of model matches the data. Our exercise above, for example, tries to match the distribution of firm sizes at a point of time, but says nothing about the path, while Buera does not try to match the data. The one exception is the papers by Robert Townsend and his collaborators based on Thai data (Jeong and Townsend (2003); Townsend and Ueda (2003)).
These papers, as well as those mentioned in the previous paragraphs, start from the assumption that every firm has a single, usually strictly concave, production technology. The only fixed cost comes from the fact that the firm needs an entrepreneur. As we saw above, this model does not do very well in terms of explaining the cross-sectional variation in the firm sector or the overall productivity gap, as compared to a model with a small number of alternative technologies and varying fixed costs. More generally, we need both a better empirical understanding of where the most important sources of inefficiency lie and better integration of this understanding when we assess the predictions of growth theory.
And perhaps above all, we need better growth theory: Our exercise at the beginning of this section was intended to advertise the possibility of a growth theory that does not assume aggregation. While we attempted to link the results to some relatively general properties of the production function, our analysis relies heavily on the fact that the inefficiency we assumed was in the credit market and that this took the form of a credit limit that was linear in wealth. One can easily imagine other ways for the credit market to be imperfect and other results from such models. Moreover, while the class of production technologies covered by our model was broader than usual, it does not include the (multiple-fixed-cost) technology that the previous section advocates.
There are, of course, other types of non-aggregative models: There are some examples of non- aggregative growth models that build on the inefficiency that comes from poorly functioning insurance markets.47 There are also interesting attempts to build growth models that emphasize the fact that some
47See Banerjee and Newman (1991) for a theoretical model of non-aggregative growth based on imperfect insurance markets. Deaton and Paxson (1994) investigate some of empirical implications of this type of model using Taiwanese data.
people are favored by the government while others are not, and especially the fact that this changes over time in some predictable way (see Roland Benabou’s contribution to this volume). Some interesting recent work has been done on the dynamic interplay between growth and political institutions (see the chapter by Acemoglu and Robinson in this volume) as well as between growth and social institutions (see Oded Galor’s contribution to this volume, as well as Cole, Mailath and Postelwaithe (1992, 1998, 2001)). However, even more than in the case of the literature on credit markets and growth, it is not clear how much the insights from these models rely on specific details of how the environment or the imperfection was modeled and to what extent they can be seen as robust properties of this entire class of models.
There are also areas where growth theory has not really reached: We have no models that, for example, incorporate reputation-building or learning into growth theory. The same can be said about the entire class of behavioral models of underinvestment.
Finally, there is the open question of whether we gain anything by building grand models that incor- porate all these different reasons for inefficiency in a single model. To answer this we would need to assess whether the fact that different forms of inefficiency interact with each other has empirically important consequences.
This is an exciting time to think about growth. We are beginning to see the contours of a new vision, both more rooted in evidence and more ambitious in its theorizing.