Empirical work suggests that larger markets tend to increase the rate of process innovation. This is difficult to square with a standard Dixit-Stiglitz model of product variety choice. In Dixit-Stiglitz, the product space is unbounded, and an increase in product variety has no effect on firm size or elasticity of demand. A Hotelling model of product variety (where consumers and firms locate on a line, or a unit circle, describing product variety) is bounded. Desmet and Parente use such a model, and show that as market size increases (say, because population went up, or because trade was liberalized), then new firms profitably enter the market, “filling in” holes in the product circle. Because the product space becomes denser, the elasticity of demand of each consumer for any given variety falls since they now have more “similar” options. This implies the partial monopoly markup falls. With free entry of firms, zero profit is made, and in order to have zero profit with a lower markup, supply of each firm must go up. If firms sell more, then any decrease in marginal cost from increased productivity (which is purchased at a fixed cost by any firm that desires) is spread over more units. Therefore all firms will innovate more, in the sense of process innovation.
My belief is that the greatest mistake of economists post-WW2 was not endogenizing growth and innovation. Even today, you read many macro models where technology is assumed to increase exogenously. But new innovations are the source of growth, the most important process economists can understand!
https://netfiles.uiuc.edu/parente/Bigger18Sept2008.pdf (WP – final version in IER 51-2)
A Fine Theorem 
For most purposes, especially at the aggregate level, assuming exogenous technological progress is fine. And, in any case, what about the endogenous growth people from the late ’80s and early ’90s?
We know that human capital is very important and we know that having something substantial to say about R&D is hard (regardless of whether you try to do with with expanding varieties, quality ladders or this type of stuff).
The Solow residual is clearly not constant, even at the world level, and especially at the national level. I’m fine with exogenizing it if you’re studying, say, monetary policy (though even there, my understanding of the evidence is that R&D drops in recessions, and effects of policy on growth do exist), but if you’re studying trade, or human capital formation, or sectoral shifts, etc., then tech progress is obviously important and not exogenous.
I agree, though, that the reason we *don’t* say something is that we have a very poor understanding (both at the theoretical and empirical level) about why technological progress happens. I think Romer-style endogenous growth is a good start, at least…
You can always put a R&D sector in pretty much any model, feed it some inputs, get some patent/monopoly rents and watch it behave. You don’t get a lot out of that exercise, I think.
I guess part of the problem is the same with the production theory issues: measurement is hard and we’re not in the business of super-micro modeling techniques but usually there’s some production function black box.
I guess we can go back to IO tables and such, but the assumptions needed are maybe worse that the alternative.
There’ve been a few papers recently putting endogenous growth in DSGE models (e.g. Comin and Gertler) or looking at business cycles in endogenous growth models (e.g. Francois and Lloyd-Ellis).
I work on similar things myself, and although I do better than the existing literature on matching the stylized facts, it’s still hard to know how seriously to take my models (or those of the literature for that matter). You can get degrees of persistence absolutely unheard of in more standard DSGE models, as well as significant amplification mechanisms, but from having worked with these models I also know how sensitive they are to small changes in modelling assumptions. The interactions between market power, research, product differentiation, relative productivity, IP policy etc etc. are unfortunately orders of magnitude more complex (not to mention subtle) than those underlying the standard new-Keynesian DSGE model.
Thanks for the heads up, Tom. I’ve seen the Gertler/Comin paper, but my knowledge of the macro literature here is deficient. I agree that endogenizing technological progress makes models perhaps too complex in some settings…what we need (and what I’m hoping to do some work on) is more micro knowledge of what matters for technological change, at which point the macro guys can focus on adding just those aspects of endogenous growth to their models.