Innovation, Reallocation, and Growth

In our paper, Innovation, Reallocation, and Growth, which was recently made publicly available on SSRN, we build a micro-founded model of firm innovation and growth, enabling us an examination of the forces jointly driving innovation, productivity growth and reallocation. In the second part of our paper, we estimate the parameters of the model using simulated method of moments on detailed U.S. Census Bureau micro data on employment, output, R&D, and patenting during the 1987-1997 period.

Our model builds on the endogenous technological change literature. Incumbents and entrants invest in R&D in order to improve over (one of) a continuum of products. Successful innovation adds to the number of product lines in which the firm has the best-practice technology (and “creatively” destroys the lead of another firm in this product line). Incumbents also increase their productivity for non-R&D related reasons (i.e., without investing in R&D). Because operating a product line entails a fixed cost, firms may also decide to exit some of the product lines in which they have the best-practice technology if this technology has sufficiently low productivity relative to the equilibrium wage. Finally, firms have heterogeneous (high and low) types affecting their innovative capacity—their productivity in innovation. This heterogeneity introduces a selection effect as the composition of firms is endogenous, which will be both important in our estimation and central for understanding the implications of different policies. We assume that firm type changes over time and that low-type is an absorbing state (i.e., high-type firms can transition to low-type but not vice versa), which is important for accommodating the possibility of firms that have grown large over time but are no longer innovative.

This selection effect is shaped by two opposing forces. On the one hand, old firms will be positively selected because low-type firms are more likely to exit endogenously. On the other hand, old firms will be negatively selected because more of them will have transitioned to the low-type status. The balance of these two forces will determine whether young (and small) firms are more innovative and contribute more to growth. This feature also implies that the key dimension of reallocation in our model is that of skilled labor used for R&D and for fixed operating costs. In particular, skilled labor is allocated for R&D across firms with different types and between R&D and operating costs. Our focus on the reallocation (and misallocation) of R&D inputs is different from that of much of the literature, which emphasizes the reallocation of production input. This focus is motivated by the importance of innovation activities for economic growth. Our model separates R&D and production inputs both for greater transparency and because the margin between R&D and non- R&D activities for production workers seems secondary for the issues at hand. Despite the various dimensions of firm-level decisions, heterogeneity, and selection effects, which will prove important in our estimation and quantitative exercises, we show that the model is tractable and that much of the equilibrium can be characterized in closed form (conditional on the wage rate, which does not admit a closed-form solution). This equilibrium characterization then enables the estimation of the model’s parameters using simulated method of moments.

We compute 21 moments capturing key features of firm-level R&D behavior, shipments growth, employment growth and exit, and how these moments vary by size and age. We use these moments to estimate the 12 parameters of our model. The model performs well and matches these 21 moments qualitatively (meaning that the rankings by firm age and size are on target) and on the whole also quantitatively. In addition, we show that a variety of correlations implied by the model (not targeted in the estimation) are similar to the same correlations computed from the data. Finally, we also evaluate the model by comparing the response of innovation to R&D expenditure and R&D tax credits in our model to various micro and instrumental-variables estimates in the literature and find that they are in the ballpark of these estimates.

We then use our model to study the effects of various counterfactual policies and gain insights about whether substantial improvements in economic growth and welfare are possible. We first look at the impacts of different types of industrial policies: subsidies to incumbent R&D, to the continued operation of incumbents and to entry. The main result here is that all these policies have small effects, and in the case of subsidies to incumbents, these are negative effects both on growth and welfare. For example, a subsidy to incumbent R&D equivalent to 5% of GDP reduces growth from 2.24% to 2.16% and welfare (in consumption equivalent terms) by about 1.5%. A subsidy equivalent to 5% of GDP to the continued operation of incumbents reduces growth by exactly the same amount, but welfare by less, by about 0.8%. A subsidy equivalent to 5% of GDP to entry increases growth and welfare, but again by a small amount (growth increases to 2.32% and welfare by 0.63%).When we consider subsidies equivalent to 1% of GDP, all of these numbers are correspondingly smaller.

These small effects might first suggest that the equilibrium of our model is approximately optimal. Though they do indeed reveal that any deviation from optimality is not just related to insufficient R&D incentives (a typical occurrence in models with endogenous innovation), in reality they mask a very substantial inefficiency in equilibrium originating from the selection effect discussed above. This can be seen in two ways. First, we compute the socially optimal allocation chosen by a planner who controls R&D investments, and entry and exit decisions of different types of firms. We find that such an allocation would achieve a 3.8% growth rate per annum (relative to 2.24% in equilibrium) and a 6.46% increase in welfare. The social planner achieves this by forcing low-type incumbents to exit at a very high rate and reducing their R&D, and increasing the R&D of high-type incumbents, thus inducing a strong selection from low-type firms where the productivity of skilled labor is low to high-type firms.

Second, we look at the effect of using optimal levels of incumbent R&D, entrant and operation subsidy/tax. We find that with all three, or just with taxes on continued operation of incumbents and subsidies to incumbent R&D, growth can be increased to about 3.11% and welfare can be increased by almost 5%. This can be achieved by having a huge tax on the continued operation of incumbents combined with a modest subsidy to incumbent R&D (between 12 and 17%). Such a policy strongly leverages the selection effect just like what the social planner was able to achieve directly. In particular, the high tax on the continued operation of incumbents encourages exit, but much more so for low-type firms, and the incumbent R&D becomes effectively directed towards high-type firms (since the low-type ones are exiting). If allowed, optimal policy also subsidizes entrants, but this is fairly marginal (about 6%, equivalent to about 1% of GDP). Though entry and incumbent R&D play pivotal roles, it turns out to be much better to support these by freeing resources from inefficient, low-type incumbents rather than subsidizing entry or incumbent R&D directly (and this is the reason why the incumbent

Overall, our policy analysis leads to a number of new results (relative to the literature and beliefs and practices in policy circles). First, industrial policy (support to existing firms and industries) is damaging to growth and welfare, and at best ineffective. Second, the equilibrium is inefficient, but in contrast to other models of endogenous innovation, this cannot be rectified by R&D subsidies. Third, the allocation of resources and growth can be significantly improved by exploiting the selection effect, which is only weakly utilized in equilibrium. This involves encouraging the reallocation of R&D resources (skilled labor) from low-type incumbents to high-tech incumbents and entrants, and if done effectively, it can increase growth and welfare by a significant amount.

The full paper is available for download here.