A theory of growth and volatility at the aggregate and firm level

1. A theory of growth and volatility at the aggregate and firm level By Comin and Mulani Comments by: Claudio Raddatz

2. What does the paper do? • Presents an endogenous growth model that: • Simultaneously addresses first and second moments of growth at the firm and aggregate level • Endogenously links aggregate and firm level volatility are • Can account for some puzzling patterns of the data in the US: • Increases in R&D investment are not associated with increases in productivity at the aggregate level • Decline in aggregate volatility occurring simultaneously with an increase in firm level volatility • Provides some empirical validation for some of the model’s predictions

3. The basic mechanism • Quality ladders model of endogenous growth • Leader with superior product and followers with standard (inferior) one • Leader and followers can engage in two types of R&D driven innovations • Patentable innovations (PI) that topple the leader • GPT that benefit everybody by reducing MC • PI akin to idiosyncratic shock, GPT akin to aggregate shock • Trade-off between both types of investment • Under particular functional forms and some extra assumptions: • Only the followers invest in PI • Only the leader invests in GPT • Investment in GPT depends on the value of being the leader

4. These 3 results are important for the comparative statics What happens after an increase in the productivity of PI (λ0q) Increases arrival rate of PI (idiosync. vol.) Increases turnover Reduces value of being leader Reduces investment in GPT Reduces arrival rate of GPT (agg. vol.) The basic mechanism

5. Comments on the model • Model is complex and has several non-standard aspects that deserve a more thorough discussion • For instance: • Why the negative externality in PI? • Why the fixed cost in GPT innovation?

6. Comments on the model… • Result (CS) seems to hinge crucially in • Leader does not do PI • Followers do not invest in GPT • Evidence suggests that leaders do PI • Followers and GPT: • Not only leaders do GPT • Later aspect seems to depend importantly on the fixed cost. • Does GPT investment happen in equilibrium?

7. Model • Overall: • Model carefully crafted and delivers the point • Is this the simplest model that can do the job? • It is complicated and with many non-trivial parameterizations • Seemingly, it could be made more parsimonious • If not, a more thorough discussion of the role of some of the choices would help the reader • How robust are the result to allowing the leader do PI and followers GPT?

8. Evidence • Expected growth • Positive relation btw. R&D and growth at firm level • Ambiguous at aggregate level • Turnover • Increase in λ results in more turnover • R&D and firm level volatility positively associated • R&D and sector volatility ambiguous • Negative relation at aggregate level between λ and volatility • Comovement • Increase in λ reduces correlation across sectors • R&D negatively associated with correlation

9. Evidence • In the model R&D intensity (λq /λ0q) is not a deep parameter • RF relations true if changes in R&D result from increases in λ0q. They are conditional predictions • Even within the model the relation between R&D and λ0q is conditional on the interest rate being relatively high: • Determining the empirical predictions of the model requires us to know how all parameters have moved • Is it the case that λ0q has been the main driving force in the last 30 years?

10. Evidence • Is λ0q the main driving force? • Some of the evidence for an increase in λ0q seem also to apply to λ0h (e.g. higher education) • Changes in turnover cited as evidence of changes in λq • But increase in turnover is the flipside of an increase in firm level volatility • It does not tell us anything about the causes • It does not imply that “leadership” is less persistent (there is just more noise)

12. Evidence • Turnover and volatility regressions are largely the same • What is driving identification? • Reverse causality (lagging partly takes care of it) • Comment on reverse causality seems incorrect • Fluctuations around trend or differences in trends?

13. Evidence • How should we read the evidence? • Interesting and compelling circumstantial case • All the reduced form correlations can be explained by the model if, among other things, the main driving force is an increase in λ0q • Determining whether they are actually consistent with the model would require us to know how all the different deep parameters have changed and determining the signs of the total derivatives • Other option would be a fully fledged calibration exercise • Quickly disregarded • There are several moments available • Can also explore reasonable values for rest of parameters

14. Taking stock • Very interesting paper • Addresses both productivity growth and volatility simultaneously and relates them to deep parameters • Has enough flexibility to match interesting aspects of the data under some parameter combinations • Model is complex and some non-trivial aspects could be either simplified or more thoroughly addressed • Role of some modeling aspects and parameter restrictions • Suggestive empirical evidence but not a slam-dunk • Empirical implications presented are conditional and do not necessarily validate the model • Perhaps a more standard calibration could be a way forward