The Effect of High-Tech Clusters on the Productivity of Top Inventors: Comment

This paper is a comment on Moretti (2021b), which studied agglomeration effects for innovation by testing whether the size of technology clusters causes patenting. The original paper (M21) used US patent data from 1971 to 2007 (Zucker and Darby, 2014) and reported a baseline elasticity of patenting with respect to cluster size of 0.0676, along with event study and instrumental variables (IV) evidence supporting a causal interpretation.

Wiebe identifies two major methodological problems that undermine M21’s causal claims.

Problem 1 — Misspecified event study. M21’s event study (Figure 6) was designed to test for selection bias from “rising star” inventors sorting into large clusters. The event is inventors moving across cities exactly once. However, M21’s specification interacts pre-move average cluster size with pre-move event-time indicators and post-move average cluster size with post-move event-time indicators separately — it does not exploit the change in cluster size generated by the move itself. Following the standard “mover” design literature (Finkelstein et al., 2016; Molitor, 2018; Cantoni and Pons, 2022), the correct specification uses the change in average cluster size as the treatment variable, interacted with event-time indicators. Wiebe implements this corrected event study and finds no statistically significant pre-trend and no statistically significant treatment effect post-move. Notably, the baseline elasticity estimated on the mover sample using all observed variation is large and significant at 0.3145 (SE 0.0953), but no effect is detected when variation is restricted to that generated by moving. The null result could also partly reflect attenuation bias from misclassified moves, since the dataset does not distinguish inventors who share the same name.

Problem 2 — Coding error in IV. M21’s Table 5 instruments cluster size using variation in the number of inventors in other cities employed by firms also active in the focal inventor’s city, with the instrument calculated via first-differencing. Due to a coding error, M21 sorts data by firm, field, and year but not by city before first-differencing, so the differencing is taken across cities rather than within cities. Because firm-field-year is not a unique sorting key, Stata’s sort command pseudo-randomly orders observations with tied values, making the results unreproducible across runs. When Wiebe corrects the code to sort by city and compute first-differences within city, the 2SLS estimates become unstable and nonsignificant, with the first-stage F-statistic falling to approximately 7. This means M21 provides no valid IV evidence against confounding from city-field-year shocks such as local subsidies.

Beyond these two major problems, the Appendix documents seven additional issues. The positive effect of cluster size on patent quality (M21 Table 6) disappears and reverses when the log transformation is corrected from log(y + 0.00001) to log(y + 1) or Poisson regression — the corrected estimate is negative and significant, implying that cluster size reduces citations per patent along the intensive margin and the overall quality effect is negative. Heterogeneous elasticity estimates (M21 Table 8) contain a coding error; corrected estimates show substantial heterogeneity. The distributed lag model (M21 Figure 5) uses an incorrectly defined lag structure in an unbalanced panel; corrected estimates yield nonsignificant contemporaneous effects. Cluster quality estimates (M21 Table A.8) use a cluster size definition differing from the text, and corrected elasticities are approximately half as large. M21’s claimed extensive margin effect in Table A.7 is logically unsupported since no zeros are observed. The team size robustness check is conceptually flawed because it controls twice for per-coauthor adjustment. A gap-interpolation coding error in Table A.6 biases estimates downward. Broader computational reproducibility failures arise from many-to-many merges with non-unique sort orders. Wiebe explicitly notes that the null IV and event study results are not evidence against agglomeration effects per se.

Q: What is the baseline finding in M21 that Wiebe contests? A: M21 reports a baseline elasticity of patenting with respect to cluster size of 0.0676, estimated from linear regressions with extensive fixed effects including inventor fixed effects. M21 presents an event study and IV strategy as additional evidence supporting a causal interpretation of this elasticity.

Q: What is wrong with M21’s event study specification? A: M21’s event study interacts pre-move average cluster size with pre-move event-time indicators and post-move average cluster size with post-move event-time indicators, but never uses the change in cluster size associated with moving. The standard mover design (Finkelstein et al., 2016; Molitor, 2018) uses the change in average environment as a constant treatment variable interacted with all event-time indicators. Because M21’s specification does not exploit moving-induced variation, it would be identified even if moving induced no change in cluster size.

Q: What does Wiebe’s corrected event study find? A: Wiebe’s corrected mover event study shows no statistically significant pre-trend (consistent with no systematic sorting of rising-star inventors into large clusters) and no statistically significant post-move treatment effect. In contrast, the baseline fixed-effects elasticity on the mover sample using all observed variation is 0.3145 (SE 0.0953) — large and significant — indicating the null result is specific to the moving-generated variation.

Q: What alternative explanation does Wiebe offer for the null event study result? A: The null result could be partly explained by attenuation bias from misclassified moves. M21’s code creates inventor identifiers based on names, but the COMETS dataset does not distinguish inventors who share the same name, so an apparent cross-city move may simply be two different inventors with the same name living in different cities.

Q: What is the coding error in M21’s IV strategy? A: M21 constructs the instrument by first-differencing a variable measuring inventors in other cities working for firms also active in the focal city. The code sorts by firm, field, and year before differencing, but omits city from the sort key, so first-differencing is computed across cities rather than within cities, generating an instrument that does not match the definition in the text.

Q: Why does the coding error also cause non-reproducibility? A: Firm-field-year is not a unique sorting key because multiple cities can share the same firm-field-year values. Stata’s sort command pseudo-randomly orders observations with tied values, so each run produces a different city ordering within tied groups and therefore a different instrument and different estimates.

Q: What do the corrected IV results show? A: After correcting the sort order to include city and computing first-differences within city, the 2SLS estimates are unstable and nonsignificant. The first-stage F-statistic falls to approximately 7, indicating a weak instrument. This does not constitute evidence against agglomeration effects, but means M21’s IV strategy provides no valid evidence against confounding from city-field-level shocks such as local subsidies.

Q: What happens to the patent quality results when the log transformation is corrected? A: M21 uses log(citations + 0.00001), which assigns very large weight to the extensive margin. When Wiebe uses log(citations + 1) or Poisson regression instead, the estimated effect of cluster size on patent quality is negative and statistically significant, reversing M21’s finding. The corrected result implies that while cluster size may raise the probability of producing any cited patent, it reduces citations per patent for inventors who do produce cited patents, and the overall effect is negative.

Q: What are the corrected aggregate agglomeration loss estimates? A: Using the corrected constant elasticity, the estimated output reduction from equalizing cluster sizes is -9.15% (slightly smaller than M21). Using corrected heterogeneous elasticities based on within-field-year size quartiles, the output loss is -23.75% (about twice as large). Using elasticities based on global size quartiles, the loss is -35.11%.

Q: What is wrong with M21’s distributed lag model (Figure 5)? A: M21’s code defines lags and leads using sequential observations in the panel rather than calendar years. Because the inventor-year panel is unbalanced, a coded “one-year lag” can refer to any number of years prior. When Wiebe restricts to inventors with 11 consecutive years and correctly defines year-based lags, confidence intervals widen substantially and the contemporaneous effect estimate becomes nonsignificant.

Q: What is the conceptual flaw in M21’s team-size robustness check? A: M21’s Table A.8 controls for the number of coauthors on a patent, but the dependent variable is already measured as patents per coauthor. Controlling for team size after already dividing by team size effectively controls for the same variable twice.

Q: What are the broader computational reproducibility problems in M21? A: The cleaning code uses many-to-many merges with non-unique sort orders, generating slightly different datasets on each run. For example, when merging inventors with patent assignees, patent identifiers are not unique because multiple firms can be assigned to a single patent. Removing name suffixes also causes distinct inventors (e.g., Paul H. Hamisch Jr. and Sr.) to be assigned the same identifier. Additionally, using reghdfe with the keepsingletons option retains singleton groups explicitly warned against by the package due to biased standard errors.

Agglomeration elasticity: The elasticity of an inventor’s patent output with respect to the size of the technology cluster (city-field-year cell) in which they work; reported as 0.0676 in M21’s baseline and 0.3145 on the mover sample with all observed variation.

Mover event study design: An event study specification in which the treatment variable is the change in an individual’s average environment (here, cluster size) before and after a geographic move, interacted with event-time indicators — the standard design used in Finkelstein et al. (2016) and Molitor (2018), which M21’s specification does not follow.

Cluster size: The number of inventors (or cluster density) active in the same city-field-year cell as the focal inventor, used as the key independent variable in M21’s regressions.

First-stage F-statistic: A measure of instrument strength in 2SLS IV estimation; the corrected instrument yields F ≈ 7 (indicating weakness), whereas M21’s incorrectly constructed instrument produced a stronger first stage by exploiting spurious cross-city variation.

Extensive vs. intensive margin (patent quality): The extensive margin captures whether an inventor produces any cited patent; the intensive margin captures citations per patent conditional on having any. M21’s log(y + 0.00001) transformation overweights the extensive margin, and the corrected intensive-margin effect of cluster size on quality is negative and significant.

Computational reproducibility: The property that running code on the same data produces identical results across runs. M21’s code fails this standard due to non-unique sort orders in merges and first-differencing steps, causing the IV instrument to differ across runs.

Rising star sorting: The hypothesized selection mechanism whereby inventors with increasing patent trajectories are preferentially hired into large clusters, which would bias OLS agglomeration elasticity estimates upward; M21’s event study was designed to test for this but is incorrectly specified and does not use moving-induced variation.