The Global Economic Impact of Private Equity Report 2008 - World ...

Estimates are reported in Table 3. One limitation of thismodel is that the intensity is a deterministic function of theobserved characteristics, Χi, and the parameters, β. Inreality, unobserved factors often affect the citation intensity,and the Negative Binomial model is an extension of thePoisson model that includes an error term in the aboveequation to capture these factors. Hence, for the NegativeBinomial model, the intensity is given as1n (λ i) = Χ í β + ε i (2)where ε i is an independently and identically distributed (i.i.d.)random variable with mean zero (and a Gamma distribution).We use these models to estimate both absolute and relativecitation intensities, where the relative citation intensities aredefined as follows. For each patent, we find the matchingpatents in the USPTO database within the same technologyclass that are granted in the same year, and we calculate theaverage citation intensity of these matching patents asγ i=Total citationsNumber of matching patentswhere Total citations is the number of citations received by allmatching patents during the three years following the grant year.By including this baseline intensity in the estimation, weestimate the relative (or abnormal) citation intensities,controlling for technology specific trends in the citations,Using either the Poisson or Negative Binomial models, weestimate the specifications(3)1n (λ i) = Χ í β + 1n (γ i ) (4)1n (λ i) = Χ í β + 1n (γ i ) + ε i (5)When Χ íβ = 0, the patent’s citation intensity equals theintensity for the matching patents. When Χ íβ is greater(or less) than zero, the citation intensity is proportionallygreater (or less) than the intensity for the matched patents.In Table 3, each patent is a separate observation. 9 In thefirst four regressions, the independent variables are dummyvariables denoting the year of the patent application relativeto that of the private equity investment. In each case,applications in the second to fifth year after the buyout arecited significantly more frequently. (In all tables in the paper,we report incidence rate ratios, where a coefficient greaterthan one means that the dependent variable is more likely,and a coefficient less than one means that it is less likely.)For instance, in the first regression, the coefficient of 1.824for a patent applied for three years after the private equitytransaction implies that these patents garner 82% morecitations than those applied for in the year of the transaction.In the first four specifications, the coefficients in the first threerows are not significantly different from zero. Hence, patentsfiled before the LBO investment are cited as frequently as thematching patents. However, the coefficients in the rows thatfollow are greater than one and consistently significant (withthe exception of the fourth row), showing that patents filedafter the investment are cited significantly more frequentlythan the matched patents. Both the absolute and relativecitation intensities show strong evidence for this pattern,although it is slightly more pronounced for the relative ones.One advantage of the Negative Binomial model is that it allowsfor unobserved factors to affect citation intensity. Empirically,the presence of such factors leads to over‐dispersion of thecitation counts relative to the dispersion specified by thePoisson model. In our sample, when testing the dispersion,the Poisson model is decisively rejected, and we turn to theNegative Binomial specification. In specification 3, we seethat this does not affect the estimated coefficients, but thestandard errors increase substantially due to the extra sourceof variance in the model. Except for the first year after thebuyout, the coefficients remain significant at the same levels.Figure 4 plots the implied absolute citation intensities inspecification 4 and their standard errors.In the fifth and sixth columns of Table 3, we employ a moreparsimonious specification, in which a dummy variable equalsone if the patent was applied for in the first to fifth year afterthe private equity investment. Again, this coefficient is greaterthan one and statistically highly significant.A concern about the specifications in Table 3 is that theremay be composition effects that lead to misleadingconclusions. We address this concern in Table 4, where were‐estimate the equations, using fixed and random effects tocontrol for the characteristics of the firms. In this way, we areasking whether there are any changes after the private equityinvestments, even after controlling for the unobservedcharacteristics of each firm.One subtle issue with the implementation of this analysis isthat the Negative Binomial model where the error terms ε iare highly correlated within each firm is implemented as aPoisson model with an additional firm effect. We implementboth a fixed‐effect specification and a random‐effectspecification, which imposes the additional assumption thatthe error terms are uncorrelated with the observed firmcharacteristics. Finally, we estimate a Negative Binomialspecification with fixed and random effects. This specificationallows for an extra source of uncertainty and the citationintensity is given as1n (λ i) = Χ í β + 1n (γ i ) + ε j +η i (6)where ε jis a firm‐specific and η iis an additional i.i.d. errorterm. The cases where ε jare fixed and random effects areboth reported in Table 4.9Because the patents must have three years after being issued to garner citations, the sample size is less than 6,398.32 Large-sample studies: Long-run investmentThe Global Economic Impact of Private Equity Report 2008