court
Stage 3: Litigation and Settlement
3.5 Model Predictions
3.4.6 Uniqueness and Accuracy of Calibration
The model can be uniquely calibrated to perfectly replicate the aggregate patent system char-acteristics defined in Section 3.4.5. While this may seem trivial at first sight, given that I am freely tuning two model parameters to essentially produce two model outcomes, one should keep in mind that the parameters influence the predictions in a highly non-linear and interde-pendent way.
Two concerns may arise with regard to fitting a non-linear model. First, the existence of several local minima may obscure the minimization algorithm’s path to the optimal point in parameter space. As a result, one may underestimate the model’s capability of reproducing empirical outcome rates. If relaxing simplifying assumptions then proves insufficient, one may even reject its general suitability to represent the litigation selection process. Second, the optimal parameters may not be unique, if several local minima exist whose depth is comparable to that of the global minimum. This may not pose a major problem as long as the predictions of the unobservable characteristics of interest are identical for all optimal parameter vectors.
Yet, if the corresponding predictions differ substantially, unambiguous conclusions cannot be drawn in a straightforward fashion. For the calibration implemented here, however, the above considerations are of no significance, since the optimum turns out to be the unique minimum, as shown in Figures C.1 and C.2 in the appendix.
Moreover, the calibration results allow to assess whether the simplifications of Section 3.4.4 are overtly restrictive. Since the simplifying assumptions prove to be sufficiently lax to allow for a calibration exactly reproducing the observable outcome rates, corresponding concerns are alleviated.
Figure 3.7: Outcome distribution (baseline calibration)
no entry settlement litigation 0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
share
valid invalid
Notes:Outcome distribution and conditional validity for the baseline calibration of the model (see Table 3.1).
Figure 3.8: Patented invention values (baseline calibration)
no entry settlement litigation 0
200 400 600 800 1000 1200 1400 1600
av. invention value v (k )
population average
Notes: Average invention values by outcome for the baseline calibration of the model (see Table 3.1).
enters the market,
P(no entry|valid) =96.0%, (3.2)
because he cannot expect to make positive profits given the large inventive step ˆıd he has observed. A large inventive step means small chances in winning a potential suit, which goes along with an unfavorable position in settlement negotiations (high bidding and expected asking prices). He will only enter if the perceived validity is sufficiently moderate in relation to the value of the patented invention; higher values potentially leading to higher returns from entry. As a result, the model’s first stage, i.e., the endogeneity of disputes, has profound implications for validity and value at later stages. While invalidity rates lie at 42.0% in the patent population and at 25.5% in the case of no entry in the baseline calibration, they are considerably higher for litigated patents (75.0%) and the highest for settled patents (91.5%).
Hence, latent invalidity is predicted to be considerably lower than estimated in Henkel and Zischka (2016) and still noticeably lower than in Schankerman and Schuett (2016), whose estimates range from 65% to above 80%. Generally, for findings based on expert interviews and surveys, differences might partly be explained by the calibration results. The rate of latent invalidity is higher in settlements than in litigation. A legal practitioner only observing patents which become subject of a dispute might thus be led to the fallacious conclusion that litigated patents on average have a smaller inventive step than the average patent in the population, and that they are accordingly less stable from a legal point of view.
Concerning the second patent characteristic, patented invention value ˆv, the baseline cal-ibration again suggests substantial selection (see Figure 3.8). Patents which never become subject of a dispute constitute the majority of all patents, with around 74.7%. They are as-sociated with an average patented invention value of 138 ke, which corresponds to 0.76 of the population mean of 180 ke. Patented invention values for settled patent disputes (24.1%) average to 244 ke, or 40% more than the population mean. While this is already indicative of selection with respect to value, the negotiation stage induces substantial value selection for litigated patents. Parties are aware of the considerably higher cost associated with trial in court as opposed to settlement. Hence, even under divergent expectations concerning validity, the infringer’s maximum settlement demandB will exceed the patent holder’s minimum set-tlement demandA, thus allowing parties to settle, unless the stakes are very high. If patents are litigated, the average patented invention value lies at 1.56 millione, or 8.7 times the pop-ulation mean. The ratio is even more extreme for litigated patents which are valid. According to the calibration, they are 14.5 times as valuable as the average patented invention. The finding that litigated patents are substantially more valuable than the average is in line with results in the empirical literature, which has found a significant, positive relationship between typical proxies for value and the likelihood of infringement and nullity proceedings (Lanjouw and Schankerman, 2001, 2003). Harhoff et al. (2003a) find that patents which have survived
Figure 3.9: Outcome probabilities as a function of patented invention value
0 200 400 600 800 1000
0.0 0.2 0.4 0.6 0.8 1.0
Conditional probability P(... | v)
P(no entry | v) P(settlement | v) P(litigation | v) f(v) (scaled)
Patented invention value v in 1000 EUR
Notes:Outcome probabilities conditional on patented invention value. The gray dotted line indicates the proba-bility density functionf(v)of patented invention values.
an annulment proceeding are 42.6 times more valuable than an unchallenged patent. In the model, the closest analogy is the ratioE[v|valid, litigation]/E[v|no entry]. According to the baseline calibration,E[v |valid, litigation] =2.62 million eandE[v | no entry] =138 ke. Hence, litigated valid patents are on average 19 times as valuable as patents that never become subject of a dispute. The two findings thus fall within the same order of magnitude.
Figures 3.9 and 3.10 provide a few further insights. First, as visible in Figure 3.9, entry becomes much more likely for valuable patents. Over a relevant range of patented invention values, the probabilities for settlement and for litigation increase by a similar amount (despite different curvature), at the expense of the probability for no entry occurring. Second, due to fixed legal costs, litigation is only entered if patented invention value is sufficiently high.
In fact, the litigation probability is zero for patented inventions below a minimum threshold value, which lies at approximately
vlit, min≈396.3 ke, (3.3)
a value which is considerably above the median of 67.44 keand the mean of 180.2 ke. This is clearly visible in Figure 3.10, which displays the value distribution conditional on litigation f(v|litigation). The existence of a threshold value is not only intuitive, it may also be testable in future empirical work. Finally, from inspecting the inset in Figure 3.10, it seems that the conditional distributions are closely related to the log-normal distribution. Deviations are the largest when conditioning on litigation, where the distribution essentially only comprises the log-normal tail.
Figure 3.10: Patented invention value distribution by outcome
0 250 500 750 1000 1250 1500 1750 2000
Patented invention value v in 1000 EUR 0.00
0.02 0.04 0.06 0.08 0.10 0.12
Conditional probability density
f(v | no entry) f(v | settlement) f(v | litigation) f(v)
101 100 101 102 103 104 0.00
0.05 0.10
Notes:Patented invention value distribution conditional on litigation (blue dash-dotted line) in comparison to the unconditional distribution (gray dotted line). Using a logarithmic x-axis, the inset additionally shows the density functions conditional on no entry (red solid line) and on settlement (green dashed line). Dashed vertical lines indicate the corresponding expectation values.
In the appendix, Figures C.3 and C.4 display the joint probability density functions of ˆıand ˆ
v. By definition, ˆıand ˆvare independent random variables and are hence uncorrelated in the patent population (cf. Figure C.3). However, due to selection, they exhibit positive correlation within each outcome subsample (cf. Figure C.4 for the subsample of litigated patents).
In summary, the calibration results suggest that the entry and the negotiation stages drive different dimensions of selection. While selection with respect to validity primarily is a conse-quence of the potential infringer’s decision at the entry stage, selection with respect to value is predominantly driven by the negotiation stage.