Patent thickets, defensive patenting, and induced R&D: an empirical analysis of the costs and potential benefits of fragmentation in patent ownership

Abstract

Patent thickets are sets of overlapping intellectual property rights that occur in fragmented technology markets. Their potential impacts on innovation have become an increasing concern in recent years. I estimate the direct and indirect effects of patent thickets on market value of publicly traded manufacturing firms. I find that patent thickets decrease the market value of firms, holding R&D and patenting activities of these firms constant. I also find that while firms do not change their R&D activities in response to patent thickets, they do reduce negative cost effects of patent thickets on market value through defensive patenting.

Appendices

Appendix 1: Derivation steps of the market value equation

Following the studies of Griliches (1981) and Hall et al. (2005), the general specification for market value function is

$$\begin{aligned} \textit{log}\,\textit{Market}\,\textit{Value}_{\textit{it}} = \textit{log}\,\textit{SV}_{\textit{it}}+\sigma \textit{log}(\textit{TA}_{\textit{it}}+ \gamma \textit{INA}_{\textit{it}}). \end{aligned}$$

(18)

The variable $\textit{log}\,\textit{Market}\,\textit{Value}_{\textit{it}}$ is the log of the market value of firm i in year t.³⁶ Following Hall et al. (2005), the market value of a firm is calculated as the sum of the current market value of common and preferred stocks, long-term debt adjusted for inflation, and short-term debts of the firm net of assets. In the analysis of Hall et al. (2005), the variable $\textit{log}\,\textit{SV}_{\textit{it}}$ includes time fixed effects ($m_t$) and the error term ($\epsilon _{\textit{it}}$). The term $\epsilon _{\textit{it}}$ denotes the other factors that influence the market value of firm i in year t. I assume that error terms $\epsilon _{\textit{it}}$ are additive, independently and identically distributed across firms and over time, and serially uncorrelated. The variables $\textit{TA}_{\textit{it}}$ and $\textit{INA}_{\textit{it}}$ are tangible and intangible assets, respectively. Their measurement is discussed shortly. The coefficient $\gamma$ is the shadow price of the intangible to tangible asset ratio. Moving the variable $\textit{TA}_{it}$ to the left-hand side in Eq. (18) allows the left-hand side of this equation to be written as $\textit{log}\left( \frac{\textit{Market}\,\textit{Value}_{\textit{it}}}{\textit{TA}_{\textit{it}}}\right)$ or Tobin’s q.³⁷ Eq. (18) then becomes

$$\begin{aligned} \textit{log}q_{\textit{it}}= \textit{log}\left( 1 +\gamma \frac{\textit{INA}_{\textit{it}}}{\textit{TA}_{\textit{it}}}\right) +m_t+\epsilon _{\textit{it}}^{\textit{MV}}. \end{aligned}$$

(19)

Following Hall et al. (2005), the variable $\textit{TA}_{\textit{it}}$ is measured by the book value of firms based on their balance sheet. The book value of a firm is calculated as the sum of net plant and equipment, inventories, investments in unconsolidated subsidiaries, and intangibles and others. All of the components of $\textit{TA}_{\textit{it}}$ are adjusted for inflation.³⁸ $\textit{INA}_{\textit{it}}$ is measured based on the approach of Hall et al. (2005), who measure the variable $\textit{INA}_{\textit{it}}$ with $R \& D$ intensity ($R \& D\textit{stock}_{\textit{it}}/\textit{TA}_{\textit{it}}$), patent intensity ($\textit{PATstock}_{\textit{it}}/R \& D\textit{stock}_{\textit{it}}$), and citation yield per patent or citation intensity ($\textit{CITEstock}_{\textit{it}}/\textit{PATstock}_{\textit{it}}$). The variables $R \& D\textit{stock}_{\textit{it}}$, $\textit{PATstock}_{\textit{it}}$, and $\textit{CITEstock}_{\textit{it}}$ measure the stock of $R \& D$, patents, and citations, respectively. These variables are constructed based on a declining balance formula with the depreciation rate of 15 %.³⁹ Hall et al. (2005) justify their method for measuring $\textit{INA}_{\textit{it}}$ of a firm by arguing that the firm’s $R \& D$ expenditures show the intention of the firm to innovate. The $R \& D$ expenditures might become successful and result in an innovation. Patents of the firm catalogue the success of the innovative activity, and the importance of each patent is measured by the number of times it is cited in subsequent patents. Therefore, I employ $R \& D$, patent, and citation intensities to measure $\textit{INA}_{\textit{it}}$, following Hall et al. (2005), and, Eq. (19) becomes

$$ \begin{aligned} \textit{log}q_{\textit{it}}= & {} \textit{log}\left( 1 + \gamma _1 \times \left[ \left( \frac{R \& D\textit{stock}}{\textit{TA}}\right) _{\textit{it}}\right] +\gamma _2 \times \left[ \left( \frac{\textit{PATstock}}{R \& D\textit{stock}}\right) _{it}\right] \right. \nonumber \\&\left. +\gamma _3 \times \left[ \left( \frac{\textit{CITEstock}}{\textit{PATstock}}\right) _{\textit{it}}\right] \right) + m_t+\epsilon _{\textit{it}}^{\textit{MV}}. \end{aligned}$$

(20)

There is usually a difference between the application and grant date of patents. Out of the patents applied close to the end date of the sample, only a small fraction is granted, and the rest are granted outside the reach of the sample. This issue indicates truncation in patent counts. Citation counts are also truncated. Truncation in citation counts happens since only citations that occur within the sample are observable. I correct for these truncations. As a result, the $\textit{PATstock}_{\textit{it}}$ and $\textit{CITEstock}_{\textit{it}}$ variables are corrected for truncations in patent and citation counts. See “Appendix 4” for detailed correction procedures.

To estimate the impact of patent thicket on the market value of firms, I augment Eq. (20) with the variables $\textit{log} F_{\textit{it}}$ as a measure of the firm’s own patent thicket, and $\textit{log}{} \textit{spill}F_{\textit{it}}$ as a measure of other firms’ patent thickets or patent thicket spillovers (the construction of these variables is explained in Sect. 2.4). To control for R&D spillovers, I include $\textit{log}{} \textit{spill}R \& D_{\textit{it}}$ in Eq. (20), and the construction of this variable is explained in “Appendix 4”. The distributed lag structure in the firm-level sales ($\textit{log}{} \textit{sale}_{\textit{it}}$ and $\textit{log}{} \textit{sale}_{\textit{it}-1}$) decreases the potential for inconsistent estimates due to demand shocks. To control for product market competition, I use a Herfindahl index that utilizes firm-level sales in four-digit SIC codes ($\textit{log}{} \textit{HHI}_{\textit{it}}$). Finally, some firms might have a permanently higher market value than others due to omitted firm specific effects.⁴⁰ To control for the firm’s unobserved heterogeneities, I include $\alpha _i^{\textit{MV}}$ in Eq. (20). Adding the above variables to Eq. (20) results in the specification

$$ \begin{aligned} \textit{log}q_{\textit{it}}= & {} \textit{log}\left( 1 + \gamma _1 \times \left( \frac{R \& D\textit{stock}}{TA}\right) _{\textit{it}}+\gamma _2 \times (\frac{\textit{PATstock}}{R \& D\textit{stock}})_{it}\right. \nonumber \\&\left. +\,\gamma _3 \times \left( \frac{\textit{CITEstock}}{\textit{PATstock}}\right) _{\textit{it}}\right) +\delta _1 \textit{log} F_{\textit{it}}+ \delta _2 \textit{log}{} \textit{spill}F_{\textit{it}}\nonumber \\&+\,\delta _{3}{} \textit{log}{} \textit{spill}R \& D_{\textit{it}}+\delta _{4}{} \textit{log}{} \textit{sale}_{\textit{it}}+\delta _{5}{} \textit{log}{} \textit{sale}_{\textit{it}-1}\nonumber \\&+\,\delta _{6}{} \textit{log}{} \textit{HHI}_{\textit{it}}+ m_t+\alpha _i^{\textit{MV}} +\epsilon _{\textit{it}}^{\textit{MV}}. \end{aligned}$$

(21)

Equation (21) could be estimated with a nonlinear least squares estimator, but it is easier to substitute the nonlinear terms with series expansions and estimate the equation with a linear estimator, following Bloom et al. (2013) and Noel and Schankerman (2013).⁴¹ This approach makes the incorporation of firm fixed effects easier. Therefore, Eq. (21) becomes

$$ \begin{aligned} \textit{log}q_{it}= & {} \delta _{1}{} \textit{log}F_{\textit{it}}+\delta _{2}{} \textit{log}{} \textit{spill}F_{\textit{it}}+\delta _{3}{} \textit{log}{} \textit{spill}R \& D_{\textit{it}}\nonumber \\&+\,\gamma _{1}\Psi \left( log\left( \frac{R \& D\textit{stock}}{TA}\right) _{it}\right) +\gamma _{2}\Omega \left( log(\frac{\textit{PATstock}}{R \& D\textit{stock}})_{it}\right) \nonumber \\&+\,\gamma _{3}\Gamma \left( log\left( \frac{\textit{CITEstock}}{\textit{PATstock}}\right) _{it}\right) +\delta _{4}{} \textit{log}{} \textit{sale}_{\textit{it}}+\delta _{5}{} \textit{log}{} \textit{sale}_{\textit{it}-1}\nonumber \\&+\,\delta _{6}{} \textit{log}{} \textit{HHI}_{\textit{it}}+\alpha _{i}^{\textit{MV}}+m_{t}+\epsilon _{\textit{it}}^{\textit{MV}}, \end{aligned}$$

(22)

where the parameters $\Psi$, $\Omega$, and $\Gamma$ denote the polynomials of the measures of intangible assets. Equation (22) is used to build Eq. (7).

Appendix 2: Indirect impacts through R&D and patenting

$$ \begin{aligned}&\textit{INDIRECT}(R \& D)\nonumber \\&\quad =\left[ \frac{\partial \textit{log}q_{i}}{\partial \textit{log}R \& D\textit{stock}_{i}} \times \frac{\partial \textit{log}R \& D\textit{stock}_{i}}{\partial \textit{log}R \& D_{i}} \times \left( \frac{\partial \textit{log}R \& D_{i}}{\partial \textit{log}F_{i}}+\frac{\partial \textit{log}R \& D_{i}}{\partial \textit{log}{} \textit{spill}F_{i}}\right) \right] \nonumber \\&\quad \quad +\left[ \frac{\partial \textit{log}q_{i}}{\partial \textit{logPATstock}_{i}} \times \frac{\partial \textit{logPATstock}_{i}}{\partial \textit{logPatent}_{i}} \times \frac{\partial \textit{logPatent}_{i}}{\partial \textit{Patent}_{i}} \times \frac{\partial \textit{Patent}_{i}}{\partial \textit{log}R \& D\textit{stock}_{i}}\nonumber \right. \nonumber \\&\quad \quad \left. \times \frac{\partial \textit{log}R \& D\textit{stock}_{i}}{\partial \textit{log}R \& D_{i}} \times \left( \frac{\partial \textit{log}R \& D_{i}}{\partial \textit{log}F_{i}}+\frac{\partial \textit{log}R \& D_{i}}{\partial \textit{log}{} \textit{spill}F_{i}}\right) \right] \nonumber \\&= \frac{\partial \textit{log}q_{i}}{\partial \textit{log}R \& D\textit{stock}_{i}} \times 1 \times \left( \frac{\theta {2}+\theta {3}}{1-\theta _1}\right) \nonumber \\&\quad +\frac{\partial \textit{log}q_{i}}{\partial \textit{logPATDstock}_{i}} \times 1 \times \frac{1}{\overline{\textit{Patent}}} \times \beta _4 \times 1 \times \left( \frac{\theta {2}+\theta {3}}{1-\theta _1}\right) . \nonumber \\\end{aligned}$$

(23)

$$\begin{aligned}&\textit{INDIRECT}(\textit{PATENTING})=\left[ \frac{\partial logq_{i}}{\partial \textit{logPATDstock}_{i}} \times \frac{\partial \textit{logPATDstock}_{i}}{\partial \textit{logPatent}_{i}}\right. \nonumber \\&\quad \left. \times \frac{\partial \textit{logPatent}_{i}}{\partial \textit{Patent}_{i}} \times \frac{\partial \textit{Patent}_{i}}{\partial \textit{log}F_{i}}\right] \nonumber \\&\quad +\left[ \frac{\partial \textit{log}q_{i}}{\partial \textit{logPATDstock}_{i}} \times \frac{\partial \textit{logPATDstock}_{i}}{\partial \textit{logPatent}_{i}} \right. \left. \times \frac{\partial \textit{logPatent}_{i}}{\partial \textit{Patent}_{i}} \times \frac{\partial \textit{Patent}_{i}}{\partial \textit{log}{} \textit{spill}F_{i}}\right] \nonumber \\&=\frac{\partial \textit{log}q_{i}}{\partial \textit{logPATDstock}_{i}} \times 1 \times \frac{1}{\overline{\textit{Patent}}} \times (\beta _1+\beta _2). \end{aligned}$$

(24)

One point to note is that the $R \& D$ variable is a stock variable in Eqs. (10) and (12), and is a flow variable in Eq. (11). Following Hall et al. (2005), I define the relation between the $R \& D$ stock and flow as

$$ \begin{aligned} R \& D\textit{stock}_{it}=(1- \delta )R \& D\textit{stock}_{\textit{it}-1}+ R \& D_{\textit{it}}. \end{aligned}$$

(25)

Using the steady state condition ($R \& D\textit{stock}_{\textit{it}}=R \& D\textit{stock}_{\textit{it}-1}=R \& D\textit{stock}_i$), and taking the logarithm of both sides, Eq. (25) becomes

$$ \begin{aligned} \textit{log}R \& D\textit{stock}_{i}=\textit{log}R \& D_{i}-\textit{log}\delta , \end{aligned}$$

(26)

where

$$ \begin{aligned} \frac{\partial \textit{log}R \& D\textit{stock}_{i}}{\partial \textit{log}R \& D_{i}}=1. \end{aligned}$$

(27)

I use Eq. (27) in Eq. (23). The same applies to the patent variable as this variable is a stock variable in Eq. (10) and is a count variable in Eq. (12).

Appendix 3: Measuring technology spillovers

Firms in different industries interact with each other. These interactions imply the possibility of R&D spillovers among firms. In order to measure the R&D spillovers, I follow the R&D spillovers literature that I explain in Sect. 1, and I measure the R&D spillovers of firm i at time t as

$$ \begin{aligned} \textit{Spill}R \& D_{\textit{it}}=\sum _{j \ne i} \rho _{ij} \times R \& D\textit{stock}_{\textit{jt}}. \end{aligned}$$

(28)

The parameter $\rho _{\textit{ij}}$ measures the closeness between firm i and j, and the variable $R \& D\textit{stock}_{\textit{jt}}$ stands for the R&D stock of firm j at time t. According to Jaffe (1986), firms mostly benefit from R&D of the firms that are closer to them in their technological field. Jaffe names $\rho _{\textit{ij}}$ the technological proximity between firms i and j, and he explains that $\rho _{\textit{ij}}$ is built based on the uncentered correlation coefficient of the location vectors of firms i and j ($S_i$ and $S_j$). For example, the location vector of each firm i ($S_i$) based on the distribution of the share of the firm i’s patents across N different technology classes is $S_i=\lbrace s_{i1},s_{i2},\ldots ,s_{\textit{iN}}\rbrace$, where $s_{\textit{ik}}$ shows firm i’s share of patents in the technology class k.

Fig. 8

Patents per $R \& D$ with corrected and not corrected patent counts

Bloom et al. (2013) use a modified version of Jaffe’s (1986) measure for the parameter $\rho _{\textit{ij}}$. Their measure is

$$\begin{aligned} \rho _{ij}=\frac{S_i^\prime S_j}{(S_i^\prime S_i)^{1/2} (S_j^\prime S_j)^{1/2}}. \end{aligned}$$

(29)

The range of $\rho _{\textit{ij}}$ is between 0 and 1. It is closer to 1 for the firms that are closer to each other in their technological field, and it is zero if the location vectors of firms are orthogonal.⁴² Noel and Schankerman (2013) suggest using the distribution of the citations in the patents of each firm across N different technology classes for location vectors. This means $s_{\textit{ik}}$ is the share of all citations in the patents of firm i that belong to a technology class k. These citations reflect the benefits that the firm enjoys from the research activity of others in the same technology field, because they exactly show the previous patents that the firm is using in its innovation. Therefore, I follow Noel and Schankerman (2013) and utilize the distribution of citations across 426 different technology classes of the USPTO in the sample of my analysis to build the location vectors. Then, I use the proximity measure in Eq. (29) to calculate the R&D spillovers that firm i receives at time t from other firms based on Eq. (28).

Appendix 4: Correcting truncation in patent and citation counts

To correct for truncation in patent counts, I follow the approach of Hall et al. (2000), which defines weight factors to correct for truncation in patent counts. Their weight factors are calculated according to

$$\begin{aligned} \textit{patent}_{t}^*= & {} \frac{\textit{patent}_{t}}{\sum _{k=0}^{1999-t} \textit{weight}_k} \nonumber \\ 1996\le & {} t \le 1999, \end{aligned}$$

(30)

where $\textit{patent}_{t}$ is the number of patents granted at time t to all firms and $\textit{weight}_k$ is built based on the average of citations in each lag for the patents of firms.⁴³ Hall et al. (2000) multiply patent counts in ending years of the sample with the inverse of the weight factors ($1/\textit{patent}_{t}^*$) and correct for the truncation. I only correct patent counts for 1996 to 1999 because from 2000 to 2002 (end of my sample) the results are under the “edge effect” (Hall et al. 2000). This means the 2002 data will not be usable and the 2001 data will have large variance. Figure 8 displays a comparison of original and corrected patent counts for truncation.

To correct for truncations in citations, I have employed the method of Hall et al. (2000). I calculate the distribution of the fraction of citations received by each patent at a time between the grant year of the citing patents and the grant year of the cited patent. Using this distribution, I predict the number of citations received for each patent outside the range of the sample, up to 40 years after the grant date of the patent. Figure 9 displays a comparison of original and corrected citation counts. I use the truncation corrected patent and citation counts in my analysis.

Fig. 9

Citations per $R \& D$ with corrected and not corrected citation counts