Discussion Papers In Economics
And Business

Patent Acquisitions under Uncertainty:
The Case of Requests for Examination
Masayo Kani

Discussion Paper 07-06

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANPatent Acquisitions under Uncertainty:
The Case of Requests for Examination
Masayo Kani

Discussion Paper 07-06
February 2007

この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANPatent Acquisitions under Uncertainty:
The Case of Requests for Examination
Masayo Kaniy
Graduate School of Economics, Osaka University
February, 2007

Abstract

Under the Japanese patent system, an applicant has to request examination within a given period of time after application. This paper studies
the timing of a request for examination when return on patent is uncertain.
When a …rm …les a patent application, it acquires a timing option limited
for a …xed period and can exercise it at anytime. After modeling a real options model of the request for examination, we estimate it based on micropatent application data. The paper …nds that the request for examination
is deferred when uncertainty increases. We also …nd that the probability ofrequesting examination rises as the time limit approaches since the option
value declines with time and falls down to zero at the time limit.
JEL classi…cation numbers: C41, L21, and O34
Keywords: patent, request for examination, real options, and duration analysis
I would like to thank Kazuo Ogawa for the valuable comments and encouragement. I am also
grateful to Sadao Nagaoka, and other participants in the 2006 Autumn Meeting of Japanese Economic
Association for the helpful comments. I also thank Hitoshi Inoue, Yusuke Kinari, Masahiko Shibamoto,Takanori Tanaka, and Junmin Wan for their valuable comments. All remaining errors are naturally myown.
yGraduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka 560-0043,
Japan. E-mail: mkani@iser.osaka-u.ac.jp

1. Introduction
Much attention has been paid to the importance of Intellectual Property Rights ineconomic activity. Patent rights are the representing one, and also in Japan patents
has been emphasized. Even if statistically, the number of Japanese patent applications
is highest in the world according to World Intellectual Property Organization Patent
Report 2006. Such a case of the high number of Japanese patent applications is afrequent issue in the …eld of patent management. As one opinion, Pitkethly (1997)
suggests a deferred examination system in Japan; "the system must act at least as
a potential incentive to …le patents which in a less ‡exible system might not be …ledbecause they would be less valuable. "Before describing the system, we illustrate the procedures for obtaining a patentright in Figure 1. To put it brie‡y, we can whether to …le a patent application for new
invention, and then we request examination if we hope the patented invention. A patent
will be granted only after examination as to patentability which may be requested by
the applicant or by a third party.
Therefore, provide further details of the patent system, especially a request for examination. Under the system, an applicant has to request examination within a given
period of time after …ling. Otherwise the patent is deemed to be withdrawn1 . With
respect to a given period of time, for the patent applications …led on or before September 30, 2001, the time limit of seven years from the …ling date is to be applied, and theabove revised time limit is to be applied for patent applications …led on or after October
1, 2001. It is the most unique point that Japanese Patent Law allows examination to bedeferred for up to certain …xed period while most other countries do not. That is, under1
An applicant does not expect patenting all applications. In fact the proportion of requests for
examination to all applications is half.

1the other patent systems an applicant must decide to continue applications with continued cost of applications, but under Japanese patent system a continuance procedure is
not needed.
We discuss how …rms accounting for 95% of the patent applications perform under
the unique system. As shown in Figure 1, the Japan Patent O¢ ce publish the content
of an application in the O¢ cial Gazette after 18 months have elapsed from the dateof …ling2 . Therefore, as the …rms defend patenting the invention by the rival …rms,
they take time and select the pro…table patent applications slowly and carefully. At thetime of invention, …rms can not assess precisely return on patenting because the returnis uncertain. Under the Japanese patent system the …rms can decide the timing of arequest for examination with no deferral charge. That is, when the …rms …le patents,
they acquire timing options limited for a …xed period and can exercise in at anytime, or…nite American call option. This paper studies the timing of a request for examination
when return on patent is uncertain using real options approach.
Provided that the concept of viewing patents as options is expressed, Pakes (1986)
presents the value of patents in Europe derived from renewal from data in aspects oftheoretical and empirical study. Pakes (1986) shows that the view of the options represented by holding a patent is that payment of a renewal fee for a granted patent not only
buys the coming years monopoly pro…ts but also buys in all but the …nal year an option
on renewing the patent at the end of the year, exercise price for which is the renewal
fee then payable. The patent renewal model contribute to our study on a request for
examination, but it has the di¤erent points, for example whether an owner has to pay
fee every year is di¤erent. We seek a more suitable model to represent the Japanesesystem.
Meanwhile, in Japan the empirical studies have been di¢ cult due to the problem
of utilizing statistical data. However, recently the patent-a¢ liated organizations are
2

After the publication of unexamined application, an applicant obtains the right to demand (paymentof ) compensation. Note that the compensation is claimed after a patent right is established.

2

promoting the data, for example "Results of the Survey of Intellectual Property-Related
Activities" conducted by Japan Patent O¢ ce, and "The Institute of Intellectual Property(IIP) patent Database " provided by the IIP. The research reports (published in 2004,
2005) examine the Japanese patent activity empirically using individual data of "Resultsof the Survey of Intellectual Property-Related Activities". As mentioned the studies, inJapan it is expected that empirical study on patent activity will accumulate. In thispaper, after modeling a real options model of request for examination, we estimate it
based on micro patent application data collected from "The IIP patent Database ".
Section 2 provides an overview of the request for examination model used in thispaper. In Section 3, we explain estimation method, or duration analysis. Section 4
describes the data and the descriptive statistics, and then Section 5 shows the results ofboth nonparametric estimation and the regression model. Section 6 contains concluding
remarks.

2. Theoretical Model
When we consider requests for examination under the uncertain returns, especially inJapan, the real options model by Paddock, Siegel and Smith (1988) is useful. The
model is the most popular (or mentioned) model for petroleum real options applications,and has practical advantages (when compared with others options models) due to its
simplicity and few parameters estimation. It is suitable for the case of the requests for
examination since the option to develop the reserve is not a perpetual one3 .That is, themethod is to exploit the power of the analogy with a …nancial American call option on astock paying a continuously compound dividend yield4 . Following Paddock, Siegel and3O¤shore leases are usually subject to relinquishment requirements, which limit the time that the…rm can hold the tract before developing it.
4
An American call option is an asset that gives the holder the right (not the obligation) to buy one
stock for a …xed exercise price, until a certain date (expiration ).

3

Smith (1988), the close connection between the value of the request for examination andthe call option on stock is illustrated in Table 1.
Moreover, Paddock, Siegel and Smith (1988) consider the valuation and exploitationof an o¤shore oil tract as a multistage problem: exploration, development, and extraction. Similarly, in the case of patents, applicants and patentees confront the following
decision types: whether to …le a patent application, whether to request examination,
whether to keep any patent granted in force or let it lapse, and how to exploit the patent
one granted (direct commercialization, licensing, a combination or outright sale)5 . Dixit
and Pindyck (1994) describe that the solution to the multistage investment problem hasexactly the same form as the solution to the single stage problem, and the only thingthat changes is the amount of the investment; the solution for the …rst stage uses thetotal investment cost and the solution for the second stage uses the second-stage cost.
Therefore, when we consider the …rm’s decision on requesting examination after …lingof patent applications, the cost includes not only the fee of requesting examination but
also the cost of patenting and the commercialization cost. That is, consider that the…rst stage is a request for examination, and second stage is a patent commercialization.
In particular, we focus on the valuation of waiting the request for examination.
The …rm’s problem is to decide on whether to request examination in considerationof the following situation. Filing a patent application provides the timing option torequest examination, which is the right to decision-making for patenting the invention
due to acquiring the monopoly pro…t from the invention in the future. At any time t
up to a given expiration date , the …rm can pay I including the cost of patenting
and the commercialization cost, for which the expected future net cash ‡ows conditionalon undertaking the request have a present value Vt ; it represents the appropriately
discounted expected cash ‡ows, given the information available at time t. For the …rm,
5

Lambrecht (2000) analyzes the sleeping patent phenomenon, which involves the consideration of the
optimal timing of two sequential investment decisions: patenting and commercialization of the productinnovation.

4

Vt represents the market value of a claim on the stream of net cash ‡ows that arise
from patenting the inventory. Typically, Vt is stochastic. We assume that Vt follows ageometric Brownian motion of the form,

dV = V dt + V dz;

where

is the drift (or growth rate) parameter,(1)

the proportional variance parameter,and dz the increment of the standard Wiener process.
Given equation (1) for the value of a patent , we can now determine the value of
waiting a request for examination. Let F (V; t) denote the value of waiting the request
for examination. Using equation (1) and going through the usual steps, we can verify
that F (V; t) must satisfy
12

2

V 2 FV V + (rwhere r is the riskless interest rate, anddo not need to know

)V FV + Ft=

rF = 0;(2)

is the dividend rate6 . Note that weor , but only the di¤erence between them, . Equation (2) is apartial di¤erential equation; since the option to request examination expires at time ,the value of the option depends on the current time t.
6

We can write equation (2) down immediately by noticing the formal analogy between this partial
di¤erential equation and the one obtained using the dynamic programing approach,1
2

2

V 2 FV V + V F V + Ft

F = 0;

where is a discount rate. In equation (2), the exogenously speci…ed discount rate is replaced by theriskless rate r, and the growth rateof the geometric Brownian motion of V is replaced by (r):
In other words, we can evaluate the future payo¤ by discounting it at the riskless rate r, provided weare willing to pretend that V follows a process with a di¤erent growth rate parameter 0 = r. We
have here an instance of "equivalent risk-neutral valuation," a procedure with much wider applicability
and interest in …nancial economics; See Dixit and Pindyck (1994, Chapter 4 and 5) for the relationshipbetween dynamic programing and contingent claims valuation.

5

Equation (2) must be solved subject to boundary conditions as following.

F (0; t) = 0;

F (V; ) = max [VF (V ; t) = V(3)I; 0] ;

(4)

I;

(5)

FV (V ; t) = 1:

(6)

Condition (4) just says that at expiration, the option will be exercised if V > I.
Equation (2) cannot be solved analytically, but it is not di¢ cult to obtain a solution
numerically using …nite di¤erence methods. The numerical solution will help to illustrate
the results and show how they depend on the values of the various parameters. As wewill see, these results are qualitatively the same as those that come out of standard
option pricing models. Table 2 reports the solutions of numerical analysis by case, andFigure 2.1 to 2.4 show the threshold values.
The Basic Model
The basic model showed by the column 1 in Table 2 and Figure 2.1 is based on thefollowing parameter values: the total cost I = 1, the pro…t volatility (or uncertainty)= 0:2, the time to expirationrate= 7, the riskless interest rate r = 0:04, the dividend= 0:04. In Table 2, the value of the threshold is higher than the cost, V > I = 1.

That is, the value is higher than the threshold value in the standard NPV rule, V=I = 1. Figure 2.1 shows the threshold value V as a function of the number as years to
expiration. Note that at expiration, V = I = 1 which follows from boundary condition(4), so that the standard NPV rule applies. The threshold declines toward unity as the
expiration approaches since the option value declines with time and falls down to zeroat the time to expiration. In particular, it declines drastically close to the expiration.
6

The Case of Larger Uncertainty
The column 2 in Table 2 and Figure 2.2 report the case of lager uncertainty, for
The uncertainty increases the threshold value V= 0:4.

and the option value F in Table 2.

Therefore, it is di¢ cult for a …rm to request examination. Along with these value, thethreshold curve showed by Figure 2.2 is upper than Figure 2.1. Thus, it is known thatthe uncertainty increases the value of a …rm’s investment opportunity, but decreases theamount of actual investing that the …rm will do.
The Case of Larger Opportunity Cost
The parameterstock,

plays an important role. If V were the price of a share of common

would be the dividend rate on the stock. The total expected return on thestock would be=+ ; that is, the dividend rate plus the expected rate of capital

gain. If the dividend rate

were zero, a call option on the stock would always be held

to maturity, and never exercised prematurely. The reason is that the entire return on
the stock is captured in its price movements, and hence by the call option, so there isno cost to keeping the option alive. However, if the dividend rate is positive, there is an
opportunity cost to keeping the option alive rather than exercising it. That opportunity
cost is the dividend stream that one forgoes by holding the option rather than the stock.
Since

is a proportional dividend rate, the higher is the price of the stock, the greater isthe ‡ow of dividends. At some high enough to make it worthwhile to exercise the option.
If> 0, the expected rate of capital gain on the projectis less than the expected

rate of return from owning the completed project . Henceis an opportunity cost of

delaying construction of the project, and instead keeping the option to invest alive. If
were zero, there would be no opportunity cost to keeping the option alive, and one
would never invest, no matter how high the NPV of the project. That is why we assume> 0. On the other hand, if

is very large, the value of the option will be very small,because the opportunity cost of waiting is large. As
7! 1, the value of the option goes

to zero; in e¤ect, the only choices are to invest now or never, and the standard NPV ruleagain applies. In the case of a request for examination, there could be an opportunity
cost to delay the request. Since the deferred request for examination leads to take along time to grant a patent from the …ling date, in the meantime a …rm might let theopportunity of pro…ts go to waste and also period of patent right is shorter7 . Thus, thepatent applications with the large opportunity cost, including the shorter life cycle of atechnology, should be requested immediately, while others with small opportunity cost,
including the defensive patent applications, should be held until close to the time limit
for requesting examination.
The column 3 in Table 2 and Figure 2.3 show the case of a larger opportunity cost,for= 0:08. When the opportunity cost is large, the threshold value and the option

value are lower than the basic model, that is, a …rm requests examination at an earlier
date.
The Case of Shorter Expiration Date
As we saw in section 1, the time limit for submitting a request for examination for apatent application is to be changed as of October 1, 2001 from "within seven years"
from the …ling date to "within three years" from the …ling date. In response to this, thepatent applications waiting the examination at Patent O¢ ce jump. We can examinesuch a revision using our model, and show in column 4 in Table 2 and Figure 2.4, for= 3. As compared with seven years, or the basic model, the threshold value andthe option value slightly decrease. It is implied that such revision promotes requestingexamination, therefore, raises the number of requests for examination.
7

The term of patent is 20 years from the …ling date. Note that there is no case of patenting by thethird party after …ling.

83. Estimation Method
In the previous section, we capture requesting examination as exercising the call option,and show how to decide the timing of it under uncertainty when a …rm is allowed
examination to be deferred for up to certain …xed period. In this section, we brie‡ydescribe duration analysis ,which use models of the length of time spent in a given state
before transition to another state, such as duration unemployed or alive or without healthinsurance. Considering such econometric models, the problem is that the distributions
for time to an event might be quite dissimilar from the normal. Then, we should use
the methods substituting a more reasonable distributional assumption, called parametricmodels, or relaxing the speci…cation of the model, called semiparametric models.
We begin with explaining the basic concepts. Now consider that a patent application
has not yet requested examination for T periods. Duration T is nonnegative randomvariable and has the cumulative distribution function F (t) and the density function
f (t) = dF (t)=dt. Then, the probability that the duration is less than t is

F (t) = Pr[T

t] =

Z t

f (s)ds:(7)0

A complementary concept to the cdf is the probability that the duration exceeds t,
called the survivor function, which is de…ned by S(t) = Pr[T > t] = 1

F (t) . A key

concept is the hazard rate (or function), which is the instantaneous probability of leaving
a state conditional on survival to time t. This is de…ned as(t) = lim

Pr[t

t!0

T <t+
t

tjT

t]

=

f (t)
:
S(t)

(8)

We can obtain estimators of the survivor and the hazard function by using nonparametric analysis. Let t1 < t2 << tj <of the spells in a sample of size N; NtJ denote the observed discrete failure times
J. We de…ne it as follows,9dj= the number of spells ending at time tj ;

(9)

mj

= the number of spells censored in [tj ; tj+1 );rj= the number of spells at risk at time tj=

X(dl + ml ) ;ljl j

where "at time tj " means "just before time tj ." In this paper, tj is a period from a …lingdate to a requesting date or a censoring date, N is the number of patent applications, dj
is the number of patent application requesting examination at time tj , rj is the numberof patent applications which still have deferred requests for examination at time tj
Since

j = Pr [T = tj jT.

tj ], an estimator of the hazard function is the number ofspells ending at time tj divided by the number of spells at risk at time tj , or b = dj =rj .
The Kaplan-Meier estimator or product limit estimator of the survivor function is the
sample analogue,
Sb =

Y

1

jjtj tbj =Y rj

jjtj t

dj
rj

:

(10)

In section5.1, we report this estimator based on our data set.
On the other hand, usually in econometric models we are interested in hazard functions conditional on a set of covariates or regressors. Perhaps the most widely used
formulation used in regression analysis of durations is the proportional hazard model. A
proportional hazard can be written as(tjx) =0 (t;) (x; )

(11)

where (x; ) > 0 is a nonnegative function of x, which is a vector of covariates, and0 (t;) > 0 is called the baseline hazard. In addition,andare vectors of parameters.

The baseline hazard is common to all individuals in the population and is a functionof t alone. The individual hazard function di¤ers proportionately based on a function10(x; ) of the observed covariates.
Furthermore, we can classify the methods of duration analysis into two groups. In
parametric models an appropriate hazard function is speci…ed, such as the exponential or Weibull distribution. We should use the distribution with due consideration forcharacteristics of our duration data.
Such fully parametric models are relatively simple to estimate but produce inconsistent parameter estimates if any part of the parametric model is misspeci…ed. Fortunately,
there is a semiparametric method that requires less than complete distributional speci…cation because the baseline hazard is no particular parametrization and, in fact, is left
unestimated. The model makes no assumptions about the shape of the hazard over time.
This is called the Cox proportional hazards model. To keep the distribution of duration
data ‡exible, we adopt the Cox proportional hazards model.
Following Cameron and Trivedi(2005, Chapter 20), we mention the Cox proportional
hazards model along the analysis in this paper. The proportional hazard denotes(tjx) =

This replaces

00 (t) exp(x

):

(12)

(x; ) with exp(x0 ) in the general form (5). That is, This model isconsidered, with the functional form for0 (t;) unspeci…ed and the functional form for(x; ) fully speci…ed. Suppose the kth regressor xk increases by one unit and other
regressors are unchanged. The change in the hazard is 1

exp( k ) times the original

hazard then.
To estimate

in the proportional hazard model, we set up a partial likelihood

function. Let t1 < t2 << tj << tJ denote the observed discrete failure

times of the spells in a sample of size N , N

11J. Additionally, we de…ne to be the set

as follow.

R(tj ) = fl : tl

tj g = set of spells at risk at tj(13)

D(tj ) = fl : tl = tj g = set of spells completed at tjX
dj =1 (tl = tj ) = number of spells completed at tj :l

Now consider the probability of requesting examination at time tj . ThenPr [Tj = tj jR (tj )] ==Pr [Tj = tj jTj tj ]tj ]l2R(tj ) Pr [Tl = tl jTlPPj (tj jxj )l2R(tj )=(14)l (tj jxl )(xj ; )
l2R(tj ) (xl ; )P

where in the last line the baseline hazard factor

0 (tj ) has dropped out, as a consequenceof the proportional hazard assumption, (t) = .
Furthermore, we should modify a partial likelihood function on the basis of equation(14) so that it adapts to three characteristics of our data described in next section.
First, we should control for tied durations. If there is more than one failure at a given
time, an adjustment is needed. It is possible that multiple patent applications request
examinations at the same time. Then, the partial log-likelihood function denoteln L ( ) =

k
X
j=1

2
4

X

ln (xm ; )m2D(tj )0

dj ln @X

l2R(tj )13(xl ; )A5 :(15)

Second, our data have right censoring data described in detail in next section, anduntil they are censored a¤ect the size of the risk set, or the second in (15). Then, we

12should rewrite it asln L ( ) =

N
X
i=1

where the indicator variables

2

i 4ln

0

ln @

(xi ; )X

l2R(tj )13(xl ; )A5

(16)

i = 1 for uncensored observation and equal zero otherwise.

Third, this paper focuses on the point what kind of technology is. We therefore
allow the baseline hazards to di¤er by technical classi…cation, but the coe¢ cientsareconstrained to be the same8 . This method is called strati…ed estimation. The hazard
function for technical classi…cation gth denotes0g (t) exp (x) ; g = 1; : : : ; 8. Then, thepartial log-likelihood function isln L( ) =8
X

ln Lg ( ):

(17)

g=1

Using the equation (17), we perform maximum likelihood estimation.

4. Data
We use rich data set to study the timing of the request for examination under unique
Japanese patent system. The data set link Japanese …rm-level data to patent data, thatis, each observation has not only the information about a patent application but also
the applicant’s, or …rm’s characteristics. We collect patent data from the Institute ofIntellectual Property (IIP) Patent Database (DB) provided by Institute of Intellectual
Property, and …rm-level data from NEEDS …nancial database. We describe a making
method of our data set as follows.
To begin with, we describe a outline of IIP patent DB. The DB is developed forpatent statistics analysis based on arrangement standardization data, and covers the8

We classify the pantent applications according to International Patent Classi…cation. 1.Human
Necessities, 2.Performing Operations; Transporting, 3.Chemistry; Metallurgy, 4.Textiles; Paper, 5.Fixed
Constructions, 6.Mechanical Engineering ;Lighting; Heating; Weapons; Blasting, 7.Physics, 8.Electricity.

13

observations which have been published the contents of applications or registered by
January, 2004 from January, 1964. It consists of the following …ve data …les; Application
File, Registration File, Applicant File, Patent Holder File, and Citation File9 . In thispaper, we use Application File and Applicant File, which are connected with the applicant number. Then, we obtain the information about the date of …ling and requesting,the International Patent Classi…cation, and the applicant’s name.
From NEEDS …nancial database, we extract the manufacturing …rms which published
the …nancial data from 1990 to 2005. By matching the …rm’s name including NEEDS
database and the applicant’s name recorded on IIP patent DB, we can make the richdata set including the patent data and the …rm-level data10 .
Here we consider a revision of the time limit for submitting a request for examination.
The time limit, which represents the time to expiration in section 2, is to be changed
as of October 1, 2001 from "within seven years" from the …ling date to "within three
years" from the …ling date. To avoid a problem with having two limits, we use the data
which were …led from April 1, 1990 to September 30, 2001.
In this study, dependent variables are the durations which are the days from the …lingdate to requesting date. As described in the previous section, we should identify the twokinds of right censored data. One is the data of the application which has not beenrequested within a period of seven years from …ling date. That is, it is the withdrawn
one. The following reasons are thought; the business or right hopeless, or a defensive
application. The other is the data which are right censored at a data collection time
before the time limit for submitting a request for examination. In this study, we set thedata collection time of November 20, 2003, on which we can observe the latest sample.
As discussed in the previous section, the empirical model is appropriate for censoreddata.
9

Goto and Motohashi (2005) gives a complete description of IIP patent DB.
In matching of an applicant’ name and a …rm’s name, we are careful to the following points. We
accommodate a di¤erence of …rm’s name notation and a change of a …rm’s name. However, a merger
and holding company are removed from our sample.
10

14

Using our data set, Figure 3 provides the number of applications and the rate ofrequests for examination, which denotes the number of requests for examination divided
by the number of applications11 . Electrical Machinery and Precision Instruments havethe large number of applications, but lower value in terms of the rate of requests for
examination. Due to constantly advancing technology …elds in such high-tech industries, they might not make a former application a patent if a more valuable technology
invent after …ling. Thus, the performance of applications and requests for examination
is implied technical characteristics by industry.
In this paper, we suggest one explanation for the timing of a request for examination
when returns on patents are uncertain. In section 2 we present the theoretical model,
and show that the higher uncertainty of returns is, the more di¢ cult it is to request
examination. To analyze evidence empirically, we use the standard deviation of thegrowth rate of real sales within the duration as the uncertainty measure12 . In terms ofpredictions in the theoretical model, it has the negative e¤ect on the hazard rate which
denotes the probability of requesting examination.
Besides the implications from our model, we investigate the e¤ect of the average ofthe real sales growth rate within the duration. We consider that in the growth stage a…rm requests examination actively because of making the patent strategy with an eye
to the future. Therefore, it is expected that the higher growth rate …rms perform, theshorter the duration is, that is positive e¤ect of the hazard rate.
In addition, we show whether the number of employees has the e¤ect on the hazard
11

We calculate the rate of requesting examination in Figure 3 using the observation having expired by
the collection date, or before November 20,1996. If we use the total observations, the rate is underestimated because of including the observations before the time limit.
12
As discussed even by Pitkehly (1997), it is di¢ clut to assess the value of individual patents. For
example, Pakes (1986) estimates the value of patents in Europe using the patent renewal model. Therefore, we face the problem of measuring the uncertainty of patent value. However, we cannot use theinformation after requesting because the feedback from the duration to the future value of the covariate
violates strictly exogenous. In this paper, we asssume that a …rm calculates the pro…t ‡ow from a patenttechnology based on the performance of itself when decides a request for examination. Then, leaving it
as a subject of future investigation, we use tthe standard deviation of the growth rate of real sales as theproxy of the uncertainty. The measure basically follows that of Ogawa and Suzuki (2000), except thatthe empirical study shows capital investment under uncertainty.

15

rate. This hypothesis is basically followed by Nagaoka and Nishimura (2005), who estimate the patent acquisition function and the patent use function using Japanese patentdata. Although the size of complementary assets increases the number of application,
the rate of requesting examination decreases, because of including the lower quality or
unpatentable applications. We predict the negative e¤ect on the hazard rate. As for the
rest, some kind of dummy variables are provided. One is the technical dummy due tocontrolling the technical characteristics of applications. We take in 527 dummy variables
based on International Patent Classi…cation. The others are industrial dummy variables
and …ling year dummy variables which control the situation associated with economic
and patents.
In duration analysis, the regressors contain the time-invariant covariates which denote the vector of regressors at time t and the time-varying covariates which denote thecovariate path up through time t13 . In this study, all dummy variables are clearly timeinvariant covariates because they do not take di¤erent values over the duration. On theother hand, sales and the number of employments are observed each …scal period, but
we can consider them as time-variant covariates by transforming into the average andthe standard deviation, that is, we look on their measures as the constant performanceof the …rm over the duration. In fact Cameron and Trivedi (2005) describe using the
average over the duration as the easy method to deal with time-varying covariates bysome software.
Table 3 and Table 4 show descriptive statistics and correlation coe¢ cients, respectively.
13
We can obtain the data after a request for examination from Registration File in IIP patent DB.
However, they may exihibit feedback so that patent registration is involved in whether it requests examination or not. Lancaster (1990) provideds a de…nition that rules out feedback from the duration to
future values of the covariates. Therefore the information on registration is not appropriate as covariates.

16

5. Results
5.1. Fact Finding
Figure 4 shows the rate of requests for examination by …ling year, which denotes thenumber of requests for examination divided by the number of applications. Although
in the …rst year it is little high 8%, after that decreases, just before time limit rises
again. That is, the rate of request for examination draws the U-curve14 . Such a uniquesituation might imply the Japanese system of request for examination.
The rise in the latter half is corresponding to the discussion in section 2; the numberof requesting examination increases as the time limit approaches since the option value
declines with time and falls down to zero at the time limit.
Furthermore, the high rate in the …rst year suggests the two factors. One is the valueof the valuable patent is requested immediately. Pakes (1986) shows that there are a
few highly valuable patents and many relatively worthless ones since the distributionof the potential returns skews towards as the patent ages. The other is that the highopportunity cost leads to request examination at once. Since we cannot identify the two
factors, we need to undertake an additional analysis forward15 .

5.2. Nonparametric Estimation
Using the data of duration including censoring data, in Figure 5 we present the KaplanMeier estimator of survival function by industry. As the de…nition is showed in section
3, it provides the probability not requesting examination at the time. No regressors
14

Note that such a curve is the …nding by data of the Japan Patent O¢ ce Annual Report. Our data
set cannot capture the curve, although the rate rises as time passes.
15
We make table of it.
Value of patent Opportunity cost
Request for examination
High
High
ImmediateHigh
Low
Immediate
Low
High
Immediate
Low
Low
Deferred17

are included. The estimator is often insightful to know the shape of the raw hazardor survival function before considering introducing regressors. In addition, it is notcorresponding to the rate of requesting examination in Figure 4, because denominators
are di¤erent. The denominator of the rate is total number of applications, on the other
hand, the estimator uses survival number of application at the time. That is, the rate is
unconditional probability, and the estimator is conditional probability. Then, we should
be careful to interpret the estimator.
Figure 4 shows that the estimator of the survivor decreases drastically over 7 years, orfrom 2191 days to 2557 days. To defend entry of other …rms, a …rm gets a large numberof complement patents to encircle core patents. In such a case, representing the low
opportunity cost, the …rm is not always have to patent immediately, therefore requests
for examination have been deferred until the time limit for requesting examination, thatis, until the option value lowers enough.

5.3. Decision of timing to request examination
We report estimation results based on the Cox proportional hazard model described in
section 3, using a 5% random sample of total population of our data set. Table 5 shows
two estimation results. First, in the non-strati…ed estimation we assume that all patentapplications have the same baseline hazard. Uncertainty, growth rate, and number of
employees coe¢ cients are signi…cant at 5%, which are consistent with our view. However,
we cannot pass the speci…cation tests of the proportional hazards assumption that thecoe¢ cients are constant over time, H0 : (t) = . The test statistic using Schoenfeld
residuals by Grambsch and Terneau (1994) is reported in the last row of Table 5. As aresult of it, we …nd the speci…cation problem, and it suggests that the proportional hazard
assumption is violated for some covariate. In such cases, it may be possible to stratify
on that variable and employ the proportional hazard model within each group (or called
stratum) for the other covariates. Figure 5 represents the baseline cumulative hazard
18

function under the assumption that all observations face the same baseline hazard16 . Itis very restricted.
As discussed in section 3, in the strati…ed estimation the individuals in the gthgroup have an arbitrary baseline hazard function. And so, the baseline hazards areallowed to di¤er by technical classi…cation based on International Patent Classi…cation;g = 1;; 8. The coe¢ cients are constrained to be the same. The estimation results

reported by Table 5 are signi…cant at 5%. Moreover, the coe¢ cient estimators do notchange as such non strati…ed estimation results. Cleves et al. (2004) recommend thatthe proportional hazards assumption be checked separately for each group. In Table
6 the speci…cation tests of the proportional hazards assumption are passed except for"Physics".
In the result for the strati…ed estimation, we interpret the e¤ects on the probabilityof requesting examination. The uncertainty increases the probability, then it is impliedthat a …rm with larger uncertainty for project returns delays a request for examination,and it is consistent with the theoretical implication. For example, in the …rm that theuncertainty is 0.1 points larger, the probability of requesting examination falls by 16.7%
at any given point in time. The growth rate coe¢ cient is positive, meaning that growing…rms tend to promote requesting examination, and also as for the number of employee,
we …nd that in the …rm with larger complementary assets the probability of requestingexamination is lower.
As another meaningful point described in section 2, we want to examine that thehazard, that is, the probability of the requesting examination is increasing over timesince the threshold declines as the expiration approaches, especially close to the expiration. The cumulative hazard does appear to be increasing and at an increasing rate,
meaning that the hazard itself is increasing (recall that the hazards is the derivative of
16

Although the Cox model produces no direct estimate of the baseline hazard, estimates of functions
related to 0 (t) can be obtained after the fact, conditional on the estimates of from the Cox model.
One of them is the estimates of the baseline cumulative hazard.

19the cumulative hazard). Then, we should examine the estimate of the baseline cumulative hazard because the baseline hazard is a function of time alone, that is corresponds
to the overall hazard when x = 0. Figure 6 represents the estimates of the baseline
cumulative hazard by technical classi…cation. Unlike the rate of requesting examinationin Figure 4 and the estimator of Kaplan-Meier in Figure 5, calculating the functions
by technical classi…cation, we can show the results taking into accounts the di¤erenceof the opportunity cost to some extent. We …nd that the probability of the requestingexamination is increasing over time since the curves appear that they have the convex
functions. In particular, the estimates explode cross over 2000 days, and then it should
be showed that the option value declines with time and option value falls down to zero at
the time limit. Between technical classi…cation the order of the estimator di¤ers vastly,
In Electricity, Human necessities and Textiles; Paper, we can consider that the probability of requesting examination depend on time largely because the baseline hazard isa function of time alone.

6. Conclusion
In this paper, we have examined the timing of a request for examination under Japaneseunique patent system both theoretically and empirically. We can explain the …rm’s
decision taking into account a deferred examination system in Japan by the timing
option with the dividend and the time to expiration. Our model shows that 1) the
number of requests for examination increases as the expiration approaches since theoption value declines with time and falls down to zero at the time to expiration, 2) the
large uncertainty leads to defer requesting examination, 3) with the high opportunity
cost a …rm request examination immediately.
Using the rich data matching patents and …rm-level data, we …nd empirical evidence
supportive of predictions in respect of declining the option value over time and the20uncertainty. Note that as far as the opportunity cost concerned, we cannot identify thee¤ect on requesting examination empirically.
As the results of this study, it is implied that a …rm decides to request examination inconsideration of the timing option. Therefore, we should provide the evidence that theunique system of requesting examination in Japan causes the high number of Japanese
patent applications, "…le a patent application in the meantime", since it generates avaluable option.
There are several future directions to take this study. First, we must …nd the measureof uncertainty of individual patent value. Second, we show the e¤ect of opportunity cost
empirically.

References[1] Cameron, A.Colin and Trivedi, Pravin K. (2005), Microeconometrics: Methods andApplications.
[2] Cleves, Mario A., Gould, William W. and Gutierrez, Roberto G. (2004), An Introduction to Survival Analysis Using STATA, STATA Press.
[3] Dixit, Avinash K. and Robert S. Pindyck (1994), Investment and under Uncertainty, Princeton, New Jersey: Princeton University Press.
[4] Goto, Akira and Motohashi, Kazuyuki (2005), "Tokkyo Database no Kaihatu toInnovation Kenkyu," Chizaiken Forum, Vol.63.
[5] Grambsch, P. M. and Therneau, T.M. (1994), “Proportional Hazards Tests andDiagnostics Based on Weighted Residuals,” Biometrica, Vol.81, No.3, pp.515-526.
[6] Lambrecht, Bart (2000), “Strategic Sequential Investments and Sleeping Patents,”
in Project Flexibility, Agency, and Competition, ed.by Brennan,Michael J. andTrigeorgis, Lenos, pp.297-323. Oxford University Press, Oxford.
21

[7] Lancaster, Tony (1990), The Econometric Analysis of Transition Data, Cambrigdge University Press.
[8] Nagaoka, Sadao and Nishimura, Yoichiro (2005), “Acquisitions and Use of Patents:
A Theory and New Evidence from the Japanese Firm Level Data,” IIR Working
Paper WP#05-14.
[9] Ogawa, Kazuo and Suzuki, Kazuyuki (2000), “Uncertainty and Investment: Some
Evidence from the Panel Data of Japanese Manufacturing Firms,” Japanese Economic Review, Vol.51, No.2, pp.170-192.
[10] Paddock, James L., Siegel, Daniel R., Smith, James L. (1988), "Option Valuationof Claims on Real Assets: The Case of O¤shore Petroleum Leases," The Quarterly
Journal of Economics, Vol. 103, No. 3, pp. 479-508[11] Pakes,A. “Patents as options: some estimates of value of holding European patent
stocks,” Econometrica, Vol.54, No.4, pp.755-784.
[12] Pitkethly, Robert (1997), "The VALUATION OF PATENTS: Areview of patentvaluation methods with consideration of option based methods and the potential
for further research," Judge Institute Working Paper WP 21/97.

22

FIGURE 1

Source: "Procedures for Obtaining a Patent Right," by Japan Patent Office.
http://www.jpo.go.jp/tetuzuki_e/index.htm
Note: To the patent applications filed before September 30, 2001, the time limit ofseven years from the filing date is to be applied.

23

TABLE 1
Comparison of a call option with a delayed request for examination
Call option on stock

Delayed request for examination

Current value of stock(Gross) PV of expected cash flow creating patent

Exercise price

Cost, including fee for requesting examination

Time to expiration

Time limit for requesting examination

Stock value uncertainty

Patent value uncertainty

Dividend on stock

Net production revenue from patent less depreciation

24

TABLE 2
Parameters and Numerical Solutions for Four Cases

Column No.

1
Basic

2

3
4
Larger dividendrate, or
Shorter expiration
Larger uncertainty opportunity cost
date

1.Parameter
The present value (at current date) of
the operating project
The present value (at current date) of
the investment cost (net of tax credits)
The volatility of the project V ' or amarket variable as a proxy of the
The time to expiration of the rights ofinvestment
The riskless interest rate (real andafter-tax)
The dividend yield of V (orconvenience yield from the commodity)

V

1.2

I

1

σ

0.2

τ

7

r

0.04

δ

0.04

V*

1.653

0.4
3

0.08

2.Numerical solution

The value of the threshold (level of
optimal immediate investment)
The value of the option to invest (orthe value of the investment
Threshold value × Time

F

2.473

1.337

1.5

0.292
0.462
0.223
0.252
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Note: We find the solutions using the shareware file for real options analysis provided by Marco A.G. Dias.
See http://www.puc-rio.br/marco.ind/main.html#contents.

25

FIGURE 2.1
Threshold Value over Time: part 1

Threshold Value
(V*)

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.00

0.70

1.40

2.10

2.80

3.50

4.20

4.90

Time (Years)
Note: The value is based on the basic case, Column 1 in Table 2.

26

5.60

6.30

7.00

FIGURE 2.2
Threshold Value over Time: part 2

3

Threshold Value
(V*)

2.5
2
1.5
1
0.5
0
0.00

0.70

1.40

2.10

2.80

3.50

4.20

4.90

5.60

Time (Years)
Note: The value is based on the larger uncertainty case, Column 2 in Table 2.

27

6.30

7.00

FIGURE 2.3
Threshold Value over Time: part 3

1.6

Threshold Value
(V*)

1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.00

0.70

1.40

2.10

2.80

3.50

4.20

4.90

5.60

Time (Years)
Note: The value is based on the larger dividend rate case, Column 3 in Table 2.

28

6.30

7.00

FIGURE 2.4
Threshold Value over Time: part 4

1.6

Threshold Value
(V*)

1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.00

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

Time (Years)
Note: The value is based on the shorter expiration date case, Column 4 in Table 2.

29

2.70

3.00

FIGURE 3
Number of applications (per Firm) and Rate of Examination Requests

3500

80.0%

3000

70.0%
60.0%

2500

50.0%

2000

40.0%
1500

30.0%

1000

20.0%

Number of applications per firm

Precision
Instrument(20)Transportation
Equipment(37)Electrical
Machinery(97)GeneralMachinery(77)Metal
Products(25)Non-Ferrous
Metals(23)Iron and Steel(14)Ceramic(17)Petroleum andCoal Products(2)Chemical(83)0.0%Pulp and Paper(8)0Textile(15)10.0%
Food(45)500

Rate of examination requests

Note: The figure is based on a part of data set in this paper, specifically having expired by the collection date; the observations of before
November 20, 1996. The rate of examination requests is the number of examination requests divided by the total number ofapplications. The values in parentheses are number of the firms. Total number of application, examination requests, and firms is588,496 and 273,471, and 463. Then average of application and rate is 1271, and 46.5%.

30

TABLE 3
Descriptive Statistics
Variable
Duration
Uncertainty
Growth Rate
No. Employees (log)Mean1918.193
0.084
0.035
9.288

Standard
deviation
663.330
0.053
0.055
1.238

Minimum

1
0.000-1.517
1.989

Maximum
2557
1.090
0.608
11.222TABLE 4
Coefficient Correlation
Variable
Uncertainty
Growth Rate
No. Employees (log)

Uncertainty
1
0.024-0.269Growth Rate

No. Employees
(log)

1
0.235

1

FIGURE 4
Rate of Examination Requests
14.0%
12.0%
10.0%

1996
1997
1998
Dataset

8.0%
6.0%
4.0%
2.0%
0.0%
0

1

2

3

4

5

6

7

Passed year

Note: “1996”, ”1997” and ”1998” show the rates of requesting examination by application
year, respectively. These data are obtained from the Japan Patent Office Annual Report
2006 (Statistical data). On the other hand, “Dataset” is calculated using a part of data
set in this paper, specifically having expired by the collection date; the observations ofbefore November 20, 1996. The rate of requesting examination is the number ofrequesting examination divided by the total number of applications.

31

FIGURE 5

0.00 0.25 0.50 0.75 1.00

Kaplan-Meier Survival Estimates by Industry

0

500

1000

1500
Time (Days)

2000

Food(5013)

Textile(3842)

Pulp and paper(2931)

Chemical(60038)

Petroleum and coal products(380)

Ceramic(7904)

Iron and steel(25199)

Non-ferrous metals(27188)

Metal products(5102)

General machinery(42941)

Electrical machinery(311949)

Transportation equipment(39348)

2500

Precision instruments(59028)

Note: Number of observations is 588,496 , with 273,471 of requesting examinations. Note that we limit the sample period until
November 20, 1997 in consideration of censoring at the collection date, as in Figure 3 and 4. Values in parentheses are number ofobservations.

32

TABLE 5
Determinants of Requesting Examination

Non stratified estimation
Variable

Coefficient

Stratified estimation

Standard error

exp(0.1*β)-10.205-0.160CoefficientStandard error

exp(0.1*β)-1-1.831***0.207-0.167**

Uncertainty-1.747***Growth rate

0.595

**

0.231

0.061

0.541

0.232

0.056

No. Employees-0.052***0.008-0.005-0.053***0.008-0.005Observations（Exits）

49755(19637)

49755(19637)

Log likelihood-200727.05-167015.41

3023.75***

Table 6

Global test of proportionality overall covariates:Χ2

Note: Hetroskedasticitic-consistent standard errors. *, **, *** denote significant at the 10%, 5%,and 1% levels, respectively. The
dummy of industry, application year, and technology are dropped. The degree of freedom for the specification test is 552.

33

TABLE 6
Specification Test; in Stratified Estimation
Human
necessities

Global test of proportionality
over all covariates:Χ2

139.99Performing
operations;
Transporting

273.39Chemistry;

Textiles;Fixed

Mechanical;

Metallurgy

Paper

Constructions

et al.

216.2

35.22

43.37

144.71

Physics

671.95***

Electricity

391.23

Note: *, **, *** denote significant at the 10%, 5%, and 1% levels, respectively. The dummy of industry, application year, and technology
are dropped. The degree of freedom for the specification test is 552.

34

FIGURE 6
Estimated baseline cumulative hazard: Non-stratified estimation

All (49755 )

cumulative baseline hazard

1.000e-22

8.000e-23

6.000e-23

4.000e-23

2.000e-23

0

0

500

1000

1500

2000

Time

Note: Values in parentheses are number of observations.

35

2500

FIGURE 7
Estimated baseline cumulative hazard: Stratified estimation

Chemistry;Metallurgy(5283)

Electricity(13870)
60

2.000e-10
1.500e-10
1.000e-10
5.000e-11
0

40
20
0
Fixed constructions(1008)

Human necessities(1761)
40
30
20
10
0

1.500e-09
1.000e-09
5.000e-100Mechanical engineering; et al.(3604)

Performing operations; et al. (8748)

1.500e-07

8.000e-08
6.000e-08
4.000e-08
2.000e-08
01.000e-07
5.000e-080
Physics(15016)

Textiles;Paper(465)

1.000e-10

.02
.015
.01
.005
0

5.000e-11
0

0

1000

2000

3000

0

1000

Time
Graphs by nameNote: Values in parentheses are number of observations.

36

2000

3000