High stakes in high technology: high-tech market values as options.

Darby, Michael R. ; Liu, Qiao ; Zucker, Lynne G. 等

I. INTRODUCTION

High-technology industries are frequently formed or transformed as a result of scientific breakthroughs that open new technological opportunities. Major technological innovations are extremely important for the success of a high-tech firm, particularly innovations that other firms cannot easily emulate, either because of broad patent protection or because the underlying technology requires important tacit knowledge unavailable to potential emulators. Firms exploiting such legal or natural excludability enjoy a higher rate of return until other firms are able to catch up or overtake the firm's growing technology portfolio with similar or more advanced technologies.

In this article we argue that the firms with access to the very best scientific minds and cutting-edge technologies will be more likely to pursue a high-stakes "bet the firm" research and development (R&D) strategy which will be characterized by both a higher expected value and a greater probability of discrete stock-price jumps (up or down) as it is revealed whether the bets win or lose. It is not surprising that firms with more knowledge capital are typically more successful, but it is a novel result that these firms have inherently more idiosyncratic risk. These considerations lead us to an option pricing approach to valuing knowledge capital, which we will show fits very well the data for publicly traded biotech firms.

Related Firm Value to Knowledge Capital

There is a substantial body of literature that attempts to improve on accounting-type measures of the value of the firm's intangible knowledge capital. (1) Austin (1993) and Chan et al. (1997) apply a conventional event study approach to estimate the values of intangible assets, such as patents and joint ventures with other firms. Another line of research assumes there is a linear or log-linear relationship between the firm's market value and its knowledge capital measures. By regressing Tobin's q against the knowledge asset variables, this method measures the effects of knowledge assets on the firm s market value. (2) A common problem with this line of research is that it has to fall back on fairly ad hoc functional forms between the firm's market value and the measures for knowledge assets and fail to capture an important component of high-tech firms' market values: Firms with more knowledge capital tend to choose relatively riskier R&D projects, and therefore may face a higher probability of large successes or failures than firms pursuing incremental research strategies.

We build on this work by adding an important omitted consideration: Firms with a strong science base and great scientists make repeated breakthrough discoveries and--whether we call it, like Merton, an "attractive arrogance" or simply rational calculus--are much more likely to engage in high-risk and high-return research (Merton 1968). (3) Firms with the most knowledge capital are most likely to pursue and succeed in a high-stakes R&D strategy and then use what they have learned to launch further major projects. These firms, accordingly, are more likely to undertake significantly costlier and riskier R&D projects given the fact that the expected rewards rise with knowledge capital. Therefore, a market valuation model should take account of this endogeneity in the firm's project selection.

Jump-Diffusion and the Option-Pricing Framework

Because we know that achievement of technological breakthroughs--or failure to achieve them in a major R&D project--affects the firm's market valuation, we expect that a certain type of discontinuity in the firm's market value will occur whenever the firm makes frontier discoveries or announces failure. In this article, we take a traditional view of treating the firm's equity value as a call option written on the firm's valued assets with exercise price equal to the firm's outstanding debt level. In addition, there is a technological breakthrough or impasse component embedded in this call option, which affects the firm's market value. In our model, we assume that the firm's valued assets follow a jump-diffusion process with jump intensity endogenously related to the firm's knowledge-asset measures. We do not specify when or how the firm would achieve a technological breakthrough or reach an impasse, we simply assume that the firms with a strong science base are more likely to do that and the firms' market value, therefore, should include this part of the option premium.

Cox and Ross (1976) and Merton (1976) were among the first to apply a jump process to option pricing models. Bates (1996), Bakshi et al. (1997), and Heston (1993) use the inverse characteristic function method to obtain the closed-form solution for the price of a call option. This article follows the same structure except that the jump intensity in our model is related to the firm's knowledge assets. By applying the inverse characteristic function technique, we are able to overcome the complexity brought along with this endogenized jump intensity assumption and obtain a closed-form solution. Unlike the one in Merton (1976), the jumps in our model are not diversifiable. Earlier studies have found similar evidence. For example, Kim et al. (1994) study the jumps in stock market index and its component stocks and find that the jumps in stock returns are not diversifiable. As to biotech firms, even though the firms can diversify across research projects, whether to make a success or reach impasse to certain degree depends on the firm's linkage to tacit knowledge. The number of great minds is always limited. Therefore, the jump effect in biotech firms could not be diversified and the risk premium adjustment should be positive.

The key to our empirical tests is to find appropriate measures or proxies for the high-tech firm's knowledge capital. We estimate the model using four alternative measures drawn from the literature on R&D: counts by application date of patents eventually granted, patent counts weighted by the number of times each patent is cited subsequently by other patents, patent counts weighted by the number of claims in the granted patent (indicative of patent scope), and the number of genetic-sequence discovery articles authored by a star scientist as or with a firm employee as proof of bench-science involvement in the firm. All of these measures are scaled by a depreciated (at 20%/year) sum of past R&D expenditures.

The first three measures attempt to identify the firm's knowledge-capital intensity by looking at patent output relative to R&D expenditures, lf a simple patent count worked (we will see that it does not), it would be an excellent measure because it is nearly knowable as shares are being valued. We say "nearly knowable" because the firms typically tout to the financial markets the progress of their R&D programs and particularly which patents they have applied for; however, the market still must assess whether patent applications still pending will ultimately be granted.

Citation-weighted and claim-weighted patent counts, as discussed, have been pretty well established in previous studies--whether used separately or together--as better indicators than simple counts of the output of R&D process and particularly of more important breakthroughs. Thus, we hypothesize that citation-weighted patent counts and/or claim-weighted patent counts are also better indicators than simple patent counts of the firm's success in creating valuable inventions and hence its likelihood of actually pursuing a high-stakes strategy. However, future patent citations to presently granted and pending patents appear over many years, and Lanjouw and Schankerman (1999) show that it takes about five years after the patent grant date (typically seven to nine years after the application date) before cumulative citations are a reliable measure of patent quality. Therefore, citation-weighted patents are useful for testing the theory but cannot provide much real-time guidance to investors.

In a series of studies, Zucker and Darby (1996; 1998) and Zucker et al. (1998a; 1998b; 2002a) have demonstrated the key role of "star scientists" who act as scientist-entrepreneurs in determining the time and place of entry and the success of firms exploiting the biotechnology revolution. In particular, their measure of "tied articles" (the cumulative number of genetic-sequence-discovery-reporting research articles written by these stars either as or with firm employees) seems to be a direct measure of knowledge capital located on the scientific frontier. One problem of using the Zucker-Darby data set on star scientist articles is that the stars are identified by counting the articles published up to 1990, with articles fully tabulated only through 1992. This definition of star scientists imparts a downward bias for the firms that were founded late (most of them are very small in size).

Using data for the publicly traded biotech companies, we estimate our model by application of the generalized method of moments (GMM). We find several interesting results: (1) In estimates using only one measure of the firm-specific knowledge capital, the claims measure alone works well, although the star ties measure also is acceptable if the observations for very small firms (less than $2 million total assets) are dropped from the sample. (2) In our preferred estimates using simultaneously two measures of firm-specific knowledge capital, either claims and ties or claims and citations provide a good explanation of firm valuation and clearly indicate the empirical importance of the jump process. (3) A simple count of patents is an unsuccessful measure of the firm's knowledge capital; so is a zero-one dummy variable that indicates the existence or absence of nonzero values for either "tied article" or "patent" variable.

The results from the robustness analyses demonstrate that our jump-diffusion option-pricing model correctly specifies the actual process of the firm's market value. The option model based values fit the true market values well, and, on average, the jump premia account for about 5% of the firm's total market value.

The rest of the article proceeds as follows. In section II, we lay out the model and then derive the solution to the model. We provide a detailed description of the data we used in this paper in section III. Econometric methods and the empirical results are provided in section IV. Section V further analyzes the robustness of our model and also contains the results of sensitivity analyses. Section VI concludes. An appendix contains the details of the proof.

II. THEORETICAL FRAMEWORK

A typical model of market value hypothesizes that the market value of a firm is a function of the set of assets that it comprises

(1) C = G([a.sub.1], [a.sub.2], [a.sub.3],...),

where C is the firm's market value, [a.sub.1], [a.sub.2],... are various assets the firm invests in, and G is unknown function that describes how the assets combine to create value. Most empirical study on this line of research has to fall back on fairly ad hoc functions, such as linear or Cobb-Douglas (linear in logs). In this section, we aim to find a near-structural model, which is able to capture the technological innovation nature of high-tech firms. We think this endeavor is able to overcome the naivete of making ad hoc assumptions about the functional form, G; it is also important to help people precisely measure the returns of innovative activities.

The Model

Considering the R&D-intensive nature and the importance of intangibles per se in high-tech industries, we define a high-tech firm's valued asset as follows:

(2) V(t) = [alpha]A(t) + [beta]S(t),

where A(t) is the value of the firm's tangibles at time t and S(t) is the value of the firm's intangibles at time t. (4) V(t) in Equation (2) is the value of the firm's valued assets. It captures the total value of the firm's assets that are valued by the shareholders. Note that in Equation (2), [alpha] and [beta] can be thought of as the shadow prices of the firm's tangibles and intangibles, respectively. They capture the weights the investors put on the firm's assets when they value the firm.

We follow the standard practice and specify from the outset a stochastic structure under a risk-neutral probability measure. The existence of this measure is equivalent to the absence of free lunches, and it allows us to value future risky payoff as if the economy were risk-neutral. We prespecify that the firm's valued asset, V(t), evolves according to the following process:

(3) dV(t)/V(T) = (R[t] - [lambda][[micro].sub.J])dt + [square root of (sigma)]dz(t) + J(t)dq(t),

and

(4) ln[1 + J(t)]~N[ln(1 + [[micro].sub.J]) - ([[sigma].sup.2.sub.J]/2), [[sigma].sup.2.sub.J]],

where

R(t) is the time-t instantaneous spot interest rate;

[lambda] is the frequency of jumps per year (jump intensity);

[sigma] is the diffusion component of the firm's return variance (conditional on no jump occurring);

z(t) is standard Brownian motion;

J(t) is the percentage jump size (conditional on jump occurring) that is log-normally, identically, and independently distributed over time, with unconditional mean [mu.sub.j]. The standard deviation of ln[1 + J(t)] is [[sigma].sub.j];

q(t) is a Poisson jump counter with intensity [lambda], that is, Prob[dq(t)= 1] = [lambda]dt and Prob[dq(t) = 0] = 1 - [lambda]dt. We also assume the probability of more than one jump is Prob[dq(t) [greater than or equal to] 2] = o(dt), where a function f(h) is o(h) if [lim.sub.h][right arrow]0]f(h)/h = 0.

Note that [[sigma].sub.j] also captures the dispersion of jump size.

We further assume

(5) [lambda] = [[lambda].sub.0] + [[lambda].sub.1]X,

where X is the firm-specific knowledge asset measure.

An intuitive interpretation of this process is the following. Most of the time, the firm's total valued assets evolve continuously, but jumps occur occasionally. The frequency of jump occurring is endogenously determined by the firm's intellectual capital state, the X in our model. Thus, the model is able to capture the technologically innovative nature of high-tech firms. Because we specify our model under risk-neutral probability measure, [lambda] is not the actual jump intensity. It is the jump intensity under the risk-neutral probability adjustment; similarly, taj does not capture the actual jump size either. What it captures is the risk-adjusted jump size. It is important to realize that the exogenous valuation framework can be derived from a general equilibrium in which all risks are rewarded. Bates (1991; 1996) demonstrates how risk premiums for each factor could be derived from a general equilibrium model. (5) In our model, the jump risks related to the firm's intellectual human capital have both systematic and unsystematic components. So the risk premium for each risk factor is not zero. As Merton (1976) and many other researchers have pointed out, a firm's equity market value could be regarded as a European call option written on the firm's valued assets with strike price equal to the firm's outstanding debt level and maturity equal to the maturity of the firm's debt. Therefore, we can value the firm's equity market value in a option-pricing framework.

We have

(6) C(t,[tau]) = [e.sup.-R[tau]]E[max(V[t + [tau]] - D[+ [tau]], 0)],

where V(t + [tau]) is the value of the firm's valued assets at time t + [tau], D(t + [tau]) is the firm's debt level at time t + [tau], [tau] is the maturity of firm's debt, and C(t, [tau]) is the price of the European option, and it measures the firm's equity market value in our model. Note that in Equation (6), E is the expectations operator with respect to the risk-neutral probability measure.

Equations (2), (3), (4), (5), and (6) summarize the model. Valuation is related to the firm's intellectual human capital state through the jump component that appears in the dynamics of the firm's valued assets. This captures the fact that frontier discoveries in science and technology and subsequent commercialization made possible by the firm-specific intellectual capital (great scientists, great ideas, etc.) have dramatically changed the high-tech industries.

The Solution to the Model

Applying the generalized Ito's lemma, we know a European call option written on the firm's valued asset with strike price D and term to expiration x could be solved through the following partial differential equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

subject to C(t, [tau]) = max{V(t + [tau]) - D(t + [tau]), 0}.

Note that in Equation (7), we assume that the risk-free spot interest rate, R(t), and the volatility of the return of the firm's valued assets, [sigma], are deterministic. This will reduce the complexity of our model dramatically and will not change the results qualitatively.

In appendix, it is shown that the formula for the price of the European call option is

(8) C(t, [tau]) = V(t)[[PI].sub.1](t, [tau], V, X) - D(t)[e-.sup.R[tau]][[PI].sub.2](t, [tau], V, X),

where the risk-neutral probabilities, [[PI].sub.1] and [[PI].sub.2], are recovered from inverting the respective characteristic functions: (6)

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

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From the appendix, we also know:

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

and

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Equations (8)-(12) provide the solution to the European call option. As discussed, the price of this European call option is the same as the firm's market valuation if we take the firm's equity as a call option written on its valued assets with exercise price equal to its debt level. Therefore, if we can estimate the implicit parameters ([alpha], [beta], [[micro].sub.J], [sigma], [[sigma].sup.2.sub.J], [[lambda].sub.0], [[lambda].sub.1]) in the equations, then we are able to use this formula to estimate the firm's market value. But first, we use the actual data to estimate the model and to test whether it is correctly specified.

III. DATA

This article focuses on the biotechnology industry to estimate our model. The period of analysis for each firm is from the year of founding through 1992. The year 1992 was chosen because it was the last date for which we have full information on the star ties variable and because we needed to allow five years forward to accumulate patent grants and citation data. Although we apply our model here only to the biotech industry, we believe that its applicability is more general. In science-driven high-tech industries undergoing entry-generating metamorphic progress (those with similar technological opportunities incongruent with the science base of any industry incumbents), the essential features will also be present: (7) (1) The firms in such industries have substantial intangibles that have not been valued appropriately by traditional accounting procedures. (2) The firms are competing with others in an R&D-intensive and technologically innovative environment, in which frequent breakthrough innovations based on the firms' intellectual capital generate discrete jumps in the firms' asset values.

The Biotechnology Firms

The starting point for our firm data set is the list of 752 firms used in the Zucker et al. (1998b) and Brewer (1998b) analysis of the adoption of biotechnology. Some of these firms are incumbents in biotech-using industries, such as pharmaceuticals, food processing, beverages, and agriculture. For these incumbents, biotech operations are often a small part of the total value of the firm. To focus on the influence on the firms' stock market performance of innovations in biotechnology, we limit our sample to the 511 entrant firms founded after 1975, the "new biotechnology firms." Combining reports in the industry directory Bioscan (1988-97) with those drawn from the IPO Reporter (1976-92) and from the Securities Data Company's Global New Issues database, we find reports that 156 of the 511 firms went public during the 1979-92 period. However, we can only find subsequent trading records and complete firm data for 129 firms in the COMPUSTAT database. (8) For those 129 firms, we retrieve such data as number of outstanding shares, closing stock price, total assets, debts with different maturities, and R&D expenditures.

Measures of the Firm-Specific Knowledge Capital

Given the purpose of our study, knowledge capital is the key explanatory variable. We try four different indicators of knowledge capital: counts by application date of patents eventually granted, the patent counts weighted by the number of times each patent is cited in subsequent patents, the same counts weighted by the number of claims, and the number of the firm's ties to star scientists. All of these measures are scaled by division by a depreciated sum of past R&D expenditures.

Ties to Star Scientists. The most novel of these measures of knowledge capital, we believe, is a count of the number of times a star scientist appears on a research article reporting a genetic-sequence-discovery listing his or her affiliation as at the firm or writing with another scientist who lists his or her affiliation as at the firm. Each article represents substantial bench-science-level collaboration (and tacit knowledge transfer) between a star scientist and one or more firm employees. We cumulate these ties to year t to obtain an input-based measure of the firm's knowledge capital in that year. (9) A firm's star ties (as just defined) have been shown to be a principle determinant of firm success in biotechnology in both the United States and Japan (Zucker et al. 1998a, 2002a; Darby and Zucker 2001; Zucker and Darby 2001). Star scientists were defined in Zucker et al. (1998b) on the basis of the number of genetic-sequence-discoveries up to April 1990 (see the appendix for detailed discussion). To control for the firm's size and R&D investment, we use the cumulative number of ties up to year t scaled by corresponding depreciated cumulative R&D expenditures in our estimations and denote that variable ties/R&D. (10)

Patent Variables. We obtained our patent variables by connecting to the U.S. Patent and Trademark Office's Internet homepage and searching the database for each of the firms in our sample. For each firm, we obtained a list of all the patents granted up through 1997. We are interested in measuring the firm's knowledge stock as of a certain date and accordingly date the patents by the year in which the application was filed because the underlying R&D would have to be done before application. For each patent granted, we count the number of claims covered by the patent. Simple patents have only one claim, whereas broader patents may cover a number of separable inventions, each spelled out in a separate claim. Patent claims have been increasingly used in the R&D literature as an important indicator of the patent's quality. (11) We also recorded for each patent the number of times it was cited in subsequent patents granted through 1997. Patent applicants are legally required to disclose relevant prior art, and patent examiners also search for other prior patents to clearly delineate the new rights. As a result, the number of patent citations is a standard indicator of a patent's significance. Let Cit(t, s) be the number of citations received in year s to the patents applied for in year t. We define

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where T = 1997. Thus, Cit(t) is the total number of future citations (up to 1997) to patents applied for by the firm in year t. We also define Clm(t) as the total number of claims to patents applied for by the firm in year t.

Because the knowledge value represented by patents declines over time, it is customary in the literature to assume a depreciation rate of g (we assume a conventional value of 0.2; see Griliches 1990). (12) Thus, the patent, citation count, and claim count measures of the firm's knowledge capital are based on

(14) Patent [Stock.sub.t] = (1 - g)Patent [Stock.sub.t-1] + Patent(t)

and

(15) Citation-weighted Patent [Stock.sub.t] =(1 - g)Citation-weighted Patent [Stock.sub.t-1] +Cit(t)

and

(16) Claim-weighted Patent [Stock.sub.t] = (1 - g) Claim-weighted Patent [Stock.sub.t-1] + Clm(t).

Because we are attempting to get a measure of relative intensity of knowledge capital to the size of the R&D expenditures, in estimations we use the patent stock, claim-weighted patent stock, and citation-weighted patent stock divided by the firm's (similarly depreciated) R&D stock. We denote these variables by patent/ R&D, claim/R&D, and citation/R&D, corresponding to the star-based measure ties/R&D.

Other Variables

Some of the variables used in this study are also taken from the data sets Zucker and Darby have constructed for their ongoing project "Intellectual Capital, Technology Transfer, and the Organization of Leading-Edge Industries: Biotechnology." To summarize: A dummy variable (Recombinant Technology) captures whether or not a firm uses recombinant DNA technology, which is a straightforward indicator of whether the firm is using advanced technologies. Also, to control for the effects of technology spillover, we count the number of universities with top-quality bioscience programs in the same region as the firm (Top-quality Universities).

Other variables used in our study include the observed market value of the firm (C), the debt level (D), the maturity of the firm's debt ([tau]), (13) the book value of the assets (A), discounted cumulative R&D expenditures, (14) and, from Bioscan, the age of the firm. In this article, we also use the reputation rank of the lead underwriter that brought the firm public (rank). It follows a 1 to 9 scale with 9 representing the most reputable underwriter. The variable is from Carter et al. (1998).

IV. STRUCTURAL PARAMETER ESTIMATION AND TESTS OF HYPOTHESES

Econometric Method

In applying options pricing models to estimate the effects of intellectual human capital on firm's market value, one always encounters the difficulties that the structural parameters are unobservable. In our model, the spot volatility of firm's valued assets (conditional on no jump), [sigma]; the jump-related parameters [[lambda].sub.0], [[lambda].sub.1], [[micro].sub.J], [[sigma].sup.2.sub.J] (also) [[lambda].sub.2] when we use two science-based variables to explain the jump probability), the shadow prices of the firm's tangible assets and intangible assets, [alpha] and [beta], need to be estimated. In this article, we employ GMM to obtain the structural parameter estimates by implementing the following steps.

Step 1. We treat the firm's market valuation as a European call option written on its valued assets with strike price equal to the debt level. Because the firm normally issues debts with different maturities, we compute the firm's total debt level by calculating the present value of the different types of debts. We discount the debts that will mature in the future by using a short-run risk-free interest rate. The firm's maturity is calculated as the McCauley duration of the firm's debts, as detailed in section III. This measure can be interpreted as a weighted average of the maturities of the firm's different types of debts.

We stack the observations. Note that with an average of only 5.64 annual observations per firm, we do not attempt to estimate time-series effects and treat each observation as if an individual firm. However, we do employ industry age as an instrument to control the year-related effects on the biotech firm's market value. For each of the 727 observations for 129 biotech companies, we calculate the debt level, D, and corresponding maturity, [tau], and observe one of the alternative measures of knowledge capital intensity (Ties/R&D, Patent/R&D, Citation/ R&D, Claim/R&D). Based on this, we calculate the theoretical market value for the firm's equity by using Equations (8)-(12). In other words, we calculate [C.sub.i] (t, [[tau].sub.i], [X.sub.i], [D.sub.i], [V.sub.i]). Let [C.sup.*.sub.i] be the observed market value for observation i, calculated by multiplying the closing stock price by the number of outstanding shares. The difference between [C.sup.*.sub.i] and [C.sub.i] (t, [[tau].sub.i], [X.sub.i], [D.sub.i], [V.sub.i]) is a function of the values taken by [X.sub.i], [A.sub.i], [S.sub.i], [D.sub.i], [[tau].sub.i], R(t), and by [PSI] = ([alpha], [beta], [[lambda].sub.0], [[lambda].sub.1], [[micro].sub.J], [[sigma].sup.2.sub.J], [sigma]). For each i, define

(17) [[epsilon].sub.i][[PSI]] = [C.sup.*.sub.i] + [C.sub.i](t, [[tau].sub.i]; [X.sub.i], [D.sub.i], [V.sub.i]),

where [[epsilon].sub.i] denotes the absolute estimation error of our model.

Step 2. If our model is correctly specified, we expect

(18) E[[epsilon]] = 0.

We assume that

(19) E[[epsilon][epsilon]'] = [OMEGA],

where [OMEGA] is unrestricted. Suppose now for each observation, i, we observe a vector of J variables, [z.sub.i], such that [z.sub.i] is uncorrelated with [[epsilon].sub.i]. The assumptions imply a set of orthogonality conditions:

(20) E[[z.sub.i] [[epsilon].sub.i]] = 0,

which constitutes the moment conditions in our study. It is straightforward that the sample moments will be

(21) m(1/n) [summation over i][z.sub.i][[epsilon].sub.i].

For our model, we assume that the weighted matrix has the following form:

(22) [W.sub.GMM] = (1/[n.sup.2)[summation over i] [summation over j] [z.sub.i][z'.sub.j] x Cov[([C.sup.*.sub.i] - [C.sub.i)]) ([C.sup.*.sub.j] - [C.sub.j)]].

The minimum distance estimator will be the [[PSI].sup.*] that minimizes

(23) q = m([[PSI].sup.*])'[W.sup.-1]m([[PSI].sup.*]).

Estimation and Results

When implementing the procedures, we assume that the set of instruments, z, consists of the following 14 variables: the firm's total physical assets, A; the firm's discounted cumulative R&D expenditures, S; the dummy variable Recombinant Technology, indicating whether the firm uses this technology; the number of local universities with top biotech-related doctoral programs; the number of local top-quality universities; the number of years that the firm has been practicing biotechnology; the age of the firm; the firm's debt level, D; the maturity of the firm's debt, "c; the reputation rank of the lead underwriter; Rank; the age of biotech industry; a constant; and four current-year-flow versions of the knowledge related variables: patent(t)/R&D, clm(t)/R&D, cit(t)/R&D, and dties/R&D.

If our model is well specified, we expect to be orthogonal to these variables. Table 1 presents the sample statistics for the variables used in our estimation. The full sample has 727 firm-year observations for 129 biotech firms. Each firm has one observation for each year from the year it goes public through 1992. The year 1992 was chosen because it was the last date for which we have full information on the ties variable and because we needed to allow another five years beyond patent grant date to accumulate patent citation data. In Table 1, we also report the means of the variables for a truncated sample where 117 observations are deleted because they represent firm years with total assets less than $2 million.

We use the Davidson-Fletcher-Powell (DFP) algorithm to estimate the implicit parameter vector [PSI]. There are two reasons that the DFP algorithm is attractive in our study. (1) The DFP algorithm has very strong convergence ability, which is important for our parameter estimation. (2) When we do the iteration, we have to update the Hessian matrix, H. In most algorithms, this means that we need to calculate the second-order derivatives of our objective function with respect to the implicit parameters. It is a very demanding task given the complexity of the objective function in our model. Using DFP avoids this problem.

We adopt the sequential optimization technique in our estimation. We start from certain starting values and then use GMM to estimate the parameters. After the parameters converge, we use those estimated values as the starting values and repeat the same procedure. We repeat this process until we can no longer improve the estimates. All programs are written in MATLAB. Normally, it takes 7-18 hours to finish one convergence on a devoted Sun workstation.

Are There Discrete Jumps in the Firm's Market ValueL We first use the four knowledge-capital variables separately to explain the jumps in the biotech firm's market value. Table 2 reports the results for the six models we estimate.

Let us look at models II-V first. For these models, we use the full sample to estimate the implicit parameters. The estimation minimizes the criterion or goodness-of-fit statistics. These statistics are distributed [chi square](7) if the data are consistent with the model specification. Thus a significant value of this statistic rejects the model, whereas an insignificant value supports the model. Simple patent counts (model III) are rejected even at the relatively forgiving 1% significance level. On the other hand, when we use claims-weighted patents as our knowledge-capital variable (model V), the model is accepted at both the 1% and the 5% levels of significance, and all the parameter values are significant at the 1%. Using the ties/R&D or citation/R&D indicators gives an intermediate result: The models are rejected at the 5% but not at the 1% level of significance. Because we know that our ties/R&D variable may be biased against new, small firms, we tried dropping the 117 observations corresponding to firm assets less than $2 million. The resulting estimates, reported as model I, are consistent with the bias hypothesis because the [chi square](7) statistic is no longer significant at either the 1% or 5% level and we can accept the model for ties/ R&D using the restricted sample. (15) It is also interesting to know whether knowledge capital only plays a signaling role. In other words, the presence or absence of knowledge capital, rather than the degree of knowledge capital, drives the results. In model VI, we use a dummy variable that equals to one if "ties" or "patent" is positive. The hypothesis is rejected at 1% level. Obviously, the degree of knowledge capital matters. This also reflects the fact that the distribution of knowledge capital on any measure is so skewed and only knowledge capital in the upper tail pays off.

In Table 3, we report the results of combining the claims measure with one or the other of the ties/R&D and citation/R&D measures. (16) While claim/R&D is clearly a useful indicator of knowledge capital, citation/R&D or ties/ R&D may also have some marginal explanatory power. Accordingly, we use two science variables to capture the firm's knowledge capital.

Table 3 reports the results. For model VII, we use ties/R&D and claim/R&D to estimate the option-pricing model. The [chi square] (6) statistic from model VII is 12.26, which passes at both the 1% and 5% significance level. For model VIII, we use claim/R&D and citation/ R&D as the science variables to estimate the model. Now, the [chi square] value drops further to 10.48, which also passes at both the 1% and 5% significance level. (17)

In the first two columns of Table 4, we use the Newey and West (1987) method to test whether ties/R&D and cit/R&D provide additional explanatory power over and above that provided by claim/R&D. Both tests confirm that the additional variable provides some additional power over the fit for model V. Although the criterion value is lower for model VIII than VII, model VII uses variables that can be reasonably estimated contemporaneously, whereas VIII requires a wait of seven years or more. For this reason we consider both models reasonable ways to approximate the firm's unobservable knowledge capital, with model VII more attractive to the practitioner and model VIII to the econometrician or cliometrician. Both models clearly indicate that there are discrete jumps in the firm's market value.

Are the Jumps Technology-Related? Let us focus on the jump-related parameters in our models. Note that the estimated value of [[micro].sub.J] is negative in all models. This sign may seem counterintuitive. But consider the fact that we start our model from a risk-neutral probability framework, so [[micro].sub.J] here does not capture the real jump size, it only captures the adjusted jump size, which already incorporates the positive risk premium of jump risk.

Examining models VII and VIII, we find in each case that both [[lambda].sub.1] and [[lambda].sub.2] are significantly positive, which implies that the probability of jump occurring is positively related to the firm's intellectual capital measures. Again, we use the method proposed by Newey and West (1987) to test the hypothesis:

(24) [H.sub.0]: [[lambda].sub.1] = [[lambda].sub.2] = 0.

By applying the same weighted matrix, W, to both unrestricted model and restricted model, we obtain the minimum distances defined in Equation (23) for both models. The difference between these two should follow a [chi square] distribution with degrees of freedom equal to the number of restrictions imposed if [H.sub.0] holds. In this case there are two restrictions imposed on the model.

Columns 3 and 4 of Table 4 present the results of this test. Obviously, the null hypothesis should be rejected for both models VII and VIII. Therefore, we conclude that discrete jumps in the firm's market value are positively related to the firm's knowledge-capital intensity.

In concrete terms, we have shown not only that firms with greater knowledge-capital intensity are more highly valued by investors, but also that those values are more subject to discrete jumps. We believe that before this article, it was far from obvious that the Genentechs and Chirons should have greater risk than lesser firms. Furthermore, these greater risks are inherent in the very same frontier-moving R&D, which makes these firms so valuable.

V. FURTHER EMPIRICAL ANALYSIS

Robustness Analysis' of the Model

Our model captures the innovative nature of high-tech companies; it also captures the subtle role played by the firm's stock of intellectual capital. The empirical results in section IV also reject the hypotheses that there are no jumps and no intellectual capital related jumps in the firm's market valuation. Despite this success, we must address one remaining question about our model. Table 1 shows that biotech firms' average debt level is far smaller than the firm's underlying assets. Therefore, the call options in our study are deep in the money. Given that, people may suspect that the option characteristics of equity are minimal and the "moneyness" of the options may bias our model estimation. In option pricing framework, "moneyness" is a variable used to measure how deep in or out of the money the option is. In this article, strike price is the debt level, D. The underlying asset price is defined as the firm's valued assets, V = [alpha]A + [beta]S. We define D/V as the moneyness in our model. If our model is correctly specified, the remaining pricing errors of our model should be uncorrelated with the main explanatory variables in our model estimation. This subsection addresses these issues.

We use the implicit parameters estimated from models VII and VIII and calculate the models' proportionate pricing error, Price-error, as follows:

(25) Price-error = (model value - observed value) /observed value

In Table 5, we report the following regression, which tests for each model whether or not the remaining pricing errors of the model, "Price-error," are uncorrelated with the main explanatory variables in the model estimation:

(26) Price-[error.sub.j] = [[beta].sub.0] + [[beta].sub.1] [Moneyness.sub.j] + [[beta].sub.2-12] Year [Dummies.sub.j] + [[beta].sub.13-20] Other [Variables.sub.j + [epsilon]].

Of the 42 coefficients estimated in the two regressions only 3 (7% of 42) are significant at the 5% level and of these 1 (2% of 42) is significant at the 1% level. These results are pretty much in line with probability theory if the errors are in fact unrelated to these right-hand variables. We are particularly pleased to note that moneyness is not a source of error for our model. Note that Price-error is also generally uncorrelated with the variables measuring firm's knowledge assets, such as citation/ R&D, ties/R&D, claim/R&D, Patent/R&D, Top-quality Universities, and Recombinant Technology, which implies that our model has correctly captured the roles played by firm-specific intellectual capital in the firm's valuation. If there is any indication of further work to be done on the model, it is to further incorporate the information implicit in the ranking of the underwriter which brought the firm public.

Finally, note that the adjusted [R.sup.2] of the regression is less than 2% for model VII errors and less than 1% for model VIII errors. A natural interpretation is that our models already capture the explanatory power of those variables, so nothing has been left in the remaining pricing errors.

How Economically Significant Is the Technological Jump Component?

In this subsection, we explore how economically significant the technological jump component is. We estimate the firm's theoretical model value based on model VII (using the claim/R&D and ties/R&D measures to capture the firm's knowledge capital) and on model VIII (using claim/R&D and citation/R&D). Here the economic value due to knowledge capital based jump is calculated as the difference between the model value and the value from the same model with the parameters [[lambda].sub.1] and [[lambda].sub.2] set equal to zero. Table 6 and 7 report our analysis for models VII and VIII, respectively.

The Descriptive statistics portions of the tables provide the statistics of the model values, premia for the selected sample (with the 1989-92 Amgen outliers dropped). (18) The mean value of the knowledge capital based jump is $1.34 million for model VII and $5.25 million for model VIII, which is 1.2% and 5.0% of the firm's total market value, respectively. Although the two models do about equally well at predicting market values of the biotech firms, the model relying on ex post (future citation) information about the value of patents attributes substantially more of market value to the technological jumps.

To look at how knowledge capital affects the variability of the firm's market value, we look at a hypothesized firm with mean values of all the explanatory variables in our pricing model VII or VIII, respectively. We find that this firm's market value derived from our model is given as $112.30 million in Table 6 and $119.98 million in Table 7. The estimated value would be $1.89 million or $10.97 million lower, respectively, if this mean firm has no measurable knowledge capital. (19)

Consider the effect on the firms (bottom part of tables) of increasing each of their knowledge capital measures to levels 1 standard deviation above the mean: The firm's estimated market value goes up by $5.72 million to $118.02 million using model VII and by $28.56 million to $148.54 million using model VIII. If each of their knowledge capital measures is increased by 2 standard deviations, these firms' market values will increase by a total of $13.25 million or $79.78 million, respectively, relative to the case with zero-values for each of the knowledge capital measures.

As we increase the number of patent claims, star ties, or patent citations, the firm's market value keeps on increasing. The approach used in our empirical study provides a possible way of pricing a firm's technology stock. We can value the importance of a star scientist or patent by considering the contribution they may make to the firm's market value. Traditional accounting procedures fail to capture the tangible value of the firm's intangibles, especially knowledge assets. The methodology employed in our study, however, values a firm's intangible assets by taking into account their contribution to the firm's market value.

VI. SUMMARY AND CONCLUSIONS

In this article, we identified empirical evidence of Poisson-distributed jumps in biotech firms' market valuation. We demonstrate that these discrete jumps are related to the firm's knowledge-capital intensity, as measured by ties to star scientists and by patent variables.

Firms with 2 standard deviations more knowledge capital are valued 10-50% more than firms with mean values of all variables (refer again to Tables 6 and 7). The approach we used herein can also be generalized to value other types of intangible assets, especially when they have the same sort of innovative frontier nature with associated higher risks. Further, our approach provides a method to value a firm's intangible assets, an issue on which traditional accounting theory provides little guidance.

We take firm-specific knowledge capital measures as exogenously given. This is consistent with the view that they largely measure the quality of the scientist-entrepreneurs who start the firm (or, less frequently, join it later) and determine its technological identity. This approach was suggested by our data, because the first articles tied to stars usually appear very soon after the firm is founded, usually with the star as a founder receiving a substantial share of the value they generate. (20) These stars may later recruit other stars, but the technological identity of these firms is shaped by their founders. Occasional cases of initial ties to stars substantially after founding does suggest an alternative model, however. This model would analyze knowledge capital as endogenously chosen by firms trying to maximize the associated benefits. In other words, the firms will also take into account the effects of knowledge capital on their stock prices when they decide whether to increase their investment in obtaining more advanced technology. We will address this issue in future research. Meanwhile, we are not sure whether our results can be generalized to different time periods in biotechnology other than the period that includes the very hot market period of the late 1980s and early 1990s. We intend to attack this issue in future research, too. Last, besides the four knowledge measures used in our study, we wonder whether there are some other measures that can better capture the degree of knowledge capital of a high-tech firm. As research in this line evolves, we believe better measures will emerge and can be used to test our model. Of course, this is also a challenging task we plan to pursue in the future.

ABBREVIATIONS

DFP: Davidson-Fletcher-Powell

GMM: Generalized Method of Moments

R&D: Research and Development

APPENDIX: PROOF OF THE OPTION PRICING FORMULA

The valuation partial differential equation can be rewritten as

(A-1) 0=[R - [lambda][[mu].sub.J] - (1/2)[sigma]]([delta]V/[delta]L) + (1/2)[sigma]([[delta].sup.2]/[delta][L.sup.2]) - ([delta]C/[delta][tau]) - RC+ [lambda]E[C(t,[tau],L+ln(1+J),X) - C(t,[tau],L,X)],

where we have applied the transformation L(t)=lnV(t). Inserting the following conjectured solution

(A-2) C(t,[tau]) = V(t)[[PI].sub.1](t,[tau],V,X)-[De.sup.-R[tau]] [[PI].sub.2](t,[tau],V,X)

into (A-1) produces the partial differential equations for the risk-neutralized probabilities, [[PI].sub.j], for j = 1, 2:

(A-3) 0=[R - [lambda][[mu].sub.J] - (1/2)[sigma]]([delta] [[PI].sub.1]/[delta]L) + (1/2)[sigma]([[delta].sup.2][[PI].sub.1]/ [delta][L.sup.2]) - ([delta][[PI].sub.1]/[delta][tau]) - [lambda][[mu].sub.J][[PI].sub.1] + [lambda]E[(1 + ln[l + J])[[PI].sub.1](t, [tau], L + ln(1 + J), X) -[[PI].sub.1](t,[tau],L,X)]

and

(A-4) 0 = [R - [lambda][[mu].sub.J] - (1/2)[sigma]]([delta] [[PI].sub.2]/[delta]L) + (1/2)[sigma]([[delta].sup.2] [[PI].sub.2]/[delta][L.sup.2]) - ([delta][[PI].sub.2]/[delta][tau]) + [lambda]E[[[PI].sub.2](t,[tau],L+ln[1+J],X) - [[PI].sub.2] (t,[tau],L,X)].

Equations (A-3) and (A-4) are the Fokker-Planck forward equations for probability functions. This implies that [[PI].sub.1] and [[PI].sub.2] must indeed be valid probability functions with values bounded between 0 and 1. These equations are separately solved subject to the terminal conditions

(A-5) [[PI].sub.j] (t + [tau], 0, L, X) = [1.sub.L(t+[tau]) [greater than or equal to] ln[D]],

where j = 1, 2. The corresponding characteristic functions for [[pi].sub.1] and [[pi].sub.2] will also satisfy similar partial differential equations:

(A-6) 0 = [R - [lambda][[mu].sub.J] - (1/2)[sigma]]([delta] [f.sub.1]/[delta]L) + (1/2)[sigma]([[delta].sup.2][f.sub.1]/[delta][L.sup.2]) - ([delta][f.sub.1]/[delta][tau]) - [lambda][[mu].sub.J][f.sub.1] + [lambda]E[(1 + ln[1 + J])[f.sub.1](t, L + ln[1 + J], X, [tau]) - [f.sub.1](t,L,X,[tau])]

and

(A-7) 0 = [R - [lambda][[mu].sub.J] - (1/2)[sigma]]([delta] [f.sub.2]/[delta]L) + (1/2)[sigma]([[delta].sup.2][f.sub.2]/ [delta][L.sup.2]) - ([delta][f.sub.2]/[delta][tau]) + [lambda]IE|[f.sub.2](t, L + ln[1 + J], X, [tau]) - [f.sub.2](t, L, X, [tau])]

subject to the terminal conditions

(A-8) [f.sub.j](t + [tau], 0, X; [phi]) = [e.sup.i[phi]L(t+[tau])

for j = 1 and 2. Conjecture that the solutions to the (A-6) and (A-7) are respectively given by

(A-9) [f.sub.1](t,[tau]) = exp{u([tau]) + [y.sup.*]([tau])X(t) + I[phi]ln[V(t)]

and

(A-10) [f.sub.2](t,[tau]) = exp{z([tau]) + [y.sub.x]([tau])X(t) + i[phi]ln[V(t)] - R[tau]

with u(0) = [y.sup.*] (0) = 0 and z(0) = [y.sub.x] (0) = 0. By the separation of variable technique, we can solve the equations as follows:

(A-11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

TABLE 1
Variables List with Descriptive Statistics

Variable Mean SD Minimum

Equity market value, C 135.19 468.26 0.15
Total assets, A 41.63 97.19 0.18
R&D stock, S 17.02 45.17 0.00
Underwriter reputation 5.63 3.42 1.00
Debt level, D 5.64 17.49 0.03
Maturity, [tau] 1.26 0.42 1.00
Age of firm 6.69 3.09 1.00
Age of biotech industry 12.06 2.93 1.00
Top-quality universities 1.44 1.11 0.00
Interest rate, R 0.07 0.02 0.04
Recombinant technology 0.56 0.50 0.00
Ties/R&D stock 0.09 0.54 0.00
Patent/R&D stock 0.38 1.02 0.00
Citation/R&D stock 2.17 9.01 0.00
Patent claim/R&D stock 6.65 20.40 0.00
Dties/R&D 0.04 0.46 0.00
Patent (t)/R&D 0.18 0.61 0.00
Cit (t)/R&D 0.74 2.98 0.00
Clot (t)/R&D 3.10 13.84 0.00

 Mean
Variable Maximum (truncated sample, N=610)

Equity market value, C 7334.00 198.76
Total assets, A 979.57 71.56
R&D stock, S 623.11 27.34
Underwriter reputation 9.00 5.92
Debt level, D 292.19 8.71
Maturity, [tau] 4.32 1.29
Age of firm 16.00 7.33
Age of biotech industry 16.00 12.34
Top-quality universities 3.00 1.79
Interest rate, R 0.14 0.07
Recombinant technology 1.00 0.61
Ties/R&D stock 9.00 0.11
Patent/R&D stock 16.57 0.41
Citation/R&D stock 178.53 2.19
Patent claim/R&D stock 301.85 6.79
Dties/R&D 8.95 0.05
Patent (t)/R&D 7.38 0.19
Cit (t)/R&D 35.05 0.78
Clot (t)/R&D 205.10 3.15

Notes, The table defines all the variables used in this study. The
first four columns of descriptive statistics are for the full sample
with 727 firm-year observations. The last column of the table reports
the variables means for a subsample with 610 observations, where the
117 observations with total assets less than $2 million are dropped.
All dollar values are given in millions of 1984 U.S. dollars (current
dollar values divided by the Consumer Price Index CPI-U). C is defined
as observed market value: C=closing price x number of shares
outstanding. Total assets, A, is the book value of the firm's total
assets (Compustat item 6). The R&D stock is the discounted cumulative
value of the firm's R&D expenditures with 20%, annual discount rate.
It is based only on R&D expenditures reported in Compustat (normally
begins two years before firm goes public). Underwriter reputation is
the rank (9 top to 1 bottom) of the lead underwriter in Carter et al.
(1998). The firm's total debt level includes debt-like liabilities. D
is calculated as the discounted cumulative value of the firm's debt
where the interest rate on six-month Treasury bill is used as the
discount rate. Maturity, [tau], is calculated as the McCauley duration
of the firm's debts. Age years that the firm has been practicing
biotechnology. Age of biotech industry is year-1975. Top-quality
universities is a count of universities in the same functional economic
area as the firm that have any biotech-related programs rated 4.0
higher in the National Research Council 1982 survey of doctoral
programs. R is defined as short-run instantaneous interest rate: we
use the interest rate on six-month Treasury bill. Recombinant
technology equals 1 if the firm applies recombinant-DNA technology
and 0 otherwise. Ties/R&D stock is the cumulative count of articles
by star scientists as or with firm employees/S. Patent/R&D stock is
the discounted (at 20% per year) stock of patents assigned to the
firm dated at application/S. Citation/ R&D stock is Patent/ R&D stock
with patents counted by number of citations by other patents up to
1997. Patent Claim/R&D is Patent/R&D stock with patents counted by
number of claims granted in the patents. Lines, Patent (t), Cit (t),
and Clm (t) are the inputs to the numerators of the four cumulated
variables, respectively. They are scaled here for comparability by
dividing by S.

TABLE 2
GMM Estimates of Implicit Parameters ([lambda]=[[lambda].sub.0]+
[[lambda].sub.1][X.sub.1])

 Model I Model II Model III
 (N=610) (N=727) (N=727)
 [X.sub.1]= [X.sub.1]= [X.sub.1]=
Parameters ties/R&D ties/R&D patent/R&D

[alpha] 1.8576 ** 2.4931 ** 2.4803 **
 (0.0000) (0.0000) (0.0000)
[beta] 0.8643 ** 0.6134 ** 1.0048 **
 (0.0000) (0.0000) (0.0000)
[sigma] 0.0880 ** 0.0905 ** 0.1008 **
 (0.0000) (0.0002) (0.0003)
[[lambda].sub.0] 0.5013 ** 0.1952 ** 0.1565
 (0.0000) (0.0002) (0.1763)
 0.2626 ** 0.3471 ** 0.1988 **
 (0.0000) (0.0004) (0.0283)
[[lambda].sub.1] -0.6012 ** -0.3504 ** -0.0652 **
 (0.0000) (0.0003) (0.0056)
[[micro].sub.J] 0.0800 ** 0.0884 ** 0.1288 *
 (0.0001) (0.0005) (0.0508)
[chi square](7) goodness- 13.9600 18.0133 * 23.7667 **
 of-fit statistic

 Model VI
 (N=610)
 Model IV Model V [X.sub.1]=1
 (N=727) (N=727) if ties or
 [X.sub.1]= [X.sub.1]= patent > 0;0
Parameters citation/R&D claim/R&D otherwise

[alpha] 2.5028 ** 2.2456 ** 2.0136 **
 (0.0000) (0.0000) (0.0000)
[beta] 0.6400 ** 1.1382 ** 0.8134 **
 (0.0000) (0.0000) 0.0000
[sigma] 0.1074 ** 0.1101 ** 0.1165 **
 (0.0000) (0.0000) (0.0003)
[[lambda].sub.0] 0.3078 ** 0.0837 ** 0.3014 *
 (0.0010) (0.0000) (0.1510)
 0.1056 ** 0.2851 ** 0.2842 **
 (0.0004) (0.0001) (0.0475)
[[lambda].sub.1] -0.2319 ** -0.1492 ** -0.3705 **
 (0.0008) (0.0000) (0.0037)
[[micro].sub.J] 0.1290 ** 0.1283 ** 0.0938 **
 (0.0006) (0.0000) (0.0321)
[chi square](7) goodness- 17.0754 * 12.7405 19.2907 **
 of-fit statistic

* Significant at the 5% level.

** Significant at the 1% level.

Notes: We use GMM to estimate the seven unknown parameters implicit in
the option-pricing model. For all five models, 14 instruments are used
to construct the moment conditions: constant; total asset, A; R&D
stock, S; dummy whether the firm applies rDNA technologies,
recombinant technology; Number of patents firm applied for in year t
scaled by R&D stock; citation-weighted patent counts applied for in
year t/R&D stock; claim-weighted patent counts in year t/R&D stock;
the age of firm; the age of the biotech industry; number of tied
articles in year t scaled by R&D stock; top-quality universities;
underwriter reputation; debt level; debt maturity. For each model; the
degrees of freedom for the [chi square] is 7. Model I is estimated for
the truncated sample with 610 observations (the firm-year observations
with total asset less than $2 million are dropped). The rest are
estimated for the full sample, which includes 129 firms and 727
observations. Standard errors are in parentheses.

TABLE 3 Estimation of Implicit Parameters ([lambda]=[[lambda].sub.0]+
[[lambda].sub.1][X.sub.1]+[[lambda].sub.2][X.sub.2])

 [alpha] [beta] [sigma]

Model VII ([lambda]=[[lambda].sub.0]+[[lambda].sub.1], ties/R&D +
[[lambda].sub.2] claim/R&D)

Estimate 2.5361 ** 0.6465 ** 0.0915 **
Standard error 0.0000 0.0000 0.0004
[chi square](6) statistic=12.2606

Model VIII ([lambda]=[[lambda].sub.0]+[[lambda].sub.1] citation/R&D +
[[lambda].sub.2] claim/R&D)

Estimate 2.2744 ** 1.1318 ** 0.1102 **
Standard error 0.0000 0.0000 0.0000
[chi square](6) statistic =10.4784

 [[lambda]. [[lambda]. [[lambda].
 sub.0] sub.1] sub.2]

Model VII ([lambda]=[[lambda].sub.0]+[[lambda].sub.1], ties/R&D +
[[lambda].sub.2] claim/R&D)

Estimate -0.1109 ** 0.8969 ** 0.0626 **
Standard error 0.0005 0.0041 0.0000
[chi square](6) statistic=12.2606

Model VIII ([lambda]=[[lambda].sub.0]+[[lambda].sub.1] citation/R&D +
[[lambda].sub.2] claim/R&D)

Estimate 0.0784 ** 0.1688 ** 0.2377 **
Standard error 0.000 0.0001 0.0001
[chi square](6) statistic =10.4784

 [[sigma].
 [[micro]. sup.2.
 sub.J] sub.J]

Model VII ([lambda]=[[lambda].sub.0]+[[lambda].sub.1], ties/R&D +
[[lambda].sub.2] claim/R&D)

Estimate -0.0758 ** 0.1262 **
Standard error 0.000 0.0000
[chi square](6) statistic=12.2606

Model VIII ([lambda]=[[lambda].sub.0]+[[lambda].sub.1] citation/R&D +
[[lambda].sub.2] claim/R&D)

Estimate -0.1084 ** 0.1283 **
Standard error 0.000 0.0002
[chi square](6) statistic =10.4784

* Significant at the 5% level.

** Significant at the 1% level.

Notes. We use GMM to estimate the eight unknown parameters implicit in
the option-pricing model with two science variables explaining the
jump probability. Fourteen instruments are used to construct the
moment conditions: constant; total assets, A; R&D stock, S; dummy
whether the firm applies rDNA technologies, recombinant technology;
number of patents applied for in year t scaled by R&D stock; future
citation-weighted patent counts applied for in year t/R&D stock;
claim-weighted patent counts in year t/R&D stock; the age of firm; the
age of the biotech industry; number of star articles scaled by R&D
stock; top-quality universities; Underwriter reputation; debt level;
maturity of debt. For each model, the degrees of freedom is 6. Both
models are estimated for the full sample with 727 firm-year
observations.

TABLE 4
Newey and West Tests of Several Hypotheses

 (1) (2)

Benchmark model Model VII Model VIII

Null hypothesis [H.sub.0]: [H.sub.0]:
 [[lambda].sub.1] = 0 [[lambda].sub.1] = 0
 (ties/R&D does not (citation/R&D does
 explain the jump not explain the jump
 probability) probability)

[chi square] statistics [chi square](1)=12.45 [chi square](1)=19.41

Accept or reject? Reject Reject

 (3) (4)

Benchmark model Model VII Model VIII

Null hypothesis [H.sub.0]: [H.sub.0]:
 [[lambda].sub.1] = 0, [[lambda].sub.1] =
 x2=0 (no science 0, 22-0 (no science
 variable-related jump) variable-related
 jump)

[chi square] statistics [chi square](2)=22.13 [chi square](2)=
 27.86

Accept or reject? Reject Reject

Notes: This table computes the [chi square] statistics proposed in
Newey and West (1987). The first column tests the null hypothesis that
ties/R&D does not provide additional explanatory power in determining
the jump probability; the second column test the null hypothesis that
citation/R&D does not provide additional explanatory power; column (3)
tests against the hypothesis that there is no science variable-related
jump based on model VII; column (4) tests the hypothesis that there is
no science variable-related jump based on model VIII. All three
hypotheses are rejected.

TABLE 5
Ordinary Least Squares Analysis of the Estimation Price-error
for the Option Pricing Model

Explanatory Coefficient (SE) for
Variable Model VII errors

Constant -0.2553 (0.4024)
Moneyness (D/([alpha]A+[beta]S) 2.2889 (1.4284)
Year dummies Omitted, none is significant
Other variables
Citation/R&D stock -0.0473 (0.0595)
Ties/R&D stock 0.0695 (0.2287)
Clam/R&D stock -0.0168 (0.0183)
Patent/R&D stock 0.4793 (0.4854)
Industry age 0.0113 (0.0435)
Total assets, A -0.0027 (0.0036)
R&D stock, S 0.0009 (0.0058)
Recombinant technology -0.2576 (0.2176)
Top-quality universities -0.2212 * (0.1046)
Age of the firm 0.0829 (0.0436)
Debt level 0.0036 (0.0119)
Underwriter ranking 0.1041 ** (0.0342)
Debt maturity 0.1023 (0.3421)
[R.sup.2] 0.03388
Adjusted [R.sup.2] 0.01626

Explanatory Coefficient (SE) for
Variable Model VIII errors

Constant -0.3118 (0.7997)
Moneyness (D/([alpha]A+[beta]S) 2.7822 (2.0230)
Year dummies Omitted, none is significant
Other variables
Citation/R&D stock -0.0392 (0.0298)
Ties/R&D stock 0.2525 (0.2866)
Clam/R&D stock -0.0111 (0.0179)
Patent/R&D stock 0.5903 (0.4293)
Industry age 0.0001 (0.0695)
Total assets, A -0.0053 (0.0047)
R&D stock, S 0.0050 (0.0075)
Recombinant technology -0.2643 (0.2848)
Top-quality universities -0.2462 (0.1370)
Age of the firm 0.0978 (0.0566)
Debt level 0.0058 (0.0155)
Underwriter ranking 0.1042 * (0.0443)
Debt maturity 0.1112 (0.3301)
[R.sup.2] 0.03362
Adjusted [R.sup.2] 0.00765

N = 727.

* Significant at the 5% level

** Significant at the 1% level

Notes: This presents the results of the OLS analysis to see which
variables contribute to the pricing errors of the option-pricing model.
The option model values are calculated from model VII and Model VIII,
respectively. The estimation errors, Price-error, are defined as:
Price-error-(option model value observed market value)/observed market
value. The regression in this table is specified as:
Price-[error.sub.j] = [[beta].sub.0] + [[beta].sub.1] [Moneyness.sub.j]
+ [[beta].sub.2-12] Year [Dumnues.sub.j] + [[beta].sub.13-20] Other
[Variables.sub.j + [epsilon]]. Moneyness in the regression is defined
as the ratio between the debt level and [alpha]A + [beta]S (the
underlying asset in the option model: the weighted sum of the firm's
tangible and intangible assets). Standard errors are in parentheses
to the right of the parameter estimates.

TABLE 6
The Effect of Intellectual Capital on the Firm's Market
Valuation--Estimated from Model VII Based on claim/R&D
and ties/R&D

 Mean SD Minimum Maximum

Descriptive Statistics (N = 723)
Firm's market value 105.21 238.03 0.15 3007.00
Option model value 104.91 237.38 0.30 2683.00
The value of technological jumps 1.34 5.21 0.00 77.20

 Number of Option Marginal
Number of ties/R&D claim/R&D Modal Value Increase

The Effect of Knowledge Capital on the Variability of Biotech Firm's
Market Value

0 0 110.41 0.00
Mean 0.09 Mean 6.65 112.30 1.89
Mean + 1*SD 0.63 Mean + 1*SD 27.05 118.02 5.72
Mean + 2*SD 1.17 Mean + 2*SD 47.45 123.66 5.64

Notes: In this table, we study the effect of knowledge capital on the
biotech firms' market value based on model VI. In the top, we report
the statistics of the estimated values for the select sample (four
outliers are dropped). Here, the option-pricing model values are
calculated based on the estimates of model VII in Table 3. We define
the option premium of knowledge capital as the difference between
model values estimated from model VII and the model values estimated
from model VII but with the constraints [[lambda].sub.1] =
[[lambda].sub.2] = 0 imposed. The lower part reports how the changes
in the firm-specific knowledge capital measures (ties/R&D, claim/R&D)
affect the variability of the biotech firm's market values. The
calculation is also based on the model VII in Table 3. Here, we study
a hypothesized firm, which has the mean values for the variables. We
calculate how the increase in the firm's intellectual measures changes
the market value of this hypothesized firm. All nominal variables are
in terms of million U.S. dollars.

TABLE 7
The Effect of Intellectual Capital on the Firm's Market
Valuation--Estimated from Model VIII Based on claim/R&D
and citation/R&D

 Mean SD Minimum Maximum

Descriptive Statistics (N 723)
Firm's market value 105.21 238.03 0.15 3007.00
Option model value 105.28 234.14 0.30 2783.00
The value of technological jumps 5.25 12.34 0.00 174.00

Number of Number of Option Marginal
citation/R&D claim/R&D Model Value Increase

The Effect of Knowledge Capital on the Variability of Biotech
Firm's Market Value

0 0 109.01 0.00
Mean 2.17 Mean 6.65 119.98 10.97
Mean + 1*SD 11.18 Mean + 1*SD 27.05 148.54 28.56
Mean + 2*SD 20.19 Mean + 2*SD 47.45 179.79 31.25

Notes: In this table, we study the effect of knowledge capital on the
biotech firms' market value based on model VIII. In the top, we report
the statistics of the estimated values for the select sample (four
outliers are dropped). Here, the option-pricing model values are
calculated based on the estimates of model VIII in Table 3. We define
the option premium of knowledge capital as the difference between
model values estimated from model VIII and the model values estimated
from model VIII but with the constraints [[lambda].sub.2] =
[[lambda].sub.2] = 0 imposed. The lower part reports how the changes
in the firm-specific knowledge capital measures (citation/R&D,
claim/R&D) affect the variability of the biotech firm's market
values. The calculation is also based on the model VIII in Table 3.
Here, we study a hypothesized firm, which has the mean values for the
variables. We calculate how the increase in the firm's intellectual
measures changes the market value of this hypothesized firm. All
nominal variables are in terms of million U.S. dollars.

(1.) For example, Lev and Sougiannis (1999) show that the omission of R&D capital is the key factor explaining the falling relevance of accounting earnings and book values to stock prices.

(2.) Griliches (1981), Jaffe (1986), Megna and Klock (1993), Hall (1993), and Hall et al. (2000) all follow this basic approach.

(3.) Merton (1968, 61) on risk-taking by Nobel laureates: "They display a high degree of venturesome fortitude. They are prepared to tackle important though difficult problems rather than settle for easy and secure ones." An example may help. Early on, Genentech elected to attempt to make the fundamental breakthroughs required to produce human insulin from bacteria because the firm's cofounder and scientific leader, Herbert Boyer, saw it as the highest-payoff research program. Though many scientists thought it was impossible, the coinventor of genetic engineering was able to put together a team to make it happen.

(4.) Lev and Sougiannis (1999), for example, suggest that S(t) could be proxied by the firm's discounted cumulative R&D expenditures.

(5.) Bates (1991) shows the relationship between the actual jump components and the risk-adjusted jump components. He convincingly demonstrates that the actual jump probability normally has the same sign as the risk-adjusted jump probability, but the risk-adjusted jump size is always downwardly biased compared to actual jump size.

(6.) Bates (1996), Heston (1993), and Bakshi et al. (1997) use the same approach.

(7.) See Darby and Zucker (2002) for a full discussion of metamorphic technological progress and the predominance of its entry-generating (as opposed to incumbent-enhancing) form.

(8.) Some of the public firms were traded in local exchanges or through OTC. This explains why we can only find trading information for 129 out of 156 firms from CRSP and Compustat.

(9.) As an input measure, it is uncertain whether a depreciation rate or appreciation rate applies in cumulating tied articles. Sensitivity experiments discussed in the appendix led us to accept prior practice and cumulate without adjustment.

(10.) We also tried total assets and the number of employees to control for firm size. The empirical results are qualitatively the same whichever variable is used to scale the knowledge capital measures.

(11.) See, for example, Hall et al. (2000).

(12.) We try g = 0.3 or even g = 0.5 and find the estimated results are not sensitive to the values of g.

(13.) Debt maturity is calculated as the McCauley duration of the firm's debts with different maturities. Let [C.sub.t] stand for the level of debt that matures in t year. We have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

(14.) When we calculate the firm's cumulative R&D expenditures, we assume that the firm's R&D investment depreciates, like knowledge represented by patents, by 20% annually.

(15.) It is difficult to distinguish between this simple statistical bias explanation and one based on fraudulent initial public offerings because the 117 excluded observations in model I are primarily for firms brought public by less reputable underwriters.

(16.) All four of the knowledge capital measures are correlated, and two of them at one time appears to be the limit of our ability to estimate the model given current soft- and hardware.

(17.) In regressions not reported here, we experimented with different combinations of the four knowledge-capital indicators examined in Table 2, but only the two combinations reported in Table 3 passed the [chi square] test.

(18.) Amgen's market value in 1989 was $73.34 billion, which represents a sudden increase from $16.23 billion in 1988. However, Amgen's knowledge capital, measured by citation/R&D or ties/R&D, did not change so dramatically. The major change was the Food and Drug Administration's June 1989 licensing under the U.S. orphan drug program of Epogen for treatment of anemia associated with end-stage renal disease. Medicare's program for this disease ensured a large growing market for this vital drug. Obviously, it is not due to any technology reason. Therefore, we delete Amgen from our sample.

(19.) Because the distribution of knowledge capital on any measure is so skewed, there is a relatively small difference between the firm values estimated for the mean and zero-value of knowledge capital. It is only in the upper tail that knowledge capital really pays off.

(20.) We believe the ties measure works well because it measures the extent to which star scientists are participating in bench-level science with firm employees and thus transferring their crucial tacit knowledge protected by natural excludability. Stephan and Everhart (1998; see also related work surveyed in Stephan 1996) have attempted to link academic scientists to firms using such devices as participation in scientific advisory boards; but these relationships are typically shallow and frequently overlapping. (For example, the same scientist is frequently a member of more than one scientific advisory board at the same time.) In contrast, tied articles indicate deep relationships (shown through fieldwork often to include equity stakes) and are almost always monogamous or at least serially monogamous (Zucker et al. 2002b). These scientists strongly tend to stay involved with the firms they found or collaborate with, getting greatly increased research support and wealth as a result (Zucker and Darby 1996).

REFERENCES

Austin, D. H. "An Event-Study Approach to Measuring Innovative Output: The Case of Biotechnology." American Economics Review, 83(2), 1993, 253-58.

Bakshi, G. S., C. Cao, and Z. Chen. "Empirical Performance of Alternative Option Pricing Models." Journal of Finance, 52(6), 1997, 2003-49.

Bates, D. S. "The Crash of 1987: Was It Expected? The Evidence from Options Markets." Journal of Finance, 46(3), 1991, 1009-44.

--. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschmark Options." Review of Financial Studies, 9(1), 1996, 69-107. Bioscan. 1988-1997. Vols. 2-11.

Carter, R. B., F. H. Dark, A. K. Singh. "Underwriter Reputation, Initial Returns, and the Long-Term Performance of IPO Stocks." Journal of Finance, 53(1), 1998, 285-311.

Chan, S. H., J. W. Kensinger, A. J. Keown, and J. D. Martin. "Do Strategic Alliances Create Value?" Journal of Financial Economics, 46(2), 1997, 199-221.

Cox, J. C., and S. A. Ross. "The Valuation of Options for Alternative Stochastic Processes." Journal of Financial Economics, 3(1), 1976, 145-66.

Darby, M. R., and L. G. Zucker. "Change or Die: The Adoption of Biotechnology in the Japanese and U.S. Pharmaceutical Industries." Comparative Studies of Technological Evolution, 7, 2001, 85-125.

--. "Growing by Leaps and Inches: Creative Destruction, Real Cost Reduction, and Inching Up." Economic Inquiry, 41(1), 2002, 1-19.

Griliches, Z. "Market Value, R&D, and Patents." Economic Letters, 7(2), 1981, 183-87.

--. "Patent Statistics as Economic Indicators: A Survey." Journal of Economic Literature, 28(4), 1990, 1661-707.

Hall, B. H. "The Stock Market Valuation of R&D Investment during the 1980s." American Economic Review, 83(2), 1993, 259-64.

Hall, B. H., A. B. Jaffe, and M. Trajtenberg. "Market Value and Patent Citations: A First Look." National Bureau of Economic Research Working Paper No. 7741, 2000.

Heston, S. L. "A Closed-Form Solution for Options with Stochastic Volatility with Application to Bond and Currency Options." Review of Financial Studies, 6(2), 1993, 327-43.

IPO Reporter. 1976-1992, various issues.

Jaffe, A. B. "Technological Opportunity and Spillovers of R & D; Evidence from Firms' Patents, Profits, and Market Value." American Economic Review, 76(5), 1986, 984-1001.

Kim, M.-J., Y.-H. Oh, and R. Brooks. "Are Jumps in Stock Returns Diversifiable? Evidence and Implications for Option Pricing." Journal of Financial and Quantitative Analysis, 29(4), 1994, 609-31.

Lanjouw, J. O., and M. Schankerman. "The Quality of Ideas: Measuring Innovation with Multiple Indicators." National Bureau of Economic Research Working Paper No. 7345, 1999.

Lev, B., and T. Sougiannis. "Penetrating the Book-to-Market Black Box: The R&D Effect." Journal of Business Finance and Accounting, 26(3&4), 1999, 419-42.

Megna, P., and M. Klock. "The Impact of Intangible Capital on Tobin's q in the Semiconductor Industry." American Economic Review, 83(2), 1993, 265-69.

Merton, Robert C. "Option Pricing when Underlying Stock Returns Are Discontinuous." Journal of Financial Economics, 1976, 3(1), 125-44.

Merton, R. K. "The Matthew Effect in Science." Science, 159(3810), 1968, 56-63.

Newey, W. K., and K. D. West. "Hypothesis Testing with Efficient Method of Moments Estimation." International Economic Review, 28(3), 1987, 777-87.

Stephan, P. E. "The Economics of Science." Journal of Economic Literature, 34(3), 1996, 1199-235.

Stephan, P. E., and S. Everhart. "The Changing Rewards to Science: The Case of Biotechnology." Small Business Economics, 10(2), 1998, 141-51.

Zucker, L. G., and M. R. Darby. "Star Scientists and Institutional Transformation: Patterns of Invention and Innovation in the Formation of the Biotechnology Industry." Proceedings of the National Academy of Sciences, 93(23), 1996, 12709-16.

--. "Entrepreneurs, Star Scientists, and Biotechnology," NBER Reporter, Fall 1998, 7-10.

--. "Capturing Technological Opportunity via Japan's Star Scientists: Evidence from Japanese Firms' Biotech Patents and Products." Journal of Technology Transfer, 26(1/2), 2001, 37-58.

Zucker, L. G., M. R. Darby, and J. Armstrong. "Geographically Localized Knowledge: Spillovers or Markets?" Economic Inquiry, 36(1), 1998a, 65-86.

--. "Commercializing Knowledge: University Science, Venture Capital, and Firm Performance in Biotechnology." Management Science, 48(1), 2002a, 138-53.

Zucker, L. G., M. R. Darby, and M. B. Brewer. "Intellectual Human Capital and the Birth of U.S. Biotechnology Enterprises." American Economic Review, 88(1), 1998b, 290-306.

Zucker, L. G., M. R. Darby, and M. Torero. "Labor Mobility from Academe to Commerce." Journal of Labor Economics, 20(3), 2002b, 629-60.

MICHAEL R. DARBY, QIAO LIU, LYNNE G. ZUCKER *

* This research has been supported by grants from the University of California Systemwide Biotechnology Research and Education Program, the University of California's Industry-University Cooperative Research Program, and the Alfred P. Sloan Foundation through the NBER Research Program on Industrial Technology and Productivity. We are grateful to Hongbin Cai, Harold Demsetz, Josh Lerner, Philip Leslie, David Levine, Shijun Liu, Ren6 M. Stulz, and an anonymous referee for useful suggestions. We also thank participants in various UCLA seminars, especially Marc Junkunc and Yuan Gao, for helpful comments. Andrew Jing and Marc Junkunc assisted in developing new elements of the Zucker-Darby database for use in this article. Any errors and omissions are our own responsibilities. This study is a part of the NBER's research program in productivity. Any opinions expressed are those of the authors and not those of their universities, McKinsey & Company, or the National Bureau of Economic Research.

Darby: Warren C. Cordner Professor of Money and Financial Markets, Anderson Graduate School of Management, UCLA Box 951481, Los Angeles, CA 90095. Phone 1-310-825-4180, Fax 1-310-454-2748, E-mail [email protected]

Liu: Assistant Professor of Finance and Economics, School of Economics and Finance, University of Hong Kong, Pokfulam Road, Hong Kong and McKinsey & Company, Inc., Asian Corporate Finance and Strategy Practice, 25/F Cheung Kong Centre, 2 Queen's Road, Central, Hong Kong. Phone 852-2859-1059, Fax 852-2548-1152, E-mail [email protected]

Zucker: Professor of Sociology and Policy Studies, UCLA Box 951551, Los Angeles, CA 90095. Phone 1-310-825-9155 Fax 1-310-454-2748, E-mail zucker@ ucla.edu