MARKET VALUE AND PATENTS A Bayesian Approach. Mark HIRSCHEY * 1. Introduction

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1 Economics Letters 27 (1988) North-Holland 83 MARKET VALUE AND PATENTS A Bayesian Approach Robert A. CONNOLLY University of Cal~fornm, Irvine, CA 92717, USA Mark HIRSCHEY * Unmwity of Kansas, Lawrence, KS , USA Received 16 December 1987 This paper finds a large, positive and statistically significant effect op patent statistics on firm market values. Furthermore, these effects are robust to a variety of alternate specifications of our underlying model. We conclude that patent data provide economically meaningful information on the scope and relative effectiveness of a firm s R&D program. 1. Introduction The market value of the firm embodies those factors with systematic influences on expected future profits. In addition to tangible assets, intangible factors which reflect output market power and/or superior operating capabilities will also be reflected. There are important reasons for considering patents as an example of such intangible factors. First, patents represent a limited (17 year) government grant of monopoly with the expressed intent of generating monopoly profits as an inducement to invention and innovation. Therefore, considering the link between patents and market value is a partial evaluation of patent law effectiveness. Second, patent statistics can provide a useful indicator of the relative success of a firm s R&D program. Especially effective R&D personnel, management, or strategies will be reflected in supernormal rates of valuable patent output and/or higher quality patents. Therefore, any valuation effects of patents will encompass both market power and efficiency (Ricardian) influences. 2. The model We hypothesize an effect of patent statistics on the market value of the firm, measured using Thomadakis (1977) relative excess valuation (EV/S), only in the event that these data are surprising in the following sense. When an individual firm is able to produce a relatively large number of patents from a given level of resources, holding patent quality, technical opportunity, and all else equal, then this superior R&D efficiency will be reflected in E V/S. Conversely, when only a relatively small number of (high quality) patents are produced from a given level of resources, then this relative R&D inefficiency will be reflected in lower EV/S. This approach is based on the presumption that a portion of current patent output is expected and already capitalized in the firm s * We thank Ken Snowden and C.J. LaCivita for helpful comments, and Robin O Leary for research assistance /88/$ , Elsevier Science Publishers B.V. (North-Holland)

2 x4 R.A. Connol(~~, M. Himchyp / Market rulue mdputents stock price. That is, in an efficient capital market the expected component of patents statistics is reflected in equity values on an ex ante basis. An ex post evaluation of the information content of patent statistics therefore depends on patent surprises defined as the number of unanticiputed patents. Our market value model is given by eq. (1) and our conditioning equation for patents is described by eq. (2): EV/S=u,,+a,P/S+a2R&D/S+u,AD/S+u,CR+u,GR+u,B+e,, (1) 24 P/S=h,,+h,EV/S+h,R&D/S+h,CR+h41/S+ c b,i,+e,, 1=5 (2) where S is firm sales; EV/S is relative excess value given by market value of common plus book value of debt minus the book value of tangible assets, P is total patents; P/S is unanticipated patent intensity given by actual patent intensity less expected patents [or P/S - E( P.S ( X)(from (2)]; R&D/S is R&D expenditures normalized by sales; AD/S is advertising expenditures normalized by sales; CR is concentration measured by the weighted top four-firm sales in the firm s various four-digit census industries; GR is geometric sales growth ; B is the firm s stock market beta; I is a dummy variable for each two-digit industry to capture industry-specific differences in the propensity to patent ( technical opportunity ); and D is diversification measured as 1 - CyZ,(S,/S)2 and where S, is sales in the jth four-digit industry and 0 < D < 1 with diversification increasing as D + 1. This model is an extension of work by Connolly and Hirschey (1984) Hirschey (1985) and Pakes (1985, 1986). Our earlier paper provides a considerable analysis of the basic forms of the basic model and a complete description of our 390 firm sample taken from the 1977 Fortune Estimation method and results Our patent equation was employed to generate estimates of expected and unexpected patents (P/S) to be used in our second round market value model. Given the potential for simultaneity bias (see our earlier paper). the Hausman (1978) test was used to determine whether an OLS approach to estimation is appropriate. A joint test that the effects of P/S and R&D/S are correctly estimated using OLS generated and an insignificant test statistic of only F,,,,, = Consequently. there is no apparent need to employ simultaneous equations methods in our estimation of the market value effects of patents. To investigate the valuation effects of patents, we adopt a Bayesian approach. Beginning with a multivariate normal prior for p, the coefficient vector, and a gamma prior for the disturbance, the mean of the resulting posterior distribution for /? is given by [see Learner (1978, p )] p= (fj, x, xp+u -2x x)-i( up- x, xppp + u-2x x~(),,s), (3) where a is the standard error of the estimate, p indicates prior and X is the sample data matrix. To implement this estimator, we formulated prior opinions about the subjective elements of the estimator, p,,,( Xix,,), and u,. For both AD/S and R&D/S, we assumed that a one-dollar increase adds two dollars to EV/S. We chose the prior standard errors so that with 95 percent certainty, an extra dollar of advertising or R&D added at least one dollar to El//S. For unexpected patents, we assumed that each unexpected patent added $3 million to EV/S and our prior standard error was

3 R.A. Connolly, M. Hirschey / Market calue und putenrs x5 chosen so that with 95 percent certainty, each unexpected patent adds at least $1 million to E V/S. For concentration, our prior mean effect is zero, and our prior standard error is one. Therefore. the 95 percent prior confidence interval encompasses a number of different points of view. Numerically, we found the growth rate prior mean by assuming that a 10 percent increase in sales growth adds one percent to El//S. We chose the prior standard error to put zero on the very edge of a 95 percent prior confidence interval. Our prior mean on risk presumes that risk has no influence on EV/S, but the large prior standard error (a = 1) admits substantial uncertainty about this effect. Finally we adopt a zero mean prior for the intercept with a wide prior confidence interval to reflect our uncertainty about the value of this coefficient. In this analysis we assume (,8,\ u,,, that is, we Table 1 Estimation and sensitivity analysis results. (a) Senstttotty of posterior means to changes in o, Variable 0, : P/S (16.00) (12.50) (11.60) (11.10) (10.80) (11.00) R&D/S (17.90) (11.10) (9.12) (9.04) (9.14) (8.73) A D/S (17.00) (9.81) (7.14) (6.62) (6.67) (6.83) CR ~ ( ) (- 0.22) ( ) (-1.34) (-1.77) (-2.25) GR (8.22) (4.44) (2.87) (2.67) (3.55) (6.91) B ~ (1.04) (0.81) (0.28) (-0.36) (- 0.74) (-1.16) ( h) Extreme bounds ifprror curiance - cocw%mre matru VO IS bounded X ~ V,, < V < X2 l$ Variable X: p/s U L R&D/S U L AD/S U L _ CR U L GR U L B U L * Approximate r-scores are reported in parentheses below coefficient estimates.

4 86 R.A. ConnolIy. M. Hmchq / Market value and patents expect our coefficient estimates to fall between and 1.96, Consequently, we selected 0; = 1 as a first approximation. This amounts to saying our prior covariance matrix is proportional to (XiX,)-. Later we show the effect on p of varying up. We can evaluate the sensitivity of results to specification of up 2 in the following way. Define u, = a, /~. For a given a2, Learner and Leonard (1983) shows how a set of estimates of p can be found by varying u2. - As u, -+ 0, the variance of the sample information increases relative to the prior information, and p is being computed with a sharper prior. As u, -j cx), the prior becomes more diffuse and the sample data, rather than prior information, become more important in determining P. Learner (1982) has also shown how to summarize the sensitivity of p to a range of different prior covariance matrices. Essentially, Learner shows that if the prior covariance matrix V can be bounded V* < I/< v*. where A < B means B - A is positive definite, this implies upper and lower bounds on the posterior means. Given an initial prior covariance matrix, v:, and prior bounds given by V, = X- V0 and V * = X2&, an entire range of prior covariance matrices can be found by varying h. If the resulting bounds on the Bayes estimates do not vary substantially, then our inferences are not affected by the arbitrary specification of the prior covariance matrix. Table 1 presents estimates for our excess value equation and sensitivity analysis results. At u, = 1, the Bayes estimate with equal weights on the prior and sample information is listed. At u, = w, the Bayes estimate of,b with a diffuse prior (the OLS estimate), is listed. Intermediate positions reflect different weightings of the prior and sample information. For unexpected patents, the equal-weight estimate, where u1 = 1, indicates that each unexpected patent adds $5.33 million to excess value. An extra dollar of R&D expenditure adds $3.60 to excess value, while an additional dollar of advertising adds $2.99. Growth has a small positive effect, but neither concentration nor stock-price beta have any discernible influence. OLS estimates, where (Jl = CD, suggest somewhat larger effects for each variable. In particular, an excess value effect for patents of $5.74 million is indicated. Most importantly, the inference of a positive excess value effect for patents seems relatively unaffected by the different weightings of prior and sample information shown in table la. The prior variance-covariance matrix is shown in table lb. At h = 1, the pooled (Bayes) estimate for u, = 1 is listed. Estimates reported for X = cc are the bounds from using any prior covariance matrix. While some coefficient estimates display considerable sensitivity, the valuation effects of unexpected patents and R&D/S are quite robust. We also checked the sensitivity of our estimates to changes in p,, and found virtually no change except for the growth coefficient (details are available upon request). We conclude that our estimate of a large, positive and statistically significant effect of patents on excess value are quite robust. 4. Conclusions An attractive means for considering the information content of patent statistics is to consider their relevance within the context of a market value model. We find that unanticipated patents increase the excess value of Fortune 500 firms by roughly $5 million. While the magnitude of this effect is somewhat sensitive to aspects of our prior, the positive effect of patents on market values is robust. We conclude that patent statistics can be considered economically relevant information. References Connolly, Robert A. and Mark Hirschey, 1984, R&D, market structure and profits: A value-based approach, Review of Economics and Statistics 66, Nov.,

5 R.A. Connolly, M. Hirschey / Market value and patents 87 Hausman, Jerry A., 1978, Specification tests in econometrics, Econometrica 46, Nov., Hirschey, Mark, 1985, Market structure and market value, Journal of Business 58, Jan., Learner, Edward E., 1978, Specification searches: Ad hoc inferences with non-experimental data (Wiley, New York). Learner, Edward E., 1982, Sets of posterior means with bounded variance priors, Econometrica 50, May, Learner, Edward E. and Herman Leonard, Reporting the fragility of regression estimates, Review of Economics and Statistics 65, May, Pakes, Ariel, 1985, Patents, R&D and the stock market rate of return, Journal of Political Economy 93. April, Pakes, Ariel, 1986, Patents as options: Some estimates of the value of holding European patent stocks, Econometrica 54, July, Scherer, F.M., 1965, Firm size, market structure, opportunity and the output of patented inventions, American Economic Review 55, Dec., Thomadakis, Stavros B., 1977, A value-based test of profitability and market structure, Review of Economics and Statistics 59, May,