Invention and Discovery In Science-Based Firms

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production functions for patents and scientific papers. Even more than patents, papers depend on knowledge outside the firm. In contrast with patents, knowledge flows from universities dominate industry flows. The results suggest that inventions are determined by a sequence of research. Later on knowledge flows narrow down to industry, whereas university research is more important in the early stages. Even so, science plays an appreciable role in patents, especially high impact patents. 1 I. Introductory Remarks To what extent does new invention depend on knowledge from past inventions? How important for invention is knowledge outside the firm compared to inside knowledge? Do knowledge flows from science play an additional role in invention? How do production functions for invention compare with those for scientific discoveries? This paper seeks to provide tentative answers to these questions. Our approach builds on two literatures. The first is the search approach to technological change pioneered by Evenson and Kislev (1975, 1976), and applied to R&D by Nelson (1982) and growth by Kortum (1997). The second is the quality ladders approach to growth, in which higher quality products supersede lower quality ones. Grossman and Helpman (1991) and Barro and Sala-i-Martin (2004) contain expositions. Etro (2004) implicitly builds on this approach in his discussion of patent racing under different assumptions about industry organization. Using a sample of large R&D-performing firms in the U.S., which are observed during 1981-1999, the empirical work quantifies inventions and scientific discoveries as well as knowledge flows to both. Our evidence builds on patents and citations in the NBER Patent Citations Database and papers and citations to papers from the NBER Scientific Papers Database. In addition we draw on Compustat for firm R&D stocks and on the CASPAR database of the National Science Foundation for university R&D 1 . Main findings are as follows. Simple patent counts depend on knowledge flows from 1 See Standard and Poor 9s -Data Services Compustat (2007) for firm R&D data; the WebCASPAR Integrated Science and Engineering Resources Data System (2007) for data on R&D by university and field; and National Science Foundation (2007) for aggregate R&D by type as well as industry. Chapter 13 of Jaffe and Trajtenberg (2002) discusses the patent database. Adams and Clemmons (2006) discuss the scientific papers database at length. 2 inventions but much less on science. When we replace patent counts with patents weighted by citations received, a measure of invention weighted by impact, we find that knowledge flows from patents continue to dominate, but that knowledge flows from science now have a much greater impact. When we compare flows from inside and outside the firm, we find that outside flows have a larger effect on patents produced. When we compare industry- with university-based we find that the effects of knowledge flows from industry outweigh those from universities by a wide margin. For comparison with patents we estimate production functions for scientific papers. We find that firm 9s papers depend even more that its patents on knowledge flows from outside the firm. In addition, unlike patents, flows from universities have a larger effect on scientific papers than industry flows. These comparative findings on patents and papers suggest that innovation is a sequential process in which the scope of the firm 9s research progressively narrows as it proceeds from early to late stages. In the early going the firm 9s scientific effort depends mostly on outside knowledge, most of that coming from universities. Later on, the firm 9s inventions depend mostly on the firms 9 past inventions and on inventions elsewhere in industry, with science strictly secondary. Nevertheless, we observe that science plays an important role in patents, especially highly cited patents. The rest of the paper is arranged as follows. Section II describes the structure of firm innovation decisions. Section III discusses preparation of the data, beginning with construction of firm R&D stocks. For the purpose of matching patents to firms, we proceed to the problem of matching of firm names and their subsidiaries to patent assignees. Then, the section discusses the calculation of patent counts and citation- 3 weighted patents for the firm. Afterwards we describe flows of knowledge from patents of the same firm and other firms. Finally we turn to knowledge flows from science. We construct papers and citation-weighted papers of firms, flows of science-based knowledge from papers of the same firm, other firms, and universities. Crucially, we describe a method of mapping flows of science-based knowledge by field of science into patent categories. The section concludes with a description of the various knowledge flow indicators. Section IV discusses the patent panel, describes the main variables, and presents findings for knowledge production functions for patents. Section V describes the scientific papers panel and presents findings for knowledge production functions for scientific papers. Section VI discusses and compares findings for patents and papers and concludes the paper. II. Structure of the Firm 9s Innovation Decisions A. Overview We start by asking why a firm invests in science and technology and how this is conditioned by size and product diversity of a firm. Having addressed these questions we are better able to understand why large, diverse firms are more likely to invest in science. The theory is based on the quality ladders model (Grossman and Helpman, 1991; Barro and Sala-i-Martin, 2004), which assumes that firms compete to be the sole producer of the next level of quality of a given product. By investing in science and R&D, the current producer of the product can raise the probability that it will continue to be the monopolist. This is the question of the persistence of monopoly. According to the Arrow effect the monopolist has less of an incentive to invest than the entrant, because it forgoes a present value of profits on the current product in which it holds a 4 monopoly position. However, Etro (2004) shows that if the monopolist has an informational advantage and knows the reaction of entrants to its R&D investments, and if there is free entry to be producer of the next higher level of the product, then the Arrow effect disappears: the incumbent has a greater incentive to invest than entrants. To this theory we add economies of scope based on science and other firm-wide capabilities. The theory is consistent with the persistence of leadership of many firms in our sample and it agrees with empirical results of Blundell, Griffiths, and Van Reenan (1999), who find that market share increases innovation and enhances the impact of innovation on a firm 9s stock market value. B. Single Line of Business Consider the competition to be patent holder and producer of the next generation of the product. The present value of entrant i and incumbent L respectively are (1) F p p r R s V p PV L j n j i i i i 1 (2) F p p r R s V p PV L j n j L L L L 1 The first term in (1) is the discounted expected present value of the entrant 9s being first to invent while the second term is its fixed cost F of entering the race. The numerator of (1) is the probability i p that the entrant is first to innovate times the present value V of the next generation product, minus the cost of the two inputs, the sampling rate i s (search) and R&D i R , whose prices are both normalized to unity. The denominator is the sum of interest rate r and the probability L j n j p p 1 . This is the discount rate given the Poisson assumption on the probability of invention. Equation (2) is similar to (1) except 5 that the return includes profit from being a monopolist in the current product 2 . The probability of discovery for entrant and incumbent alike depends on search, the stock of knowledge, and R&D. We assume that (3) R S i i i R K s p ) ( (4) R S L L L R K s p ) ( for the entrant and incumbent, where K is the stock of knowledge. We can expand the search term S K s i ) ( to form a vector with no essential change in the story. Included in this are resources used to search the science literature. These may be thought of as broadly applicable to research questions in industry and not specific to any one of them. We assume that entrants search the knowledge stock and perform R&D to maximize expected profit (1), taking the actions of other entrants and the incumbent as given. First order conditions for entrant search and R&D are: (5) i s i i i L j n j i s p R s V p p p r V p , 1 , ) ( ) )( 1 ( (6) i R i i i L j n j i R p R s V p p p r V p , 1 , ) ( ) )( 1 ( The terms i s p , and i , R p are partial derivatives of (3) with respect to i s and i R . However, (5)-(6) can be simplified. Free entry drives expected profit (1) of entrants to zero. This implies that ) ( ) ( 1 L j n j i i i p p r F R s V p . Substituting into (5) and (6) we reach 2 Equations (1) and (2) derive from present values of entrant and incumbent. Under the assumption that the arrival rates L i p p , follow independent Poisson distributions the probability that the next generation product has not been discovered by time t is ] ) ( exp[ t p p L i . The present values for the entrant and incumbent are, respectively, (1*) F dt R s V p e PV i i i t p p r i L i ] [ ) ( 0 (2*) F dt R s V p e PV L L L t p p r L L i ] [ ) ( 0 If the arrival rates and the inputs remain constant over time (1*) yields (1) and (2*) yields (2). 6 (52) 1 ) ( , F V p i s (62) 1 ) ( , F V p i R Equations (52) - (62) yield solutions for search and R&D of entrants. The solutions are cpegged d: they are independent of investments by other firms and are easily found given (3). For now it is sufficient to say that incentives of entrants are given by the knowledge stock K , the productivity of search and the net value F V from entering the race. Following Etro (2004) we assume the incumbent follows a Stackelberg strategy. She anticipates the reaction of entrants to her investments in search and R&D. First order conditions from maximization of (2) are (7) ] ) / ( )[ ( ) )( 1 ( , , 1 , L R L R L L L L L j n j L s p p p n p R s V p p p r V p (8) ] ) / ( )[ ( ) )( 1 ( , , 1 , L R L R L L L L L j n j L R p p p n p R s V p p p r V p We have used symmetry, np p j n j 1 , and the fact that entrants 9 search and R&D and hence p are independent of the incumbent, to write out the terms on the right of (7)-(8). To find L p n / set (1) equal to zero using free entry and impose np p j n j 1 to reach (9) p p p r Fp R s F V n L Differentiation of (9) shows that p p n L / 1 / so the right hand sides of (7)-(8) are both equal to zero. Further simplification yields (72) 1 , V p L s (82) 1 , V p L R Given the technology (4), notice that incentives of the incumbent are given by the knowledge stock K , the productivity of search and V . The incumbent has a larger incentive to invest in research than entrants. This is because they anticipate the reactions 7 of entrants to their investment. There is a tendency towards persistence of monopoly if the difference in favor of the incumbent, due to fixed costs F , is large. C. Multiple Lines of Business We now show that the above argument understates the advantages of the incumbent. Suppose that a firm owns multiple lines of business in which it is the leader and suppose that it competes in every one to be the first to invent the next generation of higher quality product. We shall assume that search resources of the firm exhibit an economy of scope, on the grounds that science, which is included in these resources, tends to be general knowledge, along with some forms of technology, but that science is on the whole broader than technology. To see how this scenario would play out, consider an incumbent whose present value over N lines of business, indexed by superscript k , is: (10) k k L k j n j k L L k k k L N k L F p p r R N s V p PV 1 1 / Observe that the unit price of search resources is N / 1 since these inputs are used in all N lines of business. The probability of the incumbent winning patent race k is (11) R S k L k L R sK p ) ( ) ( Search spans all the different product lines of the firm, while R&D is specific to a product line. While the assumption is extreme it points out the difference between general knowledge, of which science tends to be an example, and technology, which tends to be specific to sectors. To highlight the difference between large incumbents and small entrants, we suppose that the expected present value of the entrant follows (1) and refers to a single 8 line of business. Thus, the fi rst order conditions (52) and (62) continue to apply. Given symmetry across lines of business the first order conditions for the incumbent become: (12) ] ) / ( )[ / ( ) )( / 1 ( , , , L s L s L L L L L L s p p p n p R N s V p p np r N V p (13) ] ) / ( )[ / ( ) )( 1 ( , , , L s L s L L L L L L s p p p n p R N s V p p np r V p Differentiation of (9) again shows that p p n L / 1 / so that the bracketed term on the right equals zero. Upon simplifying, the incumbent 9s first order conditions become: (122) 1 , V Np L s (132) 1 , V p L R Using (4) equations (122) - (132) can easily be solved for equ ilibrium investments in research by the incumbent. But it is already clear what we shall find. Not only is the incumbent 9s incentive V larger than the entrant 9s F V , which contributes to persistence of monopoly, but there is a further advantage to, as well as bias towards, search and science resources s owing to their use across all N business lines. These are used to search the stock of knowledge (Cohen, Nelson, and Walsh, 2002) , and the incumbent 9s size and diversity favors them over R&D specific to a line of business. This digression into the large incumbent firm 9s environment for innovation serve s three purposes. First, it shows that the assumption of informational advantage, which is based on the incumbent 9s knowledge of the market in which she is a leader, when coupled with the assumption of free entry, will give the incumbent more incentives than entrants to invest in research. Second, and perhaps more important, economies of scope associated with search give the incumbent even more of an incentive to invest in research than entrants. The search input increases because of the scope economy. But as search increases there is a secondary effect that increases R&D, owing to Pareto complementarity between knowledge absorbed and R&D specific to product lines. Thus 9 large and diverse firms invest heavily, especially in search. Third, the model suggests that science is primarily a large company affair, because large and diverse firms benefit more than small firms engaged in a single line of business. The production functions for inventions and science within firms could reflect the incentives described in this section. We shall try to find empirical counterparts to them in auxiliary data. III. Preparation of the Data A. Construction of R&D Stocks Data preparation begins with the selection of the Top 200 R&D-performing firms in the U.S., hereafter the Top 200. The firms are drawn from the year 2000 edition of Compustat and are ranked by R&D expense. For a current description of these data, see Standard and Poor 9s -Data Services Compustat (2007). Identities of the Top 200 and of the science carried on in them are described in Adams and Clemmons (2006). We deflate R&D expense using the 1992 implicit price deflator of the Bureau of Economic Analysis. Then we depreciate deflated R&D at an annual rate of 15 percent and construct five-year R&D stocks 3 . The stocks are lagged one year so for example, the 1993 stock covers 1992 back to 1988. The firm 9s R&D stock is, (14) j t i j j t i R RDK , 1 5 1 , ) 85 . 0 ( We adjust (14) to represent basic research by multiplying the R&D stock by the ratio of basic research to total R&D in the firms 9 primary industry to yield the firm 9s estimated stock of basic research. We use basic research stock to explain the firm 9s output of scientific papers 4 . Then we multiply (14) by the ratio of applied research to total R&D to yield an estimate of the firm 9s applied research stock. We use basic plus 3 The five year lagged R&D stock takes the relatively short R&D series on some firms into account. However, eight year stocks behave similarly in a smaller panel. 4 The stock of basic plus applied research performs almost as well. 10 applied research to explain the firm 9s output of patents. The industry ratios are taken from National Science Foundation (2007) 5 . While these estimates fit better than the unadjusted R&D stock (14) the difference is not essential. B. Patent Data 1. Name Match to Patent Assignees By construction Top 200 firms match Compustat, but they do not match patent assignees in the NBER Patent Citations database (Jaffe and Trajtenberg, 2002), our source for patents and the knowledge flows related to them. For this reason we undertake a name match between Top 200 names and assignee names in the NBER data. The first step in this match is to obtain subsidiaries of the firms from FIS OnLine. Since FIS later became Mergent see Mergent OnLine (2007) for a description of recent data. This step yields 13,536 subsidiaries, or about 70 per firm. Its importance is that it allows for multiple patent assignees including foreign subsidiaries owned by the firms. The second step is a name match between subsidiaries and assignees. This yields 1,549 assignees or about eight per firm. Since FIS (Mergent) assigns ticker symbols to subsidiaries, tickers are attached to matching assignees and their patents. At this point we have matched the Top 200 firms in Compustat, their assignees, and their assignees 9 patents. A ticker symbol appears in all patent records. 2. Patents and Citation-Weighted Patents Next we extract patents of the Top 200 as well as citations made and received by the patents. The result is 357,739 patents during 1975-1999 or about one-fifth of all U.S. patents during this period. Top 200 patents receive 0.9 million citations from Top 200 5 The NSF data do not exist in all years and therefore require interpolation as well as extrapolation. This is especially true in the early 1980s and in non-manufacturing but R&D intensive sectors. These data are the only data available with which to make these adjustments. 11 firms and two million citations overall. To capture their impact on industry we use forward citations received from other Top 200 firms over the first five years including the grant year 6 . Citation-weighted patents using a seven year interval perform similarly in the empirical work 7 . Given these data we accumulate patent counts and citation-weighted patents by firm, patent category, and year. The six categories are chemical; computer and communications; drugs and medical; electrical and electronics; mechanical; and other. We want to construct patents by firm and category because this helps to distinguish knowledge flows from firm level R&D. We start the panel in 1988 to allow the R&D stocks and knowledge flows to build up over time. After missing values are removed, this process yields 7,263 observations on patent counts arranged by firm, patent category, and year over 1988-1999. There are 4,615 observations on patents weighted by five-year citations received, in which the time period is 1988-1995. These two variables serve as measures of invention that are to be explained. We date patents by grant year rather than application year. This choice is dictated by the scientific papers part of our data. Use of grant year implies that patents and papers are both lagged relative to the year in which the invention or discovery is applied for. Clearly this makes it harder to synchronize patents with their effects on the U.S. economy. But part of our purpose is to link knowledge flows from scientific papers with those from patents. As it happens, papers are dated only by publication year, the 6 Trajtenberg (1990) and Harhoff, Narin, Scherer, and Vopel (1999) validate citations received as a measure of patent quality. 7 Since patents granted end in 1999 five year citations end in 1995, and seven year citations in 1993. While the seven year interval is a more accurate measure of the importance of the patents, by catching more later maturing patents, it truncates the sample two years earlier and thus causes appreciable loss of sample size. 12 analogue to grant year. Nothing is known about the year of submission, especially given that papers can be submitted an unknown number of times. If we were to use application year for patents, then we could wind up dating patents before papers, when the patents appear later. Put another way we lack application year for papers so we cannot consistently assign cgrant d dates to research. 3. Knowledge Flows Inside the Firm Throughout we assume that knowledge flows are the result of a search for useful knowledge by industrial scientists and engineers. To make this idea tangible we assume first, that citation (and collaboration) rates for patents and scientific papers measure sampling rates under search, and that estimated sampling rates are roughly proportional to the knowledge that spills over. Second, we assume that R&D stocks of cited institutions, whose science and technology is being sampled, are highly correlated with unobservable stocks of knowledge. Klette and Kortum (2004) take this point of view 8 . Third, we impose an aggregation condition in that we assume that different knowledge flows can be added up to form an overall knowledge flow to the citing firm. R&D stocks have several practical advantages as measures of accumulated knowledge. They provide an historical record of research that captures anticipated future impact. R&D stocks also avoid nominal variations in papers-R&D and patents-R&D ratios. For example, firms could shift towards higher impact science and invention so that R&D remains profitable, despite declines in these ratios. (Griliches, 1993; Lanjouw and Schankerman, 2004) 8 Klette and Kortum (2004) demonstrate the point for a stylized model of the firm. Using a depreciation rate on R&D equal to the rate of creative destruction yields a stock of firm R&D that is equal to firm knowledge, defined as the number of its innovative products. A different depreciation rate would yield a stock of R&D that is highly correlated with firm knowledge. The point is that stocks of R&D and stocks of innovative goods are different ways to measure innovation, the first by inputs, the second by outputs. 13 Given these assumptions we construct a variety of knowledge flows, all based on patents. We call these coriginal d measures in that they refer to knowledge flows before aggregation into cderived d measures. We distinguish the flows by citing firm, patent category, and year; and by cited firm, category, and year 9 . These dimensions determine observed knowledge flows by points of origin and destination. We begin with measurement of knowledge flows from patents inside the firm. The measure that we use is the citation rate times cited R&D stock, summed over cited years and categories, but within the firm. Inside knowledge flows depend on the number of citations to earlier patents in the firm, on the number of patents that could have been cited, and on the firm 9s R&D stock. Our justification is that citation rates sample the amount of accumulated knowledge captured by the stock of R&D. Therefore, inside knowledge flows by citing firm, patent category, and year are (15) 1 6 1 6 1 1 , it it ikt k ikt ijt k T INSIDE FIRM ijt RDK a n c K Firm i patents in patent category j at time t make ikt ijt c citations to ikt n 4 these are all the patents of firm i in category k at time t . Since citing and cited firms i are the same these are c in side d citations. The citation rate, the middle term on the right of (15), is an overall weighted-average. This is because cited R& D stock is at the firm level 10 . The term it a in (15) is the ratio of basic plus applied research to total R&D in the firm 9s industry, which yields an 9 Recall that the six patent categories are chemical, computer and communications, electrical and electronic, mechanical, and other. 10 If R&D stocks were distributed by patent category, then (15) would instead be (15 2) 1 6 1 1 , ikt it ikt ikt ijt k T INS FIRM ijt RDK a n c K 14 estimate of the stock of basic plus applied research when multiplied by R&D stock , 1 it RDK as defined in (14). Note that cited patents are lagged by at least one year and that R&D stock is lagged by one more year. In the empirical work we lag knowledge flows (15) by still another year relative to patents to instrument the citation rate in (15). Therefore, R&D precedes citing patents by at least two years. These lags are identical for all knowledge flows that follow. 4. Knowledge Flows from other Firms In a similar way outside knowledge flows, or flows of knowledge from other firms 9 patents , depend on citation rates to earlier patents of other firms, times stocks of basic and applied research. The measure of outside knowledge flows is (16) 1 6 1 6 1 1 1 , lt lt lkt k lkt ijt k T N i l l OUTSIDE FIRM ijt RDK a n c K Firm i patents in category j at time t make lkt ijt c citations to patents of another firm l . These lkt n are all the patents issued to firm l in category k at time t that could have been cited. Since citing and cited firms i and l differ these are coutside d citations and summation occurs over cited firms as well as cited years and patent categories. Again the citation rate is a weighted average across categories, because cited R&D is at the firm level. The term lt a is the ratio of basic plus applied research to total R&D in the cited firm 9s industry and this provides an estimate of basic plus applied research, multiplied by the lagged, cited R&D stock . 1 lt RDK Lags on R&D are the same as for inside knowledge (15) and precede citing patents by at least two years. 15 C. Scientific Papers Data 1. Papers and Citation-Weighted Papers The data that we use on scientific papers derive from Thomson Scientific. They are described in Adams, Black, Clemmons, and Stephan (2005), Adams, Clemmons, and Stephan (forthcoming), Adams and Clemmons (2006), Adams and Clemmons (forthcoming 2008) and Adams and Clemmons (2008). The data consist of 230 thousand papers of the Top 200 firms and 2.43 million papers of the top 110 U.S. universities, which are published during 1981-1999. The papers appear in 7,137 scientific journals. Each journal and the papers it contains, is assigned to a single science field. The main alternative is the assignment of papers according to authors 9 fields. But this information is not complete 11 . Top 200 firms make one million citations to papers of top 110 universities, and 0.6 million citations to Top 200 papers, including their own. Because firms rarely collaborate with one another, in this paper collaboration consists simply of joint research between firms and universities 12 . After removing missing values the data yield 4,340 observations on scientific papers arranged by firm, field, and year over the period 1988-1999; and 2,495 observations on 11 We tried to assign all papers of Harvard University to a science field using address information. About a third of the papers could not be assigned leading us to abandon this method. 12 Firm papers are 1/10 as many as university papers so collaborations between firms would be 1/10 as many as universities and firms collaborations. This assumes that the two collaboration propensities are the same. But firm-firm collaborations are rarer than this. 16 citation-weighted papers over 1988-1995 13 . These variables are observations on firms 9 scientific discoveries. 2. Knowledge Flows Inside the Firm We use S to represent knowledge flows from scientific papers to distinguish these from knowledge flows K from patents. All flows take place in one of six main fields that dominate industrial science: biology, chemistry, computer science, medicine, physics, and engineering. As before, the flows occur at the receiving firm, science field, and year level. Perhaps the most serious problem that we face in estimating knowledge production functions for patents is that there is no direct link between science fields and patent categories. We address this issue in Section III.C.5. As with patent-based flows, inside knowledge flows from papers of the firm are (17) 1 6 1 6 1 1 , it it ift f ift ijt f T INSIDE FIRM ijt RDK b N C S Firm i papers in science field j at time t make ift ijt C cinside d science citations to ift N 4 these are all the papers published by firm i in field f at time t . Again the citation rate on the right is a weighted average because R&D stock is at the firm level. The term it b is the ratio of basic research to total R&D in the firm 9s primary industry. Multiplied by 1 it RDK this provides an estimate of the firm 9s basic research. 3. Knowledge Flows from other Firms Knowledge flows from scientific papers of other firms follow a similar pattern. The measure of outside knowledge flows from scientific papers of other firms is 13 Since citations received cover the first five years after publication and since the data end in 1999, citation-weighted papers end in 1995, leading to a drop in the number of observations. 17 (18) 1 6 1 6 1 1 1 , lt lt lft f lft ijt f T N i l l OUTSIDE FIRM ijt RDK b N C S Firm i papers in science field j at time t make lft ijt C citations to firm l papers flt N , which are all the papers issued to firm i in field f at earlier time t . Since citing firm i and cited firm , , i l l are different these are coutside d citations. The term lt b is the ratio of basic research to total R&D in the cited firm 9s primary industry, which provides a n estimate of basic research when multiplied by 1 lt RDK . 4. Knowledge Flows from Universities Knowledge flows from universities take place through citation and collaboration since firms collaborate with universities on 20 percent of their papers 14 . Thus we consider two different knowledge flows from university science. The collaboration flow carries the richer connotation of sustained mutual learning, often over an extended period of time. And of course collaboration contributes to citation through references to past joint research and the learning process just alluded to. In constructing measures of knowledge flow from university science we use stocks of federally funded R&D, which the National Science Foundation collects by university, field of science, and year. To learn more about the data see WebCASPAR Integrated Science and Engineering Resources Data System (2007). We restrict university R&D to federally funded research so as to avoid double-counting with the firm R&D shown in (14)-(18). University R&D stocks are eight year, lagged stocks in millions of 1992 dollars, depreciated at 15 percent. The R&D stock in university i and field j at time t is 14 In contrast, firms collaborate in two percent of cases, many of these jointly authored with university researchers and presumably written while in graduate school. 18 (19) t ijt UR URK 1 8 1 ) 85 . 0 ( Unlike industrial R&D, which is available by firm and year, university R&D is available by university, field, and year. While this seems an advantage, errors in field-specific university R&D are a countervailing disadvantage. The measurement of knowledge flows through science citations to universities is (20) 1 1 6 1 1 , lft lft lft ijt T f N l CITES UNIV ijt URK N C S In (20) the knowledge flows are summed over cited universities l using science citations lft ijt C to university papers in field f divided by university papers in year t , times the cited, lagged university stock 1 lft URK . The citation rate is specific to field. It is not a weighted average rate because university R&D is reported by field. Knowledge flows by means of collaboration are similar to (20) except that collaboration takes place within field, occurs contemporaneously, and collaboration counts lft ijt J replace citation counts. This simplifies the measure relative to (20). It is (21) ljt ljt ljt ijt N l COLLABS UNIV ijt URK N J S 1 , In the empirical work we instrument knowledge flows in (20) and (21), as before, by lagging them by one year relative to the patent counts and citation-weighted patents that we seek to explain. The lag structure in (20) and (21) is similar to knowledge flows from firms except that eight-year stocks replace five-year stocks. Equations (18)-(21) yield knowledge flows from science at the firm, field, and year level. But this does not help us to explain patents by firm, category, and year. A 19 method for mapping patent categories to science fields is required. This problem is the subject of the next section. 5. Assignment of Science Fields to Patent Categories We assign knowledge flows from fields to categories as follows. First, we transform the knowledge flows from science in a firm, field, and year (some of which are zero) by adding 0.001 to each and taking logarithms of the result. Separately by science field we then run Tobit equations of the transformed variables on a vector of year dummies ( t D ) and a vector of proportions of the fir m 9s patents falling in different categories ( it P ), omitting the c other d patent category. The equation is: (22) ijt it t X ijt u P D S ) ln( We estimate (22) separately for each field j (biology, chemistry, computer science, medicine, physics, and engineering) and each knowledge flow from science ( FIRM, INSIDE; FIRM, OUTSIDE; UNIV, CITE; UNIV, COLLAB ). We choose patent proportions because we want to avoid a result in which knowledge depends on the volume of patents. We tabulate significant positive coefficients and rank them by size across different fields of science and thus equations, to see which sciences increase most for a one unit increase in each patent proportion. Table 1 displays the results from this exercise. To illustrate, consider knowledge flows from inside papers of the firm. The largest effect of the chemical patent share is on chemistry, the second largest is on biology, the third largest on physics, and so forth. This is shown in the first column of Table 1 under cCitations, Same Firm Papers d . 20 Typically three science fields increase in response to a given patent share. We take the top three fields, top two fields, and top field as sciences that are associated with a patent category. To illustrate, consider knowledge flows through citation to papers of the same firm, and consider the top two fields. For chemical patents, the knowledge flow comes from chemistry and biology. For communications and software patents it comes from computer science and physics. Likewise, the flow for drug and medical patents derives from medicine and biology. For electrical and electronics patents it is physics and engineering; for mechanical patents it is physics and chemistry; and for other patents it is computer science and engineering. Any of the criteria: top three, top two, and top field work well in the patent equations. As a compromise we choose the top two fields. This method almost surely creates a downward bias in the measured effect of science on patents. This is because it does not capture the use of science that is specific to patents in a particular category: the same physics knowledge flow, for instance, affects electrical and electronics patents as mechanical patents. And yet, despite this drawback, science flows are significant in the patent equations. D. Summary of Knowledge Flow Concepts Table 2 summarizes the knowledge flow indicators from Sections III.B and III.C. The first six are the c original d measures described by (15)-(18) and (20)-(21), while the final six are cderived d measures that are sums of original measures. Following (15) original measure 1 consists of knowledge flows from citations to earlier patents of the same firm. Measure 2 consists of knowledge flows from citations to patents of other firms and follows (16). The remaining four measures are knowledge flows from scientific papers. Measure 3 is (17) and is based on citations to papers of the 21 same firm. Measure 4 is (18): it is based on citations to papers of other firms. The remaining c original d measures report knowledge flows from university papers. Measure 5 is derived from citations to university papers. It follows (20). Measure 6 is derived from collaborations on university papers and follows (21). Table 2 concludes with six c derived d measures. Flows from all patents (measure 7) are the sum of knowledge flows from patents inside and outside the firm 4 measure 1 plus measure 2. Flows from all papers (measure 8) are the sum of knowledge flows from all firms and universities by citation and collaboration. They are the sum of measures 3 to 6. Measure 9 aggregates knowledge flows inside the firm from patents and papers, or measure 1 plus measure 3. Measure 10 is the sum of knowledge flows from other firms 9 patents and papers and from university papers 4 this is the sum of measures 2, 4, 5, and 6. The sum of all knowledge flows from industry patents and papers, or measures 1 to 4, yields measure 11. Flows from university papers comprise measure 12. It is the sum of measures 5 and 6. Table 2 contains all the different concepts of knowledge flow that we use in our study of patents. We now turn to estimates of patent production functions. IV. Patent Production Functions A. Patent Panel Capitalizing on the data construction, we create a patent panel that relates current patents of firms to lagged knowledge flows. Its dimensions consist of firm, patent category, and year. Table 3 describes the principal variables. At the top are patent counts and citation-weighted patents. The mean number of patents per cell is 29, while the mean number of patents weighted by five-year forward citations is 13. Citation- 22 weighted patents are fewer than patent counts, because many patents are not cited by patents of other Top 200 firms. Next we report various measures of firm R&D stock. As Section III.A explains, the basic research stock, basic plus applied stock, and stock of development are all obtained by multiplying the firm 9 s total R&D stock by proportions of each of these components of R&D in the firms 9 primary industries . The mean stock of basic research is 100 million dollars of 1992, the basic plus applied stock is 372 million, and the stock of development is 1,284 million. The three components sum by construction to total R&D stock, whose mean is accordingly 1,757 million. Knowledge flows comprise the rest of Table 3. The definitions underlying these figures consist of equations (15)-(18) and (20)-(21) in Section III. The mean flow based on citation to patents of the same firm is 101 million. For citation-based flows to other firms 9 patents it is 113 million. Now consider knowledge flows from science. The mean flow from papers of the same firm is 61 million dollars. The flow from other firms 9 papers is 32 million dollars and from university papers it is 45 million. Thus, industry patent-based flows are more than double the scientific paper-based flows, 213 million versus 92 million. Moreover, inside knowledge flows from patents and papers amount to 161 million, as compared to 144 million of between-firm or outside flows by means of patents and papers. We conclude that most knowledge flows to patents are patent-based. Even more of the flows are industry-based and only 13 percent (45/351) derive from universities. c D erived d measures complete Table 3. Outside patent and paper flows (190 million) exceed inside flows (161 million) because we group university knowledge flows 23 with flows from other firms. For convenience of interpretation we often use c derived d knowledge flows in patent production functions. The call patents d and call papers d definitions, the cinside d and coutside d measures, and the cindustry d and cuniversity d decomposition form the specifications used in the empirical work. B. Estimates Table 4 presents estimates of the patent equations in which the principal variables are the logarithm of the stock of the firm 9s basic plus applied research, the logarithm of knowledge flows through all patents, or patent-based flows; and the logarithm of knowledge flows through all papers. These are scientific paper-based flows. The dependent variable in equations 4.1-4.3 consists of patent counts. The method is fixed effects Poisson, which Cameron and Trivedi (2005) view as a robust estimation for count data 15 . Fixed effects represent both firm and patent category. In 4.1 and 4.2 we find that the elasticity of patents with respect to the firm 9s research stock is around 0.2 4 roughly equal to the elasticity of patent-based knowledge flows. Both are highly significant. When we introduce the knowledge flow from all scientific papers in 4.2, the paper-based elasticity is only 0.02, though it is significant. Equation 4.3 a dds czero interaction terms d for knowledge flows to 4.2. These are similar to a spline in which zero values and positive knowledge flows are taken into account. The rationale goes back to the transformation of the knowledge flows. We added 0.001 to the values, many of which are zero (see Table 3) in order to include the entire sample. The estimates in 4.1 and 4.2 are thus an average over zero and positive values. The zero interactions are products of dummy variables equal to 1 when the 15 Consistent with this, random effect Poisson or Negative Binomial estimates are similar to the estimates shown. The key reference on this subject is Hausman, Hall, and Griliches (1984), though Cameron and Trivedi (2005) discuss subsequent developments. 24 knowledge flow is zero and 0 when the flow is positive, and the logarithm of the knowledge flow (plus 0.001). When the knowledge flow is zero, the zero interaction term is ln (0.001), but when it is positive the zero interaction term disappears. When the knowledge flow is zero, we expect the zero interaction term to cancel out the main knowledge term. Adams and Clemmons (2006) use this specification extensively. Equation 4.3 employs zero interactions for knowledge flows from patents and scientific papers. As expected the interaction elasticities are negative and roughly cancel the main elasticities. In addition, the main knowledge flow elasticities rise sharply when interaction terms are included: the effect of knowledge is of course greater, when positive flows occur. The coefficient of the research stock drops when knowledge coefficients are measured separately over zero and positive domains. Equations 4.4-4.6 are random effects Tobit estimates for citation-weighted patents, about a fourth of which are left-truncated 16 . The method controls for random effects for the group 4 again this is the firm-patent category 4 and also for group and time. In 4.4 the elasticity for the knowledge flow from patents increases relative to the elasticity for the firm 9s research stock. In 4.5, when we include the knowledge flow from scientific papers, the research stock becomes insignificant. The relative elasticity of the science variable rises markedly compared with the results for patent counts. This could follow from a difference in techniques, in part because we cannot control for fixed effects in the Tobit equations. But the prominence of science could be a substantive difference, in that science is more productive for highly cited inventions. In 4.6 the zero interaction term for patent flows cancels the main effect, and as before, the main effect rises. 16 Fixed effects Tobit estimates are inconsistent in short panels like ours because of the incidental parameters problem. Differencing and conditioning that would eliminate the fixed effects are not available because of the nonlinearity of the likelihood. Again see Cameron and Trivedi (2005). 25 Table 5 reports results like 4.2 and 4.5 separately by industry. For patent counts (columns (1)-(3)) the research stock and flows from all patents enter with persistent positive and significant signs. A positive effect of science flows is not discernable in petrochemicals or drugs and biotechnology. This is not true for citation-weighted patents (columns (4)-(6)). Elasticities of the science flows are greatest in drugs and biotechnology, as one would think given the science linkages for this industry. Table 6 breaks up knowledge flows from patents and papers into flows inside and outside of the firm. As in tables 4 and 5 6.1 and 6.2 are fixed effect Poisson estimates for patent counts, while 6.3 and 6.4 are random effects Tobit estimates. 6.1 and 6.3 include only inside-outside knowledge flows for patents, while 6.2 and 6.4 add inside-outside knowledge flows for scientific papers. In 6.1 and 6.3 the outside knowledge elasticity is double the inside elasticity. This pattern continues when science flows are included (see 6.2 and 6.4). The pattern is still more extreme for inside and outside science, where the only significant effect is from outside science. We conclude that outside knowledge dominates invention: its elasticity is larger than the elasticity for inside knowledge. Table 7 breaks up knowledge, first, into industry knowledge flows from papers and patents together and then university papers (7.1 and 7.3); and second, into industry knowledge flows from patents and papers separately, then university papers (7.2 and 7.4). Equations 7.1 and 7.3 reveal that the elasticity of industry knowledge flows is at least four times larger than the elasticity of university flows. In 7.2 and 7.4, where we break up patent and paper flows, most of the industry premium is shown to reside in the patent- 26 based flows. Indeed the elasticity of industry flows from science is only slightly greater than the elasticity of university science flows. Table 8 reports Wald tests of coefficient restrictions where equality of the coefficients is the null hypothesis. This is done for the leading specifications of the equations in Tables 4, 6, and 7. Equality is rejected in nearly every case. On line one, the elasticity of the research stock is less than the patent flow elasticity in 4.2 but it is greater in 4.5 for citation-weighted patents. On line two, the patent flow elasticity significantly exceeds that of paper flows. The outside elasticities (Table 6, lines three and four) significantly exceed inside elasticities in every case. Then, in Table 7, the industry patent flow elasticity is significantly greater than both the industry and university paper flow elasticities on lines five and six. Finally, on line seven the industry paper flow elasticity exceeds or is equal to the university paper flow elasticity. The Wald tests in Table 8 formally confirm the significance of the differences in coefficients that we observe. V. Scientific Paper Production Functions A. Scientific Papers Panel For comparison with the patent estimates we construct a panel of scientific papers, whose dimensions are firm, science field, and year. Table 9 describes the principal variables and the panel. The six scientific fields dominate industrial science and consist of biology, chemistry, computer science, medicine, physics, and engineering. The time period is 1988-1999, except for citation-weighted papers, where it is 1988-1995. The number of observations is 4,340 for scientific papers, and 2,719 for citation-weighted papers. In both cases we have cfractionated d the papers and citation -weighted papers to avoid multiple counting of scientific output and to reflect co-authorship with other 27 institutions, increasingly common in science (Adams, Black, Clemmons, and Stephan, 2005). From an econometric point of view this also means that the paper data are continuous and not integer-valued, so that count data methods are not needed. The mean number of papers is 29 and the mean of citation-weighted papers is 74. These are dependent variables in the empirical work that follows. About one-sixth (448/2,719) of citation-weighted papers are left-truncated, suggesting the use of Tobit analysis for citation-weighted data. The various research stocks are about one-third larger than the patent panel, which shows the larger size of firms that undertake science, even among the Top 200. For instance, the stock of basic research in Table 9 is 146 million dollars rather than 100 million and the stock of R&D is 2,592 million rather than 1,757 million as in Table 3. In this data set the knowledge flows all pertain to scientific papers. All are lagged one year behind the papers and citation-weighted papers which they seek to explain 17 . Since the citation lags and the R&D stocks that enter the knowledge flow indicators are the same as the science measures expounded in section III, effective lags amount to several years. The mean knowledge flow from scientific papers is 111 million, of which 42 million is inside the firm, and 69 million outside of it. Of the 111 million, 66 million is contributed by industry papers and 45 million by university papers. This is to be contrasted with Table 3, in which 92 million was contributed by industry knowledge flows from papers and again 45 million from university paper flows. A larger proportion of science-based knowledge comes from the academic sector at the pre-invention stage. Table 10 reports production functions for scientific papers. Equations 10.1 and 10.2 use fixed-effect OLS. Here the dependent variable is the logarithm of fractional papers. 17 Exploration of the role of patents in scientific papers is beyond the scope of this paper. 28 Equations 10.3 and 10.4 use random effects Tobit. Here the dependent variable is the logarithm of fractional citation-weighted papers (plus 0.001). In 10.1 and 10.3 we employ the inside-outside knowledge flow decomposition that Table 9 explains. In 10.2 and 10.4 we use the alternative industry-university decomposition. The significance of the firm 9s stock of basic and applied research varies , perhaps because of the random effects approach used in the table 9s second half. The elasticity of inside knowledge ranges from 0.07 to 0.17, while the outside elasticity ranges from 0.45 to 0.86. Using both methods the inside elasticity is about one-sixth of the outside elasticity. In the industry-university specifications the industry elasticity is less than half the university elasticity. Thus the impact of university science exceeds that of industry science. Also interesting is the comparison between Table 6 and Table 10, for inside and outside knowledge. The comparative elasticity of inside knowledge is far larger in Table 6, implying that the relative impact of knowledge outside the firm is smaller at the inventive stage than at the pre-technology stage. Thus the scope of relevant knowledge narrows down and begins to center on the firm, as it move towards commercialization and increasingly depends on a sequence of R&D decisions. Likewise, in the comparison of industry and university elasticities in Tables 7 and 10, the industry elasticity is larger at the inventive stage, while the reverse holds at the pre- technology stage of Table 10. The scope of relevant knowledge narrows down and begins to center on industry, as the firm works through a sequence of phases that in the best of outcomes results in new products and processes. 29 Table 11 concludes the empirical work by testing a set of equality restrictions on the equations in Table 10. On line one, the hypothesis that the elasticities of the basic research stock and the inside knowledge flow are equal is rejected in 10.1 but accepted in 10.3. On average, the inside paper elasticity is found to be greater. On lines two and three equality of the elasticities is rejected. Thus, the outside elasticity significantly exceeds that of the research stock and the inside knowledge flow. Lines four and five are ambiguous as to whether the elasticity of the research stock exceeds or falls short of the industry or university knowledge flows. But line five is unambiguous in finding that the university elasticity exceeds the industry elasticity. Thus, Table 11 finds that per one percent change outside knowledge flows and university knowledge flows produce a greater percentage increase in papers and citation-weighted papers than inside knowledge and industry knowledge. VI. Discussion, Comparison, and Conclusion This paper has explored the motives behind the production of inventions and scientific discoveries in large R&D-performing enterprises and it has provided a simple framework in which research is carried out, arguing that there are reasons for the persistence of monopoly, based on the informational advantage of incumbents and economies of scope in large companies having to do with science and other general forms of knowledge. In this paper we estimate production functions for inventions and scientific discoveries in R&D-performing firms. The analysis treats patents and scientific papers, sometimes weighted by their citations, as pertinent measures of inventions and discoveries: ideas located at different removes from commercialization. In turn, ideas are 30 treated as a function of the firm 9s R&D stock, of knowledge flows from its own past inventions and discoveries, and of knowledge flows from inventions and discoveries in other firms and in universities. We capture the importance of different kinds of knowledge by the elasticity of ideas with respect to each knowledge source. Our most significant findings are first, that knowledge flows from past inventions are the most important determinant of new inventions. Second, past scientific discoveries are also important, holding patent-based knowledge flows constant, especially for highly cited, impactful patents. We also explore implications of knowledge flows inside and outside the firm for the firm 9s inventions. We f ind that outside knowledge flows from patents issued by other firms are more important than inside knowledge flows. In addition, industry knowledge flows outweigh university flows in the invention production function. Turing to production functions for fir ms 9 scientific papers we find that papers depend even more than patents on outside knowledge. In sharp contrast with patents, knowledge flows from universities are more important than knowledge flows from industry, implying that universities exert their greatest influence at early stages of industrial research, a fact that is obscured by an exclusive reliance on patent data. Together the findings suggest that firm 9s inventions are determined by a sequence of research that in late stages narrows the scope of knowledge flows to the firm and industry relative to early stages of pre-technology science. Even so, science plays an appreciable direct role in the production of patents, especially high impact patents. 31 References Adams, James D., cFundamental Stocks of Knowledge and Productivity Growth, d Journal of Political Economy 98 (August 1990): 673-702 ______________ , cLearning, Internal Research, and Spillovers, d Economics of Innovation and New Technology 15 (January 2006): 5-36 ______________, and J. Roger Clemmons, c The NBER-Rensselaer Polytechnic Institute Scientific Papers Database: Characteristics a nd Purpose, d Working Paper, September 2006 __________________________________, and J. Roger Clemmons, cScience and Industry: Tracing the Flow of Basic Research through Manufa cturing and Trade, d forthcoming 2008, Economics of Innovation and New Technology __________________________________, cThe Origins of Industrial Scientific Discoveries, d Cambridge, MA, NBER Working Paper #13823, February 2008 ______________, J. Roger Clemmons, and Paula E. 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Scherer, and Katrin Vopel, cCitation Frequency And the Value of Patented Inventions, d Review of Economics and Statistics 81 (August 1999): 511-515 33 Hounshell, David A., and John Kenley Smith, Jr.: Science and Corporate Strategy: Du Pont R&D, 1902-1980 , Cambridge, United Kingdom: Cambridge University Press, 1988 Jaffe, Adam B., and Manuel Trajtenberg, Patents, Citations, and Innovations , Cambridge, Massachusetts: MIT Press, 2002 Klette, Tor Jakob, and Zvi Griliches, cEmp irical Patterns of Firm Growth and R&D Investment: A Quality Ladder Model Interpretation, d Economic Journal 110 (April 2000): 363-387 ______________, and Samuel S. Kortum, cInnovating Firms and Aggregate Innovation, d Journal of Political Economy 112 (October 2004): 986-1018 Kortum, Samuel S., cResearch, Patenting, and Technological Change, d Econometrica 65 (November 1997): 1389-1419 Mergent OnLine (2007): www.mergentonline.com . Mueller, Willard F., c The Origins o f the Basic Inventions Underlying Du Pont 9s Major Product and Process Innovations, 1920- 1950, d in Richard R. Nelson, Editor, The Rate and Direction of Inventive Activity; Social and Economic Factors , Princeton, New Jersey: Princeton University Press for NBER, 1962 National Science Foundation (2007), Funds for Performance of Basic Research, Applied Research, and Development, by Industry and Source of Funds , Arlington, Virginia: www.nsf.gov/statistics/iris Nelson, Richard R., cThe Link between Science and Invention: The Case of the 34 Transistor, d in Richard R. Nelson, Editor, The Rate and Direction of Inventive Activity: Social and Economic Factors , Princeton, New Jersey: Princeton University Press for NBER, 1962 _______________, cThe Role of Knowledge in R&D Efficiency, d Quarterly Journal of Economics 97 (August 1982): 453-370 Scott, John T., cFirm versus Industry Variability in R&D Intensity, d in Zvi Griliches, Editor, R&D, Patents, and Productivity , Chicago: University of Chicago Press for NBER, 1984 Standard and Poor 9s -Data Services Compustat (2007), www2.standardandpoors.com S utton, John, cGibrat 9s Legacy, d Journal of Economic Literature 35 (March 1997): 40-59 Thomson Scientific (2007): http://scientific.thomson.com/isi WebCASPAR Integrated Science and Engineering Resources Data System (2007): www.webcaspar.nsf.gov 35 Table 1 Assignment of Scientific Fields to Patent Categories, By Type of Knowledge Flow Type of Knowledge Flow, Science Field Patent Category Chemical Communications & Software Drug & Medical Electrical Mechanical Other Citations , Same Firm Papers Biology 2 2 Chemistry 1 3 2 1 Computer Science 1 Medicine 1 Physics 3 2 1 1 2 Engineering 3 2 3 Citations, Other Firm 9s Papers Biology 2 2 Chemistry 1 3 1 1 Computer Science 1 3 Medicine 1 Physics 3 2 1 2 Engineering 3 2 3 Citations, University Papers Biology 2 3 Chemistry 1 2 2 1 Computer Science 1 2 Medi

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