August 10, 2004

The Location Patterns of U.S. Industrial Research: Mimetic Isomorphism, and the Emergence of Geographic Charisma*

Stephen J. Appold Department of Sociology National University of Singapore 10 Kent Ridge Crescent Singapore 119260 6874-6393 Fax: 6777-9579 http://courses.nus.edu.sg/course/socsja/ [email protected]

August 10, 2004

* I would like to thank Jack Kasarda, Eric Leifer, Michael Luger, and the anonymous reviewers of this journal for comments on an earlier draft of this paper.

The Location Patterns of U.S. Industrial Research: Mimetic Isomorphism, and the Emergence of Geographic Charisma

The emergence of new industrial spaces over the past several decades that have radically altered the economic geography of the U.S. raises questions about the mechanisms responsible for their formation. Existing theories predict either continued concentration or spatial dispersion; none predict the rise of new geographic agglomerations of establishments. A behavioral theory of agglomeration formation explains the emergence of regionally-dispersed, local agglomerations by means of mimetic behavior. A method for detecting social influence in cross-sectional data is applied to data on the 1985 locations by county of over 10,000 privately-owned research laboratories to show that the theoretical model accurately reproduces a key aspect of the existing spatial pattern. The results suggest that laboratories are, to a significant extent, reacting to each other’s actions, creating symbolic, rather than functional, communities and that the locus of power determining local growth is diffused among location decision-makers. R&D; urban agglomeration; geographic charisma; learning theory

The Location Patterns of U.S. Industrial Research: Mimetic Isomorphism, and the Emergence of Geographic Charisma

Between 1953 and 1998 (National Science Board, 2001) spending on research and development in the United States increased almost eight-fold in constant dollars – approximately 1.8 times as quickly as the growth of the GDP. Scientific research and development clearly plays a key role in the contemporary economy. Laboratories, the site of much of this formalized learning, are sometimes believed to generate significant local economic multiplier effects by attracting support services and high-skill manufacturing (Malecki, 1997). As one of the several privileged institutions in an emerging knowledge-based economy (Bell, 1973: 116) research laboratories are critical components of the emerging “new industrial spaces (Scott, 1988).” ––––––––––Map 1 about here ––––––––––Map 1 shows the 1985 location by county of the 10,393 private, industrial research laboratories in the United States that were active in ten broadly defined, overlapping, yet not exhaustive, research fields, aerospace, aviation, biological science, chemical research, communications, computer science, electric and power, electronics, engineering and medical science. Information on laboratories was collected from the 19th (1985) edition of Industrial Research Labs of the United States, the most complete enumeration of private research labs available. Each of these fields had a history that was at least decades old at the time. The year was chosen because it follows a decade or so of rapid location decisions, approximately coincides with a brief pause in the sitings of research laboratories nationally, and pre-dates institutional changes in industrial research, including the demise of the central corporate laboratory.1 The mean number of industrial research laboratories per county was 3.328 but, as 71 percent of the counties contained no labs, they were located in fewer than 900 of the approximately 3,065 counties in the continental United States. Approximately 10 percent of counties with any labs housed a single lab; Los Angeles County had the greatest number, 481. In between the extremes, numerous

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regionally-dispersed agglomerations of laboratories (19 counties contained more than 100 labs) were sprinkled across the U.S. The existence of multiple, dispersed agglomerations is difficult to explain with existing theories. The standard factors in the economic geographer’s toolkit: reliance upon natural resources and the need to interact efficiently with others (Fujita and Thisse, 2000; Mills and Hamilton, 1994) give only modest help in explaining the pattern of regionally-dispersed agglomerations seen in the map. Research scientists and engineers are not directly involved with the processing of goods and so are rarely anchored to specific sites. Moreover, since the advent of the telegraph, the ability to communicate effectively has been progressively de-coupled from physical proximity (Pred, 1967). The real costs of transportation are diminishing, leading to supply and marketing channels that are often global in scope (Frobel, Heinrichs, and Kreye, 1980; Gereffi and Korzeniewicz, 1994). Highskill (Herzog, Schlottman and Johnson, 1986) and low-skill (Martin and Widgren, 1996) labor moves in national and, as shown by the high levels of immigration, international markets. Technical knowledge flows through extra-local “invisible colleges” (Crane, 1972) and strategic alliances (Mowery, Oxley, and Silverman, 1996). Much of the available evidence on the geography of corporate control and industrial supply (e.g., Castells, 1996) suggests that contemporary cities and the regions that surround them are not tightly-interdependent economic units and research laboratories may be more tightly agglomerated than functional interdependence requires (Pascale and McCall, 1980). Just 25 years earlier than the data depicted in the map, Robert Lichtenberg (1960) termed the greater New York region, “One Tenth of a Nation,” and Raymond Vernon (1960) proposed a product cycle theory to explain that region’s continuing viability as the nation’s (and the world’s) innovation center on the basis the unduplicable advantage of amenities, rapid communication, and a rich supply of educated labor. Nevertheless, the progressive loosening over the past several decades of the constraints that have historically limited economic activities to particular places has led to neither of the most theoretically well-grounded predictions: continued metropolitanism – the increasing incorporation and subordination of peripheral places into an expanding system of dominance centered on a single core metropolitan center (Arthur, 1994) – or widespread deagglomeration – creating a

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dispersed geography of “community without propinquity” (Webber, 1967). Instead of the patterns predicted on the basis of well-developed behavioral models, multiple new dense agglomerations of economic activities have developed. Several of these agglomerations based largely on researchintensive industries, such as those centered in Silicon Valley, the Research Triangle Park, Austin TX, and a host of less celebrated places, have drastically altered America's economic landscape. The pattern in the map then presents a puzzle: these dense agglomerations have often been interpreted as a need for specific resources (such as universities) or agglomeration economies. Yet, prior to the recent maturity of these new agglomerations, such needs would have favored the Northeast and disadvantaged the rest of the country.2 Although there has been extensive discussion of local operational interdependencies that may advantage firms, these must be discounted as a cause of the emergence of new industrial places. As just mentioned, local operational interdependencies favor older, established industrial places. Such interdependencies were a crucial element of Vernon’s theory. The little evidence that exists suggests that decades are required before such localization economies emerge in new locations – if they do at all. Moreover, while there is an impressive and growing literature documenting the co-location of critical economic activities, evidence for local connections is limited. Local interaction may develop in some industrial agglomerations but not in others (Glasmeier, 1988; Saxenian, 1994). Even in the agglomerations held to have the richest inter-connections, local interdependencies appear to be limited (Oakey, 1984) and the effect of regional milieu on an organization’s research and innovation appears to be minimal (Kleinknecht and Poot, 1992; Love and Roper, 1999, Smith, Broberg, and Overgaard, 2002). Industrial location seems similar to residential choice in this regard: sometimes neighborhood ties develop and sometimes they do not. The critical task is explaining why contemporary agglomerations, typified by propinquity without functional community, persist and indeed even develop. Recognizing the weak constraints on the location of many contemporary economic activities, a number of theorists have suggested that the locations that are able to mobilize the resources firms need, rather than those that are well-endowed, will attract firms and the ensuing employment growth in the contemporary economy (Freeman and Soete, 1997). Local growth coalitions (Molotch, 1976)

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may be willing to invest considerable energy in mobilizing resources because rentiers tied to particular locations stand to profit from local employment and population growth. Entrepreneurial localities (Eisinger, 1988) might then offer incentives to firms and commission elite actors to use their personal influence to recruit firms. Research universities and government research institutes may act as institutional anchors for modern local industrial development (Etzkowitz and Leydesdorff, 1997). While some have argued that local politics is, of necessity, forced to concentrate on local development (Peterson, 1980), the evidence for the efficacy of growth coalitions – most of which comes from selected case studies of successful developments – is mixed. Pittsburgh has been recognized as having a strong elite coalition (Chinitz, 1961), but regional growth has been below the national average for many decades. A concentrated community power structure positively affects the extraction of benefits from the Federal government (Hawley, 1963) but such benefits have little effect on local employment growth (Kasarda and Irwin, 1991). Further, issuing Industrial Revenue Bonds to reduce the costs of capital to firms and tax rate differentials have had no measurable effect on employment growth (Carlino and Mills, 1987). Longitudinal investigations of the effects of research parks (Appold, 2004) and enterprise zones (Bondonio and Engberg, 2000) have not found them to be effective local development tools. It is tempting to assign causal priority to those most active in working towards development but the bulk of the evidence suggests that the locus of power in determining economic geography does not rest with local promoters (Logan, Whaley, and Crowder, 1997), whatever their motivation and institutional affiliation. Accordingly, some observers are therefore skeptical of the existence of specifically regional innovation systems (Howells, 1999). This paper explores one of the social mechanisms (Hedström and Swedberg, 1998) responsible for the development of new industrial spaces, agglomerations of industrial research laboratories in particular, in an era of eased long-distance communication and low direct dependence upon natural resources. This is an era characterized by a high level of co-location but a much lower level of operational connection. By bringing three disparate, but nonetheless related, literatures to bear on the issue of location decision-making, the paper will examine the basis for continuing and renewed spatial agglomeration. The economics of information specifies how uncertainty affects decision-making. The institutional theory of organizations explains how population-level learning

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through signaling leads to a degree of mimetic isomorphism. The study of cultural signs suggests how firms being influenced by each others’ decisions can, in rare circumstances, lend geographic charisma to particular places. The combination of behavioral uncertainty, social signaling, and cultural imaging results in the emergence of new centers that may challenge the dominance of older, established places and in a level of agglomeration not mandated by operational considerations. The hypothesis is cultural in that the critical factor determining the level and location of agglomeration development is symbolic representation, rather than collective functional interdependence. It is ecological in that the determining power is distributed diffusely among a large number of actors. The spatial distribution of establishments is, to a large extent, a consequence of firm location decisions. The character of the location decision-making process, therefore, may determine the nature of the resulting spatial structure. In many industries firms cannot optimally choose locations because the required resources are either difficult to observe or not well understood. Siting decisions are major capital investments that are infrequently made by most firms; as such, they give rise to much uncertainty. Decision-makers, therefore, search for signals – or signs (Sebeok, 2001) – to help them choose correctly. The most powerful signal, indicating that a location is an “appropriate” choice, might be the presence of other, similar, firms. Economic theory suggests why actions, which are not intended to communicate, are so effective at doing so. While location decisions are almost universally legitimated with an operational justification (and such a benefit may sometimes subsequently develop), decisions are often made on the basis of an unsubstantiated belief, indicating an influential role for signals in determining the pattern and level of agglomeration when the operational conditions for dispersion exist. Detecting the effects of cultural signals is difficult (Schelling, 1978). Therefore, the pattern of laboratory locations will be compared to simulations based on a theoretically-informed model of behavior. That model is rooted both in the theory of decision-making and in the theory of spatial point patterns (Diggle, 1983; Getis and Boots, 1978). Aggregating the outcomes of choice situations results in a frequency distribution of choices among the possible options. The nature of this distribution can reveal the degree of social influence. A family of statistical distributions, called Polya-Eggenberger distributions (Johnson and Kotz, 1969) which includes the binomial distribution

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as a special case, is useful in estimating a social influence parameter, indicating the degree of deviation from the baseline model of no influence. In the next section, I outline a simple theory of location decision-making over time that incorporates a social influence process. I then derive a method for detecting social influence in crosssectional data. Using the method derived, I test the theory on the 1985 locations of private industrial research laboratories, accounting for the role of universities and discussing the possibility of unobserved heterogeneity. Following that, I suggest an ideal-typical development sequence that places the social influence model in the context of other theories of urban development. I conclude by outlining elaborations on the basic model and further steps for research.

Location decision-making Location decisions are the result of the need for facilities. Establishing a new facility, such as a research laboratory, entails a large capital investment. Accordingly, location decisions are among the most important aspects of the strategic management of firms (Rumelt, Schendel, and Teece, 1994). To the extent that local characteristics yield advantages in the ease and costs of acquiring or distributing goods, services, or labor and the presence of other firms results in either economies or diseconomies of agglomeration, the productivity of establishments may vary by location (Hoover and Giarratani, 1984). Therefore, mangers attempt to choose the locations that will yield the greatest operating return. When information about the requirements of the production process and about the characteristics of localities is nearly complete, site choice is a relatively straightforward, albeit difficult, management decision. Land, resource, and transportation costs dominate other considerations in the capital-intensive plants utilized in heavy industrial production. Not surprisingly, they often have systematically-organized location searches and produce well-defined (“regular” or spaced out) geographic patterns. When costs are difficult to calculate and predict – as they are for research and other higherorder information-processing activities – choosing a location becomes more perilous. Information about how the potential operating environment affects those activities is inadequate because environmental feedback is slow and arrives, with experience, only after a decision is made. Local

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features, such as amenities, may be difficult to measure and their effects impossible to quantify. Moreover, because location decisions occur irregularly, if at all, during the course of a managerial career, organizational history does not provide trustworthy guidelines (March and Olsen, 1976). Accordingly, managers in many firms, particularly those engaged in high technology activities including research, have difficulty identifying their locational needs and those named could be fulfilled by almost all metropolitan areas (Schmenner, 1982). When weak or non-existent feedback results in uncertainty and blocks the ability to distinguish between alternative locations, firms may rely on signals based on each other’s behavior. Signals are “activities or attributes of individuals ... which, by design or accident, alter the beliefs of, or convey information to, other individuals (Spence, 1974: 1).” Decision-makers will attempt to observe signals when the actual characteristics of a market good, in this case a potential laboratory location, cannot be readily observed. But, because misleading signals may be purposely sent when information is known to be incomplete, the theory also suggests why local growth coalitions might have difficulty attracting firms. First, the act of recruitment itself, particularly when paired with incentives, signals a lack of desirability. Second, firms being recruited know that growth coalitions have a motivation to misrepresent their localities in a positive light. Therefore, managers will tend to look beyond the industrial recruiters and growth coalitions for credible information when the relevant local attributes cannot be readily identified. While economic theory focuses on two-person (buyer-seller) signaling, institutional theory suggests that the actions of similar actors that have faced the same situation in the past provide credible behavioral clues in the absence of direct information. The presence of other labs may serve to “filter” good from bad choice options (Arrow, 1973). When decisions are made under uncertainty, information about the state of the world can be seen as information about what ought to be done (Eco, 1976). In attempting to learn from the “best practice” of others, managers allow themselves to be influenced by each others decisions (DiMaggio and Powell, 1983). Equivalent firms (that is, those that have experienced similar situations but are not directly party to the decision) have no motivation to misrepresent themselves. The commitment and expense their presence entails therefore creates an effective signal. Mimetic isomorphism may also serve a symbolic role, enhancing legitimacy and

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providing social validation for behavior, without necessarily increasing organizational efficiency (Tolbert and Zucker, 1983), leading to a higher degree of agglomeration than that required by functional interdependence. Direct contact is not necessary for the social influence to occur. Managers may form beliefs and take actions based on what they observe. If geographic location were unimportant to productivity, managers faced with the need to chose a site for a new facility might reasonably infer that the existing establishments would be randomly distributed. If, on the other hand, location were important, it should be reflected in the choices of the firms already in operation. Therefore, without necessarily understanding why a particular site is more attractive than another, a manager could nonetheless conclude that the number of successful laboratories that are located at a particular site is an indicator of its productivity. Managers, in making location decisions, may do as many researchers have done: they examine the behavior of others, search for correlates and, in the event none are found, assume some unobserved environmental heterogeneity. That assumed and unobserved advantage may be the basis of local geographic charisma.

Social processes and statistical distributions The foregoing discussion implies that the spatial distribution of laboratories is the product of a social process and that the character of that social process – successive location decisions made by different actors under uncertainty with high costs to poor decisions – affects the nature of the spatial distribution, resulting in more agglomeration than would otherwise be expected. Analytic techniques that specify the relationship between social process and spatial outcome make it possible to identify the responsible processes even when spatial patterns are observed at a single time point only (Getis and Boots, 1978: 2-3). The nature of the social processes that create spatial distributions may be most easily envisioned using urn models, where balls are used to represent the attractiveness of spatial units (counties) and the degree of replacement after each decision captures the level of learning (influence), if any, among actors. The resulting patterns can often be characterized using statistical distributions. The level of influence can be estimated from the spatial data using a family of distributions related to the binomial (and the nearly equivalent Poisson) distribution once relevant exogenous factors have been properly accounted for.3

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Social processes result in distinctive patterns of outcomes – sometimes termed “events” or “occurrences.” Many unsystematic independent influences upon a quality or property results in a normal distribution of observed outcomes around a central true value. Similarly, many unsystematic independent influences on location decisions do not result in a uniform number of occurrences across space; they create a pattern that approximates a binomial distribution. If the location decision-making processes were perfectly modeled and all options could be perfectly ordered, there might be no need to consider what is often called the conditional (error) distribution. In practice, the modeling of decisions must reckon with the unsystematic misperceptions, optimization problems and measurement errors that bounded rationality creates. All observed decision making is, therefore, stochastic and the modeling of decisions is often based on random utility theory (Luce, 1959). The distribution of “events” (lab locations) among choice options (counties) which are essentially equivalent is key to distinguishing between independent decision-making and decisions affected by social influence. The character of the conditional distribution often indicates whether or not a given process is adequately specified. Heteroskedasticity or autocorrelation in the conditional distribution frequently indicate non-independence; that is, the “errors” are not independent of either some determining characteristic or, in the latter case, of each other. Similarly, social influence involves cases where the decisions made are not independently of each other.

Urn model representations of decision-making Probabilistic decision-making often can be represented in terms of intuitive thought experiments about different procedures for drawing balls from an urn. The hypothetical urn contains the complete set of options available to the decision-maker. These are represented as balls. The balls have colors or numbers differentiating the various options. The number of balls of each type combined with the total number of balls represents the probability of each choice possibility. The number of the balls of each color or number drawn represents the frequency distribution of choices. An urn model becomes a theory of social process whenever the essence of that process is captured by the method of drawing balls from the urn (Coleman, 1964: 517). The urn model presented here has a close correspondence to the behavioral process of location decision-making.

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Independent decision-making – wherein actors are not affected by the actions of others – results in a binomial probability distribution of choices, or “events” (laboratory locations), among equivalent options (counties) around the mean number for that type of option in repeated trials (location decisions). This corresponds to drawing balls from a uniform rectangular distribution of options in an urn with replacement. For example, if there are five equivalent options, such as identical coffee cups on a shelf, the binomial distribution describes the number of times a particular cup is selected in a given number of repeated trips to the coffee machine. Each individual cup can be expected to be chosen one-fifth of the time and the distribution around that expected value follows a predictable pattern. The simplest case, analogous to the visually distinguishable but functionally equivalent coffee cups, corresponds to the “featureless plane” sometimes hypothesized by geographers. While not a literal depiction of any geography, decision-makers could be indifferent among alternative possibilities because each offers equivalent utility and would therefore be equally acceptable. Actors may also be indifferent because they are unable to perceive differences which they believe to exist. The effect is to create a homogeneous choice situation. Webber’s “community without propinquity” argument, local amenities, and the idiosyncratic histories of particular places and people – when the fact that someone’s mother lived near Palo Alto or that another person’s vacation home was in Florida or Arizona determined the location of a company’s laboratory – would create such a random distribution of laboratories. The baseline model holds that decision-makers do not influence each other. If actors are not affected by the actions of others, the probability distribution of choices does not change through time. In fact, choices made at one time could affect the choices made at a later time, however. Making a particular choice at one time may increase – as with positive reinforcement – or decrease – as with negative reinforcement – the chances of that choice being made again in the future (Luce, 1959; Bush and Mosteller, 1955). Location choices that are made sequentially by one or more decision-makers can be seen as “chain learning” (Johnson and Kotz, 1977) or population-level learning (Miner and Haunschild, 1995) situations where the hypothetical decision urn is passed from one actor (firm) to the next.

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An urn model of social influence also begins with a uniform rectangular distribution of options but after each choice a number of balls of the same type as the one chosen are added to (or subtracted from) the urn, modifying the chance that the same option will be chosen again in the future. This corresponds to sampling with over- (under-)replacement. The number of balls added (subtracted) essentially corresponds to a social influence parameter. If decision-makers are positively influencing each other, the distribution of their choices will follow a Polya-Eggenberger – contagious binomial – distribution. Among a set of equivalent options, some may be chosen more than would otherwise be expected and many others may not be chosen at all. Each “event” will exert an attractive force on other “events.” When a social influence process operates, choices will be a function of the characteristics of the option and the force of influence. Although not immediately relevant to the present case, actors could also affect the actions of each other negatively. Actors could claim scarce resources and each unit of resources claimed by the existing occupants is not available for use by newcomers. Since resources once claimed are unavailable to others, this model corresponds to sampling without replacement. In this urn model, once a ball is chosen it is not replaced. Under these conditions the number of times the same choice is made follows a hypergeometric distribution. The early choices then tend to disperse subsequent choices through the possibility space resulting in even or “regular” distributions (Pielou, 1977). For example, housing units and jobs, once claimed, cannot be claimed by another. Returning to the coffee cup example, a decision rule “always use a dirty cup in the sink, if one is available” would produce a Polya-Eggenberger distribution of choices, while a decision rule “don’t clean a cup unless there is no alternative” would result in a hypergeometric distribution of choices among the identical cups. In the baseline model, options (counties) exert a fixed “pull” on decision-makers regardless of how many actors have or have not chosen that option. There is no positive or negative social influence. The number of individuals choosing a particular option, once the attractiveness of that option is taken into account, is determined by the number of decisions made and the number of equivalent options. In the second model, each option’s (county’s) “pull” is augmented by the number of individuals who have already chosen a particular option up to any given point in time. The working of social influence makes the conditional distribution less random than expected. In the case

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of positive influence, the more “events” an option has attracted, the more it will continue to attract.

A social influence equation Urn models provide an intuitive understanding of the influence process but do not provide an independent method of estimating the level of social influence. Fitting the parameters of a family of distributions to the pattern of choices among similar options allows for such estimates. Johnson and Kotz (1969) show the Polya-Eggenberger family of statistical distributions contains special cases associated with each of the possibilities named: negative influence (hypergeometric distribution), no influence (the binomial distribution), and positive influence (the simple Polya-Eggenberger or contagious binomial distribution). The generalized Polya-Eggenberger distribution has been previously used to model psychological theories of learning (Bush and Mosteller, 1955) and to model voting behavior in groups (Coleman, 1964). Eq. 1.1:

⎛ n ⎞ α [k] β [n- k] Pr[x = k] = ⎜⎜ ⎟⎟ [n] ⎝ k ⎠ (α + β ) Equation 1.1 shows the probability density function of the Polya-Eggenberger distribution. In equation 1.1, “n” represents the total number of trials – the number of times a decision was made regardless of the option chosen. In this case, this is the total number of laboratories nationally. Here, “k” represents the number of times a particular option (county) was selected. The brackets, “[ ]”, signify the ascending factorial.

Eq. 1.2:

⎛ n ⎞ b(b + s)K(b + (k - 1)s)w(w + s)K(w(n - k - 1)s) Pr[x = k] = ⎜⎜ ⎟⎟ (b + w)(b + w + s)K(b + w + (n - 1)s) ⎝k ⎠

The second form of the equation (Equation 1.2) clarifies the relationship between the Polya-

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Eggenberger, binomial and hypergeometric distributions to urn model representations. The parameter " is equivalent to “b/s;” ß is equivalent to “w/s.” The parameter “b” represents the attractive force of one option (county) of a particular type; “w” represents the attractive force of all other options; and “s” signifies the attractive (or repellent) force of each “event” (laboratory in a particular county). If “s” is equal to -1, the equation produces the hypergeometric distribution. If no influence behavior is taking place the parameter, “s” – the over-replacement factor, will equal zero and the equation will simplify into a binomial distribution as illustrated in Equation 2: Eq. 2:

⎛ n ⎞ bk wn-k Pr[x = k] = ⎜⎜ ⎟⎟ n ⎝ k ⎠ (b + w )

Comparing predictions to data should reveal the relative merits of each model. The parameters for the independent decision-making model and for the social influence model, " and ß, can be estimated from data using the method of moments procedure from the mean (“0”) and variance (“v(x)”) of the number of laboratories in each county. The equations of the estimators are shown below. Their derivation from the moment equations is shown in an Appendix.

Eq. 3.1:

n x2 - x( v(x) + x2 ) ˆ α= n ( v(x) - x ) + x2 Eq. 3.2:

βˆ =

n αˆ - αˆ x

The estimated parameters for each model can then be used with the distribution equations illustrated earlier (Eq. 1 and Eq. 2) to generate the full expected frequency distribution of labs among the

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counties in each county category. The predicted marginal and cumulative distributions for each model can then be compared with the actual distribution of laboratories using graphical methods and Kolmogorov-Smirnov statistics (D'Agostino and Stephens, 1986).4 Similar to log-linear models which predict frequency counts or covariance structure models which reproduce covariance matrices rather than individual outcomes, the models considered here estimate probability distributions. Because the social influence occurs between options which have been defined as equivalent, it is impossible to a priori determine which particular option (location) will be favored.

Heterogenous options These sequential decision making models are able to model the effect, or non-effect, actors have on each other through time once the exogenous factors that determine location decisions are adequately accounted for. Social processes, however, may be complex and the resulting structure may need to be decomposed into a mixture of simpler processes and distributions (Everitt and Hand, 1981). The first statistical distribution would characterize the allocation of social events (in this case, laboratory locations) across distinguishable categories of the possibility space (for example, counties that offer different levels of urbanization economies) while the second statistical distribution would characterize the allocation of “events” among equivalent options. Because estimates of the degree of influence depend upon correctly specifying those factors, a strong null model specifying the factors which should matter and which should not is needed. This model will be developed in the next section. Variations in the characteristics of options can also be represented in urn models. The difference with the preceding discussion which assumed that all options (counties) were equivalent is that the sampling space at T0 is not uniform rectangular. More desirable options, such as larger coffee cups, are represented by a greater number of balls than those less desirable but “sampling” proceeds with replacement, without replacement and with over-replacement, respectively. If homogeneous subgroups of options are examined, the conditional frequency distributions under the various models should resemble those in the case of homogeneous options.

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Explaining the agglomeration of industrial research laboratories Because the measurement of social influence in location decisions depends upon a strong baseline model that controls for exogenous factors, the level of urbanization was measured by classifying counties according to metropolitan status and size of the largest city (Beale and Fuguitt, 1978).5 The effective operation of laboratories might require the ready access to a supply of welleducated labor, the nearby availability of a wide range of high-level services, and the flow of a wide range of goods afforded by population. These factors might create economies of urbanization that could be expected to affect the location decisions of firm managers. The level of residual agglomeration was modeled; the role of universities as special signals and the possibility of unobserved heterogeneity is considered afterward. ––––––––––––––– Table 1 about here ––––––––––––––– Table 1 shows that urbanization clearly had an effect on the spatial distribution of laboratories. Almost 90 percent of all laboratories were located in metropolitan counties. Forty percent of all labs located in the 49 counties which comprise the cores of the largest metropolitan areas and over 60 percent of all labs in the U.S. were located in 181 core and outlying counties comprising the largest metropolitan areas. Only 10 percent were located in rural counties. The number of labs per million residents varied from a mean of 4 in sparsely populated counties that are not adjacent to metropolitan areas to a mean of 47 in the outlying counties of large metropolitan areas to an average of 70 in the core counties of large metropolitan areas, indicating a non-linear relationship. ––––––––––––––– Figure 1 about here ––––––––––––––– The distribution of laboratories was not determined solely by urbanization, however. A scattergram of the number of labs by county population (both logged) is heteroscedastic, revealing

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little variation in the number of labs in sparsely populated areas and an increase in the average number and in the variation in the number of labs as population rises. This suggests a limit to the number of laboratories that can be supported at given population levels but also large differences in the degree to which the local carrying capacity is approached. Figure 1 shows that a county with a population of, say, 500,000 could have as few as no labs at all or over 100. On the other hand, some counties with fewer than 8,000 inhabitants supported a lab. Variation in numbers of labs in areas with similar population levels (3-200 labs) can be quite large compared to the variation between the extremes of high and low population (0-481 labs). There was little agglomeration in the sparsely populated areas where localization economies could substitute for urbanization economies. Yet it is precisely where such agglomeration might be most valuable that it is least in evidence. (The same finding results from using a number of measures and spatial corrections.)6 ––––––––––––––– Table 2 about here ––––––––––––––– Table 2 shows the decomposition of agglomeration, measured by the Theil (1967) information statistic7, into a component accounted for by urbanization (“between county categories”) and a component that is not (“within county categories”). Urbanization (differences between county categories) explained 67 percent of the total agglomeration of labs. However, looking at the 625 metropolitan counties only (which contain 90 percent of the labs), variation in urbanization, as measured by the Beale categorization, explained only 23 percent of the agglomeration. Most of the variation in numbers of laboratories is within categories of counties which are essentially equivalent. Within each metropolitan category the distribution of labs is highly skewed with many labs locating in some counties and few or none in many others.

Testing for social influence in location decision-making The decomposition of the distribution of the spatial pattern of laboratories reveals a substantial degree of unexplained geographic concentration which may be caused by social influence during the location-decision making process. That thesis can be tested by estimating the parameters

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of the theoretical model on the basis of the mean and variance of the empirical distribution, generating the complete frequency distribution using those parameter estimates, and comparing the distribution of laboratory counts among counties to that predicted by the theoretical model. I will also compare the empirical distribution to that predicted by the independent-decision model and perform specification tests. ––––––––––––––– Table 3 about here ––––––––––––––– Table 3 shows part of the data, predictions and goodness-of-fit calculations for one of the category of counties: the outlying counties of large metropolitan areas. The actual marginal and cumulative probability functions and those calculated from the mean and variance of the data using the two models are shown. The difference between the actual cumulative probability function and that calculated from the models forms the basis for the goodness-of-fit calculations shown in the last two columns. The first row, for example, shows the proportion of outlying counties in large metropolitan areas which had no labs and the proportion predicted by each of the models. The independent decision-making model predicts that approximately half of the counties will have numbers of laboratories that are below the mean for this county category of approximately 16. The influence model predicts approximately three-fourths of the counties would have frequency counts below the mean. That closely agrees with the data. The graphic results portrayed in Figure 2 suggest that the Polya-Eggenberger distribution used in the influence model is fairly accurate in its predictions of the proportion of counties with one, two, or more labs also. The independent decision-making (binomial) model is not. That intuitive conclusion is supported by the Kolmogorov-Smirnov goodness-of-fit statistics for each model. Although the significance level for the maximum deviation from the predicted cumulative probability distribution is not exactly established, only about 20 percent of the empirical distributions generated by the theoretical model with the estimated parameters would have smaller maximum deviations. The goodness-of-fit statistic for the binomial model is an order of magnitude larger and the hypothesis that the data were generated by the independent decision-making model would have to be rejected.

17

––––––––––––––– Figure 2 about here ––––––––––––––– Table 4 summarizes the results for each of the county categories. The variance/mean ratio, three parameters for the Polya-Eggenberger distribution, the “independent” probability that a particular county of that type will be selected, the ratio of the influence parameter to the average probability of being chosen, and Kolmogorov-Smirnov goodness-of-fit statistics for the two models are given for each county category. The key information from Table 3 is reproduced in the second row of this table. The variance/mean ratio is a Poisson statistic measuring agglomeration; it provides an independent indication of the level and direction of the deviation from the independence model. A value of one indicates spatial randomness, corresponding roughly to the independent decision model. The three Polya-Eggenberger parameters are the average probability of a county being chosen divided by the influence parameter ("), the probability of a county not being chosen divided by the same parameter (ß) and the influence parameter divided by the total resource pull. (The parameter " is equal to b/s in equation 1; ß is equal to w/s in the same equation.) As described above, these were estimated from the sample means and variances for each county category and correspond closely to the parameters estimated by direct search. ––––––––––––––– Table 4 about here ––––––––––––––– For each county type the influence parameter (due to prior lab location decisions) is at least as strong as the attractive force of the county itself. Both the attractive force of the counties and the attractive force of the labs varies with urbanization. Each county has a baseline probability of being chosen as a lab location by a given decision-maker of .000318. For remote rural counties this probability decreases to .000024 (approximately 1/42,000) while core counties of large metropolitan areas the probability of being selected is approximately 350 times greater (.0084 or about 1/120). The

18

influence parameters fall into a similar range indicating that the attractive force of a lab is roughly correlated to the attractive force of the county in which it is located. The ratio of the influence parameter to the baseline average probability of being chosen ranges from just under one to over eight, from which a significant role of direct social influence can be inferred. The parameters suggest that the effects of influence of a single individual lab is greatest in the most rural counties and diminishes in the more urban counties; that result is consistent with information theory. Although the influence of individual labs diminishes in the more urban counties, the larger numbers of labs ensures that the overall level of influence has a greater effect on location decisions there. The conformity between the predicted probability distribution and the actual distribution as shown in the goodness-of-fit statistics and the graphic results (the remaining figures are included in an Appendix) provide support for the influence model. The influence model shows its strongest deviation from the data among large metropolitan area core counties. These deviations are relatively minor and may be due to the small number of counties in this category. The independence model did not fit any of the county categories. Tests for specification error indicate that the fit of the influence model is not merely due to unobserved heterogeneity.8 Similar models were estimated for the laboratories owned by firms with ten or more labs; these yielded similar results and fewer deviations. These large firms are more likely to have the resources to conduct systematic location searches; they are generally less dependent upon the urbanization economies offered by their immediate surroundings; and they are more likely to be able to offer complete attractive career paths to their employees. Yet these firms are as open to influence as the much larger set of labs in all firms. Figure 3 illustrates the results of analyses for the outlying counties of large metropolitan areas. ––––––––––––––– Figure 3 about here ––––––––––––––– These results indicate that social influence is an important determinant of location even among the laboratories connected to the firms least dependent upon agglomeration economies. Interaction – a need to share research insights and encouragement – was not a factor in determining

19

the agglomeration of laboratories (although such interaction might eventually result). If interaction were important, branch laboratories of large firms would be clustered together so that developments and knowledge could be shared in-house rather than with competitors. The average distance between branch laboratories and their headquarters is 880 miles. Among these large firms, only 16 percent of the labs are in the same county as their firm headquarters and approximately 60 percent are in another of the nine Census divisions. Even laboratories in the firms with the most resources to avoid or ignore each other, but which are also the most visible to each other, are highly likely to locate near each other, indicating that labs are taking locational cues from each other.

Universities as signals Universities are often accorded a special place in the theory of knowledge-based economies. They are sources of personnel and, hopefully, of knowledge. It is conceivable that universities are a factor in determining the location of industrial laboratories. To the extent they are, it appears they act as signals, rather than as operational resources. An analysis of the relationship between prominent university departments and laboratory location suggests that labs clustered around universities and that they clustered around some universities more than others. However, the pattern of agglomeration cannot be related to the specific resources the university has to offer. If universities served as important intellectual resources, as opposed to social signals, three outcomes would be expected. First, the mean level of labs should be higher near universities than in otherwise equivalent counties. Second, the distribution of labs should reflect the relative strengths of the academic departments and, third, since faculty time and university graduates are limited, labs should show a “regular” distribution between counties with relevant departments. Controlling for type of county, the presence of a good university – one with at least one top department as measured by the presence of PhD granting departments whose rating was at least one standard deviation above the average for “important” PhD granting departments in that field (Jones, Lindzey, and Coggeshall, 1982) – results in, on average, 3.74 (t, [mean = 1] = 6.32; p < .001) times as many labs, confirming the first expectation. Looking at the counties which contain a good university and controlling for the type of county, the presence of a top department in a field does not

20

significantly increase the number of labs in that field over the number found in counties with good universities but with no prominent department in the relevant field (t [mean = 1] = 1.25; p > .10). Further, in almost one third (9/30) of the cases, counties with good universities had fewer total labs than the average county in the same category. One university, the University of Illinois at Champaign-Urbana, which excels in several areas and has close ties to industry, appears not to have had a single private lab located in the surrounding area in 1985. Even when the county category and academic department are considered, an agglomeration of labs is evident rather than the “regular” distribution expected. These results are consistent with analyses that suggest the geographic reach of university knowledge (Feller, 1999) and personnel (Appold, 1998) spillovers can be quite large.

Considering unobserved heterogeneity The interpretation of the results depends critically upon the adequacy of the baseline model that controls for the operational advantages afforded by urbanization. In general, it is not possible to differentiate between social influence among actors and heterogeneity among choices on the basis of statistical distribution alone (Barron, 1992; Cameron and Trivedi, 1986; Xekalaki, 1983). It is often possible to reproduce a pattern with a quite different statistical distribution. The risk here is that the differences among counties are inadequately taken into account. While it is true that other distributions may exist that can reproduce the distribution of laboratories, the model presented here includes an intuitive behavioral process (represented by an urn model of sequential learning) that is closely tied to a statistical distribution with interpretable parameters. That model fails to fit in specification tests where unobserved heterogeneity is introduced. The interpretation of other distributions may be problematic. Indeed, they are often picked for expediency in estimation. (Maximum likelihood estimation encountered convergence problems with the distributions used in here.) Historical information discounts the heterogeneity model. The distribution of laboratories is more skewed than the phenomena studied by other researchers (e.g., visits to physicians) and, in the absence of social influence, would imply an extreme distribution of heterogeneity among counties. As noted in the introduction, the aggregate movement of laboratories was away from places rich in the

21

types of resources held to attract labs and towards the places, specifically the suburban counties of large metropolitan areas that lack such attractions. In that regard it is interesting to note that in 1985, Santa Clara County (Silicon Valley) contained fewer laboratories than was average for similar counties. While the increase in the number of laboratories between 1960 and 1985 was somewhat above the average for similar counties, the increase in the number of laboratories per person was lower than average and the increase in the number of laboratories over the same time period was slower than it was in a sample of 64 suburban counties in large metropolitan areas. Much of the apparent heterogeneity among counties appears to be a product of development, rather than a cause.

Social influence in the context of agglomeration growth In order to illustrate how social influence might fit into a process of local agglomeration formation, I describe an “ideal type” successful development process on the basis of data that are gleaned from case studies. The social mechanisms outlined here are not necessarily cleanly separated from each other and there is no necessary progression from one to the next. I identify three types of processes in the development trajectory of contemporary laboratory agglomerations: 1) those that directly involve the promoters of development, 2) those that are based on the social influence of local elites, and 3) those based on imitative location decision-making. The earliest phase of many contemporary agglomerations may begin with the attempt of a local growth coalition, whether led by a private investor (e.g., Cabot, Cabot and Forbes for Route 128), a non-governmental entity (such as Stanford University for Silicon Valley), or a public-private partnership (as in North Carolina's Research Triangle), to reap the benefits of employment growth. These benefits include the revenue generated by land sales and ground rent and the tax flow generated by added employment. Research-intensive, high technology industries were a major source of highwage employment growth in the several decades following the Second World War and, therefore, a fitting target for recruitment. As large, risky development investments, much of the recruitment effort needed to be underwritten by public bodies. Many localities invested heavily in recruiting research-intensive employment in the 1960s, often by creating research or technology parks. The August 1962 and August 1966 issues of

22

Industrial Development report 171 operating research parks in 116 counties. Many of these had direct or indirect sponsorship from major research universities; few were still operating in 1985. These research parks had to contend with the advantages of the traditional centers of innovation which could already boast agglomeration advantages, a supply of highly-educated labor, and a high quality of life. The economics of rents (Buchanan, Tollison, and Tullock, 1980) suggests further reasons for the lack of success. To the extent that local elites can gain by development and the firms that are being recruited are indifferent to locations, localities may need to bargain away all the potential advantage by providing incentives. It is only when firms can be attracted without compensation that development could be beneficial. Local elites can use social connections to recruit firms. The initial occupants of Stanford's industrial park had close social (but not necessarily functional) ties to the university. Many firms, including Shockley Transistor Company, recruited from almost exclusively from outside the Bay Area. Similarly, North Carolina's Research Triangle Park, first proposed by Howard Odum (a University of North Carolina administrator) and later promoted by state governors, attracted its first tenant in 1960. However, successful recruitment was limited to firms subject to influence from the regional power elite; these were mainly those involved in the research aspects of the well-established local textile industry. North Carolina's Research Triangle Park might have languished like many others were it not for an accident of history that allowed the local elite to extend its power (Moriarity, n.d.). Five years passed after the initial opening of the Park without any additional important tenants. IBM was considering locating a new facility in the South but it was unwilling to place a branch in the relatively forlorn Park. Possibly in return for political favors, a governor and a former governor who had moved to the Federal executive branch, were able to secure a major National Institutes of Health laboratory for the Park. That was sufficient to attract IBM. The many stories surrounding the recruitment of IBM to the Park belong to the lore of idiosyncratic events that would create a dispersed spatial distribution of laboratories. The next political exchange might be elsewhere or involve a different type of reward. The location decision of a large firm that did not have direct ties to the local elite, however, established an important signal

23

that the Park was a fitting site for laboratories. Social influence processes could become salient. Much later, one executive credited the presence of IBM and Northern Telecom (among other firms) with his decision to locate the U.S. branch of his optical fiber firm in the Park (personal communication). A large consulting firm had identified a dozen or so metropolitan areas fulfilling the functional requirements of his firm. Although his firm had no direct relationship with those in Research Triangle Park and did not necessarily anticipate any developing, he felt it an “appropriate” location. The business press sometimes mentions that businesses “simply have to be” in certain locations – much as a restaurant is trendy because of its customers – a place to “see and be seen” – despite the absence of interaction among tables. For much of the history of the Park, the image of the resources afforded by the three major universities and the relative absence of a blue-collar heritage have been cited as an attraction – even if functional integration between industrial research and the universities has not always been strong. While it might be tempting to cite the role of localization economies in the development of agglomeration, the time span between the initial location decisions and the critical mass necessary for such economies to emerge stretches into the decades.

Conclusions Examining successful regions and looking backward through time, it is always possible to construct coherent stories that make the employment growth seem, if not inevitable then at least an heroic accomplishment. There is a visionary leader, a foresighted coalition, a critical amenity, a local cultural tradition, and some unique local institution. Local histories construct the past after the fact (Berger, 1963: Chap. 3; Schein, 1999). A careful prospective examination of recent decades would show dozens of prominent leaders, countless critical amenities, and so on. They would be spread across a broader geography than that of the recently emerged research-based new industrial spaces. By investigating local growth after the fact and by sampling on the dependent variable, conspicuous success, researchers can mistake correlation for cause. The growth of such industrial spaces requires an explanation that is credible ex ante. A model of location decision-making based on the operational advantages of particular locations holds such a promise. But while the evidence for the co-location of related innovative

24

industrial activities accumulates (Anselin, Varga, and Acs, 1997; Feldman, 1994), there is little evidence for the local connections that are the logical basis of that co-location. Jaffe, Trajtenberg, and Henderson (1993: Table 3), for example, find that, even in the first year, 30 percent of the citations to U.S. patents originate from other countries and that less than 10 percent of such citations originate from the inventor’s metropolitan area and suggest that the more important the discovery, the more quickly it travels. The degree of localization they found is lower than would be needed to sustain a claim about regionally-bounded innovation systems. Indeed, Gertler (1995: 12) reports that small businesses are prepared to “go anywhere” for what they need even if they would prefer sources closer to home. Similarly, Almeida and Kogut (1997: 29) suggest that the entrepreneur him/herself is the primary vehicle in local knowledge spillovers and that further local linkages are minimal with successful firms connecting to national industrial networks. Because the majority of firm purchases and sales are outside the surrounding 100-mile radius (Angel, 2002), it is not surprising that there is little evidence for the positive effects of agglomeration on productivity when industries are examined carefully (Rigby and Essletzbichler, 2002). Sub-national regions are “leaky” and immediate milieus offer little special support to firms. In this research, both functional interdependence in the form of urbanization economies and social influence in the form of mimetic behavior were found to be important in determining the location of a key institution of a knowledge-based economy – research laboratories. Social influence among those making location decisions is one of several plausible social mechanisms responsible for the emergence of new geographic economic centers. Influence originates in the implications of location decision-making under uncertainty. That uncertainty is most pronounced in an expanding, restructuring economy for economic activities with poorly understood production processes. Without the need for new or additional facilities, location decisions need not be made. Without the loosening of geographic constraints, location decisions would reinforce pre-existing location patterns. Without uncertainty, straightforward technical location calculations would suffice and geographic dispersion would result. The operation of social influence results in a “star” system that makes some places much more successful than others and leads to the formation of new centers in former peripheries. The stars in the urban system are the shock cities of the urban frontier that arise with changes in

25

economic regime (Suttles, 1984). This paper used a technique for measuring social influence that conceptually links social processes and the resultant spatial statistical distributions. By specifying the entire frequency distribution of outcomes on the basis of theory and two basic parameters (the mean and variance of the empirical data), the degree to which the agglomeration of laboratories was due to social influence could be estimated from cross-sectional data. (The method can document the working of social influence but it cannot differentiate between mechanical (Tarde, 1969), emotional (Shils, 1975), and rational (Hedström, 1998; Zablocki, 1993) imitative behavior.) The method relies on a strong normative null model of decision-making behavior in forming a baseline from which the workings of social influence could be measured. By having a null model, misspecification can be discovered in much the same way that it can be detected in OLS regression. Both omitted factors and neglected social influence can lead to misinterpretation. The consistency of the results with the theoretically predicted distribution of locations and with conditions under which influence processes should be operating underpins the interpretation of the findings. Social influence research is almost always vulnerable to the criticism that the apparent results are due to some missing, unmeasured, yet crucial factor. Yet the possibility of unobserved factors is the basis for an actor’s search for signals. Observing and responding to those signals may lend a performance-based prestige (Friedland, 1964) that can result in a place being “considered extraordinary and treated as endowed with ... exceptional powers or qualities (Weber, 1978: 241).” Rituals, such as executive site visits, and narratives (Smith, 1999), such as those created by the journalists and academics who manufacture an aura of exceptionalism around places of industrial research (Kaplan, 1999) even suggesting a feverish quality (Rogers and Larson, 1984), imply that such locations confer a well-being that cannot be described in mundane terms (Weber, 1978: 11121114). The ensuing symbolic geography (Zukin, 1991) benefits elite growth machines and attracts the real estate developers who are not the originators of geographic charisma (indeed attempts at local promotion often fall flat) but who are the actors who attempt to institutionalize the charisma. Thus, the meaning of place helps us understand, not only why particular places persist in importance (Firey, 1947) but why and how they become economically important. Such charisma would, of course, be

26

rare; today it clearly centers on the cultural construction, “Silicon Valley.” A reliance on a system of visible actions for managerial guidance creates a self-regulating system of signs determining collective behavior. The act of locating, by involving physical investments (buildings), makes adjustments difficult while accompanying mobilization of productive resources and the multiplier effects resulting from investment, may create the economic conditions necessary for a stable spatial outcome. Because location decisions can create the conditions that justify the actions, the signaling can determine the pattern of development. Communication and transportation technologies have allowed contemporary agglomerations to become functionally open systems. They are not closely bounded geographically. They are not necessarily social communities. They are rarely economic units. Like many upper middle-class residential neighborhoods, the common identity in agglomerations of research laboratories may exist “mostly as a creature of romantic imagination (Dorst, 1989: 44).” If there is a locally-bounded economy, it is an economy of signs that creates a valuable identity that may be used to help recruit scientists and engineers in a competitive labor market and assist in securing credit in finance markets. The agglomerations of laboratories are largely imagined or symbolic communities (Anderson, 1991; Hunter, 1974). A simple model of influence assuming homogenous firms, a stable decision-making process, immortal firms, and no generalization has been developed and used here. Although these assumptions are pragmatic, as with many such assumptions, none are likely to be completely valid. A more complete theory explaining the emergence of new industrial spaces in the U.S. would need to take additional factors, conditions, and social processes into account. The attributes and identities of individual laboratories (IBM v. an unknown) may affect the strength of their influence on others. The strength of the influence of a location decision may decay over time and in combination with variations in the rate of facility sitings result in alternating periods of “hot potato” growth and periods of relatively unchanneled location decisions. Laboratory closure might send a strong negative signal to decision-makers about the desirability of a locality. Imitation of decision rule, rather than imitation of destination, is also possible. That is, the degree of influence might be “go South” rather than “go to the Research Triangle.” In fact, it is impossible to tell if the variation in the average number of laboratories between the county categories is due to generalization and interpretation resulting in

27

decisions to locate in places like other firms, rather than due to variations in urbanization economies. The theory of decision-making and the urn models are able to incorporate such realistic complexities but the data requirements are quite high. While stronger inferences could be made and more subtle models evaluated with longitudinal data, when an adequate sampling frame does not exist (as in much research on organizations), accounting for unknown and changing biases in data collection may outweigh the benefits of the additional data. An apparent change in aggregate behavior may be real or it may be an artifact of a changing data collection protocols. The model and findings address a question about the formation of new centers in the contemporary era posed by urbanists over a half century ago. Decades of improvements in communication and transportation technologies and the continuing economic restructuring from goods production to information processing have led to a reduction in the operational constraints on location. Yet, despite the well-founded, but contradictory, predictions of metropolitanism and dispersion to the contrary, new spatial agglomerations of employment characterized by co-location without connection have formed. A common strategy of explanation has been to postulate new forms of functional interdependence or new resource needs. The simple model of social influence presented here and supported by the analysis of a large dataset widens the discussion of the mechanisms responsible for the formation of industrial spaces and thus of renewal in large-scale social organization.

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Appendix: Derivation of parameters from moment equations Panel A:α

V(x) =

⎡ (n - 1)( α + 1) nα nα ⎤ *⎢ +1α + β ⎣ α + β +1 α + β ⎥⎦

⎤ ⎡ (n - 1)( α + 1) V(x) = E(x)* ⎢ + 1 - E(x)⎥ ⎦ ⎣ α + β +1 ⎤ ⎡ ⎥ ⎢ (n - 1)( α + 1) ⎢ V(x) = E(x)* + 1 - E(x)⎥ ⎥ ⎢ ⎤ ⎡ nα -α⎥ +1 ⎥ ⎢α + ⎢ ⎥⎦ ⎢⎣ ⎣ E(x) ⎦ ⎡ ⎤ ⎢ (n - 1)( α + 1) ⎥ V(x) = E(x)* ⎢ + 1 - E(x)⎥ ⎢ nα + 1 ⎥ ⎢⎣ E(x) ⎥⎦ ⎤ ⎡ ⎥ ⎢ (n - 1)( α + 1) + 1 - E(x)⎥ V(x) = E(x)* ⎢ ⎥ ⎢ nα + E(x) ⎥⎦ ⎢⎣ E(x) ⎤ ⎡ (n - 1)( α + 1)E(x) + 1 - E(x)⎥ V(x) = E(x)* ⎢ nα + E(x) ⎦ ⎣ E(x )2 (n - 1)( α + 1) V(x) = + E(x) - E(x )2 nα + E(x) V(x) - E(x) + E(x )2 =

E(x )2 (n - 1) ( α + 1) n α + E(x)

(V(x) - E(x) + E(x ) )(nα + E(x))= E(x ) (n - 1)( α + 1) (nV(x) - nE(x) + nE(x ) )α + (V(x) - E(x) + E(x ) ) E(x) = E(x ) (n - 1)α + E(x ) (n - 1) (nV(x) - nE(x) + nE(x ) )α - E(x ) (n - 1)α = E(x ) (n - 1) - (V(x) - E(x) + E(x ) )E(x) (nV(x) - nE(x) + nE(x ) - nE(x ) + E(x ) )α = E(x)(nE(x) - E(x) - V(x) + E(x) - E(x ) ) (nV(x) - nE(x) + E(x ) )α = E(x)(nE(x) - V(x) - E(x ) ) E(x)(nE(x) - V(x) - E(x ) ) α= 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

nV(x) - nE(x) + E(x )2

α=

2

(

nE(x )2 - E(x) V(x) - E(x )2 n (V(x) - E(x)) + E(x )2

29

)

Panel B: ß

nα α +β E(x)( α + β ) = nα nα α +β = E(x) nα β= -α E(x) E(x) =

30

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36

Notes 1

The industry share of total US research and development reached a temporary plateau in the mid1980s while the growth in the universities’ share of industrial research and development had not yet begun the acceleration that lasted for another decade. According to some industrial recruiters there was a rash of laboratory sitings prior to 1985 and a slowdown afterward. In addition, the relationship between private research laboratories and universities during the late 1980s and early 1990s may have become more direct. The post-war geographic changes through the mid-1980s arguably set the stage for the changes in the nature of the firm and the reorganization of knowledge-intensive production that have occurred since the mid-1980s (Powell, 2001).

2

Disappointingly, in attempting to model the emergence of agglomerations many accounts treat these newer locations as if they were the birthplaces of particular industries. Up through 1985, at least, they were not. The semiconductor industry, for example, did not arrive in Silicon Valley until almost 10 years after the invention of the transistor, by which time several present industry giants, such as Motorola and Texas Instruments, were already well-established in their own separate new places.

3

I will refer to the two distributions almost interchangeably. Geographers have developed the theory of spatial point processes using the Poisson family of distributions. Coleman (1964) also develops much of his argument about social influence using the Poisson family of distributions. The Polya-Eggenberger family of distributions which includes the binomial distribution as a special case more closely corresponds to the urn models discussed below and the theory of decision-making. Johnson and Kotz (1969) and Chou (1975) discuss the relationship among several discrete distributions and the conditions under which the Poisson and binomial distributions are nearly equivalent. When the probability of any particular option being chosen is small and the number of decisions, or trials, is large (as they are in the case considered here), the binomial distribution closely follows the Poisson distribution (Chou, 1975:186).

4

The large numbers of “trials” implies that Chi-squared based measures will be statistically significant even when the deviations are not substantively important.

5

The categorizations, modifications of those suggested by Calvin Beale, based on the population of the largest city and inclusion in or adjacency to a metropolitan area are as follows: Code County Type Population of largest place N 0 1 2 3 4

Large metro core counties Outlying counties of large metro areas Medium metro area counties Small metro area counties Non-metro counties adjacent to metro areas

1,000,000 plus 250,000 - 1,000,000 less than 250,000

(49) (132) (258) (186) (967)

6

Few, if any, “lab-rich” counties are not bordered by other counties containing labs. Counties containing labs are clearly agglomerated themselves. For this reason some agglomeration analysis was performed using uniform 50 mile squares as the “neighborhood”. The results did not differ substantively from the county level analysis, however, and are not reported here.

7

The Theil statistic is an “information” or “entropy” statistic. The overall Theil index is given by: Theil index = E(X/XM)*log(X/XM) The measure can be decomposed into a component representing variation between county types and variation in the number of labs among counties of the same type: Theil index = E(XK/XM)*log(XK/XM) + (X/XK)*log(X/XK) Where X is the number of labs in a county; XK is the mean number of labs within counties in a given group; and XM is the overall mean number of labs in a county. The first term constitutes the between group inequality; the second the total within group inequality. Cowell (1995, Chapters 2 and 3)

37

discusses these issues. 8

A test of specification error was performed by estimating the influence model on data known to contain heterogeneity. The cumulative probability distribution for a model, estimated on the total combined set of counties, deviates substantially from the data. This result indicates that the model is not merely capturing unmeasured environmental heterogeneity. An Appendix figure illustrates the results. As another test of mis-specification, the influence model was estimated for simulated data containing no social influence (shown in Table 4). The results are consistent with the data. It should be noted that statistical distributions with characteristics different from those used here have been most successfully used in modeling unobserved heterogeneity.

38

Figure 1

Number of research laboratories by county population (log-log scale)

1000

Number of laboratories

100

10

1 100

1,000

10,000

100,000 County population

1,000,000

10,000,000

100,000,000

Figure 2

Laboratories in fringe counties of large metropolitan areas

1

0.9

Cumulative proportion of counties

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Number of laboratories Polya-Eggenberger

Actual

Binomial

14

15

16

17

18

19

Figure 3

Laboratories in large firms that are located in outlying counties of large metropolitan areas

1 0.9

Cumulative proportion of counties

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Number of laboratories Actual

Polya-Eggenberger

Binomial

14

15

16

17

18

19

Appendix Figure 1

Laboratories in all types of counties 1

0.9

Cumulative proportion of counties

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Nunmber of laboratories Polya-Eggenberger

Actual

Binomial

14

15

16

17

18

19

Table 1 Distribution of laboratories by type of county and research field

Number Core counties of large metropolitan areas Fringe counties of large metropolitan areas Counties in medium-sized metropolitan areas Counties in small metropolitan areas Counties that are adjacent to metropolitan areas Counties that are not adjacent to metropolitan areas

Percent 4295 2145 2338 582 677 380

41.3% 20.6% 22.5% 5.6% 6.5% 3.7%

Counties in large metropolitan areas

62.0%

Counties in metropolitan areas Counties in non-metropolitan areas

90.1% 10.2%

Total

10393

100.2%

Table 2 Spatial inequality in laboratory location

Theil decompositions of spatial inequality

Between Within different county types county types

Total

Percent of total spatial inequality within county types

Percent of total spatial inequality between different county types

Laboratories in all counties

2.6101

0.8539

1.7562

0.3272

0.6728

Laboratories in metropolitan counties

1.1753

0.9045

0.2708

0.7696

0.2304

Table 3 Actual and Predicted Marginal and Cumulative Probability Distributions for Laboratories in Fringe Counties of Large Metropolitan Areas

Number of laboratories

Actual Marginal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.24428 0.13741 0.06107 0.05344 0.07634 0.03817 0.03053 0.03053 0.01527 0.01527 0.00763 0.00763 0.00000 0.00763 0.00763 0.01527 0.01527 0.02290 0.00000 0.00000 0.00000 0.01527 0.00000 0.00000 0.00763 0.00000

Polya-Eggenberger Binomial Cumulative Marginal Cumulative Marginal 0.24428 0.38168 0.44275 0.49618 0.57252 0.61069 0.64122 0.67176 0.68702 0.70229 0.70992 0.71756 0.71756 0.72519 0.73283 0.74809 0.76336 0.78626 0.78626 0.78626 0.78626 0.80153 0.80153 0.80153 0.80916 0.80916

0.30966 0.08810 0.05582 0.04186 0.03383 0.02852 0.02470 0.02181 0.01953 0.01767 0.01613 0.01483 0.01371 0.01273 0.01187 0.01112 0.01044 0.00983 0.00927 0.00877 0.00831 0.00789 0.00750 0.00715 0.00681 0.00650

0.30966 0.39776 0.45358 0.49544 0.52927 0.55778 0.58248 0.60429 0.62382 0.64149 0.65762 0.67245 0.68615 0.69888 0.71076 0.72187 0.73231 0.74214 0.75141 0.76018 0.76850 0.77639 0.78389 0.79104 0.79785 0.80436

0.00000 0.00000 0.00001 0.00006 0.00025 0.00082 0.00223 0.00518 0.01054 0.01904 0.03097 0.04577 0.06201 0.07755 0.09004 0.09757 0.09910 0.09473 0.08552 0.07313 0.05940 0.04595 0.03392 0.02395 0.01621 0.01053

Cumulative 0.00000 0.00000 0.00001 0.00008 0.00033 0.00115 0.00338 0.00856 0.01910 0.03815 0.06911 0.11488 0.17690 0.25445 0.34449 0.44205 0.54115 0.63589 0.72140 0.79453 0.85393 0.89987 0.93380 0.95775 0.97396 0.98449

Partial calculations (observed - predicted) for Kolmogorov-Smirnov goodness-of-fit test Polya-Eggenberger Binomial distribution distrbution -0.06538 -0.01608 -0.01083 0.00074 0.04325 0.05290 0.05874 0.06746 0.06320 0.06080 0.05230 0.04511 0.03140 0.02631 0.02207 0.02622 0.03105 0.04412 0.03485 0.02608 0.01776 0.02514 0.01764 0.01049 0.01131 0.00481

0.24427 0.38168 0.44274 0.49611 0.57219 0.60954 0.63784 0.66319 0.66792 0.66414 0.64081 0.60267 0.54066 0.47074 0.38834 0.30604 0.22221 0.15037 0.06486 -0.00827 -0.06767 -0.09835 -0.13227 -0.15622 -0.16480 -0.17533

0.06746

0.66792

[data and calculations omitted for clarity] Kolmogorov-Smirnov goodness-of-fit statistic: (maximum absolute difference)

Table 4 Summary of estimated parameters

Type of county

Core counties of large metropolitan areas Fringe counties of large metropolitan areas Counties in medium-sized metropolitan areas Counties in small metropolitan areas Counties that are adjacent to metropolitan areas Counties that are not adjacent to metropolitan areas

Total Simulated location pattern (no imitation)

Number of counties

Mean number of Number of labs per laboratories county

Variance in number of labs per county

Variance / mean ratio

Alpha

Imitation parameter

Beta

Baseline probability of a particular county being chosen

Imitation effect / baseline effect

KolmogorovSmirnov test Kolmogorovfor goodness-of-Smirnov test fit:Polyafor goodness-ofEggenberger fit: Binomial distribution # distribution #

49

4295

87.653

10185.106

116.198

0.746

88.183

0.011245

0.008389

1.340

0.1388

0.5952

132

2145

16.250

921.807

56.727

0.290

185.900

0.005371

0.001555

3.454

0.0675

0.6679

258

2322

9.000

352.412

39.157

0.235

272.340

0.003669

0.000861

4.259

0.0823

0.5474

186

576

3.097

27.666

8.934

0.390

1315.030

0.000760

0.000296

2.565

0.0277

0.3687

967

677

0.700

3.515

5.020

0.174

2597.609

0.000385

0.000067

5.745

0.0146

0.2439

1473

378

0.257

0.804

3.132

0.120

4898.850

0.000204

0.000025

8.312

0.0138

0.0842

3065

10393

3.328

353.674

106.272

0.031

98.184

0.010182

0.000318

31.968

0.1537

0.6764

3.409

3.408

1.000

-3.417E+19 -1.047E+23

-- *

-- *

* Cannot be calculated # Although the critical points of the distribution are not exactly defined, the Kolmogorov-Smirnov statistics for the Polya-Eggenberger distribution are within the five-percent significance level (and in most cases 20-percent level) for each of the types of counties. The Polya-eggenberger distribution does not fit for the data aggrgated cross county types. The binomial distribution does not fit the data. Cramer-von Mises statistics have been calculated for each of the types of counties. The critical values are not defined for the Polya-Eggenberger distribution but the statistics are at least an order of magnitude smaller for that distribution than for the binomial distribution.