Practical Applications of Complexity Theory in Marketing Research Rosanna Garcia Northeastern University College of Business Administration 202 Hayden Hall Boston, MA 02115 617-373-7258 r.garcia@neu.edu 1.0 Introduction Few marketing researchers have used the theories/philosophies behind complexity theory to explore the market place. The systemic approach, which is a foundation of complexity theory, is rarely taken by marketing researchers. Traditional marketing research studies take a micro or macroeconomic viewpoint of the market place. Consumers are studied as separate entities that make decisions on which products to purchase, and firms are studied as another type of entity that make decisions on what products to introduce to the marketplace. Consumer marketing research has more of a focus on the psychological perspective of consumer decision making whereas managerial researchers take more of an organizational perspective. Rarely are the two approaches studied together. Although this is a simplistic mindset to marketing research, it does exemplify the mutually exclusive approach common to marketing researchers. Complexity theory, with its systemic perspective certainly has a place in the social sciences, so why not in business applications such as marketing studies? Are there any practical applications for complexity theory in researching marketing issue? Another valid question would be, “Why hasn’t marketing researchers embraced complexity theory?” There are several good reasons. Foremost, as previously noted, marketing researchers specialize in either a micro or macroeconomic perspective of the market place. This is primarily due to the expense/complication involved with collecting data. Gathering data from consumers is cumbersome and costly so adding another layer –firms– only adds to the enormity of the task. Secondly, business researchers are rarely trained in the ‘hard’ sciences and are not familiar with simulation modeling and software programming tools necessary to adequately explore complex systems. But there are numerous reasons why complexity theory is useful in marketing research. For the researcher willing to overcome the learning curve of computer programming, it provides a method for easily evaluating how ‘micro’ elements (consumers) emerge into ‘macro’ elements (marketplaces). It provides an inexpensive vehicle to simulate ‘real’ heterogeneous consumers in ‘real’ marketplace scenarios. Data that had previously been difficult to collect, such as social networks, can now be studied at a micro-level and scaled to macro-level simulations. It also provides a practical and economical method to confirming intuition, such as existing theories regarding word of mouth and tipping points. In this paper we focus on the methodology, agent-based modeling (ABM), as a vehicle for studying complex adaptive systems. We first introduce the benefits and usefulness of ABMs. We put a particular emphasis on new product development and innovation issues as they particularly lend themselves to agent-based modeling. We also provide an example of a simple algorithm to demonstrate ABMs in a competitive R&D environment. We conclude this paper with issues and future research focused on NPD and innovation using ABMs. Agent-based modeling approaches are commonly used to represent individual actors (or groups) in a social dynamic system. 'Agents' can be consumers which act as autonomous decision-making entities Practical Applications for Complexity Theory in Marketing Research that interact with each other and/or with their environment based on a set of rules. Repetitive interaction between agents is a basic feature of agent-based modeling so it is ideal for simulating dynamic market places. From these micro-scale interactions, aggregate macro-scale behaviors may emerge. From a new products’ perspective, ABMs has been used to model the diffusion of innovations (Young, 1999, Goldenberg, et al., 2002), innovation networks (Gilbert, et al., 2001), and technological forecasting (Bhargava, et al, 1993). For example, take a simplistic (although highly unlikely, but illustrative) rule for diffusion. Imagine a marketspace where there is only one rule that all agents ‘follow’. The rule is that each agent looks at its four neighbors (the ones immediately to its left, right, above and below), and if an odd number of them (that is, 1 or 3) have adopted the innovation, it adopts the innovation. If an even number of neighbors (2 or 4) has adopted the innovation, it does not adopt the innovation. Imagine how you would expect this market to look. We obtain the following pattern as shown in Figure 1. This simplified ABM, where only two states exist (on and off) and where agents only interact with immediate neighbors, is based on cellular automata. By modeling real-world systems ABMs can potentially provide valuable information about the dynamics of the system that may not be intuitively obvious. Figure 1: Simple Model of Diffusion using – Gilbert’s (2002) Parity Model based on Cellular Automata Agent States: † ‘on – adopt also’ if odd number of neighbors have adopted innovation † ‘off – don’t adopt’ if even number of neighbor have adopted innovation 2.0 Benefits of Agent-based Modeling. The benefits of ABM over other modeling techniques are numerous. Shortcomings, of course, also exist and will be discussed in the final section. However, it is our belief that that the benefits of this methodology outweigh the shortcomings if the ABM mindset is understood. The role of simulation is not to create an exact facsimile of any particular system or environment but to assist in the exploration of the consequences of various contingencies. Or in other words, simulations should be used as a tool for the refinement of theory (Bonabeau 2002). By simulating real world behavior that may be difficult to capture in static models, the ABM approach focuses on how processes evolve over time and how policies might be changed to affect the outcomes of an evolving system. This methodology accords with Axelrod's (1997) description of the value of simulation. If ABMs are taken to be a learning tool to guide intuition in refining innovation theories, they can be useful to the new product development researcher. ABMs are best suited to domains where the natural unit of analysis is the individual (consumer, firm, employee, etc.) and when both micro-level behavior of individuals and macro-level patterns emerge from the interactions of these individuals. Modeling ABMs require understanding the behaviors of the 1 Practical Applications for Complexity Theory in Marketing Research agents and translating these behaviors into rules for agents to act upon in the modeled environment. One can easily study individual agents (micro-level), subgroups of agents and aggregated agents (macro-level) behaviors with different levels of rules coexisting in a single model. Due to this disaggregation, dynamic environments can be created where agents enter and exit the system (i.e., under performing firms leave the marketspace or new competitors enter the marketspace). The phenomena of interest are the impact at the macro-level from changes occurring at the micro-level. Tesfatsion (2002) provides an excellent summary of emergence in the related field of economics, also called agent-based computational economics. She refers to emergence in an evolving system of interacting agents as ‘growing economies from the bottom up’. ABMs are useful when individual behavior is nonlinear such as when learning and/or adaptation occurs on a microscopic level. For example, models where individual behavior exhibits memory, pathdependence, hysteresis, non-markovian behavior, or temporal correlations are easily modeled with ABMs. Stochasticity can also be applied to the agents' behavior. With ABM, sources of randomness can be applied at the appropriate decision-making level as opposed to entering noise terms more or less arbitrarily, which is typical in modeling stochastic processes. ABMs also make it easier to distinguish physical space from temporal space, which is useful in modeling social networks of diffusion and global location of innovation project team members (both issues to be further discussed below.) The study of the spatial make-up of social networks has been a major focus of study in recent years (Barabási 2002, Watts and Stogatz 1998, Valente 1995). Watts argues that local interactions between network members have global consequences, but that the relationships between local and global dynamics depend on the network's structure. Garcia, et al (2003) demonstrated how different types of social networks can affect the rate of diffusion. They tested four different network structures for effects on the diffusion process of technologically-advancing products: a random network (Erdős and Rényi 1959), a cellular automata network (Goldenberg, et. al 2002), a small world network (Watts and Stogatz 1998) and a scale free network (Barabási and Albert 1999). However, it should be noted that many ABMs are not spatially dependent. One of the reasons underlying ABMs’ popularity in other social sciences is its ease of implementation. ABMs are easier to construct than other analytic models, albeit, some computer programming knowledge is useful. ABMs do not require extensive knowledge of ordinary differential equations or other analytical modeling techniques. It is reasonably easy to create an ABM using Excel or Matlab. Additionally, several open system software programs are available for download from several sites (Netlogo, Repast, etc.). More sophisticated ABMs sometimes incorporates neural networks, evolutionary algorithms, genetic algorithms, and other learning techniques to allow realistic learning and adaptation and are, therefore, computational more complex (Bonabeau 2002). These complex models, however, are not the norm. To summarize, ABMs are useful in marketing research: when both macro and mirco-levels of analyses are of interest (e.g., adoption and diffusion of innovations). when social systems cannot easily be described by differential equations but by what-if scenarios (e.g., organizational cultures). when emergent phenomena may be observed (e.g., emergence of innovations). when co-evolving systems interact in the same environment (e.g., competitive markets). when learning or adaptation occurs within the system (e.g., R&D collaboration). when physical space and temporal space is of interest (e.g., supply chain networks). when the population is heterogeneous or the topology of the interactions is heterogeneous and complex (e.g., social networks). 2 Practical Applications for Complexity Theory in Marketing Research 3.0 Possible Applications. The possible applications for ABMs in the study of new product development and innovations have not yet been fully discovered. We provide a few examples of possible research issues that could be addressed by agent-based models. These include, but are by no means limited to: 1. 2. 3. Diffusion of innovations effects of network externalities, word-of-mouth networks, modeling tipping points, social networks and viral marketing. Organizations innovation networks & collaboration, co-evolution of competitive strategies, R&D 'emergence' of innovations, portfolio management, innovation strategies & external environmental influences. Knowledge/Information flows supply chain networks, innovation/R&D collaboration (inter and intra-organizational), technology transfer (inter and intra-organizational & to/from customers-lead users), strategy planning (organizational). Diffusion of Innovations. Modeling the diffusion of innovations in social networks has been the most common application for ABMs in marketing studies to date (e.g., Bonabeau 2002, Guardiola et. al 2002, Young 1999, Nyblom, et. al. 200x, Goldenberg, et al. 2002). It is fairly straightforward to translate the prototypical diffusion model originating from Bass (1969) into dynamic simulations of heterogeneous consumers using ABMs. Consumers are modeled as agents who make adoption/purchase decisions based on 'word of mouth' influences from local interactions with other agents. 'Other' agents can be modeled as influential consumers, seeding agents (hired guns to positively influence potential adopters), firms with marketing campaigns or other types of mass media. This is analogous to the Bass model where there are innovators and imitators, each adopting an innovation at different times. Unlike the seminal Bass model, ABMs allow the introduction of heterogeneity with respect to initial perceptions, adoption thresholds, and even individual responsiveness to information so that more realistic marketspace environments can be simulated. ABMs can readily incorporate the idea of influencing agents. Dawkins (1976) introduced the idea of 'memes' as contagious information patterns that infect a human's mind to alter their behavior causing them to propagate the patterns among a population. Typical patterns of memes are slogans, catchy-phrases, melodies, icons, inventions and fashion trends. Seeds, or carefully planted influencers, can initiate the propagation of the "memes" (rhymes with genes). The connection between memes and effective advertising campaigns is evident. Remember the "Where's the Beef?" campaign? Gladwell (2000) examined the role of memes in diffusion as the search for 'tipping points' and Rosen (2000) examined them as 'buzz' or word-of-mouth influence. Recent ABM studies have also examined the effects of different types of social networks on diffusion patterns (Valente 1995, Janssen and Jager 2002). Different types of social networks include small world networks (Watts and Strogatz 1998), random networks (Erődos and Rényi 1959), and scalefree networks (Barabási and Albert 1999). These network models have roots in social systems where most people are friends with immediate neighbors/family/co-workers, yet are also connected with people located some distance away (spatially or temporally). Scale-free networks have been used to explain the effectiveness of viral marketing (Barabási 2002). 3 Practical Applications for Complexity Theory in Marketing Research Organizations. Modeling organizational structures and innovation strategies has been other prominent applications for ABMs (Dawid 2001, Debenham and Wilkinson 2003, Garcia and Calantone 2003, Gilbert, et. al. 2001). Agents in these models represent firms, policy actors, research labs, etc. each generating knowledge bases, which lead to innovations. The dissemination of knowledge/information between agents can easily be modeled to represent collaborative or competitive strategies. Gilbert et al. considered innovation networks as evolving from the dynamic and contingent linkage of heterogeneous units each possessing different bundles of knowledge and skill. In order to study these co-evolutionary types of systems, the Self-Organizing Innovation Network (SEIN) project was established by the European Commission Framework 4 Programme. Several studies focusing on international innovation networks have come from this project (SEIN 1999). The increasing orientation towards internationalization with regards to innovation processes lead to issues not only of structure but also of time and space. Internationalization of product development teams result in globally located team members working on the same product from different localities. This global location requires coordination across time zones and geographics, as well as across cultures. ABMs can be used to answer how cooperation and communication between groups might be established to optimize design times and time to launch. Since ABMs can be modeled as heterogeneous individuals even cultural issues can be modeled into these studies. Collaboration (Gilbert, et. al 2001) and the strength of weak ties in linking innovating partners are easily modeled using agents each possessing their own decision-making criteria. Scale free networks also occur in organizations (Powell, et. al. 1996, Powell 1998). Powell and colleagues studied the formation of alliance networks in the U.S. biotechnology industry and discovered several key players or hubs; companies such as Genzyme, Chiron, and Genetech have a disproportionately large number of partnerships with other firms. Studying the role of hubs in collaboration and information dissemination can be accomplished through ABMs. Just as interorganization networks can be modeled as ABMs, so too can intra-organizational networks. Issues that can be addressed are co-location of departments, R&D-Marketing integration, information dissemination between different departments and innovation networks structures (hierarchical vs. loosely structured). It is also possible to develop simulation models to evaluate the effectiveness of different types of innovation strategies in different types of environments. Debenham and Wilkinson (2003) modeled firm survival with different strategies in competitive environments and Garcia and Calantone (2002) modeled a learning strategy for solving the innovator's dilemma (Christensen 1997). In organizational studies, the interest lies in how organizational structure and strategy should evolve as the environment (competitors, demand, regulation, technology, etc.) itself is evolving. Again, ABMs provide a unique learning environment to evaluate these different conditions. Knowledge/Information Flows. Innovation has long been recognized as benefiting from the collaboration of manufacturers with their customers, supply chain network, and other industry partners (von Hippel 1988). Tapping external knowledge sources is an important product development strategy. In this respect, innovation networks have been considered as an efficient means of studying complex R&D processes (Gilbert, et al. 2001). Researchers have recently begun to see the advantages of modeling the transfer of knowledge using agent-based modeling (e.g., Gilbert, et al. 2001, Iyer 2002). Increasing complexity of innovation networks, the accelerating rate of technology transfer, and shortening of product life cycles have been considered to be responsible for the rising importance of innovation networks (Malerba 1992). This type of complex system is ideally suited for ABMs. ABMs have also been used for modeling supply chain networks (Parunak, et.al. 1998). Parunak and colleagues used the DASCh Project (Dynamical Analysis of Supply Chain) to explore the dynamical behavior of a manufacturing supply network. From an industry perspective, Proctor and Gamble is 4 Practical Applications for Complexity Theory in Marketing Research reportedly using agent-based modeling to help it improve its supply chains. In fact, the Cincinnati-based maker of Tide, Crest, Pepto-Bismal, Clairol and 300 other household products now model its distribution channels to 5 billion consumers in 140 countries as a "supply network" (Anthes, 2003). The simulations let P&G perform what-if analyses to test the impact of new logistics rules on key metrics such as inventory levels, transportation costs and in-store stock-outs. The models, constructed in conjunction with consulting group, NuTech Solutions (2003), consider alternate rules on ordering and shipping frequencies, distribution center product allocation, and demand forecasting. Other companies that utilize ABMs include Southwest Airlines Co. to optimize cargo routing, Air Liquide America LP to reduce production and distribution costs, Ford Motor Co. to simulate buyer preferences for optimizing trade-offs between production costs and customer demands, and Edison Chouest Offshore LLC, to optimize its deployment of service and supply vessels in the Gulf of Mexico (Anthes, 2003). Key research issues regarding supply networks/webs (as opposed to chains) and ABMs include logistic network configurations, emergence of coordination and integration in supply webs, and evolution of supply network relationships through market and price signals (Lairson, 2003). 4.0 Future Research and Limitations with ABM. The use of ABMs in business applications is still in its infancy. In this paper, we have touched upon just three potential areas of research; diffusion of innovations, organizational strategy, and knowledge/information flows. There are tremendous opportunities for finding new applications for ABMs in the study of innovations. Additionally, creating user-friendly software for non-programmers should be a major goal in the development of ABMs. Simulation methods become popular as drag-and-drop tools become available for constructing and analyzing models. Comparable tools are not yet available for ABMs. An innovations researcher must have some programming knowledge or access to programming expertise in order to model with ABMs. These types of drag-and-drop tools are forthcoming (see the Appendix for a list of available software). However, even these software kits do not adequately address the issue of sensitivity analysis and cognitive maps. Bonabeau (2002) cites three areas where limitations or caveats exist with ABMs. Foremost, in business applications, agents are influenced by their social context or what others around them do. These interactions cannot always easily be modeled to emulate reality. ‘In social sciences, ABMs most often involve human agents, with potentially irrational behavior, subjective choices, and complex psychology in other words, soft factors, difficult to quantify, calibrate, and sometimes justify…Social simulation in business has not been very successful so far, because the emphasis has been on using it as a predictive tool rather than as a learning tool. For example, a manager can understand her marketplace better by playing with an agent-based model of it. Then, of course, quantifying the tangible benefits of something intangible is difficult, and a manager cannot claim to saved $X million by playing with a simulation of her customers. Still, there is a lot of value in using social simulation in a business context’ (pg. 7285). Secondly, quantitative outcomes of a simulation should be interpreted primarily at the qualitative level. There have been attempts to predict consumer behavior using ABMs. Farrell (1998) tried to predict how (and when) such movies as "Titantic" or "Blair Witch Project" become hits, but their model was not very successful. Understanding the factors that contribute to making hits happen is a better use of ABMs instead of predicting when a hit will occur. This follows likewise with using ABMs for prediction in business applications. Prediction may be more successful once calibration techniques have matured for ABMs. There have been a few successful attempts at predicting human behavior in other social sciences (see Rauch (2002) for a few examples). However, due to the immaturity of business models and "the varying degree of accuracy and completeness in the input of the model (data, expertise, etc.), the nature of the output is similarly varied, ranging from purely qualitative insights all the way to quantitative results usable for decision-making and implementation" (Bonabeau pg 7282) and are not yet proven prediction models. 5 Practical Applications for Complexity Theory in Marketing Research Lastly, Bonabeau declares that, by definition, ABM looks at a system not only at the aggregate level but also at the level of it constituent units. Although the macro level can be described with just a few equations, the micro-level description involves describing the heterogeneous behavior of potentially many individual units. Simulating the behavior of individual agents can be extremely computationally intensive and therefore time consuming. The high computational requirements of ABM remain a problem when it comes to modeling large systems. Different software programs try to remedy this problem but those that executes faster are limited on the graphical user interfaces available. Speed versus functionality is a trade-off that modelers must currently make. Despite these limitations, we believe that agent-based models have an important and distinctive place in the methodological tool kit of the innovation researchers, either in academia or industry. It appears as if industry has recognized the usefulness of ABMs (NuTech Solutions 2003, Anthes 2003) sooner than academics. The opportunities for better understanding the role of ABMs in innovation research is in its infancy and should prove to be a fascinating journey. Acknowledgements: the authors wish to sincerely thank Paul Rummel for his coding expertise in building this model and Amit Joshi for his research assistance in testing proof-of concept for several different ABMs. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Anthes, Gary H. (2003). Agents of Change. Computer World (January). Axelrod, Robert. (1997). The Complexity of Cooperation. Princeton, NJ: Princeton University Press. Barabási, Albert-Laszlo and Reka Albert. (1999). Emergence of Scaling in Random Networks. Science. 286(5439): 509-512. Barabási, Albert-László. (2002). Linked: the New Science of Networks. Cambridge, MA: Perseus Publishing. Bass, Frank M. (1969). A New Product Growth Model for Consumer Durables. Management Science. 15: 215-227 (January). Bhargava, S.C., Arun Kumar, and A. Mukherjee. (1993). A Stochastic Cellular Automata Model of Innovation Diffusion. Technological Forecasting and Social Change. 44: 87-97. Bonabeau, Eric. (2002). Agent-based Modeling: Methods and Techniques for Simulating Human Systems. Proceedings of the National Academy of Sciences of the United States of America. 99(suppl.3): 7280-7287. Christensen, Clayton, M. (1997). The Innovator's Dilemma: When New Technologies Cause Great Firms to Fail. Boston, MA: Harvard Business School Press. Dawid, Herbert, Marc Reimann and Bernd Bullnheimer. (2001). To Innovate or Not To Innovate? IEEE Transactions on Evolutionary Computation (special issue on Agent-Based Computational Economics). 5(5): 471-481. Dawkins, Richard. (1976). The Selfish Gene. Oxford: Oxford University Press. Debenham, John and Ian Wilkinson. (2003). Exploitation versus Exploration in Market Competition. SSRN Working Papers. Erdős, P. and Rényi, A. (1959). On Random Graphs. I. Publicationes Mathematicae (Debrecen). 6: 290-297. Farrell, Winslow. (1998). How Hits Happen: Forecasting Predictability in a Chaotic Marketplace. New York: Harper Business. Garcia, Rosanna and Roger Calantone. 2002. How much "R" and how much "D" is required for new product development success in competitive environments? in Product Development Management Association International Conference. Sanibal Island, FL: Product Development Management Association. 6 Research Only Practical Applications for Complexity Theory in Marketing Research 15. Garcia, Rosanna, Roger Calantone and Ralph Levine. (2003). The Role of Knowledge in Resource Allocation to Exploration versus Exploitation in Technologically Oriented Organization. Decision Science. 34(2): 323-349. 16. Gilbert, Nigel, Andreas Pyka, Petra Ahrweiler. (2001). Innovation Networks - A Simulation Approach,. Journal of Artificial Societies and Social Simulation. 4(3): 8-34. 17. Gladwell, Malcom. (2000). The Tipping Point: How Little Things Can Make a Big Difference. Boston, MA: Back Bay Publishers, 304. 18. Goldenberg, Jacob, Barak Libai, and Eitan Muller. (2002). Riding the saddle: how cross-market communications can create a major slump in sales. Journal of Marketing. 66(April):1-16. 19. Guardiola, X., A. Diaz-Guilera, C. J. Perez, A. Arenas, and M. Llas. (2002). Modelling diffusion of innovations in a social network. Econophysics Forum(April). 20. Holbrook, Morris B. (2003). Adventures in Complexity: An Essay on Dynamic Open Complex Adaptive Systems, Butterfly Effects, Self-Organizing Order, Coevolution, the Ecological Perspective, Fitness Landscapes, Market Spaces, Emergent Beauty at the Edge of Chaos, and All That Jazz. Academy of Marketing Science Review [Online]. 6. 21. Iyer, Karthik N.S. (2002). Learning in Strategic Alliances: An Evolutionary Perspective. Academy of Marketing Science Review [Online]. 10. 22. Janssen, Marco A. and Wander Jager. (2002). Stimulating diffusion of green products: co-evolution between firms and consumers. Journal of Evolutionary Economics. 120:1-23. 23. Lairson, Thomas D. (2003). Professor of International Business and Professor of Political Science, Rollins College. Personal correspondence. 24. Malerba, Franco. (1992). The Organization of the Innovative Process, In: Technology and the Wealth of Nations, N. Rosenberg, R. Landau, and D.C. Mowery (eds.). Stanford, CA: University Press, 247-78. 25. NuTech Solutions, Inc., Adaptive Business Intelligence Consultants. Headquarters Charlotte, NC 28262 USA. 26. Nyblom, Jukka, Steve Borgatti, Juha Roslakka and Mikko A. Salo. (2003). Statistical analysis of network data--an application to diffusion of innovation. Social Networks. 25:175-195. 27. Parunak, H. Van Dyke, Robert Savit, and Rick Riolo. (1998). Agent-Based Modeling vs. Equation Based Modeling: A Case Study and Users Guide. Proceedings of Multi-agent Systems and Agent Based Simulation (MABS'98). 10-25(LNAI 1534):1-16. 28. Powell, Walter W., Kenneth W. Koput, Laurel Smith-Doerr. (1996). Interorganizational Collaboration and the Locus of Innovation: Networks of Learning in Biotechnology. Administrative Science Quarterly. 41:116-145. 29. Powell, Walter W. (1998). Learning From Collaboration. Knowledge and Networks in the Biotechnology and Pharmaceutical Industries. California Management Review. 40(3):228-240 (Spring). 30. Rauch, Jonathan. (2002). Seeing Around Corners. The Atlantic Monthly. 298 (4):35-48. 31. Rosen, Emmanuel. (2002). The Anatomy of Buzz: How to Create Word of Mouth Marketing. New York: Currency. 32. Tesfatsion, Leigh. (2002). Agent-based Computational Economics: Growing Economies From the Bottom Up. Artificial Life. 8: 55-82. 33. Valente, Thomas W. (1995). Network of Models of Diffusion of Innovation. Cresskill, NJ: Hampton Press. 34. von Hippel, Eric. (1988). The sources of innovation. New York: Oxford University Press, xi, 218. 35. Watts, Duncan J. and Steven H. Stogatz. (1998). Collective Dynamics of 'Small-World' Networks. Nature. 393(6684): 440-442 (Jun 4). 36. Young, H. Peyton (1999). Diffusion in Social Networks. Washington, DC: The Brookings Institution, Center on Social and Economic Dynamics, Working Paper No. 2. 7