A RATIONAL EXPECTATIONS THEORY OF TECHNOLOGY ADOPTION: EVIDENCE FROM THE ELECTRONIC BILLING INDUSTRY Yoris A. Au Assistant Professor, Information Systems and Technology Management College of Business, University of Texas at San Antonio yoris.au@utsa.edu Robert J. Kauffman Director, MIS Research Center, and Professor and Chair Frederick J. Riggins Assistant Professor Information and Decision Sciences Carlson School of Management, University of Minnesota {rkauffman, friggins}@csom.umn.edu Last revised: April 19, 2006 ______________________________________________________________________ ABSTRACT In this paper, we draw on concepts from the rational expectations hypothesis (REH) and adaptive learning theory to introduce a new rational expectations theory of technology adoption. Although the REH and adaptive learning theory have been applied in many non-technology contexts, this research is among the first that applies rational expectations and adaptive learning theory to issues related to technology adoption. The proposed theory allows us to examine technology adoption settings where multiple parties seek to align their expectations of future value prior to making a decision to adopt. It also takes into account the learning and information sharing that generally occurs in the marketplace between multiple parties that can further influence clustered adoption and the overall adoption rate. In our effort to test our new theory, we construct several hypotheses that allow us to examine issues associated with information technology adoption that involves multiple parties (multi-partite technology adoption) and strong network externalities. We test for the existence of clustered adoption and the effects of information transmission in the electronic bill presentment and payment (EBPP) industry. We hypothesize that clustered adoption by firms will be influenced by their geographical collocation, the reach of their consumer bases, their industry sector associations, and their consensus choices of the technology vendor. Our results show preliminary evidence to support the proposed theory. KEYWORDS: Clustered adoption, economic analysis, electronic bill payment, information transmission, rational expectations theory, technology adoption _____________________________________________________________________________ ACKNOWLEDGEMENTS. The authors are grateful to Neveen Awad, Indranil Bardhan, Sanjeev Dewan, Chris Forman, Vijay Gurbaxani, Rahul Telang, Kevin Zhu, and other participants of the 2005 Workshop on Information Systems and Economics at the University of California, Irvine, where an earlier version of this paper was presented. We also thank Gordon Davis and Paul Glewwe for their helpful comments and feedback. The authors also acknowledge support from the University of Texas at San Antonio, the Management Information Systems Research Center (MISRC) at the University of Minnesota, and the third author acknowledges financial support from the 3M Corporation. i INTRODUCTION In this paper, we will do a general test of a proposed theory that is based on the rational expectations hypothesis (REH) and adaptive learning theory. We call the proposed theory the rational expectations theory of technology adoption. We will discuss how the theory allows us to look into the issues in the technology adoption that involves multiple parties (multi-partite technology adoption). We set up our discussion and test for the existence of clustered adoptions and the effect of information transmission in the context of electronic bill presentment and payment (EBPP). Much of the adoption decision depends on a firm’s expectations about the benefits and costs of the technology. In this research, we use the REH and adaptive learning theory and apply them in the adoption of IT with network externalities decision making settings that require managers (as economic agents) to have the ability to form certain levels of expectations about the value of the technology. The REH has been applied in many non-IS/IT contexts, where decision makers must estimate the benefits associated with different courses of managerial action related to their perceptions about how beliefs in the economy are shaping up. Such contexts include interest rate policy formation, financial market forecasting and money market trading, manufacturing industry investments for the production of durable goods, and policies in labor market wage-setting. Our discussion and test will center on EBPP technology, which is a relatively new technology that exhibits strong network externalities. EBPP also is an excellent example of a technology that involves multiple parties—in this case, billers, banks, technology suppliers, and customers—in its adoption process. In this kind of technology adoption context, there are needs for sharing expectations of value among these disparate parties, making EBPP representative of a 1 class of technology adoption problems that are more complex in nature than what occurs with single firm technology adoption decision making in isolation. Despite the touted benefits of ease and convenience, surveys show that the adoption of EBPP by consumers is still relatively low. Studies by the Tower Group [2002], for example, discovered that the percentage of households using EBPP had increased only modestly between 1998 and 2002, from 2% to 13.7%. Many analysts argue that the adoption of EBPP has been plagued by the “chicken and egg” syndrome. Billers are not willing to adopt EBPP until a significant portion of customers are willing to use it. However, customers are unwilling to use EBPP until they can pay most of their bills online, that is, until most billers have already adopted the technology [Au and Kauffman, 2001]. This points to the multi-partite adoption dependency that exists in the market, for which we theorize that alignment in expectations of value and willingness-to-adopt must occur. From the perspective of the billers, there are indirect network effects with regards to the adoption of EBPP. Indirect network effects arise when the value of a product increases as the number or the variety of the complementary goods or services increases [Katz and Shapiro, 1985; Economides, 1996]. In the context of EBPP, indirect network externalities occur as market-mediated effects. The more billers that adopt the technology, the more consumers are willing to use the service. This allows each biller to realize higher benefits. One of the most compelling reasons for adopting EBPP is the cost-savings that are available for billers (from the ability to greatly reduce their cost for mailing paper bills). So it follows naturally that billers are the ones that must take the initiative to adopt the technology and create the “network of billers” to attract customers. Many billers seem to have taken this stance, evidenced by the result of an 2 energy industry survey in 2000 showing that more than 90% of respondents at least had considered offering EBPP to their customers [Brown, 2001]. EBPP systems cost billers about $1.1 million on the average. At a typical recurring cost rate of 20% to 30% of the base investment annually, we can see why billers should not adopt EBPP before there are enough customers who ready to use it. If they do this, then it must be because the billers see some other convincing non-cost reasons to adopt [Gonsalves, 2003]. However, the question becomes: When should each biller adopt the technology? In the next section, we propose that each biller should wait until the other billers are ready and so that they all adopt the technology together—clustered in time. IT adopters may be clustered based on geographical regions, firm size, industry, and so on. In the EBPP case, an electric utility firm in a major city may observe a telecommunications company that serves customers in the same geographical area to see if the company is ready to adopt the technology. By adopting together, both firms reinforce one another’s evaluation of the market and increase the likelihood that more customers are using the EBPP service, an externality benefit. We have a number of specific research questions in this kind of technology adoption context. Do we actually observe the kind of clustered adoption in the real world as suggested by our theory of rational expectations? If so, then what kinds of clustering occur for technologies that exhibit strong network externalities? What kinds of factors result in variance in adoption time? What will a theory-driven conceptual model look like for this context? What facilitates information sharing by firms related to business value and technology adoption expectations for EBPP? What kind of empirical model can be used to test the theory? THEORETICAL BACKGROUND We will next review the rational expectations hypothesis (REH) and adaptive learning theory 3 that constitute the foundation of the rational expectations technology adoption theory that we propose, as well as the theory of information transmission that serves as a crucial ingredient in our theory building. Eventually, we discuss the proposed theory that we are going to test in the remainder of this paper. The Theory of Rational Expectations and Adaptive Learning Muth’s [1961] rational expectations hypothesis (REH) suggests that people are able to learn fast to adapt to changes in economic conditions, and to anticipate what will happen in the economic system by examining the patterns of economic activity. The REH effectively maintains that every individual acts as an economic forecaster, using the information he or she can collect to foretell what economic events are likely to happen. The forecasts are the individual's rational expectations. The basic assumption of the theory is that people use of all the information available to them efficiently. Consequently, an individual’s expectations are said to be "rational" if she makes efficient use of all available information, allowing for the cost of the information. Since some information can be costly and hard to obtain, expectations can be rational but still not very accurate. However, even though rational expectations may not be very accurate, at least they will be unbiased. This unbiasedness forms the basis of the central tenet of the theory, that is, the average of people’s subjective expectations is equal to the true values of the economic variables being forecast. REH’s strong assumptions fail to consider that people have bounded rationality so although all the information is available to them, they may not be able to process the information quickly and accurately. Sargent [1993] suggests the theory of adaptive learning to relax some of the strong assumptions. In adaptive learning, people are allowed some time to learn the about the economic circumstances and update their expectations about relevant parameter values on the 4 basis of newly-received information. Furthermore, unlike in the REH, in adaptive learning boundedly-rational agents are allowed to use simple forecasting strategies—perhaps not perfect, but at least approximately right—for a complex nonlinear world. A boundedly-rational agent forms expectations based on observable quantities and adapts her forecasting rule as additional information and observations become available. Adaptive learning may converge to a rational expectations equilibrium or it may converge to an approximate rational expectations equilibrium [Jordan and Radner, 1982], where there is at least some degree of consistency between expectations and realizations [Evans and Honkapohja, 2001; Hommes, 2004]. The Theory of Information Transmission For the purposes of this research, information transmission is defined as the situation where the firm in possession of information signals or transmits the information to another firm. This is also known as signaling [Spence, 1973; Kreps, 1990]. In other technology adoption decision making research, the role of information transmission has been discussed mainly in the context of information asymmetry, which refers to the situation where one firm has more information than others [Zhu and Weyant, 2003]. In this case, information asymmetry exists and persists due to the lack of information transmission. As we have discussed above, information transmission is crucial to the alignment of expectations in adaptive learning. The ability to learn what the other firms expect with regard to the value of a new technology will allow each firm to adjust its own expectations and, possibly, eventually reach an agreement with other firms about the business value of a technology. Crawford and Sobel [1982] maintain that many of the difficulties associated with reaching agreements are informational. They further suggest that sharing information makes better agreements possible. In some cases, however, revealing all of a firm’s decision-relevant 5 information to an opponent may not be the most advantageous policy [Clarke, 1983; Gal-Or, 1985]. For example, although it has been shown that information transmission among supply chain partners may be beneficial [Mukhopadhyay et al., 1995], its effects among competitors appear to be more tentative [Zhu, 2004]. These studies suggest that information sharing may not always be beneficial to a firm, as has also been noted by Han et al. [2004] for the case of Internet-based financial risk management systems; and Kauffman and Mohtadi [2004] for the case of Internet-based supply chain management. In the case of adoption of technologies with strong network externalities, however, information transmission and sharing will almost certainly benefit each firm. Why? Because their common objective is to maximize the benefit of using the technology and most of the benefit comes from network externalities. With potential adopters in a group sharing information over multiple periods, we can expect that they all will reach an informal consensus about the cost and benefit of the technology, leading to an adoption decision. This idea has been suggested by the rational expectations model discussed in Au and Kauffman [2005]. The literature on cooperative game theory and inter-firm coordination seems to support this view as well. For example, Cooper et al. [1997] present experimental evidence that pre-play communication resolves coordination problems in a “battle of the sexes” game. Allowing players to communicate prior to selecting an action almost completely resolved the coordination problems that were observed in the experimental game without pre-play communication. This permitted them to select a desired outcome. In a similar vein, Farrell [1987] presents a model in which the performance of two-way communication is improved if players are allowed additional rounds in which to communicate. 6 The Rational Expectations Theory of Technology Adoption Our rational expectations theory of technology adoption suggests that under certain conditions we can expect to observe clustered adoption, defined as the adoption of a technology by multiple firms at about the same time. Suppose there is a group of N potential adopting firms having to decide whether to adopt a new technology or wait until another, possibly better technology becomes available. The technology exhibits strong network externalities. To realize the expectations about the benefits from network externalities, a firm in the subgroup will adopt the technology only when it has learned that the other N – 1 firms are also ready to adopt the same technology. This is to prevent the firm from getting stranded with a technology that no other firm would choose. As a result, we can expect that each firm in the subgroup will adopt the technology at about the same time. Firms may initially have different levels of expectations about the value of the technology and, consequently, different levels of willingness to pay. A firm’s willingness-to-pay for a technology determines the maximum price the firm is willing to pay to purchase the technology. To achieve concurrent adoption decisions, each firm must reach a level of willingness-to-pay that is at least equal to the price set by the technology supplier. If some firms in the subgroup have a willingness-to-pay that is below the technology supplier’s price, then all firms will defer adoption. We assume that potential adopters are willing and able to freely share information with each other at no cost. The information sharing is essential for the alignment of expectations which, in turn, facilitates the adoption. HYPOTHESES Based on the REH and adaptive learning theory, Au and Kauffman [2005] suggest that IT adoption decision makers will observe the environment and try to align their expectations with 7 those of the other decision makers before making an IT adoption decision. This alignment is necessary to confirm each decision maker’s own expectations about the value of the IT being considered, due to the inherent uncertainty. Benchmarking, information sharing and clustered adoption. In their effort to align their expectations, decision makers “benchmark” against each other and share information within a targeted group. Here benchmarking refers to the process in which firms evaluate various aspects of their business processes in relation to the best practice within their own group, which consists of firms that share similar characteristics and objectives (e.g., belong to the same industry, competing in or serving the same market). In the case of the adoption process of a new technology, however, it is unlikely that the so-called “best practice” exists due to the uncertainties inherent in the new technology. Therefore, we presume that in this particular “benchmarking” process members will learn from each other by sharing information among themselves about their perception of the expected value of the technology prior to making an IT adoption decision. They may eventually reach a tacit consensus, resulting in what we would observe as time-clustered adoption in the marketplace. The information sharing will occur in the form of informal communications through email, telephone calls, conference presentations and panel discussions, and other informal individual communication. This kind of communication meets the criterion that we noted earlier for cheap talk. Although it may seem insignificant, Kim [1996] suggests that repeated interaction among firms can enhance the credibility of cheap talk and improve the efficiency in outcomes that would be infeasible otherwise. Furthermore, Jordan and Radner [1982] maintain that repeated observations of the market can smooth the process by which agents construct expectations. 8 We will directly consider the role of information transmission, and develop hypotheses on how it is likely to affect the patterns of technology adoption. We will also argue that timeclustering of adoption may occur among firms based on four critical dimensions: geographical collocation, geographical reach, industry sector, and technology vendor. We now will develop hypotheses around each of these as a means to test the conditions under which time-clustered technology adoption is likely to occur. We will also consider the role of other drivers of clustered adoption that are adapted from other theories related to technology adoption, as a means to gauge the relative strength of the different explanations of EBBP adoption. Direct effects of information sharing on clustered adoption. A central component of our theoretical argument is that expectations about the appropriate time to adopt a technology will be driven by how effectively information is transmitted and sharing among players in the technology adoption marketplace. Although it is rarely easy to identify the extent to which cheap talk is occurring in the marketplace, it nevertheless is possible to consider aspects of information transmission that are likely to support cheap talk. In particular, based on the existing theory [Seidmann and Sundararajan, 1997; Lee and Whang, 2000], we believe that the frequency of information sharing is likely to be relevant for identifying the effectiveness of information transmission. Moreover, it should relate to subsequent observations of adoption. One approach to capturing this kind of information is to measure the number of conferences that are held in the marketplace that relate to the technology under consideration. A second possible way is to identify the number of white papers and industry surveys and studies that relate to the given technology. There are other means to proxy for the unobservable cheap talk and communication. Although they are imperfect, they may nevertheless provide a useful reading on underlying conditions that support information transmission. 9 Regarding conferences, in particular, the rationale is that a conference is a good opportunity for senior managers from different firms to exchange information and ideas in an inexpensive way. Although some information transmissions are likely to incur significant costs, we consider conferences to be costless, relative to the other available means. This is because firms normally set a certain budget for conference and seminar attendance, to keep up on industry and technology developments, and so this kind of spending is probably viewed by them as a routine cost. In addition, for EBPP at least, the conference attendance costs are insignificant relative to the costs for acquiring and maintaining EBPP technology. Thus, in the EBPP case, we can use the number of EBPP-related conferences conducted in the past as a proxy of information sharing activities that occurred among potential adopters of the technology. Our first hypothesis follows from this discussion: • Hypothesis 1 (The Information Transmission Hypothesis). More information transmission in the marketplace will be positively associated with the observation of more clustered adoption. A related argument that can be made, which also can be developed in the context of the empirical model that we plan to estimate, is related to the observed rate of adoption over time. In some cases, technology adoption that is observed may not meet our requirement for clustered adoption: the time-clustering may not be tight enough, for example. Still, it may be possible to test a weak form hypothesis for clustered adoption that examines the rate of adoption. We indicate this in the second hypothesis: • Hypothesis 2 (The Information Transmission Technology Adoption Rate Hypothesis). More information transmission in the marketplace will be positively associated with faster observed rates of technology adoption. 10 Information transmission allows each firm to share its expectations about the value of the new technology with other firms. More information transmission leads to greater information sharing among the firms, which in turns leads to a faster learning process [Morishima, 1991; Creane, 1995]. With faster learning, we can expect that firms will be able to align their expectations and make an adoption decision sooner. Geographical collocation effects. Geographical collocation is a key factor that may increase the level of interaction among the firms, leading to time-clustered technology adoption. The degree of interaction and information sharing among firms can be expected to be the highest locally. This is because the transmission of new information becomes more complex and costly with increased geographical distance. As a result, the economic activity based on technology innovations is likely to be clustered geographically [Audretsch and Feldman, 1996]. Geographic proximity facilitates interaction, information exchange and technological learning [Soete 1985; Ganesh et al., 1997]. This leads us to assert our hypothesis: • Hypothesis 3 (The Geographical Collocation Clustered Technology Adoption Hypothesis). Firms in the same geographical region are likely to adopt at about the same time, resulting in clustered adoption. Geographical reach effects. Keen [1991] uses the term reach to refer to the geographical locations and the people that a firm’s IT infrastructure is capable of connecting. Similarly, the term geographical reach has been used to refer to the extent to which a firm has its presence and markets its services or products [Radecki et al., 1996]. In our case, we can group the firms into two categories based on their geographical reach: local and regional. We define local firms as firms that serve a customer base in only one state, and regional firms as firms that serve customer bases in multiple states. We maintain that local 11 firms should adopt a new technology earlier than regional firms because the latter typically go through a more complicated decision making process due to their larger operations, causing the learning process to take longer too. Our fourth hypothesis is as follows: • Hypothesis 4 (The Geographical Reach Hypothesis). Similar geographical reach is likely to result in similar underlying conditions for technology adoption, including similar dynamics for information transmission and learning, with the result that cluster adoption will be observed. Industry sector effects. The rate of technology adoption varies between industries. Some industries may find a given technological innovation more useful in their productions processes or product lines than others [Hannan and McDowell, 1984b]. Mansfeld [1968] and Romeo [1975] provide evidence supporting the hypothesis that the more competitive the market or industry, the greater the rate of technology adoption and diffusion. Kamien and Schwartz [1982] review the empirical evidence and note that technology adoption and diffusion tend to be faster in an industry where there are fewer firms in the region and where there are similarities among firm sizes. Forman et al. [2003] find that industries differ in their rates of adoption in Internet technology because they differ in their use of other kinds of IT, labor costs, and industry growth rates. The economics literature commonly identifies information transmission and sharing among firms as occurring mostly within the same industry [e.g., Doyle and Snyder, 1999; Christensen and Caves, 1997] and done through mechanisms such as industry consortia, industry conferences, and trade associations [e.g., Kirby, 1988; Vives, 1990]. Our fifth hypothesis is based on the foregoing analysis: 12 • Hypothesis 5 (The Common Industry Sector Technology Adoption Hypothesis). Since information transmission and sharing among firms in a common industry will be earlier to accomplish, clustered adoption by industry sector will be observed. Technology vendor effects. In the adaptive learning process, firms may initially have only a general idea about a new technology (e.g., the main functions of the technology, the potential benefits the technology may offer to the firms). Over time, however, these firms add, update and process information about many aspects of the technology, including information about specific vendor(s). As firms share information with each other, they will narrow their focus to a certain vendor. This will help them to be more effective in reaching a consensus on the value of the technology being considered, which will drive the outcomes to the equilibrium point suggested by rational expectations theory [Fryman, 1982]. This suggests that when a group of firms reaches a consensus to adopt the technology, they are likely to have a specific vendor in mind. Our sixth hypothesis is derived from this logic. • Hypothesis 6 (The Competing Vendor Hypothesis). Since information transmission and sharing among a group of firms typically focuses on a particular technology vendor, clustered adoption by technology vendor will be observed. Firm size effects. It is generally held that firm size is positively correlated with technology adoption. Large firms or firms with larger market shares are more likely to adopt because they are more likely to have the financial resources required for purchasing and installing a new technology. In addition, they may be better able to attract the necessary human capital and other resources. Larger firms are also more capable of spreading the potential risks associated with new projects because they are able to be more diversified in their technology choice and are in a position to try out a new technology while keeping the old one operating at the same time in case 13 of unexpected problems. Larger firms tend to adopt new technologies sooner because they have the “critical mass” and are able to capture economies of scale from production via the learning curve more quickly and can spread the other fixed costs associated with adoption across a larger number of units. The positive relationship between firm size and technology adoption has been found to occur with reasonable consistency in a variety of empirical research settings [e.g., Link, 1980, in the chemicals and allied products industry; Kimberly and Evanisko, 1981, in the health sector; Hannan and McDowell, 1984a, in electronic banking; Damanpour, 1992, in manufacturing organizations; and Karshenas and Stoneman, 1993 and 1995, in the engineering industry]. Some other literature suggests, however, that large size and market power may slow down the rate of technology adoption. Larger firms may have multiple levels of bureaucracy that can slow down technology adoption decision making processes. Furthermore, it may be relatively more expensive for larger firms to adopt a new technology because they have many resources and human capital sunk in the old technology and its architecture [Henderson and Clark, 1990]. Brynjolfsson et al. [1994] found that increases in the level of IT capital in an economic sector were associated with a decline in average firm size in that sector. This may lead to the notion that smaller firms are more likely to adopt a new technology earlier. Despite the seemingly opposing views on the effects of firm size on technology adoption, we argue that if firms of similar size display consistent technology adoption behaviors, then we should observe clustered adoption by firm size. Our seventh hypothesis is: • Hypothesis 7 (The Firm Size Hypothesis). Since firm size affects technology adoption, clustered adoption by firm size will be observed. 14 A conceptual model for EBPP technology adoption. Based on the foregoing development of hypotheses, we now are in a position to offer a more general conceptual model for EBPP technology adoption. To test our clustered adoption hypotheses, we will employ a set of crosssectional models with deviation from mean time-to-adopt as the dependent variable and a set of independent variables. The values of the dependent variable are calculated based on the mean time-to-adopt of all firms in the sample. In the other models, the values of the dependent variable are derived based on the mean time-to-adopt of each group, stratified by region, firm size, industry, reach, and vendor. In addition, we will use a duration model for survival analysis involving panel data to identify the instantaneous likelihood to adopt for each firm. This conceptual model is summarized in the following diagram. (See Figure 1.) One of the key issues with respect to this general conceptual model will be how we handle time related to the observation of clustered adoption. Our operational definition for clustering of technology adoption is based on an analysis of the empirical regularities adoption of technology in a variety of settings [Fichman, 1992; Hoppe, 2002]. We note that in the context of XML and Web services standards [Au and Kauffman, 2003; Chen et al., 2003], technologies with similar multi-partite adoption complexity issues, that adoption occurred in large measure over the course of one to two years. Other examples include DVDs, Wi-Fi and camera-phones. In the case of Wi-Fi, research firm IDC predicts that the total number of public Wi-Fi users is expected to grow from 2.4 million in 2003 to 10.4 million in 2005, a 324% growth over a period of two years [Infonet, 2003]. In addition, we also have seen this kind of time horizon for the main elements of technology adoption occurring in mobile telecommunications in Europe. Gruber and Verboven [2001] report that technology adoption was rather swift in this context also. We further note that the multi-partite adoption issues that are likely to be present here will require a 15 similar rational expectations theory interpretation of adoption-related information transmission and sharing. Figure 1. Conceptual Model to Test Rational Expectations-Based EBPP Adoption Cross-sectional Models Overall Dependent Variables Independent Variables •DevMeanTimeToAdopt •TimeToEvent •Northeast •Midwest •South •FirmReach •Telecom •Metavante •FirmSize •∆Lag2QConfDensity •∆Lag2QDJIA •∆Lag2QVendorStockPrice •Northeast •Midwest •South •FirmReach •Telecom •Metavante •FirmSize •∆Lag2QConfDensity •∆Lag2QDJIA •∆Lag2QVendorStockPrice By Region By FirmReach •Northeast •Midwest •South •FirmReach •Telecom •Metavante •FirmSize •∆Lag2QConfDensity •∆Lag2QDJIA •∆Lag2QVendorStockPrice By Industry •Northeast •Midwest •South •FirmReach •Telecom •Metavante •FirmSize •∆Lag2QConfDensity •∆Lag2QDJIA •∆Lag2QVendorStockPrice •Northeast •Midwest •South •FirmReach •Telecom •Metavante •FirmSize •∆Lag2QConfDensity •∆Lag2QDJIA •∆Lag2QVendorStockPrice By Vendor •Northeast •Midwest •South •FirmReach •Telecom •Metavante •FirmSize •∆Lag2QConfDensity •∆Lag2QDJIA •∆Lag2QVendorStockPrice Panel Data Model / Duration Model Based on our brief assessment of adoption patterns for other technologies likely to have had adoption issues caused by value flows being constrained by the adoption of different kinds of players in the same time frame, we will argue that a one-year window of time is a reasonable period within which to observed clustered adoption. We further note that this is consistent with the manner in which capital budgeting for large capital projects is done in firms: they normally must plan ahead for big investments such as EBPP, and their budgeting plans typically are done once a year. There is no requirement that their budgets all be developed over the same set of 16 months, however. Thus, we think a window of time—rather than a smaller specific period of time—ought to make the most sense for this study. DATA AND MEASURES Data Sources In this section, we will provide a description of the data set and how we collected the data as well as the descriptive statistics for the variables in the study that we will use to test the hypotheses discussed earlier. Description of the Data Set Our sample consists of EBPP adopting firms in the utilities and telecommunications industries in the United States. We focused our analysis on two major EBPP vendors: CheckFree and Metavante. To compile the sample, we used the list of corporate customers that CheckFree posted on its website, as well as a list of corporate customers that we obtained directly from Metavante. Due to the unavailability of financial information for privately-held firms, we chose to include only public firms in our base sample set. However, in our extended sample set we included all these private firms to perform a comparison analysis without any firm-specific financial information. In addition, we considered companies that had the same parent company as one company. Since CheckFree’s list did not include the adoption dates of any of the companies, we searched for the information on the Internet using multiple data sources, including Google, LexisNexis, and the annual report of each company. In this case, we defined the adoption date as the date when a company signed an EBPP agreement with the technology vendor. Furthermore, we collected information about each company including company location (city, state, and zip code), company size (in terms of the number of customers in the year adopted 17 EBPP), and company financial performance as measured in annual sales and earnings before interest and tax (EBIT). While information about company location and company size could be found on each company’s web site, we used the COMPUSTAT database to obtain the company financial performance data. For the number of EBPP conferences per quarter, we searched the Web, LexisNexis, and conference organizer web sites. We confirmed our data by contacting several major conference organizers. To determine the location of regional firms whose operations span multiple states that might fall into different regions, we used the location of the headquarters and the region where most of the operations were taking place. Our coding of regions follows the designations specified by the United States Census Bureau. (See Appendix 1.) Specification of measures for the variables included in this study Our analysis will employ two different models. The first model is cross-sectional and will be the primary means for testing the clustered adoption hypotheses. The second is a duration model involving panel data with time-varying covariates for identifying the instantaneous likelihood of adoption of a particular firm at a specific point in time. Consequently, we will specify two different sets of dependent variables to reflect the use of two different models. The sets of independent variables are almost the same between the two models. However, as the names imply, the first model uses cross-sectional data, whereas the second model employs panel data. Both models include lagged variables as explanatory variables. Table 4 summarizes the measures and definitions for the variables that are used in this empirical study. The use of the lagged value in some of the variables is based on the idea that it will take some time before conference activities are seen to affect any adoption decision by a firm. Furthermore, the use of the difference in the numbers of conferences between periods 18 captures the idea about how firm adoption decisions in certain periods were affected by the increase or decrease in the frequency of the related conference activities. Table 5 shows descriptive statistics for variables in our data set. EMPIRICAL MODELING The empirical analysis in this chapter will involve two separate models. The first is a crosssectional model set that offers a primary test of the cluster adoption hypothesis through econometric analysis of models that represent the five different clustering strata. The goal of the analysis is to estimate the extent to which the different theorized effects arise for different subgroup codings for the dependent variables, relative to deviations in time from the central tendency of firms to adopt EBPP. The second empirical analysis involves the specification of an accelerated failure time panel data model, whose structure is developed to make it possible to identify the instantaneous likelihood of adoption of a given firm in time. This analysis does not focus on deviations from time to adopt. Nor does it include sub-sample stratifications that affect the definition of the dependent variable. Instead, the dependent variable is the occurrence of EBPP adoption by a firm at a specific point in time, such that the general model can capture information about the temporal likelihood of adoption for all firms. We introduce the stratifying variables from the first model into this panel data model, as the size of the data set allows, as categorical fixed effects. However, we should note at the outset that it is not possible for us to include all of the hypothesized clustered adoption conditions; the size of the data size is insufficient in statistical power terms. 19 Table 4. Summary of Variable Definitions and Measures for This Study VARIABLE DEFINITION ISSUES Dependent Variables DevMeanTime ToAdopt The deviation from group average time-to-adopt (in quarters from the beginning of the adoption timeline). TimeToAdopt The duration of time from the start of the observation period to the event. For each firm in each time period, the event is coded with a “1” if the firm made an adoption decision, and with a “0” if otherwise. Theory-Bearing Independent Variables The difference between the number of EBPP-related ∆Lag2QConf Density FirmSize FirmReach Metavante Regional dummy variables conferences held two quarters prior to the adoption period of each firm and the number of similar conferences held four quarters prior in the region. Size of each firm, measured in terms of number of customers. Dummy variable that codes for the operational span of an EBPP adopter, with 1=regional span and 0=local span only. Local span is the base case. Dummy variable that codes for a vendor, with 1=Metavante, 0=CheckFree. Checkfree is the base case. A set of dummy variables that code for four geographic regions of the U.S. and proxies for demographic similarities in the operational environment of an EBPP adopter: • Northeast: 1=Northeast, 0=otherwise. • Midwest: 1=Midwest, 0=otherwise. • South: 1=South, 0=otherwise. The base case is the West region. Emphasis is on differences in groups, leading to different deviations for similar observations. Requires information about duration, but acts only as a technical parameter in the model. A number of different lag specifications were examined. This two-quarter lag variable was most appropriate. Proxy for firm size, since employees were not available. Span was coded based on a single state (local) or a number of states (regional). Other span definitions were possible too. No other vendors were included in this study for a lack of public information. Coding is based on regional definitions of the U.S. Census Bureau. Using the west region as the base case reflects our belief that this is the region whose EBPP growth dynamics are most well understood. Control Variables Change in quarterly average of DJIA indices compared ∆Lag2QDJIA Values computed on the basis of daily market indices. Choice of lag intended to match ConfDensity variable. Change in quarterly average of vendor stock price Values computed on the basis ∆Lag2QVendor (CKFR for CheckFree adopters and MI for Metavante of daily stock market prices. StockPrice adopters) compared to the previous quarter, measured Choice of lag intended to two quarters prior to the time-to-adopt. match ConfDensity variable. Change of a firm’s annual EBIT in the year prior to the Single-year lag used due to ∆LagFirm year-of-adoption compared with the previous year. financial reporting limitations, Profit based on annual report info. Notes: The specifications of the variables that are used in this study reflect a blend of ideal measures and pragmatic measures. The variable that codes vendor, Metavante, is an example of the former. The lag measures typically were pragmatic choices, when there were many possible measures to choose from. to the previous quarter, measured two quarters prior to the time of adoption. 20 Table 5. Descriptive Statistics VARIABLE N MEAN DevMeanTimeToAdopt Northeast Midwest South FirmReach Telecom Metavante ∆Lag2QConfDensity ∆Lag2QDJIA ∆Lag2QVendorStockPrice 80 80 80 80 80 80 80 80 80 80 0 0.275 0.225 0.275 0.663 0.188 0.113 0.150 0.019 0.330 STD. DEV 3.586 0.449 0.420 0.449 0.476 0.393 0.318 1.801 0.067 0.759 MIN MAX -6.025 0 0 0 0 0 0 -4.000 -0.060 -0.664 10.975 1 1 1 1 1 1 3.000 0.453 1.541 Note: Northeast, Midwest, South, FirmReach, Telecom, and Metavante are dummy variables and therefore have a value of either 0 or 1 only. A Cross-Sectional Clustered Adoption Model for EBPP Technology Adoption Our main premise is that in the presence of information transmission a group of firms sharing similar characteristics will adopt EBPP at about the same time, resulting in clustered adoption. In practice, some of the firms will adopt either a little earlier or a little later. In other words, clustered adoption may occur with an error term for timing, since firms with similar characteristics will not be identical, may process information differently, and so on. Nevertheless, we posit that the average time of adoption reflects the group’s rational expectations about how to maximize the value associated with technology adoption by adopting at the valuemaximizing time. A firm that adopts either earlier or later than the average time shows a deviation from the central tendency for adoption timing by members of the group. This may diminish the firm’s ability to obtain network externality-led benefits (when adoption is too early) or cause the firm to miss out on capturing value that is available in the marketplace (when 21 adoption occurs too late). The objective of our cross-sectional model is to explain the deviations for operationally-defined dependent variables that reflect different possible subgroups of firms. We base our model on the multiplicative model which takes the form of: yi = β 0 x1β, i1 x2β,2i K xKβ K, i ε where k = counter for k = 1 to K independent variables yi = deviation from mean time-to-adopt for EBPP adopter firm i among i = 1 to I firms in the sample x1,i, x2,i, …, xK,i = explanatory variable k for firm i ε = normally-distributed error term with 0 mean The multiplicative model represents interactions among the independent variables. For example, the deviation from mean time-to-adopt might be a combination effect of the location of the firm and its size. The above multiplicative form can be rewritten in the log-linear form using the variable names specified in the previous section: ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 5Telecom + β 6 Metavante + β 7 ln( FirmSize) + β 8 ln(∆LagFirm Pr ofit ) + β 9 ln(∆Lag 2QConfDensity ) + β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) + ln ε (The Basic Cross-Sectional Model) (1) This basic cross-sectional model includes all the independent variables. The value of the dependent variable for each observation (in other words, each row in the regression) is calculated based on the deviation from the mean time-to-adopt of all observations in the sample. 22 For computational purposes, to avoid an invalid operation with the logarithmic function in the model because of a negative or zero value, we add a constant (10) to each of the dependent variable DevMeanTimeToAdopt value as well as each ∆Lag2QConfDensity value. Similarly, we add 1 to ∆LagFirmProfit, ∆Lag2QDJIA as well as ∆Lag2QVendorStockPrice. These constants will be taken care of when we calculate the marginal effect of the respective coefficients later on. In addition, we also estimate four other models based on four different clustering strata: region, reach, vendor, and industry. The model based on the region stratifier excludes the Northeast, Midwest, and South dummy variables, with the Western United States region as the base case. This is because the values of those variables are reflected in the values of dependent variable, which is calculated based on the difference in mean time-to-adopt of observations per region. ln( DevMeanTimeToAdopt ) = ln β 0 + β 4 Firm Re ach + β 5Telecom + β 6 Metavante + β 7 ln( FirmSize) + β 8 ln(∆LagFirm Pr ofit ) + β 9 ln(∆Lag 2QConfDensity ) + β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) + ln ε (The Regional Stratification Model) (2) Similarly, we have a model based on the firm reach stratifier that will exclude the FirmReach variable and whose dependent variable values are calculated based on the difference in the mean time-to-adopt per reach group (regional and local). ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South + + β 5Telecom + β 6 Metavante + β 8 ln( FirmSize) + β 7 ln(∆Lag 2QConfDensity ) + β 9 ln(∆LagFirm Pr ofit ) + β10 ln( Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) (The Firm Geographical Reach Stratification Model) (3) The next model is based on the industry stratifier and it will exclude the Telecom variable. 23 The dependent variable values are calculated based on the difference in mean time-to-adopt per industry group (utilities and telecommunications). ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 6 Metavante + β 7 ln( FirmSize) + β 8 ln(∆Lag 2QConfDensity ) + β 9 ln(∆LagFirm Pr ofit ) + β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) (The Industry Stratification Model) (4) The last cross-sectional model is based on the vendor stratifier and it will exclude the Metavante variable. The dependent variable values are calculated based on the difference in mean time-to-adopt for firms by vendor group for Metavante and CheckFree. ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 5Telecom + β 7 ln( FirmSize) + β 8 ln(∆Lag 2QConfDensity ) + β 9 ln(∆LagFirm Pr ofit ) + β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) (The Vendor Stratification Model) (5) A Panel Data Model for EBPP Technology Adoption Likelihood We analyze our data using a duration model for survival analysis (Greene, 2002; Hosmer and Lemeshow, 1999; Hougaard, 2000). The data consist of a response variable that measures the duration of time until a specified event occurs, as well as a set of independent variables associated with the adoption time variable. The response variable is also known as the event time, failure time, or survival time variable. The purpose of survival analysis is to model the underlying distribution of the event time variable and to assess the dependence of the event time variable on the independent variable. We analyze our panel data using an accelerated failure time (AFT) model, also known as the accelerated time model or the ln(time) model [Cleves et al., 2002; Lee and Wang, 2003]. The 24 typical form of the model is ln(t i ) = xi β x + ln(τ i ) , where ti is time-to-adopt of firm i and τ i is the residual. The word “accelerated” refers to the fact that in such a model, the effect of a change in one of the independent variables increases with time. This is something we expect to see in many technology adoption scenarios, including EBPP adoption. This is especially true in the context of our theory, where we expect the potential adopters to go through a learning process for a while to reinforce their understanding and expectations about the technology. In addition, technologies have underlying elements that exogenously improve. As a result, as EBPP matures over time, we should observe a more profound effect of the independent variables, leading to the greater likelihood of adoption of the technology by firms. Our basic panel data model is as follows: ln(t i ) = β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 5Telcom + β 6 Metavante + β 7 Firm Re ach + β 8 ∆LagFirm Pr ofit + β 9 ∆Lag 2QConfDensity + β10 ∆Lag 2QDJIA + β11∆Lag 2QVendorStock Pr ice + ln(τ i ) (The Basic Panel Data Model) (6) In the AFT model, exponentiated coefficients have the interpretation of time ratios for a oneunit change in the corresponding covariate. For an EBPP adopting firm i with covariate values xi = ( x1 , x2 ,K, xk ) , t i = exp( β1 x1 + β 2 x 2 + K + β k xk )τ i . If the value of x1 for the firm increases by 1, then t i* = exp{β1 ( x1 + 1) + β 2 x2 + K + β k xk }τ i , and the ratio of t i* to t i will be exp( β 1 ) . Results of the Basic Cross-Sectional Model The estimation results from our basic cross-sectional model are summarized in the following table. (See Table 6.) We check for the presence of multicollinearity by calculating the variance inflation factor (VIF). Each VIF value in the table is less than two, suggesting there is no 25 multicollinearity issue with our data. The values of R2 and adjusted R2 (60.4% and 54.0%, respectively) both indicate a relatively good model fit. The value of F-statistic (9.44) is highly significant (p-value < 0.0001), suggesting that we can reject the hypothesis that all coefficients of the explanatory variables all equal to zero. Table 6. Results of the Basic Model VARIABLES Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Telecom (β5) Metavante (β6) FirmSize (β7) ∆LagFirmProfit (β8) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendorStockPrice (β11) R2 (Adj. R2) F-statistic White’s Test COEFFICIENT (STD. ERROR) 4.521*** (0.660) 0.199* (0.101) 0.176* (0.100) 0.250** (0.097) 0.182** (0.081) -0.075 (0.109) 0.228* (0.121) 0.007 (0.030) 0.029 (0.247) -1.168*** (0.197) -2.151*** (0.638) 0.094* (0.056) 60.4% (54.0%) 9.44*** 57.89 (p-value = 0.72) P-VALUE 0.000 0.053 0.083 0.012 0.028 0.491 0.064 0.816 0.908 0.000 0.001 0.102 Notes: Model: Basic Cross-Sectional Model (Equation 1). Dependent variable is ln(DevMeanToAdopt). Sample size N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Each VIF value is less than 2, suggesting there is no multicollinearity issue with our data. By observing the p-value of each coefficient, we can see that the majority of the variables are statistically significant. Three variables—Telecom, FirmSize, and ∆LagFirmProfit—are clearly insignificant. Another variable, ∆Lag2QVendorStockPrice, is marginally significant. This gives us some idea about which variables to exclude in our revised models, taking into account the key variables needed for testing our theory. 26 To provide us with a better idea about our data, we next performed the estimations based on the stratification models. The results, which are summarized in Table 7, show that the three variables—Telecom, FirmSize, and ∆LagFirmProfit—are not statistically significant in any of the models. Our revised models will exclude these three variables. Table 7. Results of the Basic and Stratification Models VARIABLES Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Telecom (β5) Metavante (β6) FirmSize (β7) ∆LagFirmProfit (β8 ) ∆Lag2QConf Density (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendorS tockPrice (β11) R2 Adjusted R2 F-statistic White’s Test BASIC MODEL Regional Coefficient Coefficient (Std. (Std. Error) Error) 4.230*** 4.521*** (0.619) (0.660) ** N/A 0.199 (0.101) N/A 0.176* (0.100) N/A 0.250*** (0.097) 0.159** 0.182** (0.081) (0.078) -0.075 -0.104 (0.109) (0.101) 0.249** 0.228** (0.121) (0.115) 0.007 0.027 (0.030) (0.028) 0.029 0.026 (0.247) (0.229) *** -1.168 -1.082*** (0.197) (0.183) *** -2.151 -2.064*** (0.638) (0.603) * 0.094 0.101* (0.056) (0.053) 60.4% 56.0% 54.0% 51.1% *** 9.44 11.31*** 57.89 45.30 (p = 0.72) (p = 0.26) STRATIFICATION MODEL FirmReach Industry Vendor Coefficient Coefficient Coefficient (Std. (Std. (Std. Error) Error) Error) 4.643*** 4.752*** 4.947*** (0.659) (0.620) (0.622) 0.131 0.142 0.202** (0.095) (0.103) (0.100) ** 0.100 0.202 0.173* (0.094) (0.101) (0.098) ** ** 0.179 0.212 0.266*** (0.091) (0.099) (0.093) N/A 0.123 0.150** (0.082) (0.076) -0.085 N/A -0.041 (0.101) (0.104) 0.212** 0.133 N/A (1.109) (0.120) 0.003 -0.027 -0.004 (0.231) (0.028) (0.028) 0.097 -0.061 0.069 (0.231) (0.249) (0.242) *** *** -1.134 -1.081 -1.191*** (0.184) (0.199) (0.192) *** *** -1.713 -2.086 -2.016*** (0.595) (0.664) (0.623) 0.070 0.059 0.086 (0.053) (0.057) (0.055) 54.5% 54.1% 59.5% 47.9% 47.4% 53.6% *** *** 8.28 8.13 10.12*** 56.95 48.08 51.40 (p = 0.44) (p = 0.77) (p = 0.68) 27 Notes. Model: Basic Cross-Sectional Model (Equation 1); Regional Stratification Model (Equation 2); Firm Reach Stratification Model (Equation 3); Industry Stratification Model (Equation 4); Vendor Stratification Model (Equation 5). Dependent variable in each model is ln(DevMeanToAdopt). Sample size in each model is N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Revised Estimation Models The results of the basic cross-sectional models presented earlier show that three variables— Telecom, FirmSize, and ∆LagFirmProfit—are not statistically significant although we have initially expected the opposite. This suggests that adoption times are not clustered by industry. In addition, firm characteristics (especially firm size and profitability) appear not to affect the time of adoption in the EBPP context. We will estimate the following revised econometric models by excluding those three variables: ln( DevMeanTimeToAdopt ) = ln β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 6 Metavante + β 9 ln(∆Lag 2QConfDensity ) + β10 ln(∆Lag 2QDJIA) + β11 ln(∆Lag 2QVendorStock Pr ice) + ln ε (The Revised Cross-Sectional Model) (7) Similarly, our revised panel data model will also exclude the three variables. ln(t i ) = β 0 + β1 Northeast + β 2 Midwest + β 3 South + β 4 Firm Re ach + β 6 Metavante + β 9 ∆Lag 2QConfDensity + β10 ∆Lag 2QDJIA + β11∆Lag 2QVendorStock Pr ice + ln(τ i ) (The Revised Panel Data Model) (8) In the following sections we will present the results of these models. Results of the Revised Models The results from the revised basic model are shown in Table 8 below. Now all coefficients are statistically significant and the adjusted R2 value is slightly higher compared with that of the 28 original basic model (55.7% versus 54.0%). The F-statistic is highly significant (13.40, p < 0.0001). All of the VIF values are below two, suggesting that there is no indication of multicollinearity. Table 8. Results of the Revised Basic Model VARIABLES Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendorStockPrice (β11) R2 (Adjusted R2) F-statistic COEFFICIENT (STD. ERROR) 4.585*** (0.444) 0.187** (0.093) 0.186* (0.096) 0.249*** (0.093) 0.170** (0.074) 0.208* (0.111) -1.143*** (0.188) -2.163*** (0.604) 0.088 (0.054) 60.2% (55.7%) 13.40 (0.000) P-VALUE 0.000 0.048 0.057 0.009 0.026 0.064 0.000 0.001 0.105 Notes. Model: Revised Cross-Sectional Model (Equation 7). Dependent variable is ln(DevMeanToAdopt). Sample size is N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Each VIF value is less than 1.8, suggesting there is no multicollinearity issue with our data. In addition to the revised basic model, we performed estimations for the revised stratification models. The results are summarized in Table 9. Notice that industry is not one of the stratifiers any more since we now exclude the Telecom variable. The results show generally consistent estimates in terms of the sign and the significance level of each coefficient across the different models. For example, ∆Lag2QConfDensity and ∆Lag2QDJIA are all negative and highly significant, and FirmReach is positive and significant. 29 Table 9. Results of the Revised Basic and Stratification Models VARIABLES Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConf Density (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendor StockPrice (β11) R2 Adj. R2 F-statistic OVERALL MODEL Coefficient (Std. Error) 4.585*** (0.444) 0.187** (0.093) 0.186** (0.096) 0.249*** (0.093) 0.170** (0.074) 0.208* (0.111) -1.143*** (0.188) -2.163*** (0.604) 0.088* (0.054) 60.2% 55.7% 13.40*** STRATIFICATION MODELS Regional FirmReach By Vendor Coefficient Coefficient Coefficient (Std. Error) (Std. Error) (Std. Error) 4.575*** 4.646*** 4.682*** (0.421) (0.399) (0.428) N/A 0.123 0.200** (0.088) (0.090) N/A 0.111 0.178* (0.090) (0.095) ** N/A 0.174 0.261*** (0.088) (0.090) ** 0.156 N/A 0.139** (0.072) (0.069) 0.199*** 0.206** N/A (0.104) (0.099) -1.063*** -1.094*** -1.168*** (0.178) (0.174) (0.183) *** *** -1.942 -1.756 -2.078*** (0.575) (0.569) (0.593) * 0.092 0.066 0.087 (0.051) (0.051) (0.053) 55.2% 53.4% 59.3% 52.1% 49.5% 55.3% *** *** 18.21 12.05 14.97*** Notes. Model: Revised Cross-Sectional Model (Equation 7). The other three models are stratification models similar to Equations 2, 3, and 5 but without the Telecom, FirmSize, and ∆LagFirmProfit variables on the right-hand side. Sample size is N = 80. Dependent variable is ln(DevMeanToAdopt). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. The following Table 10 shows the size of the marginal effect of each coefficient and its actual impact on the dependent variable. The marginal effect of the Northeast dummy variable can be calculated as follows. Let y Base be the value of the dependent variable in the base case (i.e., West region), and y Northeast be that of the Northeast region. If y Base = e (where B B represents the sum of the values on the right-hand side of the cross-sectional model for the base 30 case), then y Northeast = e B + β1 . The marginal effect of the coefficient β1 on the dependent variable is given by: y Northeast − y Base = e of e β1 B + β1 − e B = e B (e β1 − 1) . Table 10 shows the value − 1 for each model. We can derive a similar marginal effect for the other dummy variable coefficients (Midwest-β2, South-β3, FirmReach-β4, and Metavante-β6). Table 10. Coefficient marginal effects on the dependent variable VARIABLES Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConf Density (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendor StockPrice (β11) OVERALL MODEL Coefficient Marginal Effect 0.206 0.204 0.283 0.185 0.231 STRATIFICATION MODELS Regional FirmReach By Vendor Coefficient Coefficient Coefficient Marginal Marginal Marginal Effect Effect Effect N/A 0.131 0.221 N/A 0.117 0.195 N/A 0.190 0.298 N/A 0.149 0.169 0.220 0.229 N/A -0.007 -0.008 -0.008 -0.007 -0.021 -0.019 -0.017 -0.020 0.001 0.001 0.001 0.001 Note: To avoid an invalid operation with the logarithmic function in the model because of a negative or zero value, we added a constant (10) to each ∆Lag2QConfDensity value, and 1 to ∆Lag2QDJIA as well as ∆Lag2QVendorStockPrice. As a result, each constant shows up in the marginal effect for the respective coefficient as shown above in this table. The β β β marginal effects of β1, β2, β3, β4, and β6 are calculated using e 1 − 1 , e 2 − 1 , e 3 − 1 , e β 4 − 1 , and e β 6 − 1 respectively. The marginal effect of β9 is determined using e β 9 ln(10 + ∆ ) − e β 9 ln(10 ) , with ∆ = 1. The marginal effects of β10 and β11 are calculated using e β10 ln(1+ ∆ ) − 1 and e β11 ln(1+ ∆ ) − 1 , respectively, with ∆ = 1%. The results in Table 9 show that both ∆Lag2QConfDensity and ∆Lag2QDJIA have a negative coefficient and they are both significant at 0.01 level. This suggests that an increase in conference activities and a positive change in the economy in general have accelerated the 31 adoption of EBPP. This supports the Information Transmission Technology Adoption Rate Hypothesis (H2). The difference in the values of the dependent variable caused by a change in the number of conferences of ∆ is given by y * − y Base = e B+β9 ln(10+∆ ) − e B+ β9 ln10 = e B e β9 ln(10+∆ ) − e B e β9 ln10 = e B (e β9 ln(10+∆ ) − e β9 ln10 ) Therefore, the marginal effect is given by e β9 ln(10+ ∆ ) − e β9 ln 10 , where ∆ is the actual difference in the number of EBPP conferences as defined for ∆Lag2QConfDensity. (Note: The constant 10 appears in the calculation above since we added the number 10 to every ∆ prior to estimating our cross-sectional model to avoid an invalid operation with the logarithmic function in the model because of a negative or zero value.) Since β9 is negative, a positive ∆ will result in a negative marginal effect, which means earlier adoption. For example, in the overall model case, if ∆ = 1, then the marginal effect is e −1.143 ln(10+1) − e −1.143 ln 10 = −0.007 . For ∆Lag2QDJIA (β10), the difference in the values of the dependent variable caused by a change in the DJIA stock market index ∆ is given by: y * − y Base = e B+β10 ln(1+∆ ) − e B+ β10 ln1 = e B e β10 ln(1+∆ ) − e B e 0 = e B (e β10 ln(1+∆ ) − 1) Therefore, the marginal effect is given by coefficient of ∆Lag2QDJIA (β10) is given by e β10 ln(1+ ∆ ) − 1 , which also means earlier adoption for a positive change in the stock index. (Note: Similar to the number of conferences case, we added the constant 1 to every ∆ prior to estimating our cross-sectional model to avoid an invalid operation with the logarithmic function in the model because of a negative or zero value.) For example, in the overall model case, if ∆ = 0.01 32 (which means the stock market index increases by 1%, then the marginal effect is e −2.163 ln(1+ 0.01) − 1 = −0.021 . The other variables have a positive coefficient and are statistically significant at various levels. The ∆Lag2QVendorStockPrice variable has a positive coefficient and is statistically significant in two of the revised models. The positive sign is counter-intuitive since we would expect that a positive change in the vendor stock performance should accelerate the adoption of the technology; instead, the result shows the opposite. The FirmReach variable has a positive coefficient and is statistically significant at 0.05 level. FirmReach is set to “1” if a firm is a regional firm. The fact that the coefficient is significant suggests that there is a relative clustering of regional firms in terms of time of adoption because holding all other things equal, each regional firm will adopt at the same time. The positive coefficient suggests that regional firms adopted later than the base case (i.e., the local firms). Therefore, the Geographical Reach Hypothesis (H4) is supported. The marginal effect of the FirmReach coefficient for the overall model is 0.185. (See Table 10.) This means that holding all other things equal, regional firms’ deviation from the overall mean time-to-adopt is smaller than local firms’ by 0.185 times. Since the deviation from the overall mean time-to-adopt of the base case is negative, we conclude that on the average regional firms adopted later than the local firms. The Metavante variable has a positive coefficient and is statistically significant at 0.01, 0.05, or 0.10 level, depending on which model we look at. Metavante is set to “1” if a firm is a Metavante adopter. Again, the fact that the coefficient is significant suggests that there is a relative clustering of Metavante adopting firms in terms of time of adoption. The positive coefficient suggests that Metavante adopters adopted later than the base case (i.e., the CheckFree 33 adopters). This supports the Competing Vendor Hypothesis (H6). The marginal effect of the Metavante coefficient for the overall model is 0.231. (See Table 10.) This means that holding all other things equal, Metavante firms’ deviation from the overall mean time-to-adopt is smaller than Checkfree firms’ by 0.231 times. Since the deviation from the overall mean time-to-adopt of the base case is negative, we conclude that on the average Metavante firms adopted later than Checkfree firms. The Northeast, Midwest, and South variables all have a positive coefficient and are statistically significant at different levels (except in the FirmReach stratification model where Northeast and Midwest are not significant). This suggests that there is clustered adoption in each region, supporting the Geographical Collocation Clustered Technology Adoption Hypothesis (H3). The positive sign suggests that firms in each of these regions adopted later than the base case, which is the Western firms. The marginal effect of the Northeast coefficient for the overall model is 0.206. (See Table 10.) This means that holding all other things equal, Northeast firms’ deviation from the overall mean time-to-adopt is smaller than West firms’ (the base case) by 0.206 times. Since the deviation from the overall mean time-to-adopt of the base case is negative, we conclude that on the average Northeast firms adopted later than West firms. Similar arguments hold for Midwest as well as South, which marginal effects are 0.204 and 0.283, respectively. Again, the fact that each of these coefficients is significant shows that there is a relative clustering of adoption time per region. Estimations with an Extended Sample Size Since we have removed all firm-specific variables (i.e., FirmSize and ∆LagFirmProfit), we can now include all the non-public firms that were initially taken out of the original sample set. This is because we no longer have the need to include values of variables that would only be 34 typically reported by publicly-held firms. This will allow us to work with a larger sample set (118 firms versus 80 originally). Our extended sample set consists of 92 utilities and 26 telecom firms. There are now 26 Metavante firms (versus 9 in the original sample set), and 92 Checkfree firms (versus 71 in the original sample set). Although there are more observations, the results of the estimations using the extended sample set do not give us better support for our hypotheses. (See Table 11). Although there are more telecommunications firms in the extended sample set, we still do not have a statistically significant coefficient for the Telecom variable. Indeed, all three regional variables (Northeast, Midwest, and South) are now statistically insignificant. We suspect that non-public firms may behave differently than public firms in terms of deciding when to adopt a technology. Table 11. Results of the Revised and Stratification Models with Extended Data Set VARIABLES Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Telecom (β5) Metavante (β6) ∆Lag2QConf Density (β9) ∆Lag2QDJIA (β10) BASIC STRATIFICATION MODELS MODEL Regional FirmReach Industry Vendor Coefficient Coefficient Coefficient Coefficient Coefficient (Std. (Std. (Std. (Std. (Std. Error) Error) Error) Error) Error) 4.800*** 4.538*** 4.670*** 4.696*** 4.747*** (0.386) (0.392) (0.397) (0.359) (0.357) 0.108 N/A 0.145 0.076 0.091 (0.097) (0.097) (0.092) (0.090) 0.029 N/A 0.077 0.058 0.026 (0.101) (0.100) (0.096) (0.094) 0.105 N/A 0.112 0.074 0.086 (0.084) (0.085) (0.080) (0.076) ** ** 0.187 N/A 0.105 0.152** 0.158 (0.075) (0.075) (0.070) (0.064) -0.028 -0.036 0.014 N/A -0.032 (0.084) (0.086) (0.083) (0.074) 0.043 0.053 N/A 0.121 0.155** (0.095) (0.088) (0.084) (0.094) -1.193*** -1.199*** -1.130*** -1.074*** -1.148*** (0.175) (0.178) (0.176) (0.163) (0.163) *** *** *** *** -2.165 -1.839 -2.451 -2.286 -2.080** (0.683) (0.692) (0.682) (0.648) (0.637) 35 ∆Lag2QVendorS tockPrice (β11) R2 Adj. R2 F-statistic 0.033 (0.055) 52.9% 49.0% 13.49*** 0.033 (0.056) 48.6% 45.8% 17.45*** 0.039 (0.056) 50.9% 47.3% 14.13*** 0.016 (0.052) 50.9% 47.3% 14.13*** 0.028 (0.051) 52.8% 49.3% 15.22*** Notes: Model: Basic Cross-Sectional Model (Equation 1); Regional Stratification Model (Equation 2); Firm Reach Stratification Model (Equation 3); Industry Stratification Model (Equation 4); Vendor Stratification Model (Equation 5); all without FirmSize and ∆LagFirmProfit. Dependent variable in each model is DevMeanToAdopt. Extended sample size in each model is N = 118. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Panel Data Model Results We used Stata 8.0’s STREG command to estimate our panel data model. The STREG command allows the analysis of the panel data using the accelerated failure time model. Alternate Parametric Functional Forms for the AFT Model There are five parametric models that can be used: exponential, Weibull, generalized gamma, log-normal, and log-logistic. Briefly, the different parametric models permit the representation of somewhat different assumptions about τ i = exp(− xi β x ) t i in applied settings involving the adoption of IT. With an exponential parametric model, it is assumed that τ i ~ Exponential{exp( β 0 )} , i.e., τ i is distributed as exponential with mean exp( β 0 ) . With a Weibull parametric form, it is assumed that τ i ~ Weibull ( β 0 , p) , i.e., τ i is distributed as Weibull with parameter ( β 0 , p) . The generalized gamma parametric form implies that τ i ~ Gamma( β 0 , κ , σ ) , i.e., τ i is distributed as generalized gamma with parameter ( β 0 , κ , σ ) . Finally, the assumption for the log-normal regression model is that that τ i ~ Lognormal ( β 0 , σ ) , i.e., τ i is distributed as log-normal with parameter ( β 0 , σ ) . In contrast, with the log-logistic regression model, the assumption is that τ i ~ Log log istic ( β 0 , γ ) , i.e., τ i is distributed as log- 36 logistic with parameter ( β 0 , γ ) . The log-normal and the log-logistic parametric forms differ in that they increase and decrease (in this case, the log-logistic hazard increases and decreases if γ < 1 ). As a result, they may be more appropriate to represent settings in which the hazard rate is going up and then going down, a phenomenon that we would observe in many technology adoption settings where adoption is initially slow then going at a faster rate but eventually slowing down after some time. Taken together the empirical modeling choices offered by the parametric forms of the accelerated failure time model constitute a strong basis for studying a variety of IT adoption phenomena. The time option of the STREG command specifies that the model is to be estimated in the accelerated failure-time metric rather than in the log relative-hazard metric. This option is only valid for the exponential and Weibull models since they have both a hazard ratio and an accelerated failure-time parameterization. For the other three models, the STREG command always estimates the accelerated failure time model. Empirical Model Selection Procedure To determine which model to use, we followed the recommendation made by Akaike [1974]. This paper suggests penalizing each model’s log-likelihood to reflect the number of parameters being estimated and then comparing them. Although the best-fitting model is the one with the largest log-likelihood, the preferred model is the one with the lowest value of the Akaike information criterion (AIC). For parametric survival models, the AIC is defined as: AIC = −2 ln L + 2( k + c ) where k is the number of model covariates and c the number of model-specific distributional parameters [Cleves et al., 2002]. The values of c for the different distributions are shown in Table 12. 37 Table 12. AIC’s c Value for Various Distributions DISTRIBUTION C Exponential Weibull Generalized gamma Log-normal Log-logistic 1 2 3 2 2 We first performed the accelerated failure time estimation using the basic panel data model. Table 13 shows the log-likelihood and AIC values of each distribution model. We can see that the log-logistic model has the lowest AIC value. The Weibull and generalized gamma functional forms were roughly tied for second place, with some distance in terms of the AIC score that separated the log-logistic form. As a result, we selected the log-logistic model. These results practically conform with what the different parametric forms have to offer. As discussed earlier, only the log-normal and log-logistic forms are non-monotonic, which is more in line with our EBPP adoption pattern. And despite the similarities between log-normal and log-logistic, the latter allows it to increase at a slower rate initially with the appropriate value of γ (in this case, STATA reported using a value of γ of 0.138). Table 13. The AIC’s c Value for Various Distributions (Basic Panel Data Model) DISTRIBUTION Exponential Weibull Generalized gamma Log-normal Log-logistic LOG K C AIC LIKELIHOOD -233.24943 -99.06118 -98.717149 -101.67105 -98.379405 11 11 11 11 11 1 2 3 2 2 490.49886 224.12236 225.43430 229.34210 222.75881 38 Full and Revised Panel Data Model Results for the Log-Logistic AFT Model Table 14 shows the estimation results of the basic panel data model using the log-logistic model. Table 14. Results of the Basic Panel Data Model VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Telecom (β5) Metavante (β6) FirmSize (β7) ∆LagFirmProfit (β8) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendorStockPrice (β11) Log-likelihood LR(χ2) Prob > χ2 COEFFICIENT (STD. ERROR) 2.757*** (0.062) 0.030 (0.057) -0.051 (0.057) -0.006 (0.056) 0.101** (0.050) -0.010 (0.066) 0.004 (0.068) 3.18e-09 (0.000) 0.021 (0.045) -0.030*** (0.011) -0.887** (0.376) -0.057** (0.028) -98.379 33.15 0.0005*** Z 44.43 0.53 -0.90 -0.10 2.03 -0.16 0.06 1.05 0.48 -2.61 -2.36 -2.08 Notes: Model: Basic Panel Data Model (Equation 6). Dependent variable in each model is Time-to-Adopt (t). Sample size in each model is N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. LR(χ2) is the likelihood ratio χ2. Several variables have a statistically significant coefficient. They are FirmReach, ∆Lag2QConfDensity, ∆Lag2QDJIA, ∆Lag2QVendorStockPrice. In the revised panel data model, we eliminated the insignificant variables from the model. However, we still retained Northeast, Midwest, South, and Metavante to enable us to compare the results with the revised cross-sectional model. Table 17 lists the AIC value of each distribution of the revised panel data model. Again, log-logistic is the preferred distribution based on the AIC criterion. In addition, the Weibull functional form performs almost as well. 39 Table 17. AIC’s c Value for Various Distributions (Revised Panel Data Model) DISTRIBUTION Exponential Weibull Generalized gamma Log-normal Log-logistic LOG K C AIC LIKELIHOOD -233.71317 -100.06237 -99.77483 -102.53552 -99.510098 8 8 8 8 8 1 2 3 2 2 485.42634 220.12474 221.54966 225.07104 219.02020 In Table 18, we report the results of the revised panel data model. We can see that the same variables are significant. Table 18. Results of the Revised Panel Data Model VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVendorStockPrice (β11) Log-likelihood LR(χ2) Prob > χ2 COEFFICIENT (STD. ERROR) 2.757*** (0.061) 0.051 (0.055) -0.054 (0.057) -0.002 (0.056) 0.122*** (0.046) 0.003 (0.066) -0.030*** (0.011) -0.892** (0.374) -0.061** (0.028) -99.510 30.89 0.0001*** Z 44.98 0.92 -0.94 -0.03 2.62 0.04 -2.64 -2.38 -2.21 Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). Sample size in each model is N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. LR(χ2) is the likelihood ratio χ2. The marginal effects of the coefficients that are statistically significant are as follows: • FirmReach (β4): e0.122 = 1.130 • ∆Lag2QConfDensity (β9): e–0.030 = 0.970 • ∆Lag2QDJIA (β10): e–0.892 = 0.410 40 • ∆Lag2QVendorStockPrice (β11): e–0.061 = 0.941 A marginal effect that is smaller than 1 means that the variable has an accelerating effect, whereas greater than one means the variable has a decelerating effect on the time-to-adopt. Assessing Parameter Heterogeneity and Stability via Pseudo-Replicate Data Sets To estimate the accuracy of our sample statistics, we perform the jackknifing procedure. Jackknifing uses a number of pseudo-replicate data sets, each of which contains all but one of the original data elements [Efron, 1979]. Variations on this approach also permit the analyst to iteratively drop out one, then two, then three observations, etc., up to the point where it becomes impossible to establish coefficient estimates due to the lack of data. In our case, we do three types of jackknifing that we have conceptualized for the purposes of this analysis: backward, forward, and one-period-at-a-time jackknifing: • In backward jackknifing, we start with the full data set, then go backward in time and iteratively take out observations from the latest period, and estimate the remaining sample each time, until the sample becomes too small to provide any meaningful results. With this approach, fewer and fewer more recent observations of technology adoption will be included. (See Table 19.) • Forward jackknifing is the opposite of backward jackknifing. In forward jackknifing, we start with the full data set, then go forward in time and iteratively remove observations from the earliest period, and estimate the remaining sample each time, until the sample becomes too small for further useful analysis. With this 41 approach, fewer and fewer earlier observations of technology adoption will be included. (See Table 20.) • One-period-at-a-time jackknifing involves an analysis process in which we take away one period of observations from the overall sample each time and iteratively estimate the model’s coefficients on the remaining parameters. With this approach, we have an opportunity to remove observations from middle periods in the panel of data, while preserving data from the other periods with which to run the estimation model. (See Table 21.) Table 19. Results of the Panel Data Backward Jackknifing VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample No. of Firms LR(χ2) T 2.757*** 0.051 -0.054 -0.002 0.122*** 0.003 -0.030*** -0.892** -0.061** -99.510 80 30.89*** ≤ T-1 2.693*** 0.109** 0.002 0.052 0.116*** 0.016 -0.029*** -0.803** -0.051* -93.564 79 28.70*** ≤ T-2 2.627*** 0.031 0.006 0.020 0.148*** 0.090 -0.039*** -0.616* -0.026 -72.936 76 28.75*** ≤ T-3 2.561*** 0.090* 0.065 0.075 0.140*** 0.105** -0.039*** -0.539** -0.015 -66.072 75 29.34*** ≤ T-4 2.627*** 0.031 0.006 0.020 0.148*** 0.090 -0.039*** -0.616* -0.026 -61.715 74 27.53*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2. 42 Variable Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample No. of Firms LR(χ2) ≤ T-5 2.564*** 0.046 0.035 0.073 0.119*** 0.115** -0.048*** -0.428 -0.002 -56.978 72 25.46*** ≤ T-6 2.569*** 0.015 0.032 0.049 0.100** 0.130** -0.054*** -0.298 0.014 -51.252 70 26.07*** ≤ T-7 2.458*** 0.101* 0.061 0.145** 0.130*** 0.102 -0.063*** -0.082 0.031 -41.395 65 28.04*** ≤ T-8 2.448*** 0.081 0.084 0.123** 0.083* 0.125* -0.098*** -0.099 0.036 -27.926 57 36.68*** ≤ T-9 2.581*** 0.045 0.015 0.055 0.054 0.021*** -0.273*** -0.131 0.061* 8.275 43 84.41*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2. Table 19 above shows that FirmReach (β4), ∆Lag2QConfDensity (β9), ∆Lag2QDJIA (β10) are consistently significant. Metavante (β6) is also significant but shows some inconsistency. We suspect that this is due to the unbalanced sample (there are much fewer Metavante than Checkfree observations). Table 20. Results of the Panel Data Forward Jackknifing VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample No. of Firms LR(χ2) ALL 2.757*** 0.051 -0.054 -0.002 0.122*** 0.003 -0.030*** -0.892** -0.061** -99.510 80 30.89*** ≥ T-5 2.780*** 0.034 -0.070 -0.019 0.105** -0.012 -0.028*** -0.876** -0.064** -94.186 79 30.24*** ≥ T-6 2.804*** 0.018 -0.083 -0.036 0.088** -0.025 -0.026** -0.981*** -0.068*** -88.984 78 31.26*** ≥ T-7 2.871*** -0.017 -0.116** -0.074 0.038 -0.083 -0.019** -0.539 -0.083*** -74.824 74 27.74*** ≥ T-8 2.882*** -0.023 -0.124** 0.085* 0.033 -0.107** -0.015 -0.332 -0.089*** -59.844 70 30.26*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is 43 Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2. VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample # of Firms LR(χ2) ≥ T-9 2.893*** -0.031 -0.123** -0.081* 0.023 -0.113** -0.011 -0.934*** -0.106*** -43.908 67 45.10*** ≥ T-10 2.899*** -0.031 -0.102*** -0.075** 0.005 0.130*** -0.005 -1.469*** -0.108*** -17.025 59 61.32*** ≥ T-11 2.890*** -0.018 -0.113*** 0.063* 0.017 -0.141*** -0.005 -1.117*** -0.101*** -12.523 55 55.30*** ≥ T-12 2.897*** -0.019 -0.099** -0.067*** 0.022 -0.158*** -0.003 -0.662 -0.112*** -11.704 52 49.25*** ≥ T -13 2.968*** -0.036 -0.114*** -0.077* 0.001 -0.145*** 0.008 -0.129 -0.129*** -0.667 37 43.97*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2. Table 20 shows results similar to those in Table 19. In addition, Midwest (β2) and South (β3) are also significant pretty consistently when we take out observations from the earlier periods. There may be outliers in those two regions that may sway the results. 44 Table 21. Results of the Panel Data One-Period-at-a-Time Jackknifing VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample # of firms LR(χ2) ALL 2.757*** 0.051 -0.054 -0.002 0.122*** 0.003 -0.030*** -0.892** -0.061** -99.510 80 30.89*** T=3 OUT 2.780*** 0.034 -0.070 -0.019 0.105** -0.012 -0.028*** -0.876** -0.064** -94.186 79 30.24*** T=5 OUT 2.782*** 0.034 -0.067 -0.019 0.104** -0.011 -0.028*** -0.992*** -0.065*** -94.737 79 31.34*** T=7 OUT 2.825*** 0.016 -0.087 -0.040 0.071 -0.057 -0.023** -0.424 -0.077*** -87.651 76 24.67*** T=8 OUT 2.766*** 0.046 -0.060 -0.010 0.118*** -0.017 -0.025** -0.763** -0.066** -88.707 76 29.19*** Notes: Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is generally already known. When a time period is not indicated as having been dropped out, it means that there were no observations of adoption occurring in that period. LR(χ2) is the likelihood ratio χ2. VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample # of firms LR(χ2) T=9 OUT 2.785*** 0.039 -0.060 -0.007 0.104* -0.020 -0.024** -1.231*** -0.084*** -88.616 77 39.49*** T=10 OUT 2.782** 0.051 -0.035 0.000 0.100* -0.022 -0.022** -1.237*** -0.065** -86.391 72 30.52*** T=11 OUT 2.734*** 0.075 -0.060 0.019 0.144*** -0.002 -0.031*** -0.582 -0.049* -95.799 76 29.16*** T=12 OUT 2.753*** 0.054 -0.039 0.000 0.131*** 0.009 -0.029** -0.689 -0.066** -99.171 77 27.22*** T=13 OUT 2.771*** 0.063 -0.043 -0.011 0.147*** 0.081 -0.020 -1.115** -0.062* -94.010 65 23.85*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). Sample size in each model is N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and Fstatistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2. 45 VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Sub-sample # of firms LR(χ2) T=14 T=15 T=16 T=17 T=18 OUT OUT OUT OUT OUT 2.730*** 0.069 -0.055 -0.013 0.170*** 0.065 -0.046*** -1.059*** 0.018 -92.758 66 30.31*** 2.765*** 0.062 -0.060 -0.008 0.137*** -0.011 -0.030** -0.990** -0.090*** -92.996 72 35.56*** 2.701*** 0.094 -0.052 0.046 0.158*** -0.010 -0.034*** -0.819** -0.060** -93.991 75 34.50*** 2.763*** 0.044 -0.056 -0.010 0.117** 0.006 -0.034*** -0.837** -0.061** -97.580 78 30.13*** 2.766*** 0.033 -0.080 -0.000 0.110** 0.003 -0.039*** -0.864** -0.054* -94.289 77 30.10*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. Information on R2, adjusted R2, and F-statistic omitted, since model fit is generally already known. LR(χ2) is the likelihood ratio χ2. VARIABLE Constant (β0) Northeast (β1) Midwest (β2) South (β3) FirmReach (β4) Metavante (β6) ∆Lag2QConfDensity (β9) ∆Lag2QDJIA (β10) ∆Lag2QVndrStckPrc (β11) Log-Likelihood Number of firms LR(χ2) T=19 OUT 2.757*** 0.051 -0.054 -0.002 0.122*** 0.003 -0.030*** -0.892** 0.061** -99.510 79 30.89*** T=20 OUT 2.716*** 0.090 -0.016 0.036 0.118*** 0.012 -0.031*** -0.857** -0.055** -96.181 79 29.82*** T=22 OUT 2.695*** -0.027 -0.052 -0.032 0.154*** 0.076 -0.042*** -0.728** -0.036 -79.987 77 34.43*** T=24 OUT 2.693*** 0.109** 0.002 0.052 0.116*** 0.016 -0.029*** -0.803** -0.051* -93.564 79 28.70*** Notes. Model: Revised Panel Data Model (Equation 8). Dependent variable in each model is Time-to-Adopt (t). Sample size in each model is N = 80. The estimated parameter significance levels are: * = p < .10, ** = p < .05, and *** = p < .01. LR(χ2) is the likelihood ratio χ2. 46 Tables 19, 20, and 21 show relatively consistent results for the coefficients in terms of their magnitudes, signs, and significance levels. This confirms the model robustness and the parameter stability of the primary estimate of our sample. DISCUSSION We have examined clustered adoption using deviation from group mean time-to-adopt as the dependent variable in cross-sectional models. We have also employed the accelerated failure time model using panel data econometrics. In this section, we will discuss the results in greater detail, and try to wrap up the case for the observation of clustered adoption relative to our proposed rational expectation theory of technology adoption. As we hypothesized, conference activities have a significant effect on the adoption timing of the firms. As the results of the cross-sectional and panel data model show, an increase in the number of EBPP conferences decreases the time-to-adopt. In this case, we use a two-quarter lag variable, which measures the difference between the number of EBPP-related conferences held two quarters prior to the adoption period of each firm and the number of similar conferences held four quarters prior in the region where the firm is located. The use of lagged values makes sense because we believe it will take some time before information sharing facilitated by the conferences would take effect. The variable FirmReach is significant and has a positive sign, indicating that there is relative clustering with regard to the geographical reach of the firms, thus supporting our hypothesis. In this case, regional firms adopted later than local firms. Based on the adaptive learning perspective, we can argue that regional firms require more learning time due to the fact that they may need to align their expectations with more firms that serve the many regions in which they operate. Another possible explanation is that relative to local firms, regional firms probably need 47 to involve more constituents inside their own organization in their technology adoption decision making, causing the process to take more time. Contrary to our hypothesis, FirmSize does not affect time-to-adopt. We suspect it is because EBPP is still within the affordability range of small to medium firms. So firms of any size can adopt the technology whenever they feel the technology is worth adopting, i.e., whenever they think the benefits would outweigh the costs. Furthermore, firms of all size categories can be found in each region. If large and small firms tend to cluster by region, then it will be difficult to expect that they will also cluster by size. However, we did not find evidence for clustered adoption by industry. We suspect it is because there are fewer telecommunications firms (compared with the number of utilities firms) in our sample set. The reason is that the majority of the telecommunications market nationwide is served by just a few major companies (e.g., AT&T/SBC, Verizon, Sprint, and MCI). Another possible explanation is that while most of the telecommunications firms in our sample are national/regional firms, there are a few that are local, creating an imbalance in the sample. In addition to the theory-bearing variables, we included several control variables in our models to help us explain some of the variation in the dependent variables that is not otherwise explained by the theory-bearing variables. Our results show that the general economic condition (represented by the change in Dow Jones Industrial Average index) significantly impacts the adoption times. A positive increase in the DJIA index pulls the deviation away from the group mean time-to-adopt to the left, meaning that firms adopt earlier in a positive economic condition, holding all other things equal. It suggests that a positive economic condition eases and accelerates technology adoption decision making. 48 The variable ∆LagFirmProfit is not statistically significant although we had initially expected that firms that are profitable will be more likely to adopt a new technology earlier. We believe that the reason why the profitability of adopting firms does not matter in our case is because EBPP is considered a strategic necessity by many firms. Our claim is supported by interviews conducted by Celent [2002] (a Boston-based consulting firm) which revealed that most firms cite competitive pressures and strategic necessity as their primary motivators for offering e-services. We argue that because EBPP is a strategic necessity, it will be adopted by the firms when the other factors tell them to adopt, without really considering whether they have been profitable recently or not. In fact, we could argue that some firms might consider EBPP as a means for cutting costs, offering the potential for them to be profitable or become more profitable. In addition, competitive pressures—cited as the other factor by Celent—prompt firms to constantly benchmark themselves against each other in their comparison group, thus conforming to the information sharing and learning process that we have described to support our theory. Our results also show that ∆Lag2QVendorStockPrice is not consistently significant, in the sense that the results of the different models do not consistently show that this particular variable is statistically significant. We argue that this is because the observation period (1997-2002) is a period when stock prices were very volatile and it would be difficult for the potential adopting firms to base their decisions on the ups and downs of the vendor stock prices. We next discuss the results of the panel data model in the log-logistic regression. Several variables have statistically significant coefficients. They are FirmReach, ∆Lag2QConfDensity, ∆Lag2QDJIA, ∆Lag2QVendorStockPrice. Although they apply to the time-to-adopt, these variables have a similar interpretation as in the cross-sectional model. Therefore, the positive 49 coefficient of FirmReach means that regional firms adopted later than the base case (i.e., the local firms), whereas the negative coefficients of ∆Lag2QConfDensity, ∆Lag2QDJIA, ∆Lag2QVendorStockPrice mean that a positive change in the value of each of these variables will reduce the time-to-adopt, meaning earlier adoption. As discussed earlier, the cross-sectional model is the primary means for testing the clustered adoption hypotheses, whereas the duration model involving panel data is for identifying the instantaneous likelihood of adoption using a specific parametric model. Although the results are slightly different due to the different models employed, we see consistencies in some of the variables such as FirmReach and ∆Lag2QConfDensity. Overall, our results show some evidence for the rational expectations theory of technology adoption that we propose in this thesis. CONCLUSION In this section we will discuss the main findings and theoretical contributions of this research related to our application of rational expectations theory and thinking, as well as our conceptualization of clustered adoption. In addition, we will discuss contributions to practice and insights for managers. Main Findings and Theoretical Contributions This research is among the first that applies rational expectations and adaptive learning theory and thinking to technology adoption issues. The theory allows us to look into the issues in technology adoption that involve multiple parties (multi-partite technology adoption) who seek to align their expectations of value prior to making a decision to adopt. The theory further enables us to offer an alternative perspective by factoring in the complex interactions among 50 different firms over multiple periods, beyond the typical approach that involves modeling only two firms in two periods. More specifically, it takes into account the learning and information sharing that occur between multiple entities over many periods, a phenomenon that generally occurs in the marketplace. Although the alignment of expectations by multiple firms in the presence of the same information will never be the same due to bounded rationality and costs associated with processing information, the theory provides a useful characterization of the underlying dynamics that occur in the market relative to the time-clustered adoption of a technology. The resulting technology adoption theory derived from rational expectations and adaptive learning suggests that due to network externalities, it is in the best interest of each firm within a group sharing similar characteristics and/or serving similar markets to adopt simultaneously (up to the point at which bounded rationality and information processing costs become influential). This leads to our conceptualization of the clustered adoption hypotheses, which are an alternative view to those based on the rational herding behavior theory of Bikchandani et al. [1992, 1998]. Our clustered adoption theory differs in the fact that it assumes that decision makers are willing to collect more information over time and utilize all available information efficiently before making a technology adoption decision. We believe this is more in line with the basic assumption of firm value maximization. The representation of the dependent variable for empirical analysis in the cross-section models deserves special mention. Although we could have alternatively used the actual period number of the time-to-adopt of each firm as the dependent variable, we believe that using the deviation from the mean time-to-adopt allows us to better illustrate clustered adoption, since it is very easy to see how much each firm has deviated from the group mean time-to-adopt. We also 51 contribute to the IS/IT literature by showing how we can use the forward, backward, and dropone jackknifing methods to assess the robustness and the stability of the estimation models’ results, in view of their relatively small sample size. We used the multiplicative model in our cross-sectional analysis since we believe there are interactions among the independent variables, which are comprised of binary/dummy and continuous variables. The dummy variables allow us to see if there are effects of the categories on the deviation from the group mean time-to-adopt. For example, if a dummy variable for a region has a coefficient of a certain magnitude that is statistically significant, then we can argue that there is a relative clustering in that particular region. This is indeed very similar to the idea of using dummy variables to identify whether there are relative groupings of incomes of lawyers, doctors, professors, etc. A statistically significant coefficient of the dummy variable that represents the lawyer category would indicate that lawyers have a certain level of income and each lawyer’s income is expected to be clustered around that level. Contributions to Practice and Insights for Managers IT adoption is an important responsibility of IS and other managers in a firm and expectations about the benefit and cost of the technology being considered always play an essential role in the adoption decision making process. The REH offers a unique perspective by suggesting that in setting their expectations, managers should not base their decisions on the results of the past beyond the point where past information serves as an input for forming expectations about the future. We can see why this perspective is appropriate if we consider the ever-changing nature of information technologies. Technologies that worked in the past may not be relevant anymore today, let alone in the future. 52 For the EBPP technology vendors, the findings in this research suggest that it may be useful for them to identify which firms belong to which groups or subgroups. This is because we believe that each firm tries to learn about a new technology by communicating with and observing the other firms within the same group. This creates an opportunity for a vendor to eventually sign up most, if not all, of the firms in the group in a relatively short period of time. Our clustered adoption theory can be extended to some other nascent industries in which the technologies exhibit strong network externalities characteristics similar to EBPP. Such technologies include voice over Internet protocol (VoIP) and radio frequency identification (RFID). Relative to each of these cases, we would again point out that before making a decision to adopt the technology, firm decision makers will collect information over time and utilize all available information efficiently. And since there are network externalities involved, we should observe clustered adoption to some extent. 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Decision Sciences, 34, 4, (Fall 2003), 643-675. 57 Appendix 1 United States Census Bureau Regions REGION 1 (NORTHEAST) Connecticut Maine Massachusetts New Hampshire New Jersey New York Pennsylvania Rhode Island Vermont REGION 2 (MIDWEST) Illinois Indiana Iowa Kansas Michigan Minnesota Missouri Nebraska North Dakota Ohio South Dakota Wisconsin REGION 3 (SOUTH) Alabama Arkansas Delaware District of Columbia Florida Georgia Kentucky Louisiana Maryland Mississippi North Carolina Oklahoma South Carolina Tennessee Texas Virginia West Virginia REGION 4 (WEST) Alaska Arizona California Colorado Hawaii Idaho Montana New Mexico Nevada Oregon Utah Washington Wyoming Source: U.S. Census Bureau (available at www.census.gov/geo/www/us_regdiv.pdf). 58