DURATION OF INTERNET FIRMS:
A SEMI-PARAMETRIC BAYESIAN SURVIVAL ANALYSIS
Robert J. Kauffman
Co-Director, MIS Research Center
Professor and Chair
Phone: (612) 624-8562; Fax: (612) 626-1316
Email: rkauffman@csom.umn.edu
Bin Wang (contact author)
Doctoral Program
Phone: (612) 624-6041; Fax: (612) 626-1316
Email: bwang@csom.umn.edu
Information and Decision Sciences
Carlson School of Management, University of Minnesota
Minneapolis, MN 55455
Last Revised: October 8, 2003
_____________________________________________________________________________________
ABSTRACT
We test an explanatory model of Internet firm duration after their initial public offerings (IPOs) using a
Cox proportional hazards model and a semi-parametric Bayesian survival analysis. The empirical model
shows that industry-, firm- and e-commerce related variables, such as the entry of competing IPOs and the
selling of digital products or services, can reduce an Internet firm’s hazard rate. In addition, a prosperous
economy, as reflected by a high interest rate, also enhances a firm’s chance of survival. The empirical
results also suggest that the impact of the explanatory variables on different exit types, such as
bankruptcy, merger and acquisition, are different. The results demonstrate a high level of consistency
across the econometrics methods used and illustrate the validity of Bayesian analysis as a technique for
analyzing drivers of Internet firm survival.
KEYWORDS: Bayesian analysis, duration modeling, econometric analysis, electronic commerce,
empirical methods, Internet firms, morphing strategies, survival analysis.
_____________________________________________________________________________________
ACKNOWLEDGEMENTS
We thank the co-chairs of the “Competitive Strategy and Information Technology” mini-track at
HICSS-36, Eric K. Clemons and Rajiv M. Dewan, and two anonymous reviewers for their helpful
comments for a related version of this paper published in the Proceedings of the 36th Hawaii International
Conference on Systems Science, R. Sprague (Ed.), IEEE Computing Society, Los Alamitos, CA, January
2003. We thank the participants of the Information and Decision Sciences workshop at the Carlson
School of Management of the University of Minnesota for their valuable input. We also thank Rajiv
Banker, M.S. Krishnan and other participants at the 2002 Workshop on Information Systems and
Economics for their helpful suggestions on an earlier version of this paper. We are grateful to Tim Miller,
CEO of Webmergers.com, for providing us with the Internet firm failure and shutdown data.
_____________________________________________________________________________________
1
INTRODUCTION
In March 2000, Barron’s magazine published an article that painted a shocking picture of the fate of
many Internet firms (Willoughby, 2000). According to the article, 51 out of the 207 Internet firms in the
study would run out of cash soon, including some highly-touted firms such as Amazon, eToys, Peapod
and CDNow. Even though some firms on the list managed to survive, others did fail (e.g. eToys and
DrKoop.com) or were acquired by other firms (e.g., Peapod and Medscape). The subsequent large-scale
failure in the Internet sector and the depreciation of market value for public Internet firms forced many
Internet companies to come back to reality and reevaluate their business viability.
In fact, according to Webmergers.com (2002), about 900 Internet firms have shut down their Web
sites or declared bankruptcy since January 2000. Many superficial explanations have been offered about
their demise, including blindly-funded and poor business plans (Cavanagh, 2001), lack of revenuegenerating strategies and high operational costs (DeVoe, 2002; Krizner, 2001), over-optimism about
future growth (Cavanagh, 2001), and lavish work environments (Titus, 2001). How should we
understand the Internet shakeout phenomenon we observed during the past couple of years? What are the
factors that have been critical to the survivability of Internet firms?
We first use evolutionary game theory to provide a general framework for understanding “strategic
morphing” of Internet firms and the “natural selection” process that we have observed. We use the word
“morphing” in the general sense here; in fact, it can be any change in a firm’s characteristics and
strategies, such as its products or services, capabilities and resources, market and partnerships. To make
an analogy between business strategy and bio-genetics, these characteristics and strategies are similar to
the genes of an organism. They will determine whether a firm will adapt to its environment to stay alive
or be selected out by the competition. Next, we will discuss the literature on organizational change and
adaptation, which informs us how morphing occurs within an organization. Finally, we will relate the
economic literature on business survival and a recent Information Systems study on DotCom productivity
differences to identify factors that can influence the survival of an Internet firm.
In framing our explanatory model for empirical analysis, we also recognize the challenges ahead of
us. For example, we recognize the turbulence in the stock market and the weakening economy during the
last couple of years as major confounding factors. In a strong economy, even firms with relatively poor
performance will be able to remain in business. On the other hand, in a down-economy when demand is
soft and competition becomes intense, even firms with above-average performance will be touched. They
will face new pressures to remain viable and withstand market valuations that will be lower than what
makes sense in the long run. As a result, it is important to control for the impact of the macroeconomy in
our model. In addition, B2B Internet firms are not represented in our sample. This is due to a lack of exit
cases among the publicly-held B2B firms. As a result, our results may not be generalizable to B2B firms.
2
This is an issue we are unable to resolve in our current study. However, we expect to incorporate B2B
firms in it as more data become available.
Overall, we aim to answer the following research questions:
Can we build an explanatory model based on appropriate theory that adequately explains Internet
firm failures that have been observed to date?
How can evolutionary game theory inform us on Internet firm casualty? What can we learn from
the economic literature on business failure and the recent e-commerce literature on different
business models to identify the relevant industry-, firm- and e-commerce-related factors that are
crucial to the survival of an Internet firm?
What insights and modeling flexibility do Bayesian survival analysis offer?
We apply two semi-parametric survival analyses techniques—the Cox proportional hazards model
and Bayesian survival analysis—to test a theoretical model of Internet firm duration after their initial
public offerings (IPOs) of stock. Bayesian analysis offers a number of advantages, such as the capability
to make inferences even with a small sample size, the possibility of incorporating historical data, and
more flexibility for model building and analysis. The methods are widely used in the public health field
on the analysis of disease development and treatment effectiveness. In addition, our application of
multiple econometric methods allows us to cross-validate our results. Following Barua, Pinnell, Shutter,
Whinston and Wilson (2001), who defined “DotCom firms” as digital intermediaries or commerce firms
that generate 95% or more of their revenues on the Internet, we use a 90% cutoff, and restrict our sample
of Internet firms to intermediaries that provide e-marketplaces and firms that sell products and services
over the Internet.
Our empirical results indicate the entry of additional competing Internet firms through IPOs can
enhance an incumbent public Internet firm’s survival likelihood. In addition, firms selling digital
products or services via the Internet are more likely to survive than those selling physical products or
services. Interest rate, which captures the impact of the overall economy on firm performance, is also
positively related to survival. Our results also reveal the differential impact of the explanatory variables
on different exit types, such as bankruptcy, merger and acquisition. While the entry of additional
competing Internet firms into the stock market and the selling of digital goods can reduce a firm’s
likelihood of bankruptcy, size is the major factor that determines mergers and acquisitions. The high
level of consistency of our results across the two methods used suggests that Bayesian analysis is a valid
technique for the analysis of Internet firm durations. We view this as a methodological contribution to
Information Systems (IS) research, as well.
3
LITERATURE AND THEORY
We first use evolutionary game theory to provide a conceptual framework for the understanding of
Internet firm morphing and survival. Next, we cite organizational change and adaptation literature to
address the question how mutations occur in a firm. Finally, to identify the factors that relate to the
duration of an Internet firm after its IPO for our empirical model, we review previous economic research
on business survival and the recent IS and e-commerce literature on different business models. The first
stream of research informs us that both industry- and firm-related factors can affect the success and
failure of a firm. The second stream of research suggests the existence of productivity and stock return
differences between different types of Internet firms.
Evolutionary Game Theory
Evolutionary game theory focuses on the evolutionary path of organisms that compete in an
environment and the resulting equilibrium outcomes (Maynard Smith, 1982). The fundamental concepts
in evolutionary game theory are genes, mutation, the environment, competition, time and the outcome.
Genes are the key construct that differentiates individuals in a population. They determine the
characteristics an organism possesses and the strategies it employs in the game. Genes can also change in
a process called mutation due to some random stimuli either within the organism or from the
environment. Because there are only limited resources in the environment, all organisms compete for
these limited resources. Those with superior genes will outperform those with inferior genes. Over a
period of time, the outcome is the survival of the fittest. This evolutionary cycle repeats as new mutation
occurs and the survival organisms compete among themselves.
The survival of Internet firms is similar to the evolutionary process we described above. Different
firms possess different characteristics (e.g., products and target markets), resources, capabilities and
strategies. These are essentially the genes that differentiate the firms from each other. In the competition
for the limited resources in the marketplace such as customers, suppliers and financial capital, those that
occupy advantageous resources or possess unique capabilities are better positioned for survival under
tough competition. In contrast, those that adopt inferior strategies or deliver poor performance will be
selected out by the competition, which results in the Internet firm failure we observe.
Instead of assuming fully-informed and rational individuals like game theory does, evolutionary game
theory posits that individuals are not always rational. Instead, they come to realize which strategy
generates higher payoff through a learning process by trial-and-error (Samuelson, 1998). In the context
of Internet firm survival, mutation occurs when a firm discards an inferior strategy and adopts another one
that expects to generate higher payoff. This is also the morphing process that we refer to where firms
change their organizational characteristics or strategies to adapt to the marketplace.
4
Evolutionary game theory informs us that organizational characteristics and strategies are the genes
that can determine a firm’s ultimate survival in the digital marketplace. Through mutation, firms actively
adapt to the competition and adopt higher payoff strategies through trail-and-error. However, how does
mutation actually occur in an organization? What genes are important to the survival of an Internet firm?
We next discuss the literature on organizational adaptation and change, the economic literature on
business survival, and some recent IS and e-commerce research on business models. Finally, we provide
a synthesis of theories that we reviewed.
Organizational Adaptation and Change
A powerful concept in evolutionary game theory is mutation. It is through this process that firms
implement the results of their learning process and adopt strategies that generate higher payoff. However,
how does mutation actually occur in an organization? We believe the literature on organizational
adaptation and change provides an answer.
In an effort to bridge the differences among the incremental, transformational and ecological theories
of organizational evolution, Tushman and Romanelli (1985) introduce the punctuated equilibrium theory
of organizational change. According to them, organizations go through periods of reorientation and
convergence alternatively. Reorientations are the periods during which dramatic changes occur and there
are fundamental shifts in an organization’s strategy, power, structure or control. These periods are
relatively short. Convergent periods are much longer than reorientations. Changes during these periods
are characterized by incremental modifications to existing organizational form and structure. The ending
of one period and the starting of another one are determined by factors in the external environment and
within the organization. When there are fundamental changes in the social and technological
environments that deprives a firm of its fit with the environment, it will be forced to undergo a period of
reorientation. On the other hand, when a firm constantly performs poorly, reorientation is also necessary
even if there is no dramatic change in the external environment. During the convergent periods, a firm
engages in incremental changes to adapt to changes in the environment. Organizational changes affect
the strategies an organization will employ, which ultimately determines performance and survival
together with factors from both external and internal environments.
In another study of organizational adaptation and change, Rindova and Kotha (2001) compare the
trajectory that Yahoo! and Excite went through from Internet search engines to portal sites from 1994 to
1999. Yahoo! and Excite both started as Internet search engines. However, as the number of search
engines increased, a search capability could no longer differentiate the two sites from their competitors.
To keep traffic on their sites, the two firms morphed into destination sites and tried to differentiate
themselves through branding. Next, the two firms morphed into portal sites to provide a full range of
functionality including search, contents, communication and commerce. Along this path of
5
organizational changes, Yahoo! managed to stay one step ahead of Excite and sustained the competitive
advantage that it would otherwise have lost had it stopped morphing and allowed Excite and other sites to
catch up. Based on these observations, the authors introduce the concept of “continuous morphing” to
depict the process through which firms in a hyper-competitive environment try to dynamically sustain
their transient competitive advantage. By constantly changing their organizational form, firms can
regenerate its competitive advantage and succeed in the marketplace.
Overall, the literature on organizational change and adaptation suggests that organizations constantly
go through changes to sustain competitive advantage, generate higher performance, and remain
competitive.
Business Survival
Both industry- and firm-related factors can influence the survival of new businesses. Industry
characteristics include the technical regime of the industry and rate of new firm entry. Audretsch (1991,
1995) and colleagues (Audretsch and Mahmood, 1991, 1995) find that due to the high initial setup costs
and the difficulty in obtaining new technology for reaching the optimal scale of operations in an industry
that has a routinized regime, new entrants are less likely to survive. On the other hand, in an industry that
is characterized by an entrepreneurial regime where new entrants possess innovative advantage over
market incumbents, new entrants are more likely to survive. Honjo (2000) finds that a high entry rate
results in a high failure rate among new businesses due to more fierce competition.
Firm factors that influence survival include financial capital, startup size, post-entry firm size, and
founding time. Audretsch and Mahmood (1991) find manufacturing firms with a larger startup size are
more likely to survive. They argue for firms with a larger startup size, the gap between their size and the
minimum efficient scale (MES) for the industry is smaller, resulting in a higher chance of survival.
Honjo (2000) finds that firms with more financial capital and larger size incur lower failure rate. The
unique aspect of his results is that when both financial capital and size are incorporated into a model, only
financial capital is significant whereas both are significant if they are included in the model separately.
Based on the observation that smaller firms tend to have limited financial resources, Honjo concludes that
previous research that captures a significant relationship between smaller size and higher failure rate
actually reflects the impact of financial capital. He also finds that firms established around a market crash
are less likely to survive. Even though many empirical results suggest large firms are less likely to fail,
there are also contradictory results. For example, Das and Srinivasan (1997) find larger startup size is
associated with higher risk of exit in the Indian computer hardware industry. Thus we do not hypothesize
the direction for the relationship between firm size and survival.
Hensler, Rutherford and Springer (1997) analyze firm duration after their IPOs in the stock market.
The factors that can enhance a firm’s survival are firm size, the age of the firm at the offering, the initial
6
return on investment in the stock issue, the number of IPOs co-occurring in the market, and the
percentage of the firm owned by insiders. In contrast, factors such as a higher average price level in the
stock market at the time of IPO and a higher number of risk characteristics associated with the firm as
reported in their prospectus lead to higher risk of failure. The authors also find that firms in the optical or
pharmaceutical industries enjoy a longer survival time than firms in industries such as computer and data,
wholesale, restaurant, and airline.
Related to the empirical results are the econometric method used to analyze business failure data. The
method the above-mentioned economic research employs is survival analysis, especially the Cox
proportional hazards model (Cox, 1975). Survival analysis is widely used in public health to examine
drug effectiveness in the treatment of diseases. Audretsch and colleagues (Audretsch, 1991, 1995;
Audretsch and Mahmood, 1991, 1995) introduced this method to the analysis of firm duration. Since
them, it has been a widely accepted method for the analysis of business failure (Orbe, Ferreira and NunezAnton, 2001). As a result, we will also use the Cox proportional model as one of the two econometric
methods for our data analysis and we will discuss this technique in greater detail later in the paper.
Assessment of Internet Business Models
Barua, Whinston and Yin (2000) examine the productivity difference between two types of Internet
firms: digital Internet firms that sell digital products and services and directly deliver them over the
Internet, and physical Internet firms that use the digital channel to sell physical goods but deliver the
products or services through the physical world. By analyzing the production data of 199 DotComs
during the fiscal year of 1998, they find that digital firms achieved higher productivity levels. They argue
that the difference is due to a higher level of digitization of business strategies and processes at digital
firms. Because of the close-to-zero marginal cost for producing an additional copy of digital goods and
the equally small delivery cost via the Internet, digital firms incur much lower operational cost than
physical firms, which allow them to enjoy higher productivity gains. And because productivity is closely
related to profitability, which in turn influences survivability, we expect digital Internet firms to be more
likely to survive than physical firms.
In another study on the impact of e-commerce related announcements, Subramani and Walden (2001)
find that cumulative abnormal returns to shareholders are higher for B2C e-commerce initiative
announcements than those for B2B announcements. In addition, the cumulative abnormal returns to
shareholders for tangible goods announcements are higher than those for digital goods.
A Synthesis of the Literature
We cite multiple theories and results from empirical research in the previous sections. Instead of
viewing them as competing theories, we think they are complementary to each other. They share one
common goalto explain performance. In evolutionary game theory, performance is reflected in the
7
survival or distinction of an organism. In organizational change and adaptation, intermediate level of
measurements such as competitive advantages and organizational capabilities are often used as indicators
of performance. In the economic literature of business survival, survival or failure is the measure of
performance. And finally, in the two e-commerce studies on different business models, productivity and
stock prices are used as the measures for performance.
There are also unique aspects to each theory or empirical results. For example, they examine
performance at different levels. Evolutionary game theory examines the evolution of organisms at the
population level. Survival is viewed as a result of competition among individuals. Organizational change
and adaptation more often focuses on the trajectory of changes a firm goes through and the internal and
external factors that result in these changes. There can be comparisons across multiple firms, but changes
within a firm over time are more often the main concern.
Even though the economic literature on business survival and the two e-commerce business model
studies also focus on the firm level, their treatment of firms is different from the organizational change
perspective. Rather, they treat firms as black boxes that take input from the environment and generate
some output. The characteristics of the firms are usually some observable measures from an outsider
point of view. By focusing on different levels of analysis, these theories complement each other to
provide a more holistic picture of organizational performance and survival. Evolutionary game theory
depicts a general framework for our understanding of Internet firm survival. It informs us that genes and
mutations are crucial. Organizational change and adaptation theory informs us how mutations actually
occur with an organization. And finally, the economic literature on business failure and the assessment of
DotCom productivity difference and sock price change point out some factors that are either genes that
determine survival (e.g., the products a firm sells, size, and percentage owned by insiders), payoffs from a
firm’s strategies (e.g., financial capital), and significant environmental factors (e.g., technological regime
of the industry, rate of new firm entry, and industry).
THEORETICAL MODEL
In this section, we develop a new model for the duration of Internet firms that incorporates some of
the theoretical perspectives that we discussed in the prior section.
Modeling Preliminaries
Based on the above literature, we identify three types of factors that are crucial to the survival of a
new business. They include industry and market characteristics, firm characteristics and e-commercerelated characteristics.
Industry and Market Characteristics. The characteristics are the technological regime of the
industry, the rate of new firm entry, the number of IPOs co-occurring at the time of the offering, and stock
8
market index levels at the time of the offering. These factors are indicators of the external environment in
which firms reside and the level of competition in the industry or market.
Firm Characteristics. Financial capital, startup size, post-entry firm size, founding time, the age of
the firm at the time of offering, the initial return on investment in the stock issue, and insider ownership
have all been found to be explanatory of firm survival. Among these, startup size and post-entry firm size
measure the gap between a firm’s size to the industry MES. Insider ownership is an indicator of
alignment between management and shareholder interests. When the percentage of insider ownership is
high, more shares are held by the management team of a firm and the interests between the management
and shareholders are more likely to be the same. Financial capital and the initial return on investment in
the stock issue reflect the firm’s performance. Finally, the age of the firm at the time of the offering is
associated with a learning effect that makes a mature business more likely to survive.
E-Commerce-Related Characteristics. They include the business model and the types of products
or services provided. We expect Internet firms selling digital products to be more likely to survive than
those selling physical goods. Hensler et al. (1997) find an industry effect in their analysis of the duration
of a public firm after its IPO. We expect there to be a difference among Internet firms in different
industries as well. Because the electronic marketplace is still in its infancy and there are only a limited
number of public Internet firms in each industry, we use a more general categorization—business
model—which can be B2B, B2C or B2B2C. B2C firms are Internet firms that have consumers as their
customers. B2B firms are those that have other companies as their customers. And B2B2C firms target
both consumers and other businesses and may act as intermediaries.
The combined effects of the above three types of factors, together with condition of the economy,
determine the survival of an Internet firm. For example, in a prosperous economy or an industry with
high growth, even firms with below average performance may be able to survive. On the other hand,
more firms will be facing the pressure to remain viable under a weak economy.
A Theoretical Model for Internet Firm Survival
As an initial attempt to examine the impact of various factors on Internet firm survival, we propose a
model that encompasses the above three types of factors and that will permit empirical testing. We
include in our model variables that are most often used in previous research on business failure (such as
financial capital and firm size), and discard those variables that are not directly applicable in the Internet
firm context. For example, Audretsch and Mahmood (1995) define the technological regime of the
industry as the total innovation rate for the industry. It is more relevant for the manufacturing sector and
is not directly applicable in our research context. Our conceptual model of Internet firm duration after
IPO is as follows:
Prob(Survival) = f (NewFirmEntryRate, FinancialCapital, FirmSize, BusinessModel, ProductSold)
9
The probability of a firm to continue in operation up to a certain point in time is a function of five
variables: the rate of new firm entry, financial capital, firm size, business model, and the products or
services sold by the firm. Specifically, the factors that are positively related to survival include financial
capital and the selling of digital goods. A high rate of new firm entry will exert high competitive pressure
on market incumbents and is expected to increase the likelihood of failure. Because of conflicting results
from previous empirical research on the relationship between firm size and survival, we do not
hypothesize any direction for this relationship. And, because of the lack of previous research on the
effect of business model on firm performance, we do not specify any direction for the relationship
between business model and survival either. In addition, we will also include a control variable to adjust
for the impact of the macroeconomy.
We will further develop our theoretical model in the Measurement and Data Collection section. But
before we go to the definitions of the variables and the modeling details, we first introduce the basic
concepts that are generally applied in survival analysis econometrics and discuss two other semiparametric survival analyses techniques that we will use.
ECONOMETRIC METHODS
Following previous econometric research on business survival, we will use survival analysis to test
our theoretical model. In addition to using the typical Cox proportional hazards model that is frequently
used, we also introduce another method: semi-parametric Bayesian survival analysis. We will use this as
a means to cross-validate our results with the Cox model. Compared to the “frequentist approach” that is
associated with the Cox proportional hazards model, Bayesian analysis permits the analyst to fit more
complex survival models and incorporate information associated with historical data. One application
occurs when data are obtained before and after some treatment or regime change in the environment.
Another application is motivated by a need to more effectively handle missing data, and to enhance the
extent of available modeling information by retaining observations (Ibrahim, Chen and Sinha, 2001).
This approach has been applied in the public health field to clinical trials (Abrams, Ashby and Errington,
1996) and for testing time-varying coefficients in disease epidemiology (Sargent, 1997).
Survival Analysis Concepts. We first test our explanatory model using a semi-parametric survival
analysis technique called the Cox proportional hazards model (Therneau and Grambsch, 2000), and then
we apply a semi-parametric Bayesian survival analysis and compare the results from the two methods
(Ibrahim et al., 2001). There are four fundamental concepts that characterize survival analysis: duration,
censoring, the hazard rate, and the survival function. Beginning from a starting time for an observation or
for the data set as a whole, duration is either the time an event occurred or the time that the study ended,
if the subject is still at risk at that time. In the second case, the observation is said to be right-censored:
10
the event has still not happened to the subject. The hazard rate is the instantaneous failure rate at time t,
assuming survival up until that time. Finally the survival function characterizes the probability of
observing a duration time longer than t (Le, 1997).
Base Model. The Cox proportional hazards model applies a semi-parametric analysis approach. It
incorporates two components in the hazard function at time t: a non-parametric baseline hazard, h0 (t),
associated with age of the firm, and a parametric portion determined by a set of explanatory variables that
vary across firms over time:
h(t , X , β ) = h0 (t ) e
Xβ
(1)
In this expression, X is a vector of explanatory variables and β is a vector of parameters to be estimated.
The cumulative baseline hazard function is given by:
t
H0(t)= ∫ h0 ( y )dy
(2)
0
Based on the above formula, we can derive the partial likelihood function as:

n
 e xi β
L p (β ) = ∏ 
xjβ
i =1  ∑ e
 j∈R (ti )
ci


 ,


(3)
where ci is 0 if the observation is censored, 1 otherwise. Parameters are estimated using maximum
likelihood estimation methods without specifying the baseline hazard function.
Beyond Cox: Bayesian Duration Analysis. Bayes Theorem allows the update of the distribution of
a parameter given some observed data and prior knowledge about the distribution of the parameter. As a
result, Bayesian analysis is especially helpful in research contexts where historical data are available as a
good starting point for parameter estimate. In our case, even though there are no historical data available,
Bayesian analysis offers the advantage of getting stronger results for significance testing and confidence
internal estimates, even where there are asymmetrically-distributed parameters. This is especially
important since in many cases the parameters are not normally distributed and results using the frequentist
methods might be biased.
More formally, Bayesian analysis in this context specifies the posterior distribution of a parameter θ
given the observed data, D, and a prior distribution for, π(θ):
π (θ | D) =
L(θ | D)π (θ )
∫
Θ
L(θ | D)π (θ )dθ
.
(4)
The θ here is the parameter we want to estimate. π(θ) is the known prior distribution for θ, and π (θ | D)
is the updated posterior distribution for θ. L(θ | D) is the likelihood function for θ given observed data
D, with Θ the parameter space of θ (Ibrahim, Chen and Sinha, 2001). Previous data are incorporated into
11
the posterior distribution through π(θ) and the current data contribute to the posterior distribution through
L(θ | D). A Markov chain Monte Carlo (MCMC) simulation technique called the “Gibbs Sampler”
algorithm is frequently used to generate the parameter estimates (Smith and Roberts, 1993).
Bayesian Model Specification. Similar to the Cox proportional hazards model, there are also two
components in the hazard function in semi-parametric Bayesian survival analysis. The parametric part is
determined by a set of factors that vary across firms and over time. A non-parametric baseline hazard
function is also included. However, semi-parametric Bayesian survival analysis differs from Cox
proportional model in that it assumes the baseline hazard function follows a certain prior process.
Following Ibrahim et al. (2001), we employ the gamma process prior for the cumulative baseline
hazard function, H0(t): H0 ∼ GP(c0H*, c0), where c0 is a weight parameter of the mean of the gamma
process, and that H* is an increasing function with H*(0)=0. We further assume that H* is exponentially
distributed with a constant hazard rate r0. As a result, H*(y) = r0 y. Under non-informative censoring, the
counting process increment (i.e., number of subjects having events) during the time interval [t, t+dt) is
dNi(t) ∼ Poisson (Ii(t)dt), where Ii(t)dt is exp(β’xi, t)dH*t, if subject i is still at risk at time t and 0
otherwise.1 By specifying the initial values for c and r0 and giving the prior distributions for β and H*,
we can then use Gibbs sampling to generate the posterior distribution and estimate the β ’s.
We next discuss our data collection process, sample characteristics, and variable definitions.
MEASUREMENT AND DATA COLLECTION
In this section, we first discuss the data collection process and provide some descriptive statistics of
our sample. We then give detailed operationalizations of our theoretical constructs and definitions of our
variables. Finally we present the correlation matrix for our independent and control variables.
Data Collection
Due to the unavailability of financial information for privately-held Internet firms, there are only
public Internet firms in our sample. In addition, we eliminated those that were traditional firms at the
time of their IPOs and that later switched to become electronic intermediaries or e-commerce firms. We
used multiple data sources, including FIS Online, corporate filings with the Securities and Exchange
Commission (SEC), the EDGAR Online IPO Express and COMPUSTAT to gather relevant data. We
first used keywords such as “Internet,” “electronic commerce,” “Web” and “dot com” to search in FIS
1
Non-informative censoring occurs when the lack of observation of an event for a given subject fails to affect the
information provided by the likelihood function based on observing other events up to time t. The kinds of noninformative censoring are: (1) random censoring, where the subject’s lifetime and survival time are independent
random variables; (2) fixed censoring, where the subject has a maximum observation time that is fixed in advance of
the study; (3) Type I censoring, where a sample of subjects is observed for a fixed amount of time; and finally, (4)
Type II censoring, where each subject may have a different fixed observation time, but they are pre-determined. In
this research, only fixed censoring applies, but it is enough to establish the counting process increment.
12
Online to identify Internet-related firms, which resulted in about 3000 firms. We next read the
descriptions of these firms to identify those that met our criterion of being an Internet firm. For those that
had both online and offline operations, we searched their annual reports at EDGAR Online to determine if
they had 90% or higher of their revenues generated online. We dropped those firms without this
information in their annual reports. For IPO date information, we searched multiple sources, including
FIS Online, EDGAR Online IPO Express and corporate filings at the SEC Web site. Additional firms
were removed from our sample because either their IPO dates were missing or they were not Internet
firms at the time of their IPOs. We then searched COMPUSTAT for quarterly and annual financial
information and firm size figures. Our sample consists of 103 publicly-traded Internet firms. Three types
of Internet firms are represented in our sample: B2C, B2B and B2B2C firms. Table 1 provides
descriptive statistics of our sample. (See Table 1.) Later in our analysis, we drop an additional 9 firms
due to missing exit cases or unavailable two-quarter-lagged financial information.
Table 1. Descriptive Statistics
FIRM
TYPE
B2C
B2B
B2B2C
Total
NUMBER
OF OBS.
67
8
28
103
DURATION
(QUARTERS)
Mean
9.25
9.50
10.43
9.60
Std. Dev.
4.02
4.78
3.80
4.00
QUARTERLY
REVENUES
($MM)
Mean
Std. Dev.
43.73
108.67
16.08
12.97
24.31
36.87
35.86
89.03
FIRM SIZE
(# EMPLOYEES)
Mean
483
291
382
438
Std. Dev.
1023
240
625
881
Operationalizations of Constructs and Definitions of Variables
Dependent Variables. We have two dependent variables in our empirical model: durations of the
observations in the sample, and a binary variable indicating whether the firm is censored or had the
default event such as bankruptcy, merger and acquisition. Duration is defined as the elapsed number of
quarters since a firm’s IPO up to the time to when it ceased to operate as an independent corporation, or
the ending of the study period if the observation is censored, whichever occurs earlier. In the first set of
model tests, where we do not differentiate exit types, the indicator variable is 1 if the firm exited due to
bankruptcy, merger or acquisition, and 0 if it was censored at the end of the study period. In the second
and third sets of model tests, the indicator variable is 1 if the firm had the default event, 0 otherwise. The
default event is bankruptcy in Model 2A, merger in Model 2B, acquisition in model 2C, and bankruptcy
or acquisition in Model 3. Table 2 summarizes the definitions of our dependent variables. (See Table 2.)
13
Table 2. Definitions of Model Variables
VARIABLE
DEFINITION
Dependent Variables
Duration
Number of quarters from the IPO date to time of bankruptcy, merger,
acquisition, or the end of the study period, whichever occurs sooner
Status
Model 1A/1B: 1 if the firm filed for bankruptcy, merged with other
firms, or was acquired; 0 if censored.
Model 2A: 1 if bankrupt, 0 otherwise.
Model 2B: 1 if merged with another firm, 0 otherwise.
Model 2C: 1 if acquired, 0 otherwise.
Model 3: 1 if bankrupt or acquired, 0 otherwise.
Independent Variables—Industry-Related
IPOEntry
Number of competing Internet firm IPOs in the quarter
Independent Variables—Firm-Related
Size
Number of employees (in thousands)
Capital
Amount of financial capital the firm possesses (in million dollars)
E-commerce-related
Product
1 if firm sells digital goods or services, 0 if physical goods or services
B2B2C
1 if the firm is a B2B2C firm, 0 otherwise
Independent Variables—Control
InterestRate
Six-month U.S. treasury bill interest rate (in percent)
Independent Variables. We incorporate three types of independent variables: industry, firm and ecommerce. The industry-related variable in our model is NewFirmEntryRate. No data for new firm entry
for each industry for the digital marketplace were available, so we proxy it using the number of Internet
firm IPOs in each quarter. We define this for the IPO firm’s sector (i.e., the firm is a B2C, B2B or B2B2C
company). In addition, we only calculate relevant competing IPO entries. For example, a B2C firm
competes with other B2C and B2B2C firms, while a B2B2C firm competes not only with those firms but
also with B2Bs.
Firm-related variables include Size and FinancialCapital. Size is operationalized as the number of
employees in each firm, and the unit of measurement is 1000. Financial capital is calculated by deducting
a firm’s liability from its assets. This figure is reported in millions of dollars.
The two e-commerce related variables are Product and Business model. Product is operationalized as
a dummy variable, with those firms selling digital goods (e.g., portal sites, e-intermediaries) indicated by
1 and those selling physical goods (books, CDs, clothing, etc.) indicated by 0. Even though there are
three types of e-commerce firms (B2B, B2C and B2B2C), we dropped all eight B2B firms from our
14
empirical data analysis because of the lack of bankruptcy, merger and acquisition instances during our
data collection period. As a result, there are only two types of e-commerce firms in our sample for the
data analysis. We hence operationalize business model as a dummy variable with 1 for B2B2C firms and
0 for B2C ones.
Control Variables. To control for the impact of the macroeconomy, we included interest rate and
operationalize it as the six-month U.S. Treasury bill interest rate (Audretsch and Mahmood, 1995).2
We use quarterly data from 1996 to 2001. However, firm size is measured annually since public firms
only report this figure annually. We use one quarter-lagged data to predict the survival status of an
Internet firm. The only exception is financial capital. We use two quarter-lagged data since financial data
in the quarter immediately before failure usually are never available as SEC filings.
Starting from the initial 103 firms, we dropped 8 B2B firms and one other firm that existed for only
two quarters hence two-quarter-lagged financial data was not available. The final sample size is 94,
including 42 exited firms (with 13 bankruptcies, 16 merged, and 15 acquired). No two explanatory
variables are correlated beyond the 0.50 level.3 We present the correlation matrix in Table 3. (See Table
3.) Moreover, no variable has a Belsley Kuh Welsch condition index larger than 20 (Greene, 2000);
multicollinearity is not a problem.
Table 3. Correlation Matrix for the Independent and Control Variables.
IPOEntry
IPOEntry
Size
Capital
Product
B2B2C
InterestRate
1.000





Size
-0.090
1.000




Capital
Product
-0.036
0.308
1.000



-0.017
-0.233
0.053
1.000


B2B2C
0.119
-0.051
0.076
0.257
1.000

InterestRate
0.106
-0.080
0.018
-0.047
-0.019
1.000
MODEL AND RESULTS
We next test three models using the two semi-parametric approaches described above. First, we test
an explanatory model of post-IPO Internet firm duration without distinguishing different exit types. In
this test, we view bankruptcy, merger and acquisition all as instances of “default,” where a firm ceases to
exist as an independent corporation. Second, in our next set of modeling tests, we recognize that
bankruptcies, acquisitions and mergers might be due to different reasons. Although bankruptcies are
generally viewed as indicators of business failure, the drivers for mergers and acquisitions are more
2
Audretsch and Mahmood (1995) also used UnemploymentRate as a control, with a -0.62 correlation with
InterestRate in our sample. We dropped it.
3
It is important to note here the number of data pairs used to calculate the correlation matrix is not 94. Because
each firm existed for multiple quarters and all the independent and control variables were recorded during each
quarter, each firm contributed multiple data pairs to the calculation.
15
complex. They can be either the shareholders’ strategy to maximize their return or the outcomes of weak
operating results that diminishes a firm’s possibility to exist as an independent entity. As a result, we
differentiate the different exit types and test competing risks (Klein and Moeschberger, 1997) of exit due
to bankruptcy, merger, and acquisition. Third, we test different degrees of failure wherein we rank the
outcomes by degrees from bankruptcy to acquisition, to merger, and to survival.
The hazard function for estimation of the base model parameters is:
h(t ) = h0 (t ) exp[ β 1 IPOEntryt −1 + β 2 Sizet −1 + β 3 Capital t − 2
+ β 4 Pr oduct + β 5 B 2 B 2C + β 6 InterestRatet −1 ]
(5)
Time-varying covariates include IPOEntryt-1, Sizet-1, Capitalt-2, and InterestRatet-1. To avoid a Gibbs
sampling trap message displayed in the WINBUGS software that we used and to guarantee sufficient
iterations to obtain convergent results, we standardized all time-varying covariates.4 The value for a
covariate at time t is first subtracted by the mean for this covariate, and then divided by its standard
deviation. There is no standardization necessary for the two dummy variables: Product and B2B2C. We
next report our results using the Cox proportional hazards model and the Bayesian semi-parametric
survival analysis. We differentiate the hazard rate from the hazard ratio. The hazard rate as the
instantaneous risk that an event will occur at time t assuming that a subject has survived up to time t. The
hazard ratio is the marginal effect of a one unit increase in the explanatory variable on the hazard rate via
exp(βi), where βi is the coefficient estimate.
No Differentiation Among Different Default Types. We first report our results from the Cox
proportional hazards model and then discuss our results using the semi-parametric Bayesian survival
analysis.
Cox Proportional Hazards Model Results. Table 4 summarizes our results. Columns 2 through 5
represent results with the standardized time-varying covariates, and the last two columns are results that
are transformed back to their original units of measurement. Our model has an overall likelihood ratio of
21.74 (p < .01), indicating an acceptable fit. The parameter estimate for IPOEntry is -0.0747, and is
significant at the .10 level. This is consistent with a hazard ratio of 0.928, and indicates that with one
additional new Internet firm IPO, the hazard rate of an existing publicly-traded Internet firm falls to
92.8% of its original value. 5 Product is the only firm-related factor that is significant, with a parameter
estimate of -0.871 (p < .05). The estimated hazard ratio is 0.419; thus the hazard rate for an Internet firm
4
BUGS (for “Bayesian Inference Using Gibbs Sampling”) and the version of WINBUGS 1.3 that we used for
estimating are components of a statistical software package that provide the means to use Markov chain Monte
Carlo simulation methods for complex Bayesian models. See www.mrc-bsu.cam.ac.uk/bugs/winbugs/
contents.shtml for additional information.
5
We initially included percent change in the NASDAQ Composite Index, whose correlation with IPOEntry was
0.58. So, we removed it from the data analysis.
16
selling digital goods is about 41.9% of that for an Internet firm selling physical goods, ceteris paribus.
The control variable, InterestRate, is significant with a parameter estimate of -0.378 (p < .01). The hazard
ratio is 0.685, indicating that with a 1% increase in InterestRate, the hazard rate of a public Internet firm
falls to 68.5% of its original value. Firm Size and financial Capital are not significant. Even though
B2B2C firms have lower hazard rates as indicated by the estimated hazard ratio of 0.685 over B2C firms,
this parameter is not significant, as well, as so we cannot conclude anything from this.
Table 4. Cox Proportional Hazards Model Results: No Differentiation Among Failure Types
(Model 1A, N=94, 44 Defaults)
VARIABLE
IPOEntry
Size
Capital
Product
B2B2C
InterestRate
PARAMETER STANDARD
ESTIMATE DEVIATION
-0.485
-0.354
-0.169
-0.871
-0.378
-0.235
0.254
0.253
0.435
0.351
0.380
0.110
χ2
3.649*
1.957
0.152
6.165**
0.990
4.572**
HAZARD
RATIO
0.616
0.702
0.844
0.419
0.685
0.791
TRANSFORMED-BACK
RESULTS6
Parameter
Hazard
Estimate
Ratio
-0.075
0.928
-0.454
0.635
-0.0002
1.000
-0.871
0.419
-0.378
0.685
-0.378
0.685
Note: Likelihood ratio statistic for model significance: 21.74, p < 0.01; significance levels for explanatory
variables: * = p < 0.10; ** = p < 0.05; *** = p < 0.01.
In addition to age-based semi-parametric analysis using the Cox proportional hazards model, we also
performed a calendar time-based analysis.7 When we do not differentiate different exit types, Product
and IPOEntry are significant at the .05 level. The parameter estimate for Product is 0.679, indicating the
6
These transformed-back results were obtained by dividing the parameter estimate for the time-varying covariates
by the standard deviation used when standardizing the variables. Because no standardization was necessary for
Product and B2B2C, the parameter estimates remain unchanged. The transformed-back results we report later in
this paper were obtained similarly.
7
Following Honjo (2000), we develop a multiplicative hazards model based on calendar time. Instead of comparing
firms at the same age, we now compare them at the same calendar time. All observations are now aligned along
calendar quarters beginning from the second quarter of 1996, which was the earliest IPO time for the Internet firms
in our sample. For firms that went public after the second quarter of 1996, they are treated as left-truncated data and
~
do not enter the risk set before they went public. The function, h0 (~
t ) , now denotes the baseline hazard function
based on calendar time. This analysis allows us to incorporate the impact of the macroeconomy into the baseline
hazard function. Our data collection period was from early 1996 to mid 2001. This period was one of dramatic
economic turbulence, which witnessed the boom of the Internet firms in 1999 as well as the stock market crash that
started in March 2000. The economy has been relatively weak since then. As a result, the Internet firms in our
sample are likely to be greatly affected by the external environment. So, even though we include a control variable
in our age-based analysis in the main body of this paper, it may not be able to capture all the impact of the
macroeconomy on firm survival in each quarter. By performing this calendar time-based analysis, we believe that
we are able to capture more of the impact of the macroeconomy in each quarter by using the baseline hazard
function and then cross-validating our results with the age-based analysis. However, we need to point out the
control variable, InterestRate, is dropped from this analysis since it exhibits no variance across all observations in
the same calendar quarter.
17
hazard rate of a firm selling digital goods is about 51% of those selling physical goods. The parameter
estimate for IPOEntry is -0.382, indicating that with one additional competing IPO, the hazard rate of an
existing public Internet firm drops to 68% of its original value. These results are consistent with those we
obtained from the age-based analysis, which increases our overall confidence in the outcome of this
analysis.
Bayesian Semi-Parametric Survival Analysis. When no historical data is available, a non-informative
prior, such as a normal distribution with zero mean and a large variance, is often used. The large variance
gives more flexibility for parameter estimation of the posterior distribution. We specify the prior
distribution for βi (i=1, …, 6) as N(0, 100000), and assume the parameters to be independent of each
other. In addition, we give a low weight to the prior distributions by specifying a small value for c0 at
0.001 since no historical data are available and the prior distributions are just our best guesses. There are
two other hyperparameters, which are analyst-supplied and required entry parameters that seed the model
for statistical simulation. They are r0, the hazard rate for the exponential distribution, and dH*t(j), the
increment in the unknown cumulative baseline hazard function at time j. In our analysis, we assume that
dH*t(j) is a constant for all possible j’s. Because Bayesian analysis is sensitive to the initial values of the
hyperparameters and we have no prior knowledge about the underlying distributions of the Internet firm
hazard function and the hazard rate, we test multiple combinations of r0 and dH*t(j). The initial values
we used for r0 were 0.1, 0.5, 1.0, and 4.0. The initial values for dH*t(j) were 0.1, 0.5, 1.0. This resulted
in 12 possible combinations of (r0, dH*t(j)).
We performed an initial burn-in of 1000 iterations, followed by a subsequent 3000 iterations, to
generate the parameter estimates. We report in Table 5 the summary statistics for the parameter estimates
based on the above 12 combinations.8 (See Table 5.) Even though there are some variations among the
results, the consistently small standard deviations compared to the means suggests our results are
consistent across different hyperparameter values. Due to space constraint, we will only report results
from one of the combinations (r0=0.5, dH*t(j)=0.1) from this point forward. This combination is selected
because its resulting parameter estimates are the closest to the mean based on all 12 combinations.
8
The reader should note that there are tied default times in our sample. Ties occur when two firms had the default
event at the same firm age. This gives them the same survival duration. We adjusted for this problem in our Cox
model. However, in the Bayesian analysis, we were unable to adjust for this problem due to limitations in the
WINBUGS software. However, the relatively consistent results across the two methods suggest our Bayesian
results are reasonable. We think it is possible that eliminating the ties are likely to result in only very minor
changes among our parameters, with the same signs and significance levels likely to be maintained.
18
Table 5. Summary Statistics for Bayesian Survival Analysis (No Differentiation Among Default
Types, N=94, 44 Defaults)
VARIABLE
IPOEntry
Size
Capital
Product
B2B2C
InterestRate
MEAN
-0.489
-0.461
-0.355
-0.815
-0.444
-0.211
MINIMUM
-0.499
-0.477
-0.371
-0.835
-0.459
-0.215
MAXIMUM
-0.478
-0.451
-0.333
-0.783
-0.437
-0.207
STD DEV
0.006
0.009
0.012
0.017
0.006
0.002
Table 6 summarizes results of the semi-parametric Bayesian analysis based on the selected
hyperparameter values of r0=0.5 and dH*t(j)=0.1. (See Table 6.) We used a similar burn-in/simulate
technique to establish the means for the parameter estimates as the average for 3000 iterations. The last
two columns report values for the mean parameter estimates and the hazard ratios, after the estimates
were transformed back to their original units of measurement. A comparison between the results from
Cox proportional hazards model and the semi-parametric Bayesian survival analysis indicates the results
are consistent across the two methods. In the Bayesian analysis, IPOEntry is significant at the .05 level
with a parameter estimate of -0.074 (-0.075 in the Cox regression). Product is significant at the 0.05 level
with a parameter estimate of -0.818 (-0.871, Cox). InterestRate is significant at the .10 level with a
parameter estimate of -0.339 (-0.378, Cox). In addition, Size is also significant at the .05 level with a
parameter estimate of -0.593 (-0.454, Cox, but not significant). The corresponding hazard ratio is 0.553,
indicating as a firm’s number of employee increase by 1000, its hazard rate decreases to 55.8% of its
original value.
Table 6. Bayesian Analysis Results: No Differentiation Among Default Types (Model 1B, N=94,
44 Defaults)
VARIABLE
IPOEntry
Size
Capital
Product
B2B2C
InterestRate
MEAN
PARAMETER
ESTIMATE
STANDARD
DEVIATION
-0.477**
-0.463**
-0.336
-0.818**
-0.435
-0.210*
0.254
0.257
0.408
0.349
0.392
0.111
TRANSFORMED-BACK RESULTS
Parameter Estimate
Hazard Ratio
-0.074
-0.593
0.0004
-0.818
-0.435
-0.339
0.929
0.553
1.000
0.441
0.647
0.712
Note: Significance levels for explanatory variables: * = p < 0.10; ** = p < 0.05. Note the absence of any
significance levels of p < .01. The WINBUGS software we used only displays confidence levels for up
to 95% level. As a result, we were unable to obtain any better significance levels than that.
Figures 1 and 2 display the trace plots and the marginal posterior densities for the parameters. These
are produced by WINBUGS iteration-by-iteration throughout the process of its MCMC simulation and
19
Gibbs sampling. After standardizing the time-varying covariates, we were always able to run 10,000
iterations to establish the means. However, for our data with 3,000 simulation iterations, the trace plots
suggested to us that the parameters converged well enough across a smaller number of iterations. From
the marginal posterior density plots displayed in Figure 2, we can see the marginal posterior distributions
for our parameters are not always symmetric. However, because Bayesian analysis is able to produce the
marginal posterior distribution of the parameter based on a large number of iterations, the significance test
and the calculation of the confidence interval can be carried out based on the true distribution instead of
assuming a normal one. As a result, the parameter estimates are not biased by asymmetric distributions.
This is one of the advantages of Bayesian analysis over the Cox model.
20
Figure 1. WINBUGS Traces of the β Parameters in the Estimation Model, Iterations 1001 to 4000
β1: IPO Entry
β2: Size
β3: Capital
β4: Product
β5: B2B2C
β6: InterestRate
Note: WINBUGS computed a total of 4,000 parameter estimates for each of the six model variables. However, the
first 1,000 were used to establish a burn-in basis for the simulations, and permitted us to diagnose whether
there were any problems with establishing parameter estimation stability. The reader should note that
although there is considerable variation in the estimated values of the model parameters, the track behavior is
similar to what we would see if the estimates had been established with bootstrapping or jackknifing
methods.
21
Figure 2. WINBUGS Marginal Posterior Densities for β Parameters in the Estimation Model,
Iterations 1001 to 4000.
β 1: IPOEntry
β2: Size
β3: Capital
β4: Product
β5: B2B2C
β6: InterestRate
Note: All marginal posterior densities for the estimated parameters were established on the basis of 3,000 iterations
in WINBUGS.
Testing for Competing Risks. In this analysis, we differentiate among three exit types
(bankruptcies, mergers and acquisitions) and examine the drivers behind each type of outcome. In the
analysis of each specific default type, we treat the occurrence of that exit type as the event for a given
firm in the data set and all the others as censored observations. Table 7 summarizes the results from the
Cox model and the Bayesian analysis. (See Table 7.) Due to space constraints, we only report the
parameter estimates after they have been transformed back to the original units of measurement from their
standardized values to quantify the marginal impact of the explanatory variables.
Model 2A—Bankruptcies Only. In Model 2A tests for exit due to bankruptcy only, IPOEntry and
Product are the two significant variables and the results are consistent across the two methods. The
parameter estimate for IPOEntry is -0.929 in the Cox model (-1.063 in the Bayesian analysis), with a
hazard ratio of 0.395 (0.346, Bayesian). This indicates that with one more competing IPO entry in the
stock market, an incumbent public firm’s hazard rate decreases to 39.5% (34.6%, Bayesian) of its original
value. Product has a parameter estimate of -1.277 in the Cox model (-1.278, Bayesian). The hazard ratios
22
from the two methods are the same at .279, indicating the hazard rate for Internet firms selling digital
products is 27.9% of those selling physical products. The Cox model has an overall likelihood ratio of
19.82, which is significant at the 5% level.
Table 7. Results of Testing Three Models for Competing Risks (Models 2A, 2B and 2C)
VARIABLE
COX MODEL
Parameter Estimate
Hazard Ratio
BAYESIAN ANALYSIS
Parameter Estimate
Model #2A -- Exit due to bankruptcy (N=94, 13 events)
IPOEntry
-0.929*
0.395
Size
0.168
1.183
Capital
-0.0008
0.999
Product
-1.277**
0.279
B2B2C
-0.535
0.586
InterestRate
0.229
1.258
Likelihood ratio
19.82***
-1.063**
0.142
-0.0015
-1.278**
-0.761
0.279
Model #2B -- Exit due to merger (N=94, 16 events)
IPOEntry
0.010
1.010
Size
-2.145*
0.117
Capital
0.0004
1.000
Product
-0.846
0.429
B2B2C
-0.387
0.679
InterestRate
-0.542*
0.582
Likelihood ratio
10.57
0.016
-2.482**
-0.0003
-0.794
-0.600
-0.506
Model #2C -- Exit due to acquisition (N=94, 15 events)
IPOEntry
-0.148
0.862
Size
-0.952
0.386
Capital
-0.0026
0.997
Product
-0.330
0.719
B2B2C
-0.060
0.942
InterestRate
-0.487
0.614
Likelihood ratio
14.39**
-0.193**
-1.871**
-0.0036*
-0.273
-0.171
-0.451
Hazard Ratio
0.346
1.153
0.999
0.279
0.467
1.322
N/A
1.016
0.084
1.000
0.452
0.549
0.603
N/A
0.825
0.154
0.996
0.761
0.843
0.637
N/A
Note: The likelihood ratio statistic for the hypothesis of equal parameters across default types in the Cox model is
18.63, and is significant at the .10 level; significance levels for the explanatory variables in this table are
given by: * = p < 0.10; ** = p < 0.05; *** = p < 0.01.
Model 2B—Mergers Only. In Model 2B where we test for exit due to mergers only, the significance
levels are not exactly the same across the two methods, even though the parameter estimates are close. In
the Cox model, Size and InterestRate are significant with parameter estimates of -2.145 and -0.542
respectively. In the Bayesian analysis, only Size is significant with a parameter estimate of -2.482,
23
indicating a 91.6% decrease in hazard rate with each additional 1000 employees. In this analysis, the Cox
model has an overall likelihood ratio of 10.57 and is only marginally significant (p = 0.10).
Model 2C—Acquisitions Only. In Model 2C where we test for exit due to acquisitions only, the
parameter estimates again show consistency across the two methods, even though three variable are
significant only in the Bayesian analysis. IPOEntry has a parameter estimate of -0.193 and is significant
at the .05 level. Its corresponding hazard ratio is 0.825, which indicates with each additional competing
Internet firm IPO, an existing public Internet firm’s hazard rate due to acquisitions decreases to 82.5% of
its original value. Firm Size has a parameter estimate of -1.871 and is significant at the 0.05 level. When
a firm’s number of employees increases by 1000, its likelihood of being acquired decreases by 84.6%.
Capital is significant at the 0.10 level with a parameter estimate of -0.0036. The corresponding hazard
ratio of 0.996 suggests an Internet firm’s hazard rate due to acquisition decreases by 0.4% with each
additional $1 million of financial capital available. Even though no explanatory variable is significant in
the Cox model, the overall model has a likelihood ratio of 14.39 and is significant at the 0.05 level.
The overall test of equal parameters across exit types in the Cox model has a likelihood ratio of 18.63
and is significant at the 0.10 level. This indicates the impact of the explanatory variables on bankruptcies,
mergers and acquisitions are different.
Testing for Different Degrees of Failure. In this analysis, we rank the outcomes from the most
desirable to the least desirable as survival, merger, acquisition and bankruptcy. Bankruptcy indicates a
firm is no longer able to remain viable and hence is the worst outcome. Survival is the best outcome since
it suggests the firm is still able to operate under its current condition. Acquisition and merger lie in
between survival and bankruptcy. We view merger as better than acquisition since merger is usually the
formation of one corporation between two firms with roughly equal resources, whereas acquisition
indicates the focal firm is weaker than its counterpart. However, we note that the founders of some
Internet firms actually viewed acquisitions of their firms as wealth-generating exit strategies. Viewed this
way, we can perform the following three analyses.
First, when we only consider the worst outcome, bankruptcy, and treat the other three outcomes
(acquisitions, mergers, and survival) as the better alternatives, we only need to perform a test of drivers of
bankruptcy only. We have reported these results earlier in the paper.
Second, when we combine the two least desirable outcomes (bankruptcies and acquisitions) as one
group and treat the other two (mergers and survival) as the other group, we can perform a test on the
drivers of bankruptcy and acquisition versus merger and survival. We report these results in Table 8. (See
Table 8.) Results from the two methods are consistent in this analysis with the same two variables turning
out to be significant. IPOEntry is significant at the 0.05 level with a parameter estimate of -0.269 in the
Cox model (-0.304 in the Bayesian analysis). Product is also significant at the 0.05 level with a
24
parameter estimate of -0.922 in the Cox model (-0.893 in the Bayesian analysis). Overall, the likelihood
ratio statistic for the Cox model is 23.60, which is significant at the 0.01 level.
Table 8. Drivers for Default Due to Bankruptcy and Acquisition (Models 3, n=94, 28 events)
VARIABLE
IPOEntry
Size
Capital
Product
B2B2C
InterestRate
Likelihood ratio
COX MODEL
Parameter Estimate Hazard Ratio
-0.269**
0.764
-0.186
0.831
-0.0006
0.999
-0.922**
0.398
-0.302
0.739
-0.245
0.783
23.60***
BAYESIAN ANALYSIS
Parameter Estimate
-0.304**
-0.320
-0.0010
-0.893**
-0.372
-0.209
N/A
Hazard Ratio
0.738
0.726
0.999
0.409
0.689
0.811
Note: Significance levels for the explanatory variables in this table are given by: * = p < 0.10; ** = p < 0.05;
*** = p < 0.01.
Third, when we treat the three least desirable outcomes (bankruptcies, acquisitions and mergers) as
one group and survived firms as the other group, the test is essentially the same as Models 1A and 1B,
where we do not differentiate the exit types. So we do not include those results here.
DISCUSSION
In this research, we test multiple models of Internet firm survival using the Cox proportional hazards
model and the semi-parametric Bayesian analysis. Even though we were unable to adjust for the tied
duration data in our sample in the Bayesian analysis, our results across the two methods show a high level
of consistency, which alleviates our concern for the flaw in our data analysis.
In our first set of modeling testing where we do not differentiate among the default types, the three
variables that are significant in the Cox model (i.e. IPOEntry, Product, InterestRate) are all significant in
the Bayesian analysis. Counter-intuitively, the entry of competing public firms can reduce an existing
public firm’s hazard rate. There are two possible reasons for this result. First, our operationalization of
the rate of new firm entry as the number of competing IPOs in each quarter might not be correct. Hence
is might not capture the competitive aspect of the picture. It would be desirable if we had the rate of new
firm entry information for both public and private firms. Unfortunately such data is unavailable.
However, when we examine our quarterly IPO entry data for the three types of Internet firms in our
sample, 1999 witnessed the largest number of B2C and B2B2C firm IPOs and the IPOs of B2B firms
peaked in the first quarter of 2000. We think this is consistent with the Internet firm boom around the end
of the last century. In addition, even though our use of IPOEntry does not capture the portion of
competition coming from private firms, it does reflect the competition for market capital among public
firms. Based on the above two considerations, we view IPO entry as a reasonable indicator of rate of new
25
firm entry for the whole Internet sector and also being relevant for public Internet firms. Then our results
suggest the second reason might be true: some other effect related to the entry of competing IPOs might
dominant the impact of the competitive pressure due to the entry of competing firms. In a recent study of
B2B market crowdedness, Croson et al. (2001) found that access to perceived opportunities for
extraordinary financial returns from the IPOs drove firm entry into B2B electronic markets more than
profit maximization. Considering the IPO gold rush during our study period, abundant market capital,
rather than the competitive pressure due to the entry of additional firms, is critical in determining Internet
firm survival. As a result, IPOEntry during our sample period might mainly reflect the effect of the
abundance of market capital. Public firms are more likely to survive when market following in high and
they can easily obtain capital infusion.
The direction for the relationship between product and survival is within our expectation. Because
Internet firms selling digital goods or services have much lower operational cost, they enjoy higher
productivity and profitability, ceteris paribus. However, is there anything that physical Internet firms can
do to enhance their chance of survival? We believe the answer is yes. Since our results suggest the
reason that digital Internet firms incur lower hazard rate is because of the high level of digitization of
business processes and lower operational costs, physical firms can also reduce their hazard rate by
digitizing their processes and reducing costs. For example, by integrating with their suppliers, physical
firms can reduce their cost associated with maintaining the supply chain. Physical firms can also provide
as much customer service information as possible on their site and encourage their customers to use the
digital medium to interact with the companies. Amazon.com is one such example. On their Web site,
Amazon no longer lists their customer service 1-800 numbers. Instead customers are forced to email the
customer service department if they do not know the number to call.
The control variable InterestRate is positively related to survival. A high interest rate is an indicator
of a prosperous economy where the demand for capital is high. As a result, firms are more likely to
survive.
The results from our second set of model testing where we test the competing risks of exit due to
bankruptcy, acquisition, and merger show that impact of the explanatory variables on the different default
types are different. IPOEntry and Product are the two significant predictors of exit due to bankruptcy. In
the testing of exit due to merger, size is significant in both the Cox model and the Bayesian analysis.
When a firm gets larger, it is less likely to merge with another firm. In the analysis of exit due to
acquisition, no variable is significant in the Cox model while IPOEntry, size and capital are significant in
the Bayesian analysis. We consider the different impact of the explanatory variables on the different
default types to be reasonable. Even though bankruptcies generally indicate the firms are no longer viable
as an independent business, the same cannot be said for mergers and acquisitions. The complex nature of
26
the latter two types of exit makes them hard to predict. In the context of Internet firms, we see examples
of those that are seeking acquisitions or mergers after experiencing financial difficulties (e.g., Peapod),
but there are also firms that were acquired or merged with another business simply because they show
potential of growth and complement the resources of the other firms (e.g., Geocities.com). As a result,
when analyzing Internet firm exits, it is important to look at each default type separately.
Finally, in our model testing of bankruptcy and acquisition vs. merger and survival, IPOEntry and
product are significant, and their impact is similar to what we discussed earlier.
CONCLUSION
In this research, we test an explanatory model of Internet firm duration after their IPOs using a Cox
proportional hazards model and a semi-parametric Bayesian survival analysis. Our results show high
level of consistency across the methods used. This provides us support for the results we get and
validates the methods we used to perform the data analysis. We have the following interesting results.
Key Results
First, our results suggest factors that can influence an Internet firm’s hazard rate include entry of
competing Internet firm IPOs, the kinds of products or services the firm provides, size of the firm and
interest rate. Entry of additional Internet IPOs (counter-intuitively) tends to reduce the hazard rate.
Instead of reflecting the increased competition due to the entry of competing firms, IPO entry is an
indicator of the abundance of market capital in our sample period. Our results also suggest digital goods
sellers incur lower hazard rate and are more likely to survive. This result is consistent with the Barua et
al. (2000) study where they found digital firms enjoyed higher productivity gains. Internet firms selling
digital goods can take advantage of the digital channel and hence have lower operational costs, which in
turn results in higher productivity and profitability. Higher interest rates, reflecting a high capital demand
in a prosperous economy, also reduce hazard rates for Internet firms. In addition, our testing of failure
due to mergers only or acquisitions only suggest a larger firm is less likely to be acquired or merger with
another company.
Second, our testing of drivers for different exit types suggests the influences of the explanatory
variables on bankruptcy, merger and acquisition are different. As a result, it is important to differentiate
the different outcomes in future research in order to pinpoint the impact of the explanatory variables. In
the analysis of mergers and acquisitions, it is especially important to examine the rationale behind the
observed actions.
Third, as the first attempt to apply semi-parametric Bayesian survival analysis to Internet firm
duration, our research show consistent results with the Cox model, which has been the major technique
used in empirical analysis of business failure. This consistency in the results suggests semi-parametric
27
Bayesian analysis can be used to analyze firm duration. In addition, it allows researchers to incorporate
historical data and to test more complex model structures. We expect to extend our research toward these
directions.
Methodological Contributions to Empirical IS Research
The methodological contributions of this research are two folds. First, we illustrate how survival
analysis can be applied to the analysis of duration of Internet firms. Even though there are previous IS
research that utilizes the survival analysis technique to study the adoption of innovation (Kauffman,
McAndrews and Wang, 2000) and the business value of call centers (Subramanyam and Krishnan, 2001),
none has been applied to the Internet firm survival setting. By cross-validating our results using two semiparametric techniques, we illustrate the validity of using both the Cox proportional hazards model and the
semi-parametric Bayesian survival analysis. Our second and more important contribution is the
application of Bayesian survival analysis. Through Bayesian analysis, we were able to perform
significance testing and estimate the conference intervals without assuming a normal distribution. This is
done through the large number of iterations that each generates a parameter estimate and when aggregated
allows us to plot the marginal posterior distributions for the parameters. In addition, Bayesian analysis
offers advantages such as incorporating prior knowledge about the parameters when historical data is
available, more flexible model testing and the handling of missing data.
During our data analysis process using the WINBUGS software, we also learned the following
important techniques in order to successfully carry out the data analysis. First, it is important to
standardize the variables to avoid a WINBUGS software crash, especially when the number of
observations and covariates in the sample is large. Second, because Bayesian analysis results are
sensitive to the initial values used to seed the simulation, it is important to try out different combinations
of the hyperparameters to test the consistency of the results across different starting values. In our
research, the results turned out to be quite stable across the 12 combinations of values used. Third, in
addition to reading the estimation statistics for the parameters, it is also important to look at the trace for
the parameter estimation throughout the iterations to check for convergence of results.
Limitations and Future Research
The current study has the following limitations. First, the Internet sector is still in its infancy and the
results may not be generalizable to later stages as the sector matures. However, we still view this research
as important given the magnitude of the failure in the Internet sector. Second, B2B firms are not
represented in our sample. As a result, our findings might not be applicable to B2B firms. Third, because
we were did not adjust for the tied default time problem in the Bayesian analysis, we caution the reader
with respect to the extent to which the Bayesian results should be viewed as “final.” However, because
our Bayesian analysis results are consistent with the corresponding results across the different Cox
28
proportional hazard models tested, we believe our results are likely to approximate the results of the
Bayesian analysis with tied duration-adjusted results.
Our next steps in this research will involve data collection to support the analysis of B2B firm
survival. That will not only enrich our data set, but also allow us to validate our results with additional
B2B firms and compare the differences among B2C, B2B and B2B2C firms. In addition, as we collect
more data and our sample size gets larger, we plan to partition our data set into two parts. One of them
will be used as the historical data set to generate the prior distributions of the parameters. The other one
will be used as the current data to obtain the posterior parameter distribution based on the estimation
results from the historical data. This will allow us to take advantage of the updating aspect of the
Bayesian analysis.
REFERENCES
Abrams, K., Ashby, D., and Errington, D. A Bayesian Approach to Weibull Survival Models: Application
to a Cancer Clinical Trial. Lifetime Data Analysis, 2 (1996), 159-174.
Audretsch, D.B. New Firm Survival and the Technological Regime. The Review of Economics and
Statistics, 60, 3 (August 1991), 441-450.
Audretsch, D.B. Innovation and Industry Evolution. Cambridge, MA: MIT Press, 1995.
Audretsch, D.B., and Mahmood, T. The Hazard Rate of New Establishments. Economic Letters, 36, 4
(August 1991), 409-412.
Audretsch, D.B., and Mahmood, T. New Firm Survival: New Results Using a Hazard Function. The
Review of Economics and Statistics, 77, 1 (February 1995), 97-103.
Barua, A., Pinnell, J., Shutter, J., and Whinston, A.B., and Wilson, B. Measuring the Internet Economy,
2001, available on the Internet at www.internetindicators.com.
Barua, A., Whinston, A.B., and Yin, F. Not All Dot Coms Are Created Equal: An Exploratory
Investigation of the Productivity of Internet Based Companies. Working paper, Center for Research on ECommerce, McComb School of Business, University of Texas at Austin, Austin, TX, May 2000.
Cavanagh, L. From Dot Coms to Dot Bombs: Have We Learned Anything? Seybold Report Analyzing
Publishing Technologies, 1, 5 (June 4, 2001), 28-29.
Cox, D.R. Partial Likelihood. Biometrika, 62, 2 (August 1975), 269-275.
Croson, D.C., Jacobides, M.G., and Nguyen, A. T. Explaining Entry Decisions and Crowdedness in
Business-to-Business E-Commerce Markets. 13th Workshop on IS and Economics (WISE), New Orleans,
LA, 2001.
Das, S., and Srinivasan, K. Durations of Firms in an Infant Industry: The Case of Indian Computer
Hardware. Journal of Development Economics, 53, 1 (June 1997), 157-167.
DeVoe, D. Surviving the Shakeout. InfoWorld, 24, 4 (January 28, 2002), 42-43.
Greene, W.H. Econometric Analysis. Upper Saddle River, NJ: Prentice Hall, 2000.
Hensler, D.A., Rutherford, R.C., and Springer, T.M. Survival of IPOs in the Aftermarket, Journal of
Financial Research, 20, 1 (Spring 1997), 93-110.
29
Honjo, Y. Business Failure of New Firms: An Empirical Analysis Using a Multiplicative Hazards Model.
International Journal of Industrial Organization, 18, 4 (July 2000), 557-574.
Ibrahim, J.G., Chen, M.H., and Sinha, D. Bayesian Survival Analysis. New York, NY: Springer-Verlag,
2001.
Kauffman, R.J., McAndrews, J., and Wang, Y.M. Opening the “Black Box” of Network Externalities in
Network Adoption. Information Systems Research, 11, 1 (March 2000), 61-82.
Klein, J. P., and Moeschberger, M. L. Survival Analysis: Techniques for Censored and Truncated Data.
New York, NY: Springer-Verlag, 1997.
Krizner, B. Dot-Com Carnage Yields Lessons. Frontline Solutions, 2, 12 (November 2001), 1, 35.
Le, C.T. Applied Survival Analysis. New York, NY: John Wiley and Sons, 1997.
Maynard Smith, J. Evolution and the Theory of Games, Cambridge, UK: Cambridge University Press,
1982.
Orbe, J., Ferreira, E., and Nunez-Anton, V. Modeling the Duration of Firms in Chapter 11 Bankruptcy
Using a Flexible Model. Economic Letters, 71, 1 (April 2001), 35-42.
Rindova, V.P., Kotha, S. Continuous “Morphing”: Competing from Dynamic Capabilities, Form, and
Function. Academy of Management Journal, 44, 6 (December 2001), 1263-1280.
Samuelson, L. Evolutionary Games and Equilibrium Selection, Cambridge, MA: MIT Press, 1998.
Sargent, D.J. A Flexible Approach to Time-Varying Coefficients in the Cox Regression Setting, Lifetime
Data Analysis, 3 (1997), 13-25.
Smith, A. F. M., and Roberts, G. O. Bayesian Computation Via the Gibbs Sampler and Related Markov
Chain Monte Carlo Methods, Journal of the Royal Statistical Society, Series B, 55, 1 (1993), 3-23.
Subramani, M., and Walden, E. Impacts of E-Commerce Announcements on Market Value of Firms.
Information Systems Research, 12, 2 (June 2001), 135-154.
Subramanyam, R., and Krishnan, M.S. Business Value of IT-Enabled Call Centers: An Empirical
Analysis. In Proceedings of the 22nd International Conference on Information Systems, New Orleans, LA,
December 2001.
Therneau, T. M., and Grambsch, P. M. Modeling Survival Data: Extending the Cox Model. New York,
NY: Springer, 2000.
Titus, J. Some Dot Coms Deserve to Fail. Test & Measurement World, 21, 12 (October 2001), 5.
Tushman, M.L., and Romanelli, E. Organizational Evolution: A Metamorphosis Model of Convergence
and Reorientation. Research in Organizational Behavior, 7 (1985), 171-222.
Webmergers.com. Q3 Report: Shutdowns Down Sharply from 2001, San Francisco, CA, October 2002.
Available on the Internet at www.webmergers.com/editorial/article.php?id=64.
Willoughby, J. Burning Up -- Warning: Internet Companies Are Running Out of Cash – Fast. Barron’s,
80, 12 (March 20, 2000), 29-32.
30
METHODS APPENDIX. AN OVERVIEW OF BAYESIAN SURVIVAL ANALYSIS METHODS
Bayesian survival analysis combines Bayesian analysis with survival analysis. It is based on the
Bayes theorem, which allows the update of the posterior distribution π (θ | D) of a parameter θ given
some observed data, D, and a prior distribution for θ, π(θ) (Ibrahim, Chen and Sinha, 2001). The Gibbs
sampler is a Markov chain Monte Carlo (MCMC) sampling scheme for Bayesian analysis. Given a qdimensional vector of parameters to be estimated, the Gibbs sampler, θq, performs thousands of iterations
to generate a parameter trace history and a posterior density given the observed data. In each iteration,
every parameter is estimated by treating the other parameters as known. A value that fits the observed
data the best given the other fixed parameters is generated as a new estimated value for the current
parameter. All parameters are visited in turn so that after one iteration, their values are all updated. These
new values are used as the starting values of the next iteration. To start the Gibbs sampler, an initial set
of parameter values are necessary to seed the first iteration.
Similar to other survival analysis, Bayesian survival analysis offers researchers the ability to carry out
semi-parametric and fully parametric analyses. The methodology that we illustrate in this paper is the
Bayesian counterpart of the widely-used semi-parametric Cox proportional hazards model. A nonparametric prior process, most often the gamma process, can be used for the baseline hazard function. In
fully parametric models, the hazard functions can be assumed to follow a specific distribution, such as the
exponential distribution with a constant hazard rate λ, or the Weibull distribution with a shape parameter
α and a parameter λ. These parameters are assumed to follow certain prior distributions such as the
gamma distribution and the normal distribution. Based on these assumptions, we can derive the posterior
distributions of these parameters and carry out the simulation process.
In addition to the basic semi-parametric and fully parametric analyses, Bayesian survival analysis also
allows for the estimation of more complex models such as frailty models (i.e., models that cope with
unobservable characteristics that affect survival by subgrouping the sample subjects) and cure rate models
(i.e., a fraction of the sample are exempt from a disease after receiving some treatment). More detailed
discussion on the whole spectrum of analysis techniques that Bayesian survival analysis offers can be
found in Ibrahim et al. (2001).