Spillover Asymmetry and Why It Matters
Anne Marie Knott
Olin School of Business
Washington University
Campus Box 1133
One Brookings Drive
St. Louis, MO 63130-4899
314.935.4679
knott@wustl.edu
Hart E. Posen
Stephen M. Ross School of Business
University of Michigan
701 Tappan Street, D3212
Ann Arbor, MI 48109-1234
734-764-1349
hposen@umich.edu
Xun (Brian) Wu
Stephen M. Ross School of Business
University of Michigan
701 Tappan Street, D3212
Ann Arbor, MI 48109-1234
734-647-9542
wux@umich.edu
April 25, 2008
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Spillover Asymmetry and Why It Matters
While spillovers are a crucial factor in determining the optimal environment for innovation, there is
no consensus regarding their impact on firm behavior. One reason for this may be that models differ in
their assumptions for the functional form of the spillover pool. In industrial organization and economic
geography, for example, the predominant convention is that all innovation within an industry/region
contributes to a spillover pool that has a common value for all firms. An alternative convention prevalent
in endogenous growth and evolutionary economics is that spillovers have directionality—the size of the
relevant pool differs across firms.
We believe that knowing the correct functional form may facilitate theoretical consensus—either
analytically (by modifying models’ assumptions) or empirically (by supporting a critical test of competing
theories). We characterize and test the functional form of spillover pools across fifty markets in the
banking industry. Our results for firm efficiency improvement in that setting are consistent with
expectations for asymmetric spillovers and inconsistent with expectations for pooled spillovers.
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1. Introduction
Spillovers (the leakage of knowledge across firms) are one of the central constructs in the
economics of innovation. Romer (1986) relies on spillovers to explain increasing economy-wide returns
to innovation in the presence of decreasing firm-specific returns to innovation. Spillovers have two effects
on aggregate innovation (Spence 1984), an efficiency effect and an incentive effect. The efficiency effect
is that spillovers reduce the expenditures necessary for firms to achieve a given level of innovation. The
incentive effect is that imitation by rivals reduces the potential returns to innovation and therefore the
incentives to innovate. Accordingly spillovers are a crucial factor in determining the optimal environment
for innovation.
Two conventions have developed around the directionality of spillovers. One convention,
prevalent in industrial organization (Griliches 1979, Levin & Reiss 1984, 1988, Spence 1984, Jaffe 1988,
Adams and Jaffe 1996) and economic geography (Ellison and Glaeser 1997, Black and Henderson 1999)
is that spillovers are non-directional (pooled). All innovation in an industry/region contributes to a
spillover pool that has a common value for all firms. Firms may differ in their access to the pool (if, for
example, they are geographically distant), or the relevance of the pool (if, for example, they use chemistry
as their basic science while other firms use biology). However, if the pool is proximate and relevant to all
firms, then they draw equal benefit from the contributions of all other firms. In other words, there is no
sense of a leader/follower relationship for spillovers as there is for the flow of knowledge in the diffusion
and imitation literatures.
An alternative convention prevalent in the endogenous growth literature (Jovanovic and Rob
1989, Jovanovic and MacDonald 1994, Eeckhout and Jovanovic 2002) is that spillovers have
directionality. This view preserves the notion of an innovator and an imitator inherent in the diffusion
literature (Mansfield 1968), the evolutionary economics literature (Nelson and Winter 1982, Klepper
1996), and the international trade literature (Krugman 1979, Abramovitz 1986, Baumol, Blackman, and
Wolff 1989, Grossman and Helpman 1992). Under this view some firms/nations have superior knowledge
relative to other firms, and knowledge flows exclusively from those with superior knowledge to those
with inferior knowledge.
Thus despite the fact that spillovers are central to models of innovation/growth across all these
literatures, there is no consensus on their functional form. Correspondingly there is no consensus
regarding their impact on firms’ innovative behavior. Predictions are that they increase (Ellison and
Glaeser 1997, Black and Henderson 1999, Jovanovic and Rob 1989, Grossman and Helpman 1992),
decrease (Spence 1984, Levin and Reiss 1988, Eeckhout and Jovanovic 2002), decrease then increase
(Nelson and Winter 1982), and increase then decrease (Aghion et al. 2001) innovation/growth.
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While it is possible to resolve the controversy via empiricism, the empirical record is similarly
equivocal. Studies of spillovers consistently indicate that R&D intensity and outcomes increase with the
size of the spillover pool (Jaffe 1986, 1988). However the studies exhibit an apparent anomaly where the
output elasticity of spillovers is comparable to and sometimes greater than that for the firm’s own R&D
(Jaffe 1986, Adams and Jaffe 1996). Given the spillover pool in these studies is on average n-1 times the
firm’s own R&D, where n is the number of firms in the industry, the economic contribution of spillovers
is sometimes orders of magnitude greater than that from the firm’s own R&D spending. If this were true,
few firms could justify R&D investment.
One explanation for the empirical anomaly may be that spillovers are capturing market size
effects, as suggested by Levin (1988). An alternative explanation for the anomaly is that the large
coefficients on spillovers reflect estimation bias from using a pooled spillover specification when in fact
spillovers are asymmetric (see derivation in Appendix 1).
Accordingly, knowing the correct functional form for spillovers has the potential to resolve
empirical anomalies and thereby illuminate theory regarding their behavioral impact. The goal of this
paper is facilitating consensus in innovation theory by clarifying and testing the functional form of
spillovers. To our knowledge no empirical test of spillovers’ functional form exists.1
2. Background on Spillovers
Arrow (1962) posed the problem of appropriability and innovation, and the tension between
incentives to innovate and the diffusion of the benefits. The central concern is that since knowledge is a
public good (non-rival and non-excludable), the best means to appropriate the returns from innovation is
for a monopolist to keep the knowledge in house. However this is inefficient from a social standpoint
since the knowledge isn’t fully exploited. It also may be privately inefficient since a firm other than the
inventing firm may be able to use the knowledge more effectively.
There are four operative uses of the term spillovers in the literature: the general phenomenon of
leakage, the amount of knowledge available to rival firms (the pool), the percentage that leaks, and the
elasticity of rival knowledge to own output. We clarify these distinctions using the Levin and Reiss
expression for the contribution of rival R&D to focal firm innovative output, Yi:
Yi = riα (ωSi)γ
(1)
where:
ri
is focal firm R&D
1
There is however related work pertaining to brand spillovers (Kalnins and Chung 2004) and learning curve
spillovers (Jarmin 1994). That work tends to find that spillovers are asymmetric. Other work regarding firm location
choice tests whether firms behave as if some firms differ in the value of their spillovers (Shaver and Flyer 2001,
Alcacer and Chung 2007).
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α
is the elasticity of own R&D to output
Si
is the pool of rival knowledge the focal firm draws upon
ω
is the extent of knowledge leakage between rivals
γ
is the elasticity of rival knowledge to output
Here forward we use the term spillovers to refer to the general phenomenon, the term spillover
pool for the expression Si , the term leakage rate for the expression ω, and expropriability for the
expression γ. Thus the value of spillovers may differ across firms through differences in their relevant
spillover pool, Si., differences in the ease of gaining access to the pool, ω, and differential effectiveness in
utilizing the knowledge that has been accessed, γ. This paper deals exclusively with asymmetry in the
functional form of the spillover pool, Si..
Equation 1 illustrated one source of confusion regarding the phrase “spillovers.” In addition to
this theoretical confusion is some empirical confusion in that spillovers are often defined by how they are
measured empirically. This is problematic given our goals. Much of the empirical treatment of spillovers
inherently assumes directionality in that it examines particular transfers of knowledge. For example,
studies using patent citations to study spillovers trace the source and destination of knowledge (e.g.,
Thompson 2006). Studies examining the actual mechanisms of transfer such as alliances and labor
mobility often refer to the transfer as spillovers (e.g., Rosenkopf and Almeida 2003). This empirical
approach is attractive because it allows researchers to demonstrate that particular innovations have indeed
transferred.
There are two concerns with the approach, however. First, these point-to-point transfers of
knowledge are only subsets of the theoretical definition of spillovers. As equation 1 illustrates the
theoretical concept is much broader. Spence (1984), for example, examines simultaneous R&D by all
firms in the industry whose cost is reduced by the total spillovers being generated by the set of firms
engaged in R&D. Thus there is no "innovation" that gets transferred. Second, the ability to identify a
source and destination presupposes directionality, while our goal is to determine if spillovers are better
characterized as being directional or pooled.
Because we want to determine which theories correctly model spillovers, we adopt the broad
definition of spillovers implied by equation 1: knowledge generated outside the firm exploited to generate
either new products (increase demand) or new processes (decrease cost). Thus our definition includes
point-to-point transfers and imitation, but is not restricted to them. Rather we test where a firm's
extramural knowledge appears to originate (from the set of all firms in the market or the set of firms with
superior knowledge).
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2.1 What do we mean by spillover pools?
There are two basic conventions in modeling the spillover pool, Si. The first convention, shared
by industrial organization and economic geography, is to treat all economic activity as contributing to a
pool that is equally accessible/valuable to all firms. We refer to this convention as pooled spillovers. The
second convention assumes that economic actors differ in their level of knowledge and that knowledge
flows exclusively from those with more knowledge to those with less knowledge. This convention is
shared by evolutionary economics, endogenous growth, and trade theories.
The lack of consensus may reflect fundamental differences in beliefs; however it is possible that
it reflects simple measurement problems – researchers can’t identify knowledge sets. This means that
modelers and empiricists must make simplifying assumptions about differences in knowledge sets. Thus
the argument of functional form may be largely one of the better simplifying assumption.
Perhaps the best means to make this argument is by fictitious example. The radar diagram in
Figure 1 is intended to capture all available knowledge. At any given time there is a knowledge frontier
defined by the perimeter of the union of all knowledge sets. The example depicts a universe of two firms.
In general, the knowledge frontier is defined by Firm 1’s knowledge set. However, Firm 2 has greater
knowledge in political science, sociology, and classical studies. Thus while knowledge flows
predominately from Firm 1 to Firm 2, in these three domains it is possible for knowledge to flow from
Firm 2 to Firm 1.
------------------------------Insert Figure 1 about here
------------------------------Probably everyone would agree that if you could actually construct this map, then a firm’s
spillover pool would be defined as the complement of its knowledge within the current frontier. The
practical problem isn’t as simple as the example, however. We can’t characterize the knowledge set for
each firm. Even if we could, the computational task of pair-wise comparing all knowledge sets in an
industry would be overwhelming. The practical problem of spillover pools then is one of choosing the
best simplifying assumption. Are we as researchers better off ignoring redundant knowledge, or are we
better off ignoring the superior knowledge of a firm who in general has less knowledge. The pooling
convention corresponds to Figure 2a – it assumes that knowledge is largely unique and therefore the
tolerated error is the redundant area (that shaded). In contrast the asymmetry assumption corresponds to
Figure 2b – it assumes that knowledge is largely redundant and therefore the tolerated error (the shaded
area) is the knowledge unique to firm 2.
-------------------------------
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Insert Figure 2 about here
------------------------------2.2 Is knowledge redundant?
One way to choose the better simplifying assumption is to gauge the extent to which knowledge
is redundant. We tackle this by examining the patent record. We consider the relationship between R&D
spending and patenting in the chemical industry (ISIC 2400). We limit the analysis to one industry
because we need a setting where patenting is a good proxy for knowledge amounts and types. Of the three
industries where we expected this to hold (chemicals, medical products, electronic components),
chemicals was the industry where firms were most likely to have at least one patent (35%), and where the
number of patents was most closely correlated with R&D (R2 = 0.79). Figure 3 is a matrix comparing
patenting activity with R&D expenditures for the chemical firms in the sample. Patent classes are
captured by columns and firms are captured by rows, where firms are listed in ascending order of their
1995 R&D expenditures. Each cell in the matrix is the number of patents granted to a given firm between
1995 and 1999 in a given patent class. While there are exceptions, the figure tends to suggest that firms
doing R&D are engaged in subsets of the activity of those doing more R&D. This implies the assumption
of redundancy is plausible. The redundancy assumption is reinforced by the observation that most firms
(65%) do no patenting. Given the high propensity to patent in this industry, we would expect firms to
patent if their knowledge were unique and valuable to rivals.
----------------------------------Insert Figure 3 about here
-----------------------------------
2.3 Theoretical differences regarding the impact of spillovers
As mentioned previously subfields differ in their approach to modeling spillover pools. These
differences in conventions yield different propositions regarding the impact of spillovers on innovation.
Industrial Organization. IO models tend to examine R&D spending by profit maximizing firms
among a set of homogeneous rivals in the presence of spillovers. The pool of spillovers is symmetric
across firms (the sum of rival R&D), but conditioned by the percentage of the pool that leaks to rivals.2
Spence (1984) considers dynamic cost competition among firms who maximize profits by choice of R&D
taking rival behavior as given. Because rival R&D substitutes for own R&D, investment decreases in the
leakage rate.
2
Note that in duopoly models spillovers are asymmetric in that the R&D of firm A becomes the pool for firm B and
vice versa.
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Levin and Reiss (1984, 1988) model a profit maximizing firm choosing levels of R&D, taking
into account the elasticity of own investment as well as that from spillovers of rival R&D. As with
Spence, firms are identical and the available spillover pool is defined as the sum of all rival R&D adjusted
for leakage. What differs from Spence is that own R&D and rival R&D are imperfect substitutes, each
with their own elasticity. They reach the same conclusion as Spence that R&D intensity decreases in the
leakage rate; however, they show that higher elasticity of rival knowledge increases R&D intensity.
Economic Geography. Economic geography examines geographic concentration of economic
activity to understand both the prevalence of agglomeration and its relationship to economic growth. Both
are linked to Marshall’s (1890) hypothesis that cities offer close contacts that generate local spillovers.
These spillovers include gains from sharing a labor market, from inter-firm trade, and from local
knowledge. While there is some acknowledgement that spillovers may be asymmetric, e.g., the benefits of
locating near one plant may differ from locating near another (Ellison and Glaeser 1997), models and
empirics tend to adopt a pooled spillover convention.
Ellison and Glaeser (1997) model geographic concentration of industries through the lens of firms
maximizing profits through choice of plant location. The profits associated with each location comprise a
“natural advantage component,” e.g., weather/soil in Napa Valley, the effects of spillovers (characterized
as profit elasticity on the aggregate activity of existing firms), and an idiosyncratic firm-location specific
component. Profits and concentration both increase with aggregate activity and spillover elasticity.
Black and Henderson (1999) model the spatial growth of economic activity under exogenous
population growth and endogenous economic growth. They develop a two good/two city model where
firm output is a function of local sectoral employment, the corresponding level of human capital, and the
firm’s own human capital. The output elasticities of employment and human capital capture scale
economies from the total volume of communication (Romer 1986) and knowledge spillovers (Lucas
1988), respectively. Thus returns to own human capital are increasing in the extent of local human capital.
Cities grow at a rate proportional to human capital accumulation.
Evolutionary economics. Evolutionary economics examines how firm behavior, market structure,
and outcomes are jointly determined in models of innovative and imitative activity by profit-maximizing
firms competing along a downward-sloping demand curve. A major distinction from IO models is that
firms differ in their levels of knowledge, and accordingly their cost functions and profits. Of the
evolutionary economics models, only Nelson and Winter (1982) treat spillovers parametrically. 3 When
industries are concentrated, spillovers (captured as ease of imitation) have no apparent impact on the level
3
Klepper (1996) does not parameterize spillovers (leader technology is freely imitated following a one year lag),
and thus offers no propositions about its impact.
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of innovative R&D. When industries are more competitive, R&D investment is decreasing then
increasing in the ease of imitation.
Endogenous growth. Endogenous growth theory consists principally of stochastic models that
cast innovation by profit-seeking firms as engines of growth. These models share many features of
evolutionary economics: 1) characterization of knowledge as an intermediate good produced by profitmaximizing firms through imitation and invention, 2) heterogeneity in the distribution of knowledge, and
3) imitation that depends on the level of heterogeneity.4
Grossman and Helpman (1992) capture spillovers through the imitation rate – the proportion of
innovator products copied per unit of time. Since imitation and innovation are modeled identically to one
another, their model concludes that innovation and growth are increasing in imitation.
Jovanovic and Rob (1994) model the ease of expropriating rival knowledge similarly to Spence,
but with two important distinctions. First, in Spence, the leakage rate is applied to the pool of all rival
knowledge, while in Jovanovic and Rob espropriability is applied to the share of knowledge obtained
from a random rival. Second, spillovers are asymmetric – firms can’t learn from rivals with less
knowledge. Innovation and growth are increasing in expropriability.
Aghion, Harris, Howitt, and Vickers (2001) model firms who maximize the net present value of
profits taking into account profit from any current knowledge gap, profit from moving ahead, cost of own
R&D, and losses associated with followers catching up. Spillovers are modeled as the ease of imitating
the leader’s technology. Growth is increasing then decreasing in imitation.
Eeckhout and Jovanovic (2002) examine investment choice by firms who maximize the present
value of profits in a model where firms can expropriate knowledge from rivals. Like Levin and Reiss,
they distinguish between the leakage rate and the elasticity of rival knowledge. They reach conclusions
similar to Levin and Reiss: Investment decreases with the leakage rate but increases with the elasticity of
spillovers.
2.4 The empirical record on spillovers
The lack of theoretical consensus regarding spillovers is matched by an equivocal empirical
record. Studies break down into three classes: Those examining the impact of spillover pools on R&D,
those examining survey-based measures of learning and imitation, and those examining spillovers and
growth. The studies of spillover pools consistently indicate that R&D intensity and outcomes increase
with the size of the spillover pool (Jaffe 1986, 1988). However the spillover pool as constructed in these
4
Romer (1990) captures spillovers as the pool of knowledge underlying the “designs” that have been produced. This
pool is freely available as a non-rival input in the creation of new designs. Since there is no parameterization of
spillovers the model offers no propositions about their impact.
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studies (sum of R&D spending by firms in the industry) is highly correlated with market size, and thus the
spillover coefficient may be capturing market size effects. Moreover the empirical tests examine the
impact of pool size, whereas propositions in the models pertain to the behavioral (percentage of pool that
leaks) or technological (elasticity of the pool on focal firm output) dimensions of spillovers.
In contrast, the survey-based studies examine the behavioral and technological dimension of
spillovers. The behavioral and technological dimensions are captured through questions regarding
learning mechanisms and imitation lags. The learning measures are self-reports by R&D managers of the
mechanisms that are most effective for learning about technology; the imitation lag measure is a selfreport of the time it takes to imitate a major patented new product invention. Levin, Cohen, and Mowery
(1985) find that the imitation lag measure has no significant effect on R&D intensity. Levin (1988)
looking at the learning mechanisms finds none of them to be significant in explaining R&D intensity.
Cohen, Nelson, and Walsh (2000) using new survey data find that R&D intensity increases with the
importance of ideas from rivals, but decreases with the importance of information from suppliers and
market mediated information from rivals. Finally, Levin and Reiss (1988) identified three survey
measures potentially related to the elasticity of spillovers (the importance of rivals to technological
progress, the importance of government research to technological progress, and technological maturity).
None of these explained variation in the elasticity of the spillover pool.
In studies of spillovers and growth, Ellison and Glaser (1997) test whether observed levels of
industrial localization are different from what would be expected to occur randomly (without
agglomeration effects) given the Herfindahl index of industry plant sizes. They find that concentration is
non-random, but only slightly so. A coarse decomposition of concentration effects into natural advantages
versus spillovers (using decay in elasticity over expanded geographic region) suggests evidence of
spillover effects.
While Black and Henderson (1999) don’t directly test their conclusion that cities grow at a rate
proportional to human capital accumulation, they show it matches the stylized fact that city populations
increase in the percentage of the population that is college educated. This lends support to their model of
returns to own human capital which are increasing in the extent of local human capital (spillover pool).
While these growth studies provide evidence consistent with local spillover effects, other tests,
e.g., Klepper (2002) and Zucker, Darby, and Brewer (1998), indicate there is no effect of spillovers after
controlling for the local origin of firm founders.
In summary, there is no empirical consensus on spillovers with which to illuminate the theoretical
schism. One reason for this may be that the empirics capture spillovers as the sum of economic activity
(pooled spillovers). Thus the empirical measure differs from at least some of the theories (those which
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assume asymmetric spillovers). It also may differ from the actual functional form of spillovers.
Accordingly our empirical strategy is to test the functional form of the spillover pool.
3. Empirical Tests
We test the functional form of the spillover pool by examining firm innovation rates as a function
of relative knowledge in a market. To do so we begin by characterizing general functional forms in the
literature and then specifying our empirical implementations of those forms.
3.1 Functional forms of spillovers
A general functional form for spillovers allows the knowledge for each rival firm j, kj, to leak to
focal firm i by a pairwise specific parameter φij, such that the total spillovers available to firm i are
characterized by:
Si = Σj=/=i φij* kj
(2)
Note that the general form in equation 2 supports an infinite set of specific functional forms for
spillovers. Rather than examine an exhaustive set of possibilities, we restrict attention to those forms
currently employed in the innovation literature.
Pooled spillovers. As noted previously the predominant convention in IO and economic
geography (both theory and empiricism) treats φij = 1 for all i and j, as long as firms i and j are technically
and geographically proximate.5
Spi = Σj=/=i kj
(3)
Asymmetric spillovers. A broad definition of asymmetric spillovers suggests all matrices where
φij is not constrained to a single value. However the theoretical presumption that knowledge flows from
firms with more knowledge to those with less knowledge sets φij = 0 for all rivals whose knowledge is
below that of the focal firm:
Sai = Σj=/=i φij* kj
V kj > ki , and 0 otherwise
(4)
3.2 Empirical implementation of the functional forms
Within the general restriction for asymmetric spillovers in equation 4, the theoretical literature
has utilized two specific functional forms: leader-distance from evolutionary economics, and densityabove from endogenous growth. Our empirical implementation of these forms follows theoretical
convention (Spence 1984, Levin and Reiss 1984, Nelson and Winter 1982) in that we define relative
knowledge in terms of firm cost efficiency. Cost efficiency allows us to capture differences in cost for the
5
When firm are not proximate then spillovers decay with geographic and/or technical distance (see, for example,
Jaffe 1986 and 1988)
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same quality or differences in quality for the same cost. Following the same convention we measure
innovation as cost reduction.6 Our approach therefore preserves the primary theoretical foundations of
spillovers.
The first empirical form, leader-distance, matches the spillover construct in Nelson and Winter
(1982), where firms have likelihood p of imitating last period’s best practice (lowest cost function across
all rivals). Accordingly, we capture the leader-distance spillover pool as the cost distance between the
lowest cost firm and focal firm from the prior period:
Sldri = ci - minj ( cj )
(5)
A companion measure, laggard-distance, is the difference in cost efficiency between the least efficient
firm in a market and the focal firm.
Slgdi = maxj ( cj ) - ci
(6)
We test how a firm’s innovation (cost reduction) is affected by both distance measures. If
innovation is driven by spillovers and if spillovers are shared equally across firms (pooled), then we
expect distance to be insignificant. If instead innovation is driven by mean reversion, we expect the
coefficients on the two measures to be equal but of opposite sign. If, however, innovation is driven by
imitating best practice we expect the coefficient on leader-distance to be positive, but not equal to the
coefficient on laggard-distance. Such a result implies 1) that the laggards have more to gain from
industry knowledge than do leaders, and 2) that the amount they gain increases with their distance from
the leader.
The second empirical form, density-above, matches the spillover construct implicit in the
endogenous growth models where firms randomly encounter rivals and the amount of knowledge they
expropriate is a function of the rival’s surfeit knowledge (Jovanovic and Rob 1989, Jovanovic and
MacDonald 1994, Eeckhout and Jovanovic 2002). Density-above is the sum of the differences in cost
inefficiency between focal firm i and rival firm j for all firms more efficient than the focal firm. However,
by its nature, density confounds two fundamentally separable constructs – average knowledge stock of
competitors with higher efficiency and the number of such firms. The number of competitors above, na,
captures the likelihood of encountering a competitor with superior knowledge, while the average stock
captures the expected amount of knowledge gained per encounter. To isolate the effects of competition
from those of spillovers we decompose density into these two constituent elements. Accordingly, we
capture the density-above spillover pool with two variables: (a) count-above the number of firms with
lower costs than the focal firm, na; and (b) average-above the average difference in cost inefficiency
between focal firm i and rival j for all firms more efficient than the focal firm:
6
Cost efficiency can be improved by many factors other than innovation. Rather than treat those factors here in a
discussion of functional form, we deal with them later in the discussion of controls.
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Saai =(1/na)Σj ( ci - cj ) V cj< ci , and 0 otherwise
(7)
A companion measure for the nb firms with higher costs than the focal firm, average-below is the sum of
the cost distances for all firms whose cost is above the focal firm.
Sabi=(1/nb)Σj ( cj - ci )
V cj> ci , and 0 otherwise
(8)
We are interested in testing the null hypothesis of non-directional (pooled) spillovers using the
density measure, just as we were using the distance measure. While the distance test was principally one
of directionality, the density test will be more compelling because it implicitly tests equation 2, the
functional form for pooled spillovers. Under this form, the entire density of firm knowledge contributes to
the spillover pool, Spi. Since the entire spillover pool is the pool to the right of the focal firm plus that to
the left, we can express pooled spillovers in terms of the average knowlege measures:
Spi = Saai +Sbai
(9)
Thus to test the null hypothesis that spillovers are pooled, we compare the coefficients for
average-above and average-below. We accept the null hypothesis if the coefficients for average-above
and average-below are of equal magnitude.
As mentioned previously, equations 5 through 9 capture functional forms currently found in the
innovation literature. Since our goal is facilitating consensus within the existing literature, this seems to
be the right set of forms. However, we add a final form to show the potential payoff to reopening the
functional form question entirely. Our final form is a simple rank ordering of firms in the industry, count
above. While this measure is primarily used as a component of density above, it is potentially interesting
in its own right. It preserves directionality (it increases with the number of superior rivals) but fails to
capture the amount of rival knowledge.
Scai = count (j) V cj < ci , and 0 otherwise
(10)
For consistency with the other functional forms, we include the mirror image, count below:
Scai = count (j) V cj < ci , and 0 otherwise
(11)
Note that the sum of count-above and the count-below equals the number for firms (minus the focal firm)
in the industry and thus is also a measure of competition.
3.3 Industry
We conduct our tests in the banking industry following de-regulation. The industry was chosen
because it is fragmented with localized competition and has substantial innovation. Furthermore, because
banking is regulated, we can obtain quarterly cost data for the full census of insured banks.
Fragmentation is important because it allows us to compare discrete markets within the same
industry, where each market faces the same inverse demand function and shares the same technology.
Thus we can compare differences in spillover pools while controlling for other factors affecting cost
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improvement across distinct industries. We can also control for differences in level of demand through
differences in economic conditions across markets.
Cost data. The FDIC collects extensive data on bank inputs and outputs for all banks in its
insurance program (over 99% of all banks). We use the raw data on inputs and outputs to form a cost
efficiency measure that is comparable across firms. The use of cost as the measure of knowledge and
change in cost as the measure of innovation preserves the conventions in Spence (1984), Nelson and
Winter (1982) and Levin and Reiss (1984, 1988), where the goal of innovation is to reduce cost. The
measure is flexible in that it accommodates both process innovation (directly aimed at cost reduction) and
product innovation (higher price premium for given cost). An additional advantage of a cost efficiency
measure is that it is one-dimensional. Knowledge of all types gets collapsed into a cost equivalent.
Therefore we can feasibly define a knowledge (cost) frontier and have a meaningful reference for
direction and distance to that frontier. Such a measure is less feasible for multi-product industries, or for
industries comprising diversified firms with consolidated reporting.
There are two discrete definitions of market appropriate for banking: the state, representing
certificate/headquarters-level competition, or the municipality, representing branch-level competition.
Following Morgan, Rime, and Strahan (2004) our primary definition of a market is the state. However as
a robustness check we replicate all tests using Metropolitan Statistical Area (MSA) as the market
definition.
3.3.1. Innovation and spillovers in banking
The intent of this section is three-fold. First, we wish to reinforce the idea that banking has a high
level of innovation – thus an appropriate setting for a study of spillovers. Second, we want to argue that
banking is particularly appropriate for the study of spillovers because at any time there is as a body of
innovations at various stages of diffusion (spillover pool) as opposed to a single innovation that is
innovated and then imitated. Finally, we want to identify (and ultimately control empirically) factors other
than spillovers affecting firm innovation.
Level of innovation. Because banking is not a science-based industry, it doesn’t come to mind
when we list innovative industries. However, banking has had tremendous innovation and productivity
growth over the past 100 years (Batiz-Lazo and Wood 2001). Lerner (2002) documents 651 financial
services innovations of sufficient quality to merit reporting in The Wall Street Journal and 922 patents
awarded to financial services firms over the period 1990 to 2002. Indeed the annual growth rate in this
mature industry (6.6%) has outstripped GDP growth over the past twenty years. By way of comparison,
this growth rate places banking in the top third of the industries in the Carnegie Mellon Survey of R&D
managers (Cohen, Nelson, and Walsh 2000).
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To aid intuition about the nature of innovation in banking as well as its rate of diffusion, we offer
the example of check processing. Paper check processing in the U.S. peaked in the mid 1990s at fifty
billion transactions. The rate in 2004 was thirty-seven billion transactions. This rate corresponds to 101
million transactions representing 163 tons of paper per day. These paper transactions are being replaced
by two extremely important innovations: automated clearing house (ACH) transactions (direct deposit,
online banking, automatic bill payment, and E-checks) and ATM/debit card transactions. ACH
transactions have grown from 5.7 billion in 2000 to an estimated 8 billion in 2004, while ATM/debit card
transactions have grown from 10 billion to 19 billion over the same period. These innovations offer two
benefits over paper checks. First, they reduce costs for the bank. The average cost per electronic
transaction is $0.02, versus $0.16 per paper transaction. Second, the innovations offer convenience and
cost savings to the customer—not having to write checks or pay postage to mail them. Accordingly the
innovations also have the potential to enhance demand.7
Body of innovation. Most studies of innovation in banking examine diffusion of innovations
rather than invention (with noted exceptions, Lerner 2002, Frame and White 2004). Theories of spillovers
accommodate both invention and imitation (diffusion). Imitation is direct use of embodied knowledge
whereas invention combines knowledge underlying an existing invention with the firm's own R&D to
create new inventions. Thus imitation/diffusion is a subset of the innovative activity arising from
spillovers.
The prevalence of diffusion studies stems from the natural-experiment quality of the data:
Diffusion of any one innovation allows researchers to control for its intrinsic quality, while examining
how firm and market characteristics affect innovative behavior (where innovation is defined as adoption).
In contrast, studying invention would have to compare innovations of different qualities arising in
different contexts from different firms. While focusing on diffusion can be viewed as a limitation, it
covers a substantial share of banks’ innovation decisions as well as their performance improvement (there
are approximately 10,000 potential adoptions for each invention). In addition, the same basic model of
firm profit maximization drives invention as well as adoption (with the exception that invention adds
uncertainty as well as concerns with appropriability).
Studies of banking diffusion pertain primarily to three important innovations: ATMs, Small
Business Scoring Systems (SBSS), and transactional Web sites. There is little need to describe ATMs
because they are ubiquitous. They were introduced by Chemical Bank in 1969, by 1979 they had been
adopted by 12% of banks (Sharma 1992), and as of 2000 were fully diffused throughout the industry.
SBSS is a scoring system for assessing the credit risk of commercial loans developed by Fair Isaac in
1993. This is the commercial equivalent of their FICO system for evaluating consumer credit. As of 2000,
7
All data in the paragraph are from the Nilson Report.
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50% of large banks had adopted SBSS (Akhavein et al. 2005). The final innovation, Internet banking, was
introduced in 1995 by Wells Fargo, initially as a means to allow customers access to their account
information. Ultimately Web sites began accommodating financial transactions. As of 2004, 75% of
banks had Web sites, 80% of which were transactional (Sullivan and Wang 2005).
The histories of ATMs, SBSS and Internet banking discussed above and captured in Figure 4,
together with the fact that these comprise only three of the 651 significant banking innovations, suggest
an environment where numerous innovations are simultaneously being generated and adopted/diffused.
Thus in any given year there are innovations at each stage of a diffusion cycle and firms are making
decisions as much (if not more) about what to adopt as whether to adopt. This is precisely the
environment of diffuse innovative knowledge that spillovers seem to connote.
----------------------------------Insert Figure 4 about here
-----------------------------------
Other factors affecting innovation. To understand other factors affecting innovation we turn to
empirical studies of these three major innovations. Studies by Hannan and McDowell (1984) and Sharma
(1992) of ATMs, by Sullivan and Wang (2005) of Internet banking, and byAkhavein et al. (2005) and
Bofondi and Lotti (2006) of SBSS identify some general firm and market level factors affecting the
adoption of banking innovations.
Across these studies, the only market factor consistently associated with adoption is market
concentration. Higher concentration (lower competition) increases the rate of adoption. This is consistent
with the Schumpeterian market power hypothesis. Market size (in the few studies where tested) tends to
decrease adoption. This may mean that competition is suppressed in large markets. Factors that are
significant in some studies but not others are wages, market growth and urbanism.
Not surprisingly, firm effects have a greater influence on innovation. Factors that consistently
predict speed of adoption are firm size, membership in a bank holding company, and years since
introduction. Their directions match expectations from adoption models. Adoption increases with firm
size, reflecting the large customer base over which to reap the marginal revenues or cost savings. Time
since introduction is a proxy for falling adoption costs. That the holding company is significant above and
beyond scale suggests something about the value of headquarters in either evaluating the merits of a large
body of innovations or providing scale economies or learning curves across adoptions.
Taken together the results suggest the adoption process reflects profit maximization logic, and
that there is greater heterogeneity within markets than across markets in the factors affecting profitability.
Nevertheless, since our empirical strategy is to attribute efficiency gains not otherwise accounted for to
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spillovers, we control for all these time-varying market and firm-level factors. In addition we employ an
Arellano-Bond specification which inherently controls for permanent differences across firms (and by
extension markets) through first differencing.
3.3.2 Trends in banking during the period
A number of industry changes occurred during the period we examine. We want to understand the
extent to which these, rather than spillovers, are driving improvement in bank efficiency. The primary
exogenous force affecting the industry was deregulation. Branching restrictions of U.S. banks were
gradually relaxed between 1979 and 1997 first through changes in state regulations and ultimately
through the Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994 which repealed all
limits on branching across states by January 1, 1997. The intent of the changes was to offer U.S. banks
scale economies to compete more effectively with foreign banks and non-bank intermediaries. The net
effect of both threats had been a decrease in banks’ commercial/industrial lending share from 30% to 16%
over the period 1983 to 1991.
Deregulation had the intended effect of increasing the number of branches from 38,738 in 1980 to
64,079 in 2000. This heightened branch-level competition fueled consolidation (Figure 5), initially
through failures (1,352 through 1993) but ultimately through mergers. These mergers were initially
motivated by cost savings. When banks acquired competitors they consolidated back office operations
and closed branches in overlapping territories. These efforts reduced costs in the target by about 20%, and
also reduced the number of competitors. Thus scale economies are a competing explanation for improving
cost efficiency.
----------------------------------Insert Figure 5 about here
----------------------------------The banks also responded to competition by adopting a client-based approach to banking. The
client-based approach (in conjunction with legislative changes from the Glass Steagel Act allowing banks
to underwrite securities) led banks into new areas (underwriting, derivatives, investment management,
mutual funds, insurance, and annuities). The complementarities between the areas (the ability to cross-sell
and leverage customer knowledge and monitoring from one area to another) yielded scope economies in
relationship management. These scope economies provided additional rationale for acquisitions, since
each acquired customer carried higher lifetime value.
The aforementioned motivations for merger ignore additional advantages ultimately realized by
the large banks: risk reduction through geographic and product diversification, scale economies in
operations, information technology, and ability to amortize marketing and R&D expenditures over
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broader output. Further, the ability to exploit innovation over a broader output increased the returns to
innovation and accordingly increased the incentives to innovate.
Thus a number of things were occurring in banking during the period we examine. The picture we
want to paint is that these forces created the stimulus for innovation. When these factors act as a stimulus
they aren't really a competing explanation to spillovers. Rather they are a complement – firms need a
means to respond to the stimulus. There are three means to innovate at the bank level. The most difficult
means is innovation driven exclusively from own efforts. A marvelous example of this is the John Reed’s
conceiving of Citibank’s (then First National City Bank) back room as a factory and completely
reconfiguring operations accordingly (HBS 9-474-166). The easiest means to innovate is to imitate or
adopt the innovations of rivals. An intermediate strategy is to combine knowledge of rivals’ innovations
with own efforts to generate new inventions. Competition may stimulate all three, but the role of
spillovers differs across the approaches.
One fairly immediate mechanism for gaining rival knowledge is merger – the acquiring bank
either obtains knowledge from the target and exploits it in the parent, or diffuses the parent’s knowledge
throughout the target, as in Bank One (HBS 9-394-043). While such direct transfers of knowledge are
often treated as spillovers, we take the conservative view that purchasing knowledge is an interesting but
distinct phenomenon from spillovers. Accordingly we control for these effects in stage 2 tests.
In summary, trends in the industry suggest that in addition to the market and firm controls
identified in the diffusion studies, we add controls for competition, scale economies, and mergers.
3.4 Empirical Model
Analysis proceeds in two stages. In the first stage we model an industry cost frontier to collect
measures of cost efficiency for each firm in each year. In the second stage, we model changes in a firm’s
efficiency (derived from stage 1) as a function of its spillover pool, where the spillover pool is
alternatively defined as each of the three functional forms characterized in section 3.1.
Stage 1-Firm efficiency.8 We follow convention in studies of bank efficiency by modeling a
stochastic cost frontier using a translog cost function (Cebenoyan, Papaioannou, and Travlos 1992,
Hermalin and Wallace 1992, Berger, Hancock, and Humphrey 1993, Mester 1993). Stochastic frontier
analysis, developed by Aigner, Lovell, and Schmidt (1977), is based on the econometric specification of a
cost frontier. To date, more than 500 studies have employed the translog cost frontier to model banking
efficiency (EconLit), the most recent being Amiti and Konings (2007). The model assumes that the log of
firm i’s cost in year t, cit, differs from the cost frontier, cmin, by an amount comprising two distinct
8
The stage one analysis was originally conducted in Knott and Posen 2005. Accordingly this discussion, and the
later discussion of the first stage model results, follow that paper very closely.
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components: a standard normally distributed error term eit, and a cost inefficiency term modeled as a nonnegative random variable uit – which we assume to take the form of a truncated normal distribution.9
Potential problems with observations that are far from the sample means have led some
researchers to adopt non-parametric approaches to frontier analysis (Wheelock and Wilson 2006). The
advantage of non-parametric approaches is that they don't impose a functional form on the distribution of
the efficiency term. This arises from the fact that all error is ascribed to efficiency in non-parametric
models. These recent non-parametric techniques solve the problem of outlier sensitivity through partial
frontiers, but retain the problem of noise (Wheelock and Wilson 2006). Unfortunately the work does not
compare its estimates to those in prior studies, nor does it offer other approaches to validating the
methodology. The main conclusion in Wheelock and Wilson (2006) is that large firms have the greatest
efficiency improvement. This conclusion coincides with views expressed by Berger and Mester (2003)
and Bernanke (2006) that technical change has favored large banks at the expense of smaller banks, but
has not been demonstrated elsewhere.
Given broader acceptance for efficiency measures derived from the translog cost function and
given the ability of those measures to explain phenomena related to bank inefficiency such as bank failure
(Berger and Humphrey 1992, Wheelock and Wilson 1995) and problem loans (Berger and DeYoung
1997), we continue to employ them here. We address attendant concerns regarding outliers in our second
stage analysis.
One particularly nice feature of the translog cost function is its ability to accommodate the
complex array of bank inputs and outputs. In addition, the translog form accommodates tradeoffs in both
market strategies (product mixes and prices) and operational strategies (input mixes).10 The basic translog
cost function models a cost minimizing firm i in year t operating with (in log form) outputs yit and input
prices wit:
cit = β 0 + ∑ β 1 j yitj + ∑ β 2 k witk + 1 2 ∑ ∑ β 3 jj yitj yitj +
j
k
j
+
j
1
2
∑∑β
k
k
4 kk
witk witk + ∑ ∑ β 5 jk y itj witk + u it + eit (12)
j
k
where:
c it
=
log observed firm cost
9
Other distributional assumptions are also possible, the most common of which are the half normal and exponential
distributions. All results are robust to these alternative distributions.
10
Note that the translog model used in panel studies of the banking literature does not include a fixed effect. The
objective of their studies, and ours, is to capture between firm differences in efficiency over time. The inclusion of a
fixed effect would remove mean firm efficiency differences and thus only capture variation within firms over time.
We remove mean firm differences in the second stage of our analysis.
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yitj
=
vector of log output levels - j indexes output elements
witk
=
vector of log input prices - k indexes input elements
u it
=
cost inefficiency with truncated normal distribution
e it
=
error term with normal distribution.
We pool data for all firms over fourteen years using the model to capture firm-year measures of
cost inefficiency relative to a global and permanent cost frontier. We collect the estimates of the expected
value of firm-year cost inefficiency in stage 1, E(uit | eit), which for convenience we continue to label as
uit. We then use these estimates as the dependent variable in stage 2 to test the functional form of the
spillover pool.
Stage 2-Test of spillover pool. We model innovation (improvement in firm cost efficiency) as a
function of three specifications for the firm’s spillover pool. Equation (13) tests for spillover symmetry,
while controlling for time varying firm and market characteristics:
ρ
u i ,t +1 = β 0 + β1 S it + β 2 Fit + β 3 M jt + ∑ ( β n u i , t +1−n ) + ε
(13)
n =1
where:
uit
=
firm cost inefficiency
S it
=
the spillover pool for firm i under the various functional forms
Fit
=
vector of time-varying firm characteristics
=
vector of time-varying market characteristics.
M
jt
In the above time series model innovation is captured as current period cost (on the left hand side)
relative to cost in the prior periods (on the right hand side). This lagged dependent variable serves to
capture the significant persistence in the data generating process – in that firm efficiency changes only
slowly over time.11 In addition to the persistence of the dependent variable, our key independent variables
(spillover pools) are constructed from a lag of the dependent variable. As such, our model is inherently
dynamic. The use of lagged dependent variables in a fixed-effects estimation leads to biased estimates
(Nickell 1981). In order to account for this, Holtz-Eakin, Newey, and Rosen (1988) and Arellano and
11
In section 4 of the paper – during our discussion of the first stage estimation results – we provide explicit data on
the extent of persistence.
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Bond (1991) develop a Generalized Method of Moments (GMM) estimator (Arellano-Bond estimator),
which has since become a standard procedure in estimating dynamic models with panel data. The
Arellano-Bond model controls for endogeneity by estimating a first difference model using lagged values
of the dependent variable as instruments for the lagged difference. Because our spillover pool variables
are derived from the cost variables, they too suffer from estimation concerns. We treat the spillover
variables as endogenous (correlated with both current and prior period error terms). As such, we
instrument the differences in the spillover variables with further lags of the levels of the spillover. Our
primary model uses two lags of the dependent variable to capture the dynamics of the efficiency
adjustment process, although the results are robust to a variety of alternative lag structures.
3.5 Data and Measures
The data for the study comes from the FDIC Research Database that contains quarterly financial
data for all banks filing the “Report of Condition and Income” (Call Report). Upon entry into the market,
each bank is allocated a unique certificate number by the FDIC – and we take the bank (certificate
number) as our fundamental unit of analysis. The FDIC classifies and compiles data on two distinct types
of banking entities: (a) Commercial banks, which include national banks and state-chartered banks
(excluding thrifts) insured by the FDIC; and (b) Savings banks which operate under state or federal
banking codes related to Thrift institutions. Commercial banks, which are the focus of this paper, differ
from Savings banks in that Savings banks have traditionally been limited in both the types of deposits
they could accept and the types of loans they could provide. Given the well-known irregularities in the
Thrift industry during the 1980s, we confine our analysis to commercial banks. We examine each of the
fifty states plus the District of Columbia for the period 1984 to 1997. This initial data set contains
694,587 firm-quarter observations. Following convention in the banking literature we aggregate to annual
data by averaging the quarterly data (Mester 1993). The final first stage data set comprises 170,859 firmyear observations.
While there is considerable debate as to the choice of inputs and outputs in the banking sector, a
review of the literature suggests some convergence around a model that sees capital and labor as inputs to
the production process and various forms of loans as outputs (Wheelock and Wilson, 1995). We collect
data to construct seven variables related to banking efficiency in log thousands of constant 1996 dollars.
The dependent variable is total cost – total interest and non-interest expenses. The six independent
variables are divided between input prices and output quantities. Input prices are: (a) labor price – salary
divided by the number of full-time-equivalent employees; (b) physical capital price – occupancy and
other non-interest expenses divided by the value of physical premises and equipment; (c) capital price–
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total interest expense divided by the sum of total deposits, other borrowed funds, subordinated notes, and
other liabilities. Output quantities are stocks ($1000) of: (d) mortgage loans, (e) non-mortgage loans, and
(f) investment securities.
In order to test the hypotheses in the second stage model, we create year-specific spillover pools
for each firm in accordance with equations 5 through 11. To test the leader distance spillover
specification, we calculate leader-distance as the cost efficiency of the focal firm less that of the leader.
The laggard distance is calculated in an analogous manner.
To test the density above and below specification, we disaggregate density into its constituent
parts – count of competitors and average knowledge stock of competitors. Count captures the likelihood
of encountering a rival; average captures the expected value of knowledge from that rival. To disentangle
pooled from asymmetric spillovers, we disaggregate count into count_above – the number of firms more
efficient that the focal firm, and count_below – the number of less efficient firms. We also disaggregate
average into average_above – the average difference in cost efficiency between the focal firm and each
lower cost rival and average_below (calculated in an analogous manner).
We add to the spillover pool variables a number of firm-level and market-level controls. At the
firm level, we control for bank scale with seven measures: (a) assets -in log thousands of constant 1996
dollars; (b) branch_count - number of branches operated by the bank and (c) market_share – as the share
of the total market size based on loan volume. In addition, because approximately one-third of banks are
owned by a bank holding company that controls more than one bank (certificate), we include (d)
holding_company – as a dummy variable for holding company ownership, as well as a number of
measures of the size of the holding company: (e) hc_certificates – the number of additional banks
(certificates) held by the holding company; (f) hc_branches – the number of additional branches in the
bank holding company system beyond the number of branches in the observation certificate; and (g)
hc_states – the number of additional states in which the holding company operates banks. All count
variables are logged, but all results are robust to the use of levels.12
At the market level we control for demand and supply-side factors affecting the firms' incentives
to innovate. Controls for demand include: (h) population – log of market population; (i) permits – logged
number of building permits (capturing growth); and (j) market size – logged total market value of loans.
Controls for supply side include: (k) count_firms – logged number of firms in market; (l) Herfindahl –
market concentration; (m) entered – logged number of banks entering the market; (n) failed – logged
number of failing banks; and (o) merged – logged number of bank mergers. In addition to these time
12
All variables are in log form except those that inherently take on values between 0 and 1. Where there is the
potential to log a zero measure, one is added to the variable prior to logging.
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varying controls, Arellano-Bond estimation inherently controls for permanent characteristics of firms and
markets via first differencing.
4. Results
Stage 1 - Firm Cost Efficiency. Table 1 provides variable descriptions and summary statistics of
the data used in the Stage 1 stochastic frontier model. We specify a truncated normal distribution for the
inefficiency term and a normally distributed error term. Estimation is conducted using maximum
likelihood techniques. Results from the stage 1 analysis using equation 12 are given in Table 2. The
objective of the stage 1 analysis is to provide the firm-year cost inefficiencies for stage 2. While a
discussion of the estimated coefficients for the frontier model is outside the scope of this paper, the
coefficient estimates are consistent with expectations as: (a) total costs appear to rise with output and
increases in the price of capital, and (b) firms substitute labor and physical capital in response to changing
prices for these inputs.
The more important result of the stage 1 frontier estimation is the expected value of the
inefficiency terms, uit. The distribution of the cost inefficiency is given in Figure 6a and the mean value
over time is depicted in Figure 6b. Note that the inefficiency metric, uit, is by construction a log-based
measure of the cost multiplier in a multiplicative form (unlogged) of equation 12. The mean uit over the
entire period is 0.171, which indicates that the mean firm has a cost structure 18.6% above that of a firm
on the cost frontier. The data also indicate that while the mean cost inefficiency changes over time in
response to changing technologies and demand conditions, the general trend is toward increasing
efficiency (decreasing cost), which is as expected.
------------------------------Insert Tables 1 and 2 about here
------------------------------------------------------------Insert Figure 6 about here
------------------------------While changes in cost efficiency are a standard measure of innovation in the banking literature,
their use in other sectors is less common. In order to provide intuition for this measure, we compare its
dynamics to productivity dynamics in other sectors. Our approach is to mimic longitudinal micro-data
(LMD) studies and present a transition matrix of firm efficiency (Table 3). The transition matrix
characterizes how a firm’s efficiency in one period is related to its efficiency in the subsequent period.
The table decomposes firm efficiency into quintiles, then depicts year-to-year movements across quintiles
by comparing rows and columns. As an example, take the row labeled 1. This represents the highest-
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performing (lowest cost inefficiency) firms in a given year. The table indicates that the majority of firms
(78%) remain in the top (lowest cost) quintile in the subsequent year, 15% drop one quintile, 2% drop two
quintiles, less than 1% drop to each of the bottom two quintiles, 2.7% merge with other firms, and 0.5%
fail outright.
------------------------------Insert Table 3 about here
------------------------------The table indicates three patterns of interest. First, relative firm efficiencies are fairly stable. The
highest percentages are along the diagonal, meaning that in general firms remain in the same cost quintile.
This exemplifies the persistence of firm efficiencies driving the need for lagged dependent variables in
the model. Second, failures and mergers increase with firm cost. The highest percentage of mergers and
failures are coming from the highest-cost firms. Third, new firms tend to enter at the industry extremes;
27% enter the lowest cost quintile, while 60% enter the highest cost quintile. These three patterns are
similar to those found in LMD studies of other sectors (See Bartelsman and Doms 2000 for a review.) We
include this table to convey two ideas: 1) Efficiency trends in banking are representative of general trends
in productivity/efficiency in other settings; 2) Our translog cost measure captures these trends.
Stage 2 – Arellano-Bond Estimation of the Test of Spillover Functional Form. Table 4
provides variable descriptive statistics for the approximately 122,000 bank-year observations used in the
Stage 2 analysis, and Table 5 provides the correlation table. Results for tests of spillover form (equation
13), estimated using our primary specification, are presented in Table 6. We first review models with
controls to show the effects of other factors affecting improvement in bank efficiency. We then turn to our
main test.
------------------------------Insert Tables 4, 5 and 6
------------------------------Control variables
Looking first at the control variables in isolation in models 1 through 4, we note that these
variables behave as one would anticipate. In model 1, we note that the lagged dependent variables were
both significant. The first lag was positive and significant. The second lag was negative and significant,
but an order of magnitude smaller than the first lag. We examined further lags of efficiency, but found
them to be largely non-significant. This suggests that the adjustment period for shocks to efficiency is
approximately two years. Also of note in this model are the tests for autocorrelation in first differenced
error terms. For the moment conditions of Arellano-Bond estimation to be valid, second order
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autocorrelation must be non-significant. In our estimation models, while first order autocorrelation was
significant (Table 6 presents z statistics), second order correlation was non-significant, suggesting the
moment conditions hold. This remained true for all models in Tables 6-8.
Model 2 adds the firm controls. Of the two size metrics, the number of branches was negative and
significant (reflecting cost reduction), while assets were non-significant. The negative sign on branches
suggests that innovation is increasing in the size of the bank. (The lack of significance for assets is largely
expected as assets and branches are correlated at 0.79). The coefficient on holding company is significant
above and beyond the number of branches. Both results match studies of innovation diffusion in banking
discussed in section 3.3.1 (as well as innovation theory, where the returns to innovation are defined as
unit margin increase times output scale). We included additional controls for holding company scale
(number of banks, number of states, and number of branches); however, because these variables are
correlated above 0.9, their coefficients should not be interpreted separately. Finally, market share was
positive and significant suggesting that market power inhibits innovation. This result conflicts with
conclusions from the diffusion studies that market concentration (reflecting market power) increases
innovation.
Model 3 adds controls for market demand. Of the two measures for market size, population is
positive and significant while industry size was negative but not significant. Since these variables are
highly correlated, they are not separately interpretable. However, the joint effect of the two controls
indicates innovation decreases with market size. This matches results from the diffusion studies discussed
in section 3.3.1. Market growth, as captured by building permits, was negative and significant indicating
that growth increases innovation (decreases cost) which matches Sharma (1992) and Hannan and
McDowell (1984) results for adoption of ATM technology.
Model 4 adds controls for market supply. While the coefficients for the number of firms (count)
and market concentration (Herfindahl) are both negative, neither is significant in this model (although
both become marginally significant in later models). Of these two measures for competition, only
concentration has been included in prior studies. Concentration has tended to increase innovation in those
studies. This had been interpreted as evidence of the Schumpeterian market power hypothesis. The fact
that market share decreases innovation in all our models tends to argue against that interpretation. The
other obvious interpretation for the market concentration result is that lack of competition dulls the
incentives to innovate. The fact that number of firms (often viewed as an inversed measure of
concentration) also increases innovation suggests something more nuanced about the effects of
competition. Of the remaining supply variables, only failure is significant. Failures decrease the efficiency
of incumbents, possibly by reducing competitive pressure.
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Main Test
Models 5 through 7 test the probability density form of spillovers. Recall that density has two
components – count above, which captures the likelihood of encountering a more efficient rival, and
average above, which captures the expected efficiency difference of those rivals. We test each variable
separately, then test them jointly. In model 5, we disaggregate the number of firms into count_above and
count_below. While both were negative and significant, the coefficient on count_below was an order of
magnitude larger (more negative) than was the coefficient on count_above. A chi squared test rejects the
equality of the coefficients (p<0.0001). This result suggests that the influence of the number of firms is
asymmetric. Firms respond more to competition from laggards than from leaders.
An alternative interpretation of the result is that it is picking up effects from asymmetric
spillovers (since count is one of the components of probability density). However, the result is
inconsistent with an asymmetric spillover story (unless one believes that less efficient firms somehow
offer more useful knowledge than more efficient firms). The most likely explanation for this result is that
count not only captures the likelihood of encountering a rival, but also captures competition. From that
perspective the results suggest firms respond more strongly to competition from less-efficient rivals than
from more-efficient rivals.
Model 6 presents the results of the average_above and average_below elements of probability
density using aggregate firm count rather than decomposed firm count. The coefficient on average_above
is negative and significant. In contrast, the coefficient on average_below is positive and significant –
although an order of magnitude smaller than average_above. These results are consistent with
expectations for asymmetric spillovers – the knowledge above is more valuable than the knowledge
below.
Model 7 includes both elements of probability density – count and average – in the same model.
While average_above remained negative and significant, average_below became non-significant. Once
again, a chi square test confirms that the coefficient on average_below is significantly smaller than that of
average_above (p<0.0001). The coefficients on count-above and count-below are negative and significant
as they were in model 5, but count-below remains significantly larger (factor of three) than count-above.
Thus again competition from below seems to provide greater stimulus to innovation than competition
from above. In sum, models 5 through 7 provide significant evidence for asymmetric spillovers of a
probability density form.
Model 7 also allows us to test the null hypothesis that the entire rival pool (pooled spillovers)
drives innovation. We do this by comparing the coefficients on average_above and average_below. If the
null hypothesis is correct, then the coefficients on average_above and average_below should be of equal
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magnitude. Tests that the two coefficients sum to zero were rejected at the 0.001 level in both models 6
and 7. Thus pooling all rival knowledge does not appear to be the correct functional form for spillovers.
We examined the marginal effects of the main variables in model 7. A one percent increase in
average_above leads to a 0.06 percent decrease in cost. Of the significant control variables, only the
marginal contribution of market share was larger (at 0.4 percent). Indeed, the marginal effect of
average_above was 14 times larger than that of concentration, 15 times larger than that of
holding_company ownership, and at least 32 times larger than the marginal effect of any of the entry and
exit measures.
In model 8, we present the results of the leader_distance spillover specification. The coefficient
on leader_distance was negative and significant, while the coefficient on laggard_distance was nonsignificant. A chi-squared test of the difference between leader_distance and laggard_distance was
highly significant (p<0.0001), providing further evidence in support of asymmetric rather than pooled
spillovers. The marginal effect of a one percent increase in leader distance was a 0.04 percent decrease in
cost. Thus, the marginal contribution of leader_distance was similar to that of average_above.13
Stage 2 – Robustness Models. We conducted two broad sets of robustness analyses – first to
alternative constructions of the data sample and second to alternative estimation models. With regard to
the sample, we examined four alternative constructions (Table 7). First, to reduce the potential effects of
outlier markets, we dropped the three largest states (models 1 and 2). The results on average_above and
average_below were largely unchanged. Average_above remained significant and negative, while
average_below became non-significant. This continues to provide support for the asymmetric spillover
hypothesis. Moreover a test that the two coefficients are equal was again rejected at the 0.001 level. Thus
we continue to reject the null hypothesis that spillovers are pooled. Of note, however, is that with this
sample construction, leader_distance became non-significant.
Second, to reduce the potential effects of outlier firms, in models 3 and 4 we dropped bank-year
observations in the top and bottom 5 percent of the sample. The results were robust to this specification.
------------------------------Insert Table 7 about here
------------------------------13
A brief comment on the lagged dependent variables is in order. In models 7 and 8, the coefficient on the first
lagged dependent variable is greater than one. This would imply a kind of Mathew effect in which disparities in
efficiency grow over time because the efficiency of high-efficiency firms grows faster than that of low-efficiency
firms. Note, however, leader distance is constructed as own efficiency less that of the leader (and the analogous
construction for laggard distance). As such, the true lagged dependent variable efficiency in model 8 is 1.13900.3299=0.809.
7/8/2008
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Third, because patterns of entry and exit are non-random in the sense that low-efficiency firms
are more likely to exit, and entrants are less likely to be high-efficiency firms in their early years, we drop
state-years from the sample based if they exhibit high levels of churning (entry and exits). The mean level
of churn in the industry over our sample period was 0.06. That is, 6 percent of the population enter or exit
in a given year. In models 5 and 6, we drop from the sample all state-years in which churn exceeds 6%.
This reduces the sample size by approximately 40 percent. Average_above and average_below were both
highly significant. Indeed, average_above nearly doubled in magnitude from the main estimation results.
Thus in more stable markets the effects of asymmetry are more pronounced. This continues to provide
support for the asymmetric spillover hypothesis and further rejects the null hypothesis that spillovers are
pooled. As in models 3 and 4, leader_distance is non-significant.
Fourth, we assumed in our main model that the market and accordingly the market characteristics
and spillover variables were defined by state boundaries. In models 7 and 8, we reconstructed all market
characteristics and spillover variables using Metropolitan Statistical Area (MSA) as the definition of
market. The results for the probability density hypothesis are maintained. Average_above is negative and
significant, while average_below is positive and significant. Thus we continue to find support for
asymmetric spillovers and continue to reject the null hypothesis that spillovers are pooled.
Leader_distance again failed to hold – which further calls into question this spillover specification.
Our final set of robustness checks examines alternative specifications to equation 13 (Table 8). In
models 1 and 2 we replace Arellano-Bond with a simple bank fixed effect specification. The results were
robust to this alternative model specification. The coefficients for average_above, average_below, and
leader_distance are of the same sign and level of significance as in the main specification. In models 3
and 4 we test a weighted fixed effect specification with weighting by the number of banking certificates
in the state. Once again, the coefficients on average_above, average_below, and leader_distance are
significant and of the same sign as in the main specification.
------------------------------Insert Table 8 about here
------------------------------In sum, the robustness analyses provide significant additional support for the asymmetry of
spillovers. While the leader_distance result seemed sensitive to sample specification, the coefficient
estimates on average_above and below were remarkably robust. In all specifications, average_above was
negative and significant, and always significantly larger than average_below. Thus across all tests our
results reject the null hypothesis that spillovers are pooled in favor of a hypothesis that they are
asymmetric and conform to a probability density functional form.
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5. Discussion
While spillovers are a crucial factor in determining the optimal environment for innovation and
growth, there is no consensus regarding their impact on firms' innovative behavior. One reason for this
may be that models differ in their assumptions about the functional form of the spillover pool. Thus
knowing the correct functional form may facilitate consensus—either analytically (by modifying models’
assumptions) or empirically (by facilitating a critical test of competing theories).
Accordingly, we characterized and tested alternative specifications for the spillover pool in the
banking industry. We chose that industry 1) because it has one of the highest innovation and growth rates
in the economy and 2) it comprises fifty markets that share a common demand curve and underlying
technology. Thus we could exploit variance in spillover pools while controlling implicitly for technology
and explicitly for market factors affecting incentives to innovate. This is not possible for industries with a
single market (most of the manufacturing industries engaged in R&D).
Our results in that setting indicate that knowledge does appear to have directionality. The rate at
which firms increase their efficiency is related to the amount of knowledge held by more efficient firms
rather than the amount held by the entire set of firms. A test of the null hypothesis that spillovers are
pooled is rejected in all models.
In addition to the main model we conducted an extensive set of robustness checks including four
alternative sample constructions and two alternative model specifications for the main test. The
significant results for the probability density form of asymmetric spillovers are robust to all these checks,
as is rejection of the null hypothesis that spillovers are pooled.
One interesting result from the robustness checks is that the leader-distance form of spillover
pools is sensitive to sample construction. Thus it appears firms benefit from the set of knowledge held by
more efficient firms rather than their distance to the leader. This contrast is important for four reasons.
First, it means the role of spillovers is more nuanced than merely imitating best practice. Second, it means
that our spillover variables are not merely picking up an "opportunity to improve" effect (firms are not
merely improving based on how far they have to go). Third, the results suggest a model where firms are
scanning the set of more efficient firms and synthesizing what they learn with what they know/do
internally. Finally, this result together with the result that the number of superior firms has a negative
effect on innovation suggests that the underlying mechanism for spillovers is unlikely to be one of
randomly encountering a rival.
While our main interest was testing the functional form of spillovers, our efforts to isolate the
effects of spillovers allow us to say something about other factors affecting innovation. The most notable
results pertain to competition. In a model without spillovers neither market concentration nor number of
firms is significant. When we introduce asymmetric spillover pools the competition variables become
7/8/2008
Page 29
marginally significant. Thus competition seems to interact with spillovers. Competition creates an
incentive to innovate, while spillovers provide a means.
Our most interesting result regarding competition emerged when we decomposed the density
form of spillovers into its constituent elements (number of firms and knowledge per firm). We did this
precisely to isolate all potential effects of competition from our spillover measures. Because we were
looking at spillovers asymmetrically (treating firms above and below separately), we were able to
examine asymmetric effects of competition as well. Here we found that firms respond more to
competition from less-efficicient rivals than they do from more-efficient rivals. This result fits with the
intuition in "escape competition" stimulus for innovation, where firms innovate to restore lost profits
associated with laggards who have imitated them (Aghion et al 2001).
We wish to offer some caveats for the results. Our explanation for differential innovation rates
between leaders and laggards is that the cost to innovate for laggards is lower due to their ability to freeride on leader innovation. An alternative explanation relies on aspiration theory. In this view, laggard
firms are more likely to innovate because their lower profits give them greater incentive to do so
(Cockburn, Henderson, and Stern 2000). The puzzle with the aspiration explanation is that the firms with
the greatest incentive to innovate are by definition the ones with the least resources to do so. Thus
asymmetric spillovers is not an alternative to aspiration theory, it is the means (higher level of free inputs)
by which aspirations can be realized (Acs, Audretsch, and Feldman 1994).
A second caveat is that our test was conducted in a single setting – banking. What is appealing
about this setting is that market structure is not endogenously determined by technology (at least not
entirely). Accordingly it inherently controls for many unobserved factors that plague cross-industry tests
of innovative productivity. Despite the advantage, there are things unique to banking that may limit our
ability to extend results to other settings. First, this is a setting where patents don't appear to be very
important. The major innovations discussed in the paper (ATM, SBSS, and internet transactions) all
diffuse rapidly. Accordingly this is not a setting where profits are driven by patent-protected monopolies
for new products. Since patents offer temporary monopolies on inventions in exchange for full disclosure
of the knowledge underlying the invention, it is likely that spillovers behave quite differently in industries
where patenting is important, e.g., pharmaceuticals and semi-conductors.
A third caveat is that banking is an extremely dense industry – on average 10,000 banks with
60,000 branches over our sample period. Spillover patterns may differ in industries serving national or
global markets, e.g., autos, communications, and petroleum.
Fourth, this is a setting where we don't observe R&D expenditures, so we can't say anything
concrete about the link between spillovers and own R&D. Our implicit assumption in the empirics is that
R&D expenditures increase monotonically with firm size (matching the stylized fact in Cohen and Levin
7/8/2008
Page 30
1989). We have multiple measures for firm size, but the one that is consistently significant is branch
counts. Innovation increases with the number of branches in all models. If branch counts is a proxy for
R&D expenditures, then our spillover results hold in the presence of R&D expenditures. Having said that,
lack of R&D expenditures is a limitation, so to in separate analyses, we examined R&D expenditures and
spillover pools in 25 manufacturing industries. Results there are consistent with the results reported
here.14
These results have a number of implications. First, for theory, models of innovative behavior that
rely on identical firms with pooled spillovers conclude that innovation decreases with the potential for
spillovers and the number of firms. Our results indicate instead that innovation increases with the amount
of spillovers and with the number of firms (particularly less-efficient firms). Thus changing the functional
form of spillovers in such models may yield results that more closely match our observations.
Second, for the empirical anomaly of higher returns to spillovers than to focal firm R&D, the
results here imply that the anomaly is an artifact of specification error—pooling spillovers when their
correct functional form is asymmetric. Estimates of spillover elasticity using asymmetric spillovers
indicate values that are closer to expectations, i.e., less than or equal to the productivity of own R&D
(Knott and Posen 2008).
Finally, asymmetric spillovers offer a simple solution to the firm size and R&D puzzle—the
empirical regularity that large firms spend proportionately more on R&D, but that small firms have higher
R&D productivity. Asymmetric spillovers imply that small firms (those most likely to be laggards) derive
greater benefits from rival R&D than do large firms. Given that inputs from own R&D and spillovers
both contribute to innovative outcomes, estimates of R&D productivity that consider only own R&D
input (or equivalently consider own R&D plus a common spillover pool) will exhibit artificially high
estimates of R&D productivity for small firms.
14
Results available from the authors.
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APPENDIX 1. Bias in spillover coefficient estimates arising from a pooled specification
To examine possible bias arising from incorrect specification of the spillover pool, assume an
underlying Cobb-Douglas production function with the following form:15
ln Y = α ln C + β ln L + γ ln R + θ ln S U + ε1
(A1)
where S U is the ‘correct’ spillover pool (and could be the upper pool, or any other specification), and all
variables have an assumed subscripting (omitted for brevity) of firm i in year t. Assume further that:
S U = (1 − ρ it ) S T , 0 ≤ ρ < 1
(A2)
Thus the correct S U is a strict subset of the total industry spillover pool S T . We can think of ρ it , as the
proportion of the spillover pool that is redundant with firm i’s own knowledge in year t and thus S itU as
the spillover pool that firm i might make use of in period t. Substituting for S U in Equation 1:
ln Y = α ln C + β ln L + γ ln R + θ ln((1 − ρ it ) S T ) + π i + ε 1
(A3)
ln Y = α ln C + β ln L + γ ln R + θ 1 ln S T + θ 2 ln(1 − ρ it ) + π i + ε 1
(A4)
where Equation 4 is subject to the constraint that θ1 = θ 2 .
Any OLS specification that only examines S T is thus subject to an omitted variable bias as
θ ln(1 − ρ it ) is unobserved. There are two cases in which the use of S T rather than S U results in no
estimation bias. First, if ρit did not vary between firms or over time ( ρ it = ρ ), then it would be captured
in the intercept. Second, if ρit varied across firms but not over time such that ρ it = ρ i , then it would be
captured in firm fixed effects. In either of these two cases, the use of the total spillover pool S T rather
than the actual pool S U would have no effect on the outcome of the estimation. However, it seems
reasonable to assume that the amount of spillovers accessible to a firm and redundant with the firm’s
existing knowledge, changes over time. If so, estimates will be biased.
15
Note this definition of Y suffers from the conventional criticisms that in many industries the output only reflects
the appropriable portion of R&D and does not reflect quality improvements. Accordingly estimates will understate
the true value of R&D (Griliches 1979).
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Page 32
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Table 1. Stage 1 Data Summary
Variable
c
w1
w2
w3
y1
y2
y3
Description
cost
price_labor
price_physical capital
price_capital
mortgage
other loans
securities
Obs
174869
174673
173999
173789
172503
173373
173828
Mean Std. Dev.
7.98
1.27
2.97
0.28
-1.64
0.73
-3.54
0.41
9.47
1.58
9.63
1.40
9.58
1.47
Min
-0.82
-4.85
-9.93
-12.58
-1.37
-0.70
-1.27
Max
16.76
9.39
5.63
3.32
17.86
18.55
17.51
Units: ln(thousand - 1996 dollars)
Variable
c
c
1
w1
0.1929*
w2
-0.0418*
w3
0.1464*
y1
0.8640*
y2
0.9146*
y3
0.7603*
w1
1
0.2792*
0.0921*
0.1151*
0.1493*
0.0821*
w2
1
0.0452*
-0.1322*
-0.0594*
-0.0922*
w3
1
-0.0463*
0.1201*
0.0259*
y1
1
0.7711*
0.6883*
y2
1
0.6934*
y3
1
Table 2. Results from Stage 1 Regression
Dependent V ariable: ln(cost)
170859 observations
se
(2.836E-02)
w1w3
(1.188E-02)
1/2*w2sq
(2.429E-02)
w2w3
(9.368E-03)
1/2*w3sq
(1.039E-02)
y1w1
(9.163E-03)
y1w2
(5.630E-04)
y1w3
(4.992E-04)
y2w1
(5.197E-04)
y2w2
(7.419E-04)
y2w3
(5.821E-04)
y3w1
(4.637E-04)
y3w2
(4.571E-03)
y3w3
(1.854E-03)
Constant
Coef.
Coef.
w1
-8.691e-01***
-2.312e-01***
w2
-2.085e-01***
-4.964e-03***
w3
2.078e+00***
-2.519e-02***
y1
1.942e-02*
2.564e-01***
y2
4.262e-01***
3.230e-02***
y3
2.784e-01***
-7.015e-04
1/2*y1sq
9.331e-02***
-3.159e-02***
y1y2
-6.028e-02***
-2.019e-02***
y1y3
-2.049e-02***
-9.330e-03***
1/2*y2sq
1.225e-01***
2.952e-02***
y2y3
-5.541e-02***
-3.038e-02***
1/2*y3sq
8.827e-02***
1.418e-02***
1/2*w1sq
2.011e-01***
1.620e-02***
w1w2
3.016e-02***
5.320e+00***
Standard error in parentheses
+ significant at 10%; * significant at 5%; ** significant at 1%; *** significant at 0.1%
se
(3.730E-03)
(1.062E-03)
(1.612E-03)
(3.513E-03)
(1.457E-03)
(7.239E-04)
(1.286E-03)
(1.603E-03)
(9.048E-04)
(1.379E-03)
(1.402E-03)
(7.360E-04)
(1.256E-03)
(9.772E-02)
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Page 37
Table 3. Year-to-year transition matrix of firm efficiency
Next Year
Quintile
Low Cost
1
2
3
4
High Cost
5
Merge
Fail
Total
Enter
670
26.64
63
2.50
96
3.82
179
7.12
1507
59.92
0
0.00
0
0.00
2515
100
1
31,759
77.93
6,054
14.86
905
2.22
358
0.88
379
0.93
1,097
2.69
201
0.49
40,753
100
2
5,362
16.75
17,327
54.14
6,797
21.24
1,178
3.68
246
0.77
1009
3.15
86
0.27
32,005
100
3
702
2.23
6,447
20.48
15,857
50.38
6,374
20.25
770
2.45
1,187
3.77
135
0.43
31,472
100
4
254
0.84
923
3.05
6,074
20.10
16,164
53.50
5,141
17.02
1,414
4.68
244
0.81
30,214
100
5
394
1.26
346
1.10
817
2.61
4,736
15.12
22,282
71.11
1,968
6.28
790
2.52
31,333
100
39,141
23.26
31,160
18.52
30,546
18.15
28,990
17.23
30,325
18.02
6,675
3.97
1,456
0.87
168,293
100
Low Cost
This Year
Quintile
High Cost
Total
Note1: Includes firms in all states in the industry at any time from 1984 to 1997
Note2: Entrants are those entering as new certificates, but does not include conversions
7/8/2008
Page 38
Table 4. Data summary for Stage 2 test
Table 5. Correlation table for Stage 2 test
7/8/2008
Page 39
Table 6. Results: Stage 2 test of functional form using Arellano-Bond
7/8/2008
Page 40
Table 7. Stage 2: Robustness to Alternative Model Specifications
7/8/2008
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Table 8. Stage 2: Robustness to Alternative Model Specifications
7/8/2008
Page 42
Figure 1. Radar diagram
Ant hro p o lo g y
So ut h As ia Stud ies
So cio lo g y
1.4
1.2
As ian and M id d le Eas tern Stud ies
Bio lo g y
1
Slavic Lang uag es and Literatures
Chemis try
0 .8
Ro mance Lang uag es
Clas s ical Stud ies
0 .6
0 .4
Relig io us St ud ies
Earth and Enviro nment al Science
0 .2
0
Ps ycho lo g y
-0 .2
Eco no mics
Po litical Science
Eng lis h
Phys ics and As tro no my
Germanic Lang uag es and Literat ures
Philo s o p hy
His to ry
M us ic
His to ry and So cio lo g y o f Science
M athematics
His to ry o f Art
Ling uis tics
7/8/2008
Page 43
Figure 2a. The pooling assumption tolerates errors of redundant knowledge
Anthro p o lo g y
So uth As ia Stud ies
So cio lo g y
1.4
1.2
As ian and M id d le Eas tern Stud ies
B io lo g y
1
Slavic Lang uag es and Literatures
Chemis try
0 .8
Ro mance Lang uag es
C las s ical Stud ies
0 .6
0 .4
Relig io us Stud ies
Earth and Enviro nmental Science
0 .2
0
Ps ycho lo g y
-0 .2
Eco no mics
Po litical Science
Eng lis h
Phys ics and As tro no my
Germanic Lang uag es and Literatures
Philo s o p hy
His to ry
M us ic
His to ry and So cio lo g y o f Science
M athemat ics
His to ry o f Art
Ling uis t ics
Figure 2b. The asymmetry assumption tolerates errors of unique knowledge
Anthro p o lo g y
So ut h As ia Stud ies
So cio lo gy
1.4
1.2
As ian and Mid d le East ern Studies
Bio lo g y
1
Slavic Languag es and Lit eratures
Chemist ry
0 .8
Ro mance Lang uag es
Clas sical Stud ies
0 .6
0 .4
Relig ious Stud ies
Eart h and Enviro nmental Science
0 .2
0
Psycho lo g y
-0 .2
Eco no mics
Po litical Science
Eng lish
Phys ics and As tro no my
Germanic Lang uag es and Literatures
Philo s o p hy
Hist o ry
M us ic
His to ry and So cio lo g y o f Science
Mathematics
His to ry o f Art
Ling uist ics
7/8/2008
Page 44
Figure 3. Visual test of knowledge redundancy for chemicals (ISIC=2400)
patents granted 1995 to 1999 (by class) ISIC 2400 chemicals
95 R&D 2 8 15 23 29 40 43 44 52 53 55 62 65 68 72 73 106 118 126 128 132 134 137 141 148 156 162 181 204 205 206 210 211 215 219 220 222 224 239 241 242 249 250 251 252 264 300 313 324 340 343 359 383 385 401 403 422 423
0.0
0.2
0.2
0.2
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.8
0.8
0.8
1.4
3.2
4.6
1
8.4
13.2
13.7
15.5
22.3
22.3
23.2
24.0
3
1
26.5
2
1
1
1
1
26.5
27.7
1
27.8
1
1
28.0
2
2
1 2
16 4 6
1
1
7
1
2 1
1
6
29.9
1 1
5
1
4
1
1 1 1
1
30.9
44.8
156.7
6 10
1
1
1
1
1
2 3
3
1
1
2 5
1 14
6 1 1
1
1
3
236.4 1 3 1 1 3
7
1 1 18
1
13 2
1
1 3 3 4 1 11 7 1 1 3
7
1 2 1 6
13
2
3 3
1
2 3
7/8/2008
424
425
426
427
428
429
430
433
435
435
436
442
451
473
501
502
508
510
512
514
516
521
522
523
524
525
1
1
10
1
16
15
2
1
4
1
4
1 1
1
1 1
1 1
103 1 4 2 2
1 1
1
1 21 52 1 3
Page 45
2 3
2
2 1 1
6
6 22
1
1
1
4
1 5
12
13 3 4 1
241 1 17 1
2 2
3
4 2 7 39 14
total
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
24
1
15
0
7
37
99
3
1 2
47
0
0
3
1 1 450
4 9 3 2 1 1
1 1
3 3
318
526
528
544
548
549
554
556
558
560
562
568
570
604
606
Figure 4. Multiple innovations are being diffused in any given year
cumulative % of banks adopting
Diffusion of banking innovations
7/8/2008
0.7
0.6
0.5
0.4
ATM
Web trans
0.3
SBSS*
0.2
0.1
0
1960 1970 1980 1990 2000 2010
Page 46
Figure 5. Deregulation stimulated bank consolidation and branch level competition
80.0
14.0
70.0
12.0
60.0
10.0
50.0
8.0
40.0
6.0
30.0
4.0
20.0
2.0
10.0
0.0
0.0
Branches (1000)
16.0
Banks
Branches
19
198 4
198 5
198 6
198 7
198 8
198 9
199 0
199 1
199 2
199 3
199 4
199 5
199 6
199 7
199 8
209 9
200 0
200 1
200 2
200 3
200 4
05
Institutions (1000)
Branching and Consolidation
7/8/2008
Page 47
Figure 6a. Histogram of firm-year efficiency metrics
0
2
Density
4
6
8
Cost Inefficiency Density Function
0
.5
1
cost_inefficiency
1.5
2
Figure 6b. Mean Cost Inefficiency
0
.05
mean of u_tn_pl
.1
.15
.2
Mean of Cost Inefficiency
1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
7/8/2008
Page 48