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Process Innovation, Product Innovation and Firm Size*
Xin Fang†
Department of Economics, University of Illinois at Chicago
May 20, 2009
Abstract
An innovative firm allocates its research and development (R&D) investments between product
and process innovations. This paper extends the literature analyzing the determinants of a firm’s
decision to allocate R&D between process and product innovation by connecting to the literature
of incumbent’s innovation and makes predictions about the relationship between firm size and
innovation choices and outcomes. Larger firms benefit more from process innovation than
smaller firms because of the scale of their operations, while consumers’ decision to switch among
a firm’s products may reduce the size of the scale advantage. We demonstrate that larger firms
undertaking both types of innovations are still inclined to process innovation, resulting in a
smaller percentage of sales from new or markedly improved products (new product sales ratio).
However, being larger increases the probability of product invention due to the existence of a
threshold size for a firm to invest in product R&D. Therefore, the overall relationship between
new product sales ratio and firm size tends to be nonlinear. The empirical results show that the
largest firms are actually most intensive in new product sales.
* I am grateful to Prof. Richard Peck, Prof. Joshua Linn, Prof. Houston Stokes, Prof. Helen Roberts and
Prof. Anthony Pagano for their invaluable suggestions and constant encouragement. I also thank Margaret
S. Loudermilk for her helpful comments. I acknowledge data support from Center for European Economic
Research (ZEW).
† Department of Economics (M/C 144), University of Illinois at Chicago, 601 S Morgan Street, Chicago, IL
60607.
Email: xfang5@uic.edu
I. Introduction
Innovation is crucial for total factor productivity, industry and economic growth.
Firm size, in turn, is a key driver to research and development (R&D) decisions. As
Scherer (1980) states, “size is conducive to vigorous conduct of R&D.” Larger firms
have better appropriability and benefit more from the cost reduction or quality increase
due to their scales of operation (Schumpeter 1950). Therefore, larger firms tend to be
more innovative.
R&D investments are heterogeneous. An innovative firm may allocate R&D
between process innovations that “reduce the cost of producing existing products”, and
product innovations that “create new or significantly improved products”1. The existing
literature suggests firm size affect firms’ innovation choices and larger firms incline to
choose process innovation over product innovation. It naturally follows that sales of
larger firms should be less intensive in new products. However, our empirical evidence
suggests the opposite.
This paper contributes to the literature analyzing the determinants of a firm’s
allocation decision (Cohen and Klepper, 1996) by connecting to the literature of R&D
incentives of incumbents (Arrow, 1962) to innovate and derive the nonlinear relationship
between firm’s composition of sales and firm size.
Larger firms benefit more from process innovation than smaller firms because of
their operation scales. However, an incumbent firm will take into account the
competition from improved technology or products on its existing products, or
cannibalization effect. Consumers’ decisions to switch among a firm’s products trim
down the size of larger firms’ scale advantages in process innovation. Therefore, in this
1 Tirole, J., 1988. The Theory of Industrial Organization. MIT Press.
paper, the increment in a firm’s share of R&D dedicated to process innovation when firm
size increases is smaller than in Cohen and Klepper (1996a) due to the cannibalization
effect.
Our model examines corner solutions when a firm only chooses one type of
innovation and suggests the existence of a threshold size for the firm to cover the fixed
production costs of new products. Being larger increases the probability for a firm to
invest in product R&D and this increases the successes of product innovations. The
corner solution discussions lead to new insights into the nature of innovation choice. The
possibility of new product inventions increases with firm size, while for firms with new
or improved products, growth in size lowers the new product sales ratio if their
comparative advantage in process innovation is sufficiently high. Therefore, the
predicted relationship between new product sales ratio and firm size is nonlinear.
The hypothesis is tested empirically using German Innovation Survey data
(1993~2004) from ZEW (Center for European Economic Research). We use Tobit,
Hurdle Model and OLS with squared firm size to capture the nonlinearity. Alternative
econometric models, such as the General Linear Model (QMLE approach suggested in
Papke and Wooldridge, 1996) are also tried. The results show the positive effect of size
on new product sales ratio is stronger compared to the negative effect and the largest
firms are most intensive in new product sales as the result of innovation choice.
This paper is organized as follows: First, we review the background literature of
this paper. Then we show our theoretical framework and predictions. Empirical
hypothesis are put forward based on the conclusions from the theoretical model. We then
test our hypothesis and discuss the estimation results. Finally, we conclude this paper.
2. Literature
Innovation is defined as “a new or significantly improved product (good or
service) introduced to the market (product or service innovation) or the introduction
within the enterprise of a new or significantly improved process (process innovation).”
according to “OsloManual” by the OECD (1992).
Innovations are the success of R&D activities and firm size drives the decision of
R&D investment levels. It is argued in Nelson et al. (1967) that larger firms may find it
more profitable to invest more on R&D than smaller firms because of the larger market
share they have, thus “the absolute gain from a given percentage reduction in cost or a
given percentage increase in product attributes are larger for large firms”. Worley
(1961), Hamberg (1964), Scherer (1965) and Comanor (1967) analyze National Research
Council data on R&D employment for the biggest manufacturing firms in the economy,
and find that within industries, among performers of R&D, R&D rises monotonically
with firm size across all firm size ranges. They also find that firm size typically explains
over half the intraindustry variation in R&D activity.
Nelson et al. (1967) suggest a threshold on the size of an efficient program. Large
firms also have more internal funds and can finance better from external resources.
There might be significant economies of scale in R&D. In some industries, largescale
projects are important sources of technical progress. For example, in pharmaceutical
industry, a recent, widely circulated estimate put the average cost of developing an
innovative new drug at more than $800 million, including expenditures on failed projects
and the value of forgone alternative investments (CBO study, 2006). Those largescale
projects are more likely to be carried out by large firms. Empirical study by Nelson et al.
(1967) shows that the share of firms reporting positive R&D rose sharply as the size class
increased and approached one in the largest size classes.
Being large is shown to be good for innovation (Terlecky, 1982; Mansfield,
1980), and the nature or types of innovations undertaken by different sized firms draws
attention too. Composition of R&D is at least as important as the size of R&D in the
growth. Large firms might not only spend more on total R&D, but also allocate their
resources differently.
Innovations can be categorized into process and product innovations. Cohen and
Klepper (1996a) model a firm’s internal allocation of resources between product and
process innovation for price taking firms. They conclude the fraction of total R&D a firm
devote to process innovation increases with the firm’s output level if the marginal returns
to R&D in process innovation declines at the same or slower rate compared to product
innovation.
A few sources in the literature conduct empirical research on this issue. Pavitt et
al (1987) use the data for 4,000 UK manufacturing industry innovations from 1945 to
1983 and calculate process innovation fractions by innovating firmsize class. They find
out that the smallest innovators are least processoriented, followed by the largest firms
and midsized firms are most processoriented. In addition, they argue that relative
importance of process innovation increase with firm size, but very little in size when it is
compared with large intersectoral difference. Scherer (1991) also find a significant
positive relationship between firm size (measured by sales) and fraction of R&D effort
devoted to process innovation based on the data for large U.S. companies. Similarly,
Cohen and Klepper (1996a) use the same data as Scherer (1991), and derive an indirect
empirical evidence of a positive effect of firm size (measured by sales) on the share of
process R&D (measured by the proportion of patents that have been classified as
representing process innovation). Fritsch and Meschede (2001) use the data collected by
postal questionnaire from manufacturing enterprises in three German regions in 1995.
They regress the amount of process R&D expenditures on firm size (measured as number
of employees) and show that resources devoted to process R&D rises somewhat stronger
with sizes than expenditures on product R&D, therefore, they argue that small enterprises
that perform R&D tend to be more innovative than large enterprises.
Size affect firms’ allocation of resources between process and product innovation,
and the allocation of resources, in turn, will alter the product structure. We will modify
the model of Cohen and Klepper (1996a), use composition of product sales as the
measure for innovation choice to examine the relationship between firm size and
innovation inputs and output.
3. Model
An innovation is generally regarded as product innovation if the R&D activities
result in the innovation of new or improved products (Link 1975). Plasma and LCD TVs
that offer higher solutions of screens, and IPOD with videos are all wellknown
examples. We usually observe a higher price associated with new models or editions
from product innovations.
Tirole (1988) defines process innovations as those targeting at lowering the
average production cost for the existing product. The innovation of Ford Company of
assembly lines is a typical example of process innovation. Organization or managerial
changes, such as the actions of Toyota Company asking employees for costcutting ideas,
should also fall into this division. As observed, process innovations are generally
characterized with price falling.
All other applied innovations, a continuum from small improvements to brand
new products are categorized as product innovations in this paper.
Different from Cohen and Klepper (1996a), we take into account the
substitutability between established products and new products due to product innovation.
An incumbent firm will create competitors to its own established technology or products
when a new technology or new or improved product is invented. The innovation
literature states that the high substitutability between newer or improved products and
established products will cause “creative destruction”, or replacement effects mentioned
in Arrow (1962) and identified by Tirole.
In reality, we can see many new or updated version produced that are substitutes
to existing products, such as digital cameras and soft drinks. By creating the new
products and continuing to produce old products simultaneously, the firm can enlarge the
quality spectrum, also known as product line, so they can design a pricequality
combination to allocate consumers with different demands along the quality spectrum by
the process of selfselection. Therefore, the firms can partially discriminate and increase
their profits (Mussa and Rosen 1978).
Product innovation can also be used to proliferate brands, creating similar
differentiated products, and act as a strategic investment for entry deterrence. As argued
in Schmalensee (1978), ready to eat cereal companies introduce new products (CoCoa
Puff, Cherios) to take up scarce shelf space in grocery stores and prevent other firms from
entering the market.
In either situation, new products will curtail the demand for existing products.
Some consumers will switch from existing product to new product.
This “cannibalization”, or replacement effect according to Arrow, will lower the
returns to process innovation as well as firm’s incentive to invest in process R&D.
Average cost of production should fall as the result of process innovation. Given the
same level of average cost reduction, reduction in total cost is larger with higher output
level. Therefore, when the demand of existing products falls, the size of cost reduction
will drop.
This paper will investigate a firm’s allocation of R&D investment funds between
process and product innovation incorporating the replacement effect. More importantly,
we will show how composition of product sales changes as the result of the internal
allocation of the firm’s funds in process and product innovations.
We adopt the assumption of Cohen and Klepper (1996) that appropriation
conditions limit the firm’s ability to gain benefits from licensing. Firms do not license or
sell to others the process innovation in disembodied form, such as selling the “plans” or
knowledge about how the process innovation is undertaken instead of selling the
technology “embodied” in an asset like personnel or part of equipment. This assumption
is consistent with the results of a survey of CEO’s of major corporations conducted by
Levin et al (1987) in which it is indicated that managers put little faith in patent of
process innovation to prevent imitation. We will follow the arguments in Cohen and
Klepper (1996b) that firms only apply the technology towards their own production, and
firm growth due to innovation tends to be limited, so process innovation is assumed to
lower average cost for the ex ante quantities (quantity produced before the innovation).
We assume a perfectly contestable market and firms act as price takers. Each firm
has a constant marginal cost up to the capacity q, but the marginal cost becomes very
high, that is, infinite at and beyond the capacity q. Consumers are assumed to have
reservation prices for products and they would consume a certain quantity if the price
equals their reservation price. With the “Ladder” shaped demand, the best strategy of a
firm preceding innovation is to build the capacity q equal to the quantity demanded by
consumers at their reservation price.
Firms are assumed to invest in process innovations to reduce their marginal cost2.
If the firm succeeds, marginal cost is lower for the existing product’ output decided by
the demand. Total benefit equals price cost margin multiply by output (q) as shown in
blue shadowed area in Figure1.
Figure 1. Process Innovation: Demand and Marginal Costs
2 Firms might in nd to lower fixed costs, especially in rge fixed cost like
automobile industry. How er, incentives of engaging in this kind of process innovation are not influenced
by firm’s output level. Therefore, it is not the focus of this paper.
te industries with la
ev
qOutput
M
MC
1
0
Demand
Marginal Cost
p
Price
If a new or markedly improved product (indicated as “new product” in the rest of
this paper) is introduced by the same firm through product innovation, demand for its
existing products will fall because of the cannibalization effect (from Demand to
Demand’ as shown in Figure 2 below). Only part of the consumers will switch to the
new products because of their different preferences. We denote the proportion of
consumers who switch from the existing products as h (0<h<1), the ex ante quantity
(quantity before innovation) as q. Therefore, in the presence of product innovation,
benefits from process innovation should be evaluated as the reduction of marginal cost
applied to the remaining ex ante output ((1h)q). Since larger scale implies higher profits
from process innovation. Profit from process innovation is reduced due to
cannibalization.
0
Figure 2 Process Innovation: Demand (with new products) and Marginal Costs
Marginal Cost
Demand
Demand’
Price
MC0
MC1
0 (1 )hq
−
p
q
Output
Proportion of consumers who switch from the existing products (h) is supposed to
be exogenous of firm size because it should be decided by the characteristics of existing
and new products, or the substitutability.
Product innovation is assumed to increase consumer surplus and create demand
for new products at some cost level. Improvement of a product will raise consumers’
values and shift out demand (from Demand to Demand’ in Figure 3) at certain cost and
an improved product is regarded as a new product in our model.
Figure 3 Product Innovation: Demand and Average Cost
Price
q
AC Demand’
0 Output
Demand
q'
p
’
p
In this procedure, price of new product is decided by the attributes of the products
(hedonic pricing). Higher level of product R&D creates higher values as well as higher
prices for new products.
Before new products are widely imitated, the innovating firm earns temporary
monopoly profits similarly to process innovation. The transitory profits are composed by
two parts: First, values of consumers for new products above marginal cost as well as
average cost will be created due to the temporary monopoly power. Second, switched
consumers from the firm’s existing products and new customers (consumers from
competitors and new to this industry) comprise the demand for the new products.
Demand from new market (denoted as k in units of products) is irrelevant to the
firm size, since there is little empirical evidence that the ability of larger firms to do more
advertising and promoting new products using the network is superior.
Industrial level technological opportunity may affect the firm’s profits for
established products or new products unevenly and favor either process or product
innovation. This factor enters the profits but it is assumed neutral to firm size.
We assume CobbDouglas production function form for innovations with only
one input: R&D investment shown in equation (1) and equation (2).
1
1
1
11
11
1
() 1
1
br
dc r
β
β
−
=
−
& 1
1
11 11
'( )dc r b r
β
−
=
(1)
2
1
1
22
22
2
() 1
1
br
pr
β
β
−
=
−
& 2
1
2222 )('
β
−
=rbrp
(2)
, Where dc1(r1) is the absolute value of reduction in marginal cost for established
products due to process innovation. We denote p
2(r2), the price of new or markedly
improved product.
According to the definitions, R&D investments in process innovation (r1) will
lower marginal costs of producing existing products and R&D investments (r2) towards
product innovation create values (consumers’ reservation price) for the new products at
marginal cost (c2), and make the production for new products profitable. Higher R&D
investments are assumed to enlarge the size of cost reduction and the price of new
products; therefore, the first derivatives are positive. We also expect the success in both
types of innovations will increase at declining rates, i.e., the marginal returns to R&D fall
when the investments go up, so the second derivative to be negative.
The parameter bi represents the different rate of returns for type i R&D at some
industrial level technology, or technological opportunities in the industry that does not
vary with firm size. bi’s are fixed in one industry and can partially decide marginal
returns to the two types of innovation.
β
i (
β
i >1) represents the rate at which the marginal return to R&D of type i
declines, the larger
β
i, the faster the marginal returns fall. We assume that the marginal
returns to process innovation declines no faster than product innovation
(
β
1
≥β
2
). Generally, it is much harder for price increase due to quality increase to remain
increasing at high speed than to keep cutting the costs down by invest in process R&D.
In addition,
β
i is assumed to be greater than one so the marginal cost is reduced
and price (value) for new products are positive. This assumption leads to the conclusion
that R&D investments will rise more than proportionally to firm size that can be shown in
optimal R&D investment solutions. This conclusion is not against empirical evidence
found by Nelson, Peck and Kalachek (1967). They argue, “Larger firms spend more on
R&D as a fraction of sales”. Their finding show that in most industries, R&D intensity
rise as one moves from the group of firms with less than 1,000 employees to the group in
the 1,0005,000 range, while there is no clear rise for the intensities for those giants with
more than 5,000 employees compared to those with 1,0005,000 employees.
Total temporary profits include profits from process innovation and profits from
product innovation. The profits for process and product innovation are determined by
process and product R&D. The demand and profits for the established product and new
product will interact through the quantities purchased by consumers who switch from
existing products to new products.
12
11
(1 ) (1 )
111 2 22
12 1 1 1 1 2 2 2 1 2
12
(, ) (1 )[ ] ( )
11
br br
rr a hqp c r a hq k c r f f
ββ
ββ
πββ
−−
⎡⎤
⎢⎥
=− −+ −+ + −−−−
⎢⎥
−−
⎢⎥
⎣⎦
(3)
a1, and a2 capture the time lag before other firms catch up and the temporary
monopoly profits disappear. The length of time lags will affect the profits the innovating
firm can get from two types of innovation and thus the allocation of R&D resources. r1
and r2 are the R&D investments in process innovation and product innovation as we
mentioned above. p1 denote the price of established products, c1 denote the marginal cost
before process innovation. c2 denote the marginal cost of producing new products, and f1,
f2 denote fixed costs for existing products and new products. q represents the quantity of
existing products sold before product innovation takes place. Let h, as before, denote the
replacement effect measured as the proportion of quantities previously purchased by
existing consumers who now switch to new products, and k, represent the quantity of new
products purchased by new consumers.
To maximize total profits of a firm, we derive the following first order conditions
from equation (3) with respect to process and product R&D respectively.
For investments in process innovation (r1), we have:
1
1
()
111
(1 ) 1ahqbr
β
−
−=
(4)
For investments in product innovation (r2), we have:
2
1
()
222 ()abr hq k
β
−+=1
]
(5)
The left hand sides of the first order conditions can be regarded as the marginal
benefits for the R&D investments in process and product innovation, respectively. The
right hand sides represent the marginal cost measured as one more dollar spent in
innovation.
The solutions to the first order conditions (4)(5) are:
[
1
*
111
(1 )rabqh
β
=−
(6)
[
2
*
222
()rabhqk
]
β
=+
(7)
The solutions show us several things. A primary focus is the role of firm’s ex
ante size measured as q. We can conclude from (8) and (9) that larger firms invest more
in both types of innovations.
1
*111
[(1)]rabqh
qq
β
1
β
∂−
=
∂>0
(8)
2
*
222 2
[( )]rabhqk
qhqk
β
h
β
∂+
=
∂+
>0
(9)
In our model, the advantage for larger firms of process innovation comes from the
ability to gain more from marginal cost reduction because their output levels are larger,
while the advantage of product innovation for larger firms comes from the larger size of
the group of consumers who switched from established products to new products.
To investigate the relationship between internal allocation of resources between
two types of innovation and firm size, we take the ratio of R&D investments in process
innovation to investments in product innovation and then take the derivative of the ratio
with respect to firm size q:
[]
[]
1
2
** 11 1 2 1
12
22
(1 ) [( ) ]
(/)
()()
abq h hq k
rr
qab hq k hq k q
β
β
β
ββ
−−+
∂=
∂++
(10)
Therefore, if the rates at which the marginal returns to process innovation
investments and product innovation decline are equal (
β
1
=β
2
) or the marginal returns to
process innovation declines slower (
β
1
>β
2
) which is our assumption, larger firms will
proportionally invest more in process innovation. Although the sign of firm size effect
on R&D investment allocation we find is the same as Cohen and Klepper (1996), size of
the effect in our model is smaller. In particular, the comparative advantage of larger
firms in process innovation is cut down by the cannibalization effect. With new products
invented, larger firms lose more sales from established products and at the same time,
they have more demand from switched consumers for new products. However, the
demand from new consumers is neutral to firm size as assumed. Therefore, the size of
the scale advantage of large firms in process innovation is weakened.
We are more interested in the outcome of firms’ innovation choices that are
observable, and new product sales ratio (percentage of new or improved products sales) is
an appropriate one. Intuitively, with relatively less investment in product R&D, firms’
new product sales ratio will be lower.
To form our theoretical prediction for the relationship between firm size and new
products sales ratio, it is equivalent to examine the relationship between firm size and
sales ratio of established products to new products. Let R1 denote the sales from
established products, and R2 denote the sales from new products, we take the derivative
of the ratio with respect to firm size and we get:
22
12 11 2 2
(1 )
22
(/) (1 )( 1)[(1 ) ]
()( )
R
Raph hq k
qabhqk
ββ
β
β
+
∂−−−
=
∂+
+
(11)
By assumptions, we know that
β
1
,
β
2
>1. If condition as shown in (12) holds,
k>hq(
β
2
1) or
2
1
(1)
k
hq
β
>
− ` `
(12)
the ratio of sales from existing products to new or markedly improved products will
increase with firm size, new product sales ratio will fall with firm size.
2
(1)
k
hq
β
− can be interpreted as a measure for comparative advantage of small
firms in product innovation. The same change in k or q will affect the returns to
innovations the same way for different sized firms. However,
β
2
, which has an effect on
the total quantity demanded created for new products, implies a larger marginal benefits
effect for larger firms. When
β
2
becomes smaller, or the measure becomes larger, larger
firms will lose more marginal benefits in product innovation, and relative advantage in
process innovation will be enhanced. In addition, h in the denominator is the number of
consumers who contribute to the demand for new or markedly improved product. If h
decreases, or the measure increases, larger firms will have smaller reduction in the
marginal benefits for process R&D. Therefore, if the fraction (measure) increases,
comparative advantage of larger firms has in process innovation (or comparative
advantage for smaller firms in product innovation) increases. If this measure is greater
than one, larger firms have larger proportion of sales from established products as well as
a smaller proportion from new products. It is equivalently to say, smaller firms are more
intensive in new product sales.
If we take into account the possibility that the firm only invest in one type of
R&D, the conclusions above need to be modified. Fixed cost of production is irrelevant
for process innovation to take place, as long as the established good is in production. In
that case, the decision of process R&D depends only on the profits generated and R&D
expenditures. While for product innovation, fixed cost of product innovation affect the
profitability, thus it would be harder for small firms to invest in product innovation.
First, we examine situations that firms will choose to invest in one type of
innovation instead of no innovations at all. Profits with no innovations during the
transitory period will be:
0
11 1
()aq p c f
π
=−−
1
(13)
Our production function for process innovation satisfies Inada conditions. Given
that
β
1>1, it will always be profitable for the firms to engage in process innovation than
no innovations.
In the case when a firm undertakes product innovation compared instead of no
innovations, the fixed cost, f2, put a floor for firm size to make new products profitable.
The profit gain for doing product innovation only is:
2
*22
22222
2
[( )] () ()
1
ab hq k ac hq k f a p c hq
β
πβ
+
=−+−−
−11
−
(14)
If we look at the relationship of the product innovation profits and ex ante size of
the firm, we can find out that:
22 2
*1
22
22 22 21 1
2
[() ()
1
abhqk ac ap ch
q
ββ β
πβ
β
−
∂=+ −−−
∂−
]
(15)
So if
2
22
1
1
22 1 1 2
222
()(1)
{[ ] }/
ac p c
qk
ab
β
ββ
β
β
−
−+ −
>−h
(16)
If inequality (16) is satisfied, equation (15) will be positive; thus product innovation
profits will increase in q. If inequality (16) does not hold, profit gain is decreasing in q,
and we will end up with a close to Ushaped optimal profit function of ex ante quantity.
When firm size increases, the profit gain of product innovation will go down first and
then go up. Therefore, we argue that with the existence of the fixed costs of product
innovation (f2), only firms sufficiently large (or extremely small firms, that we don’t
think it would be possible in economic sense) will be able to invest in product R&D.
For both types of innovations to be undertaken instead of only one, the profits
should exceed any corner solution case. The total innovation profits are:
12
*11 2 2
11 1 22 1 2
12
[(1)] [ ( )]
()(1) ()
11
ab h q ab hq k
ap c hq achq k f f
ββ
πββ
−+
=−−+ + − +−−
−−
(17)
And we take the first derivative with respect to q, and we derive:
12
*11 1 2 2 2
11 1 22
1
[(1)] [ ( )]
()(1) (1)
ab h q ab hq k h
ap c h ach
qqhqk
ββ
πβ
β
∂−+
=−−+ + −
∂−+
β
(18)
We can see that if k is sufficiently large, larger q will increase the joint profits of
innovations.
If profits gain difference between profits from both types of innovation and
process innovation only (d
π
), a firm will choose to undertake both types of innovation
over process innovation only. We take the first derivative of d
π
with respect to q:
(19)
11 2
(1)
11 1 2 2
111
12
( ) ( ) [(1 ) 1] ( ) [( )]
() (1) (1)
dabqhabhq
ah p c
qq
ββ β
πβ
ββ
2
k
β
−
∂−−
=− − + +
∂−
+
−
We suggest that if new demand (k) is large enough, d
π
is increasing in firm size
as suggested by (20). Therefore, firm will engage in both innovations:
2
222 2
2
()[ ( )] 0
()
dabhqkh
qk hq k
β
πβ
∂+
=
∂∂ + >
(20)
This result is intuitive and consistent with what we expect on earlier results.
When demand from new consumers is sufficiently large, or we view the opportunities for
product innovation is high for the firm, the benefits gained from product innovation is
large enough to offset profit loss for existing products due to cannibalization, the firms
will conduct both innovations if it is sufficiently large. Otherwise, the firm will conduct
only process innovation. If k is insufficient to satisfy equation (20), d
π
will go up when
firm size decreases, it is possible that only small firms or entrants might choose both
types of innovation due to smaller loss of sales of existing products, and large firms only
stick to process innovation. If k is sufficiently small, d
π
could be less than zero, and all
the firms will undertake process innovation only.
The profits from new or markedly improved products is irrelevant to whether the
established products are also produced. Therefore, the decision to invest in product
innovation only or both types of innovation should be made only upon whether the
process and product innovation are both profitable.
The existence of product innovation can lower the profits for existing products as
well as the profitability of process innovation. New products reduce the demand for
established products, thus shrinking the scale of production, and raising the average cost.
At the competitive price, the firm will lose money.
The optimal profits a firm can derive from doing process innovation only with the
presence of new product is:
1
*11
111111
1
()
() 1
babq
ac p c f
β
πβ
=−−−
−
(21)
To make sure that the existing products remain in production and process
innovation will be undertaken, inequality (22) needs to be satisfied.
1
1
11
111 1
])1[(
)()1( 1f
qbah
cpqha >
−
−
+−−
β
β
(22)
Therefore, if the firm is sufficiently large, process innovation might make the
production of existing products profitable and both innovations will be undertaken.
If we are faced by a corner solution without innovations or with process
innovation only, the prediction of relationship between new product sales ratio and firm
size will be affected.
Based on the discussion and assumptions above, a firm will invest in process
R&D as long as its size is large enough. While the decision of investing in product R&D
depends on both firm size and the opportunities for new products in the industry, that is,
the demand from new consumers. If the opportunity is extremely low, then product R&D
is not profitable for any firm. Entrants, and incumbents will invest in process R&D and
invest more with firm size increase. As a result, new product sales ratio will remain zero
in this situation.
If the opportunity is medium, the chances of product innovation will be greater for
new and relatively large entrants or relatively small incumbents because they will not
suffer or suffer less from cannibalization. However, small firms have difficulty to
undertake product innovation because they will have higher average innovation costs
with presence of fixed cost. Our measure of outcome of innovation choice, the new
product sales ratio, will have a different trend when firm size increases under medium
opportunities for new products. Entrants (large enough) without established products will
invest in product R&D first, followed by established firms (large enough) when the
opportunity goes even higher. If we take a shot of picture for this stage, we should
observe new product sales ratio to rise from zero to 100% if the firm size increase across
entrants and zero to a positive number for firm size increase across existing firms. If
established products are driven out of the market, then new product sales ratio will
increase from zero to 100% or stay 100% when incumbent firm size increase more, and
then fall to zero again when firms becomes larger under the medium opportunity. It is
also possible that threshold for process innovation with new products is lower than that
for product innovation. In this case, established products will not be driven out. New
product sales ratio will fall gradually and drop to zero when the firm is too large to make
product innovation profitable.
If the opportunity for new products is high, product innovation will take place
when firm size rise above threshold and new product sales ratio will go above zero, it will
reach 100% if established products are driven out of the market. If the established
products are not driven out, new product sales ratio will fall with firm size increase,
conditioned on that marginal returns to process R&D declines at a slower or equal rate
compared to product R&D, and comparative advantage of large firms in process
innovation is sufficiently high. Otherwise, established products will become profitable
with increased firm size, both innovations will be undertaken and firms will choose
process R&D over product R&D. Therefore, new product sales ratio will fall when they
grow in size under same conditions.
We conclude firms with larger size invest more in process R&D. However, larger
firms are more likely to invest in product R&D due to the existence of fixed costs. If the
comparative advantage of larger firms in process innovation were big enough, we would
observe that sales be more “old” products (established products) intensive and less new
product intensive for larger firms or when firms grow in size. Therefore, we actually
predict a nonlinear relationship between new product sales ratio and firm size as the
combination effect of firm size on probability of product innovations and on new product
sales ratio after if the innovations take place.
Our hypothesis offers a different angle of view to discuss comparative advantages
of innovation for different sized firms. Moreover, we predict a new explanation to
reconcile the conflicts between the facts that large firms actually are possible to be an
active new product inventors and the previous literature predictions that large firms prefer
less product innovation. We will test our hypothesis empirically.
4. Empirical Tests
Empirical investigation of relationship between firm size and inclination of
process and product innovations remain largely unexplored.
Our empirical work focus on the consequences of firm’s choice on R&D
investments that varies with firm size. We choose proportion of sales from new or
improved products (new product sales ratio) as the measure for the efforts made towards
process and product innovation. The theoretically predicted relationship between firm
size and the result of innovation choices (new product sales ratio) will be estimated using
both linear and nonlinear models.
1) Empirical Model
As discussed in theoretical analysis, we hypothesize an increasing probability of
firm to engage in product R&D with firm size increase (the probability could be
nonlinear) due to the existence of threshold size. As the result of firms’ inclination to
choose process R&D over product R&D, new product sales ratio would fall with firm
size increase for firms with positive new product sales.
To test our hypothesis, we will test new product sales ratio as a function of firm
size.
Some confounding factors that could bias our estimates are controlled. Industrial
technology advances are assumed exogenous and we control for industry and year
specific shocks in our estimation. Depreciation rate of established products is also
counted as an independent variable. The cannibalization effect incorporated in our model
take into account the obsolescence of established products for a firm brought by its own
new products. While given the product life cycle, a firm without product innovation and
resulting cannibalization (replacement effect coming from its own products) are still
faced by declining sales of existing product if it is at late stage of product life cycle.
Better substitutes produced by other firms will come out when time passes (Brockhoff,
1967). We also expect that at the same stage of product life cycle, the sales will change
more for those larger, than smaller firms will. If the depreciation of sales is not
controlled for, the size effects we try to estimate will probably be upward biased. Larger
firms might end up with higher sales ratio of new products only because their “old”
product sales fall more.
All other factors that enter the change of existing product revenues and correlate
with firm size will be controlled too. Our model assume that sales for existing products
will not go up with reduction in cost due to process innovation. However, if output
increases are caused by upward sloping marginal cost curves and not constrained by
demand (although it is argued by Cohen and Klepper 1996a that it is not significant), then
the new product sales ratio of larger firms should be even lower because the proportion of
new product sales will fall even more. When the change in sales is controlled, the effect
will be controlled too.
Other possible missing variables are considered too. A case in point is life cycle
of firms. Size of firms are closely related to the years since it came into existence,
because firms generally grow in size over years, so firm size is correlated to the firm’s
life cycle. Entrants, usually small, generally enter an industry with new products, bearing
a high new product sales ratio. Without controlling for the history of firms, our estimates
will be downward biased. Unfortunately, the data for history of firms is not available.
Another factor we need to take into account is market structure or competition. It
is natural to think that concentration ratio may affect firm’s choice of innovation. Arrow
(1962) argues that the incentive to invent is less under monopolistic than under
competitive conditions. The industrial concentration ratio is controlled when we control
for industry and year specific effects, but we will not be able to evaluate the effect
brought by competition.
Factors such as firm’s productivity in process and product innovation and other
shocks to new product sales and correlated to firm size would generally be considered in
estimating a variable related to productivity. As suggested in Olley and Pakes (1996),
Levinsohn and Petrin (2003) and Ackerberg and Caves (2006), investments or
intermediate inputs or multiple proxies could be used as proxies for productivity shocks
that are observed to firms only in estimating production function. However, in our
estimation, we want to control for the shocks to relative productivity of process
innovation to product innovation, and general investments or intermediate inputs will not
fit as a proxy. Due to the limit of data, we cannot use intermediate products or R&D
investments towards new products as the proxy. Therefore, it would possibly bias our
estimation of firm size upward if larger firms respond to the shocks by investing more in
product innovation.
The following model will be estimated:
New Product Sales Ratio = f (firm size, change in established product sales)
Both linear and nonlinear regressions would be used to estimate the relationship
between new product sales ratio and firm size.
2) Data
Firmlevel data from the Mannheim Innovation Panel Manufacturing and Mining
& Services survey (MIP) that covers the years from 1993 to 2004 will be used. The
surveys was conducted annually by the Center for European Economic Research (ZEW)
and focus on all firms located in Germany that have at least five employees and are active
in the manufacturing sector, mining, knowledgeintensive services or other services.
There are 11 broad industry categories according to German WZ93 classification for
manufacturing and mining industries.
“The annual survey is designed as a panel survey and every two years the sample
is refreshed by a random sample of newly founded firms to replace those
decommissioned in the interim.” (Aschoff et al. 2006). As a result, we have an
unbalanced panel data from year 1992 to year 2003 (data provided in surveys is for the
year proceeding the survey year). The revelation of information is on a voluntary basis,
so the absences from survey do not necessarily mean that the firms exit the industry or
shut down. The response rate is between 20.623.7% for the surveys (Norbert Janz et al,
forthcoming).
For each survey year, process innovations are any new or significantly improved
production processes during the preceding two years and product innovations are the new
or markedly improved new products invented in the previous two years. With the
assumption that that firm growth due to innovation is limited (Cohen and Klepper 1996)
and innovations are applied towards the firms’ own outputs, we use the ex ante firm size
(number of employees) to evaluate the size effect when firms make innovation choices.
The survey asks firms to estimate the percentage of sales from new or markedly
improved products due to product innovation, which we would use as the dependent
variable. A firm with a zero new product sales ratio is regarded as having no product
innovation. For all the 5853 observations, there are 2455 observations of zero new
product sales.
We categorize the firm size (number of employees) in deciles for each industry
and plot the new product sales ratio as shown in Figure 4. There are some industries with
bell shaped curves indicating that new product sales ratio will rise and then fall when
firm sizes go up, which is conformed to our prediction. Other industries show an upward
trend of increasing in the new product sales ratio with firm size increase. Mean values of
new product sales ratio are affected by the number of observations and outliers. In
addition, it is desirable to derive the firm size partial effects on new product sales ratio by
holding other factors like year specific shocks constant.
Figure 4 New Product Sales Ratio with Firm Size in Deciles by Industry
0.2 .4 .6
0.2 .4 .6
0.2 .4 .6
0510
0510 0510 0510
Mining Food, Tobacco, Textiles Wood, Paper, Furniture Chem ic als
Plastic s Glass, Ceramics Met a l s Mac h i n e r y
Electrical Equi pment Medical and Other Instruments T ransport Equipment
New Product Sales Ratio
Firm Size by Employees
Graphs by ind
Table 1 shows sample statistics of average new product sales ratio, firm sales, size
of firms, R&D investments and intensity of R&D investments for 11 manufacturing and
mining industries. Industries such as Chemicals, Machinery, Electrical Equipment,
Medical and other Instruments, and Transportation Equipment have relative high average
new product sales ratio associated with high average level of R&D investments and
intensities (share of R&D investments in sales) that is a sign for high opportunities for
new products.
Table 1.
SAMPLE STATISTICS
Industry
Number
of
Observat
ions
Average
New
Product
Sales
Ratio
Average
Firm
Sales
Average
Number of
Employees
(When R&D
is
decided)
Average
R&D
Investme
nts
Average
Intensity
of R&D
Investmen
ts
Mining 921 0.065 441.479 1905.466 1.896 0.004
Food, Tobacco, Textiles 2,995 0.240 75.012 179.125 0.479 0.006
Wood, Paper, Furniture 2,313 0.260 76.902 206.334 0.770 0.007
Chemicals 1,782 0.338 445.623 999.354 23.733 0.034
Plastics 1,930 0.321 59.524 178.112 0.860 0.015
Glass, Ceramics 1,244 0.268 111.422 518.267 1.250 0.013
Metals 3,652 0.255 146.046 294.982 1.140 0.011
Machinery 4,073 0.435 134.612 429.864 3.859 0.028
Electrical Equipment 2,140 0.445 273.602 866.955 18.305 0.038
Medical and Other
Instruments 1,761 0.453 74.198 257.815 5.299 0.053
Transport Equipment 1,242 0.402 915.723 1900.374 52.378 0.024
Total 24053 0.333 199.220 529.070 7.906 0.022
3) Variables
ZEW survey builds a variable to measure the proportion of sales (turnover in their
term) including exports from “new or markedly improved product” in the past two years.
To protect the privacy of participating firms, the data is recorded into scales. We take the
means of the scales as the constructed variable for new product sales ratio that is denoted
as salesnp:
t
t
t
npsales
salesnp sales
=
(23)
npsalest denote the sales from new and improved products at time t. sales represents the
total sales of the firm at time t. We also generate salesnp1, which equals 0 if salesnp is
zero indicating no new or improved products and 1 otherwise. Mean and standard errors
of the two variables are shown in Table 2. In the 17749 observations we have, 34.4% of
salesnp are zero.
Number of employees is used instead of sales to represent the size of firms (size)
to avoid mechanical relationship between sales and new product sales ratio (salesnp) as
shown in the formula. Firm’s decision on investments of process and product innovation
is assumed to be made upon the ex ante firm size and firm size increase due to innovation
is limited. Since the surveys define innovations as those developed during the preceding
two years, we lag the number of employees for two periods to represent the ex ante firm
size and denote it as sizet2.
dost1 is a variable constructed to measure the depreciation of established
products. Because salest is by functional form related to the dependent variable, we lag
the variable for one period:
dost1=
(24)
11tt
sales npsales sales
−−
−−
3t−
1t
sales npsales
−
−1t−
represent sales of products developed before t3 (established
products). Since all the new products are developed during the preceding two years, total
sales at t3 should be the sales for “old” products as of time t at time t2.
Mean of dost1 is negative as shown in Table 2, so on average established product
sales decline over time. Smaller this variable, more reduction in established good sales,
and the larger new product sales ratio without firms’ innovation choice, therefore the
coefficient is expected to be negative. This variable will capture partial effects of sizet2,
because firm’s choice of new products will also hurt the established products due to
replacement effects. However, there is no serious collinearity problem between sizet2
and dost1. Variance Inflation Factors that shows how much the variance of coefficient
estimate is inflated due to multicollinearity, is only 2.08, which is less than 2.5, the
critical value.
Table 2
SUMMARY STATISTICS
Variable Number of
Observations Mean Std. Dev. Min Max
salesnp 17749 .3326258 .3454721 0 1
salesnp117749 .6559806 .4750608 0 1
sizet2 11313 529.0701 4238.647 .6615753 174604.6
dost1 6621 52.72846 878.7937 33841.62 8327.23
4) Estimation Methods
Small firms are not capable of making profits due to fixed costs, while larger
firms lean towards process innovation. Therefore, a bell shaped curve for new product
sales ratio is expected. The extensive margin is supposed to be positive, that is, larger
firm size increases the possibility of positive new product sales. Intensive marginal is
expected to be negative, that is, for firms with positive new product sales, new product
sales ratio should drop with firm size increase. Limit dependent variable problem will
also be dealt with. In all the estimations, we control for year and industry specific shocks
and standard errors are clustered at industry level.
First, we will estimate using the twotiered model (hurdle model) suggested by
Wooldridge (2001, P. 536538) with two steps:
(0)1(Py x x)
φ
γ
==−
(25)
2
log( )  ( , 0) ~ ( , )yxy Normalx
β
σ
>
(26)
y in equations (25) and (26) is dependent variable salesnp (new product sales ratio), and
x’s are sizet2 and dost1.
First, we estimate a Probit model to get the extensive margin from equation (25).
γ
can be derived from Probit regression. Marginal effect of firm size on the possibility of
firms’ engagements in product innovations given
γ
will be calculated. Firm size is
supposed to have a positive marginal effect on probability of positive new product sales
ratio.
Conditioned on that firms have positive new product sales ratios, new product
sales ratio and explanatory variables are assumed to follow a log normal distribution as
suggested in Wooldridge as shown in equation (26).
β
’s are the coefficients from OLS
regression. For firms active in product innovations, intensive margins are expected to be
negative, that is, increase in firm size will lower the new product sales ratio according to
our expectation.
Fitted values for new product sales ratio can be derived from formula (27)
according to Wooldridge, P537 (2002):
(27)
2
(  ) ( )exp( / 2)Eyx x x
φγ βσ
=+
where the
σ
2
, the variance, can be estimated consistently from the OLS estimator of log
normal model.
Other nonlinear specifications, such as OLS with squared term for firm size will
be used:
2
0 1 ( 2) 2 ( 2) 3 ( 1) 4 14 93 03 15 24 2 11
25 134 93 03 2 11
()
*
ttt
E
salesnp x size size dos yr ind
yr ind
ββ β β β β
β
−−−−−−
−− −
=+ + + + +
+
−
(28)
Considering new product sales ratio a fraction between zero and one, we use the
approach suggested by Papke and Wooldridge (1996). Quasi Maximum Likelihood
Estimation is used to deal with this special situation. The General Linear Model we
estimate is shown as:
2
0 1 ( 2) 2 ( 2) 3 ( 1) 4 14 93 03 15 24 2 11
25 134 93 03 2 11
()(
*)
ttt
E
salesnp x G size size dos yr ind
yr ind
ββ β β β β
β
−
−−−−−
−− −
=+ + + + +
+
−
(29)
G(.) is a cumulative distribution function which fits the limit dependent variable situation.
Logistic function and standard normal cumulative distribution function forms for G(.)
will be both estimated. Standard errors we derive will be robust to variance
misspecification.
It is possible that industries are different in the relationship of new product sales
ratio and firm size (the relative position of threshold size are different). Therefore, we
will run regression for each individual industry and test whether the slope of firm size
and sizes where the marginal effect changes signs are different across industries. In this
section, in addition to Hurdle Model, QMLE (Probit) and QMLE (Logit), we are going to
run use Multivariate Adaptive Regression Splines (MARS) procedure to automatically
detect the coefficient change of firm size variable. MARS procedure “…can detect and fit
models in situations where there are distinct breaks in the model, such as are found if
there is a change in the underlying probability density function of the coefficients and
where there are complex variable interactions.” (Stokes, 2009)
The MARS procedure will fit a spline model as shown below in equation (30)
1
()
k
ii i
i
yX
α
βτ
+
=
=+ −
∑
(30)
where i
τ
is the minimum of the i
X
vector. The y variable is the new product
sales ratio (salesnp) and i
X
is vector of explanatory variables, including sizet2, dost1 and
time dummies.
We will also use General Additive Model (GAM) to check for the nonlinearity of
new product sales ratio in firm size. A GAM model (Hastie et al, 1986, 1990; Hastie et al.
2001; Faraway, 2006) can be written as
12 0 1
(  , ,..., ) ( )
k
kj
jj
E
yxx x a x e
α
=
=+ +
∑
(31)
where the (.)
j
α
are smooth functions that are standardized so that ( ) 0
jj
Ex
α
=. These
functions are estimated one at a time using forward stepwise estimation. If (31) is
estimated with OLS, the expected coefficients are all 1.0. According to Stokes (2009),
first, the estimation will remove the means from all right hand side data, then adds the
splines to build the smoothed series that have 0.0 expectation as shown in equation (32):
*()
iiii
x
xx s=−+.
(32)
where will be an n element spline series with n observations. GAM coefficients
i
s
g
am
β
will be estimated using OLS in terms of the original explanatory variables and
remove the nonlinearity effect from dependent variable series as ,
where
*1
(, , )
k
yfx x=L
*
1
k
i
i
yy s
=
=−
∑
(33)
*01
k
gam gam
ii
i
yx
ββ
=
=+ +
∑i
e
(34)
In the GAM procedure in B34S (Stokes, 2009), a significance test is designed and
it will be used to measures the difference of the sum of squares of the residuals for the
linear restriction case allowing for a relative measure of the degree of nonlinearity, by
variable. If we define RSSr = the restricted sum of squares and RSSu= 'ee. The
significance test statistic for nonlinearity in the kth parameter can be written as
)](/)[( pnRSSRSSRSS uur −− , where
p
is the number of parameters in the model which
is checked with ()df k
χ
.
Our estimation will be organized in the following order: In the regression with
full data, we first run OLS regression, followed by the Tobit regression, then we will do
the Wooldridge approach of Hurdle Model, followed by OLS and QMLE (Logit and
Probit) with squared firm size term. In the last part of the section, Hurdle model with
firm size dummies will be launched. In the regression for each individual industry, we
will run regressions with Hurdle, QMLE (Logit and Probit) and followed by MARS and
GAM.
5) Estimation Results
Table 3 shows the estimation results for Hurdle Model. Probit regression as first
part of Hurdle Model yields the sign of the extensive margins, or marginal effect of firm
size on firms’ chances to engage in product innovation, which are positive and significant.
The marginal effects at mean values of explanatory variable shows that if the firm has
one more employee, the probability of this firm to have product innovations will go up
by .0002558.
For the second part of Hurdle Model, we also find out the outlier problem.
According to estimation using Robust Regression, the intensive margin shows negative
sign and the coefficient of firm size is statistically significant. OLS results also show
negative effect of firm size, but the coefficient is not significant. Therefore, firm size
increase decreases the new product sales ratio for firms with positive new product sales.
TABLE 3
ESTIMATION RESULTS OF HURDLE MODELa
Variable Probitb
(Hurdle I)
OLS of Log
Normalc
(Hurdle II)
OLS of Log
Normald
(Hurdle II:
Robust)
sizet2 6.72e04**
(1.42e04) 2.06e05
(1.53e05) 4.12e05**
(6.74e06)
dost1 4.87e05
(7.05e05) 8.51e05
(5.29e05) 1.49e04**
(2.30e05)
constant 2.65**
(2.22e01) 1.09e00**
(4.06e03) 2.39e00**
(8.71e01)
R2
DF
0.1266
5752 0.2338
3297 
5752
a * means the coefficient is significant at 10% level, but not 5% level.
** means the coefficient is significant at 5% level.
b Part I of Hurdle Model: Probit (with binary dependent variables) regression
c Part II of Hurdle Model: LogNormal OLS regression
d Part II of Hurdle Model: LogNormal Robust regression
The mean of new product sales ratio can be calculated using the formula given by
Wooldridge (2002):
E[yx]=
Φ
(
x
γ
)exp(x
β
+
σ
2/2)
(35)
γ, β
are coefficients from Probit and Lognormal OLS regressions respectively. Φ(.)is
the cumulative distribution function (CDF) of standard normal distribution, and Φ(xγ)is
the probability of x
γ
to be positive.. The marginal effect of firm size can also be
calculated as shown in (36):
)]()()[2/exp(][ 2
γβφγγϕσβ
xxxxxyE ++=∂∂
(36)
To make sure that the calculations are consistent, we use the OLS results instead of the
robust regression because different weights are assigned to observations in the robust
regression. The marginal effect of firm size at the mean firm size (347.2178) is 1.10514e
04, which means that if the firm hires one more employee, its new product sales ratio
tends to increase by 1.10514e04. We then plot the calculated new product sales ratio
with firm size in Figure 10. The fitted new product sales ratio rises with firm size
increase and peaks for firms with around 50,000, then fall with further firm size increase.
Figure 5. Fitted new product sales ratio for Hurdle Model
0.5 11.5
New Product Sales Ratio
050000 1000 00 150000 200000
Size
Hurdle
OLS and QMLE (Logit and Probit as the Link Functionsin Generalized Linear
Model) estimation results are shown in Table 4. In QMLE (Logit), we assume G(.) is the
logistic function, and in QMLE (Probit), G(.) denotes the standard normal cumulative
distribution function.
To check the fitness of different functional forms, we use the Ramsey’s RESET
test (1969) as suggested in Papke and Wooldridge (1996). Let , be the OLS residual
and fitted value respectively, and we obtain NR
∧
i
u∧
i
y
2 from the regression:
∧
i
uon , , i=1,2,..N
i
x∧2
i
y∧3
i
y
If the functional form is true, then NR2a
~
2
2
χ
(nonrobust form where homoskedasticity is
maintained). The RESET statistic for OLS model is 28.0944, if we check with Chi
squared distribution with two degreesoffreedom, the OLS form is strongly rejected. For
QMLE Logit and Probit, RESET statistics are .5853 and 1.1706, respectively. The
specifications cannot be rejected and we conclude that QMLE (Probit) is a better
specification.
Table 4
OLS AND QMLE RESULTSa
Variable OLSbQMLEc
(Logit)
QMLEd
(Probit)
sizet2 1.46e05**
(4.30e06) 7.73e05**
(3.22e05) 4.48e05**
(1.39e05)
size2t2 1.52e10**
(3.84e11) 9.07e10
(6.13e10) 4.90e10**
(1.72e10)
dost1 8.71e06
(9.87e06) 4.05e05
(4.90e05) 2.34e05
(2.68e05)
constant 2.59e01**
(1.04e03) 4.58**
(2.01e02) 2.33e**
(8.06e03)
R2
DF
0.2088
5751 
5751 
5751
a Note: The quantities in (.) below estimates are the OLS standard errors or, for
QMLE, the GLM standard errors robust to variance misspecification.
* means the coefficient is significant at 10% level, but not 5% level.
** means the coefficient is significant at 5% level.
b OLS regression
c QMLE (Logit) regression
d QMLE (Probit) regression
From the result of Table 4, we can see that there does exist nonlinear relationship
between size and new product sales ratio. The negative coefficients of squared term of
size indicating negative marginal effect of firm size on new product sales ratio after some
level of firm size, which is what we expect. The negative coefficient for two firm size
variables in the QLME (probit) estimation is statistically significant.
The next step is to compare the marginal effects: 2
[]/
t
E salesnp size −
∂
∂, across
three estimations. For the sample estimated, the sample mean of sizet2 is 347.2178, and
sample mean for dost1 is 44.71403. The marginal effects are compared at the means of
these variables.
In QMLE (Logit), the marginal effects should be g(x
β
)
(β1+2β2
sizet2), and
g(z)=dG(z)/dz=exp(z)/[1+exp(z)]2 . At mean values of variables, the marginal effect is
3.56e06. Similarly, in QMLE (Probit), g(z)=
φ
(x
β)
(normal density function) and the
marginal effect of firm size at mean values of variables is 5.58e06. Therefore, for mean
sized firms, firm size increase still increase the new product sales ratio. Compared to the
linear model, where the marginal effect of sizet2 is 1.46e05, marginal effects of firm size
are positive. Similar to Hurdle mode, marginal effects only turn to negative at very large
firm size. By calculation, only firms with more than 42613 employees (QLME Logit) or
45714 employees (QLME Probit) will experience decline in new product sales ratio with
firm size increase.
We plot the fitted new product sales ratio in Figure 6. From the graph we can see
that new product sales ratio peaks around 50, 000 too.
Figure 6. Fitted new product sales ratio for OLS, QMLE (Logit) and QMLE (Probit)
1
.5
0
.5
1
New Product Sales Ratio
0
50000
100000
150000
200000
Size
OLS QMLE (Logit)
QMLE (Probit)
Generally, firms with more than 5000 employees are regarded as giants.
Therefore, we might only see a very small number of firms in the downward portion of
curve. Most of the time, we might only observe an increasing new product sales ratio
with firm size increase.
In the empirical work above, we found that new product sales ratio actually rise
with firm size increase even for very large firms. Each industry could possibly have
specific type of relationship between firm size and new product sales ratio. Therefore, we
run regressions for each individual industry in this part.
Based on the analysis of the nonlinear relationship and regression results in the
previous chapters, we choose to use Hurdle Model, QMLE (Logit) and QMLE (Probit) to
empirically test our hypothesis. Besides, we will use Multivariable Adaptive Regression
Splines (MARS) technique to fit a nonlinear model for each industry.
We will also conduct tests for group differences across industries to justify the
regressions for each industry at the end of this section.
In each regression in Hurdle, QMLE (Logit) and QMLE (Probit), time effect for
each industry will be controlled and the model we estimate is:
itititit uyeardoslsizesalesnp
+
+
++= −− 039313~31210
β
β
β
β
(37)
If we run OLS, the coefficients for firm size variable are mostly not significant
(please see appendix table) and the results are different from Robust Regressions,
indicating that outliers might cause bias (LR graphs for each industry are plot and put in
Appendix). Therefore, we use Robust Regression to adjust weights for observations with
very high leverage.
From the results for Hurdle Model in Table 5, we can easily observe that for all
the industries, the extensive margins are all positive. Therefore, firm size increase tends
to raise the probability of firm to engage in product innovation. Coefficients are not
significant at 10% for Mining and Food, Tobacco, Textiles. The second part of Hurdle
models shows the intensive margins estimation. We can also see that all the coefficients
are negative. Most of them are statistically significant at 5% except for Chemicals, which
is significant at 10% level, and Wood, Paper, Furniture, Plastics, Glass, Ceramics and
Transport Equipment, which are not significant. We can conclude that in most of the
industries, firm size increase for firms with product innovation will lower the new
product sales ratio as predicted in our hypothesis.
TABLE 5
HURDLE MODEL REGRESSIONS a
Industry
Probit
(Hurdle I)
# of obs
(Degrees
of
Freedom
)
R2
(Pseudo)
LogNormal
(Hurdle II
Robust
Regression)
# of obs
(Degrees
of
Freedom
)
R2
Ratio of
positive
new
product
sales
Mining 1.86e04
(1.70e04) 145
(134) 0.1229 1.68e03**
(2.17e04) 16
(6) 0.6213
.124
Food, Tobacco,
Textiles 1.91e04
(2.23e04) 742
(731) 0.0182 7.20e04**
(3.37e04) 304
(293) 0.2240 .410
Wood, Paper,
Furniture 9.24e04**
(2.45e04) 449
(438) 0.0637 6.20e05
(1.68e04) 179
(168) 0.1200 .399
Chemicals 4.59e04**
(1.79e04) 445
(434) 0.0454 1.11e04*
(5.67e05) 298
(287) 0.2343 .655
Plastics 1.30e03**
(3.83e04) 548
(537) 0.0689 1.38e04
(1.90e04) 311
(300) 0.2241 .568
Glass, Ceramics 1.74e03**
(5.51e04) 320
(309) 0.1125 3.74e04
(2.50e04) 164
(153) 0.1755 .516
Metals 5.38e04**
(1.36e04) 891
(880) 0.0671 2.90e04**
(8.28e05) 411
(400) 0.2192 .461
Machinery 1.01e03**
(3.05e04) 1015
(1004) 0.0909 7.36e05**
(1.88e05) 739
(728) 0.2585 .728
Electrical Equipment 1.68e03**
(3.89e04) 525
(514) 0.0743 8.69e05**
(2.03e05) 410
(399) 0.3003 .781
Medical and Other
Instruments 2.92e03**
(7.52e04) 506
(495) 0.1277 2.09e04**
(1.03e04) 380
(369) 0.2339 .755
Transport Equipment 7.13e04**
(3.00e04) 267
(256) 0.1232 3.50e05
(2.76e05) 180
(169) 0.2887 .678
a The quantities in (.) below estimates are standard errors.
* means the coefficient is significant at 10% level, but not 5% level.
** means the coefficient is significant at 5% level.
Then we put the marginal effects for each industry in Table 6 as shown below.
Column (1) shows the marginal effects calculated from the Probit estimation for the
extensive margin at the mean values of firm size (shown in Column (2)) and other
variables. Consistent with the coefficients, the firm size for all the industries put a
positive effect on the possibility of product innovation at mean firm size in that industry.
And only the first two industries’ marginal effects (Mining and Food, Tobacco, Textiles)
are not statistically significant. Column (3) shows the total marginal effect of firm size at
mean values of firm size and other variables. Besides Food, Tobacco, Textiles, all other
industries’ total marginal effects at mean firm sizes are positive, although small.
TABLE 6
MARGINAL EFFECTS FOR HURDLE MODELa
a The quantities in (.) below estimates are standard errors.
* means the coefficient is significant at 10% level, but not 5% level.
** means the coefficient is significant at 5% level.
The results for QMLE (GLM Logit) and QMLE (GLM Probit) are shown in Table
7. The coefficients for size and size2 are both insignificant for Mining, Chemicals, and
Electrical Equipment in QMLE(Logit) regressions. It could be caused by possible
collinearity between size and size2 (.9746 for Mining, .9654 for Chemicals, .9413 for
Electrical Equipment) or noises in the data. In the QMLE (Probit) regressions, Mining,
Chemicals and Machinery have same situations.
For Metal industry, in both types of regressions, the firm size variable is not
significant, while the size2 is significant. We argue that the relationship between new
Industry
Probit Marginal
Effect
(Hurdle I)
Mean of size
Hurdle Marginal Effect
(ƏE[y/x]/ Əx)
Mining 3.14e05
(4.00e05) 337.498 8.61e06
Food, Tobacco, Textiles 7.43e05
(7.00e05) 136.486 7.29e05
Wood, Paper, Furniture 3.56e04**
(9.00e05) 190.924 1.67e04
Chemicals 1.63e04**
(5.00e05) 337.982 3.61e05
Plastics 5.02e04**
(1.30e04) 154.024 2.23e04
Glass, Ceramics 6.79e04**
(1.80e04) 209.385 2.89e04
Metals 2.14e04**
(6.00e05) 209.815 3.28e05
Machinery 2.80e04**
(4.00e05) 390.339 1.08e04
Electrical Equipment 1.55e04**
(3.00e05) 757.239 3.30e05
Medical and Other
Instruments 6.25e04**
(7.00e05) 222.072 3.21e04
Transport Equipment 1.24e04**
(3.00e05) 1503.61 6.41e05
product sale ratio and firm size is still nonlinear. In contrast, Plastics industry has
insignificant size2 coefficient with significant size variable. Therefore, the relationship
between new product sales ratio and firm size might actually be linear in this case.
TABLE 7
QMLE (LOGIT&PROBIT) REGRESSIONSa
a The quantities in (.) below estimates are standard errors. The subscripts are group numbers for industries.
* means the coefficient is significant at 10% level, but not 5% level
** means the coefficient is Significant at 5% level.
Industries with similar patterns of relationship between new product sales ratio
and firm size are labeled with same group number. We also calculate the marginal effects
of different industries at their mean firm size and compare with the total marginal effects
we calculate at Hurdle model as shown in Table 8.
The results of QMLE (Logit) and QMLE (Probit) are closer than Hurdle Model.
In the previous two models, marginal effects of firm size for Mining, Chemicals,
Machinery, and Electrical Equipment are negative instead of Food, Tobacco, and Textiles
Industry Sizet2
(Logit)
Sizet2
(Probit)
Sizet2
2
(Logit)
Sizet2
2
(Probit)
# of obs
(Degrees of
Freedom)
Mining19.62e04
(1.47e03) 1.81e04
(6.98e04) 1.44e07
(2.17e07) 2.03e08
(1.56e07) 145
(133)
Food, Tobacco, Textiles23.77e03**
(1.34e03) 1.85e03**
(6.19e04) 5.97e06**
(2.54e06) 2.68e06**
(9.81e07) 742
(730)
Wood, Paper, Furniture21.99e03**
(5.46e04) 1.14e03**
(2.73e04) 8.37e07**
(4.00e07) 4.43e07**
(1.46e07) 449
(437)
Chemicals34.38e05
(1.65e04) 2.48e05
(9.28e05) 2.88e09
(1.74e08) 1.20e09
(9.37e09) 445
(434)
Plastics29.07e04**
(4.55e04) 5.36e04**
(2.66e04) 4.60e07
(3.03e07) 2.68e07
(1.74e07) 548
(537)
Glass, Ceramics21.08e03**
(3.62e04) 6.79e04**
(2.07e04) 5.04e07**
(1.03e07) 2.92e07**
(5.35e08) 320
(308)
Metals22.75e04
(2.01e04) 1.85e04
(1.16e04) 1.59e07**
(5.75e08) 9.06e08**
(3.17e08) 891
(879)
Machinery13.71e05
(6.39e05) 1.83e05
(3.71e05) 3.46e10
(4.23e09) 1.59e11
(2.72e09) 1015
(1003)
Electrical Equipment37.05e05
(3.97e05) 3.92e05*
(2.10e05) 3.70e10
(1.90e10) 2.04e10**
(1.00e10) 525
(513)
Medical and Other
Instruments27.11e04**
(2.02e04) 4.38e04**
(1.12e04) 4.65e08**
(1.08e08) 2.85e08**
(6.43e09) 506
(494)
Transport Equipment22.18e04**
(6.90e05) 1.31e04**
(3.87e05) 3.76e09**
(1.31e09) 2.27e09**
(7.42e10) 267
(255)
for Hurdle Model. However, the negative marginal effects in these industries are very
small in size.
TABLE 8
MARGINAL EFFECTS AT MEAN FIRM SIZE
Similar to the approach we take in the previous section, we also calculate the
threshold size for each industry where the marginal effects will switch the sign in Table 9.
In Mining and Machinery, marginal effects of firm size will turn from negative to
positive. However, the largest firm in Machinery has 22608.14 employees and the
threshold firm size already exceeds the maximum. Therefore, in Machinery, we never
observe the positive marginal effects. In Chemical and Electrical Equipment, the
marginal effects will remain negative from the smallest firm to largest one. For other
industries, marginal effects will change from positive to negative. The size change occurs
between 3.16e+02 and 1.16e+03. Medical and Other Instruments industry is a little bit
Industry
Marginal
Effect at
Mean Size
(Logit)
Marginal
Effect at
Mean Size
(Probit)
Marginal
Effect at
Mean Size
(Hurdle)
Mean Firm
Size
Mining 8.96e05 1.02e05 8.61e06 337.498
Food, Tobacco, Textiles 2.06e04 2.19e04 7.29e05 136.486
Wood, Paper, Furniture 2.08e04 2.25e04 1.67e04 190.924
Chemicals 8.08e06 7.96e06 3.61e05 337.982
Plastics 1.38e04 1.41e04 2.23e04 154.024
Glass, Ceramics 1.16e04 1.36e04 2.89e04 209.385
Metals 2.89e05 3.71e05 3.28e05 209.815
Machinery 8.28e06 6.73e06 1.08e04 390.339
Electrical Equipment 1.67e05 1.50e05 3.30e05 757.239
Medical and Other
Instruments 1.62e04 1.62e04 3.21e04 222.072
Transport Equipment 4.55e05 4.49e05 6.41e05 1503.61
way off the range, bearing the threshold size 7.65e+03. The exception is Transport
Equipment industry, in which the threshold size is greater than the maximum firm size in
the industry. Therefore, we will not be able to observe negative marginal effects in
Transport Equipment industry.
For all the industries with a nonlinear relationship, the threshold size is very large
compared to the firm size in each individual industry (ranging from 87.5% to 99.4%),
which is consistent with the conclusion we made before.
TABLE 9
FIRM SIZE FOR MARGINAL EFFECTS SIGN CHANGE
Industry
Sign Change
Firm Size
(Logit)
Sign
Change
Firm Size
(Probit)
Maximum
Firm Size
Sign Change
Size/Maximu
m Industry
Size
Mining13.34e+03 4.46e+03 71749.13 95.4%
Food, Tobacco, Textiles23.16e+02 3.45e+02 5039.781 87.5%
Wood, Paper, Furniture21.19e+03 1.29e+03 6063.933 97.9%
Chemicals37.60e+03 1.03e+04 174604.6 
Plastics29.86e+02 1.00e+03 3167.575 97.4%
Glass, Ceramics21.07e+03 1.16e+03 49259.08 94.8%
Metals28.65e+02 1.02e+03 102359.4 95.5%
Machinery15.36e+04 5.75e+05 22608.14 
Electrical Equipment39.53e+04 9.61e+04 128319.4 
Medical and Other Instruments27.65e+03 7.68e+03 18429.68 99.4%
Transport Equipment22.90e+04 2.89e+04 157435 
Finally, we fit the MARS model allowing for 40 knots and 1 as maximum order of
interactions for each industry using B34S. The MARS model is very sensitive and offers
a totally different perspective to look at the relationship between firm size and new
product sales ratio in different industries. We also show the results of GAM model and
the nonlinearity test for size variable offered in Table 10.
TABLE 10
ESTIMATION RESULTS FOR OLS, MARS, GAM AND NONLINEARITY TEST FOR SIZE (GAM)
Industry
OLS
MARS
GAM
Size 2.55E07
(1.17E05)  1.91E05
(1.16E05)
Mining RSS (RSS_Linear in Size)
Size Nonlinearity
1.1555 1.4949 1.1054 (1.140)
(0.7420)
Size 4.93E05
(4.01E05)

2.38E03**
(6.63E04)
1.78E03**
()
If size<3.48
If 3.48<size<46.44
If 46.44<size
4.73E05
(3.94E05)
Food, Tobacco, Textiles
RSS (RSS_Linear in Size)
Size Nonlinearity
48.5546 43.7236 46.5999 (47.56)
(0.9981)
Size 8.80E05**
(3.75E05)  9.27E05**
(3.64E05)
Wood, Paper, Furniture RSS (RSS_Linear in Size)
Size Nonlinearity
28.8544 24.4683 27.0269 (27.78)
(0.9929)
Size 7.63E06
(1.70E05)
7.86E04**
(2.07E03)

If size<195.33
Otherwise
1.18E05
(1.71E05)
Chemicals
RSS (RSS_Linear in Size)
Size Nonlinearity
36.7599 33.7547 36.6719 (36.73)
(0.1104)
Size 7.59E05
(6.56E05)

4.13E02**
(1.11E02)
6.40E03
()
1.00E04
()
If size<7.91
If 7.91<size<13.02
IF 13.02<SIZE<32.79
If 32.79<size
1.19E04
(6.46E05)
Plastics
RSS (RSS_Linear in Size)
Size Nonlinearity
45.3331 38.7611 43.5513 (44.03)
(0.8788)
TABLE 10
ESTIMATION RESULTS FOR OLS, MARS, GAM AND NONLINEARITY TEST FOR SIZE (GAM) (CONTINUED)
Industry
OLS
MARS
GAM
Size 2.13E04**
(7.46E05)  1.80E04**
(6.91E04)
Glass, Ceramics RSS (RSS_Linear in Size)
Size Nonlinearity
27.8107 23.8578 23.5837 (23.87)
(0.7000)
Size 6.81E06
(2.09E05)

5.03E04**
(1.28E04)
2.94E05
()
If size< 12.41
If 12.41<size<254.06
If size>254.06
1.49E06
(2.09E05)
Metals
RSS (RSS_Linear in Size)
Size Nonlinearity
60.6126 53.8871 60.0859 (60.23)
(0.4433)
Size 5.54E06
(8.29E06)

1.13E02**
(4.93E03)
1.06E02
()
9.41E05
()
8.88E06
()
If size<20.03
If 20.03<size<30.38
If 30.38<size<46.03
If 46.03<size<1829.2
If 1829.2<size
4.26E06
(8.25E06)
Machinery
RSS (RSS_Linear in Size)
Size Nonlinearity
94.5755 83.5451 93.1253 (93.26)
(0.3084)
TABLE 10
ESTIMATION RESULTS FOR OLS, MARS, GAM AND NONLINEARITY TEST FOR SIZE (GAM) (CONTINUED)
Industry
OLS
MARS
GAM
Size 2.02E05**
(9.68E06)

4.28E02**
(1.26E02)
9.86E02
()
2.45E03
()
1.06E03
1.407E06
()
If size<7.26
If 7.26<size<14.28
If 14.28<size<15.84
If 15.84<size<64.04
If 64.04<size<282.37
If 282.37<size
1.412E05
(9.66E06)
Electrical Equipment
RSS (RSS_Linear in Size)
Size Nonlinearity
48.2242 39.0899 47.6928 (47.80)
(0.2341)
Size 9.75E06
(1.75E05)

2.29E03**
(5.26E04)
8.601E04
()
If size<212.24
If
212.24<size<295.51
If 295.51<size
5.80E05**
(1.70E05) Medical and Other
Instruments
RSS (RSS_Linear in Size)
Size Nonlinearity
46.4823 33.0859
43.6813 (44.63)
(0.9866)
Size 9.19E06**
(4.58E06)  1.55E05**
(4.47E06)
Transport Equipment RSS (RSS_Linear in Size)
Size Nonlinearity
25.8405 19.0495 24.1753 (24.75)
(0.8883)
According to the nonlinearity test of GAM, we find relatively significant (nonlinearity
probability >85%) nonlinearity in size in Food, Tobacco, Textiles, Wood, Paper, Furniture,
Plastics, Medical & Other Instruments. MARS detects nonlinearity of size also in Chemicals,
Metals, Machinery and Electrical Equipment, but not in Wood, Paper, Furniture and Transport
Equipment.
GAM results show the same signs as OLS. Comparing the Residual Sum Squares, MARS
seem to do the best job. However, the nonlinearity shown in MARS results is complicated,
although all the coefficients are significant. To investigate the pattern of relationship between
new product sales ratio and firm size for these industries, we plot the leverage graphs of firm size
for the industries with found nonlinearities in MARS as shown in Figure 7.
Figure 7. Prediction Leverage of Size
Food, Tobacco, Textiles
Contribution
SIZ E
0 500 1000 1500 2000 2500
.20
.10
0
.10
.20
.30
.40
.50
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [ lag= 0 , int= 1, o=Medians]
Page 56
Figure 15. Prediction Leverage of Size
Chemicals
Contribution
SIZE
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000
.10
.15
.20
.25
.30
.35
.40
.45
.50
.55
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [lag= 0 , int= 1, o=Medians]
Plastics
Contribution
SIZE
0 500 1000 1500 2000 2500
.30
.40
.50
.60
.70
.80
.90
1.00
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [lag= 0 , int= 1, o=Medians]
Metals
Contributi on
SIZE
0 100 0 2000 3000 4000 5000 6000 7000
0
.05
.10
.15
.20
.25
.30
.35
.40
.45
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [lag= 0 , int= 1, o=Medians]
Page 57
Machinery
Contributi on
SIZE
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000
.15
.20
.25
.30
.35
.40
.45
.50
.55
.60
.65
.70
.75
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [lag= 0 , int= 1, o=Medians]
Electrical Equipment
Contributi on
SIZE
0 20000 40000 60000 80000 100000 120000
7
6
5
4
3
2
1
0
1
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [lag= 0 , int= 1, o=Medians]
Medical and Other Instruments
Contribution
SIZE
0 2000 4000 6000 8000 10000 12000 14000 16000 18 000
0
5
10
15
20
25
M
A
R
S
Y
H
A
T
O
L
S
_
Y
H
A
T
G
A
M
_
Y
H
A
T
Prediction Leverage of SIZE [lag= 0 , int= 1, o=Medians]
The patterns of nonlinearity shown in the graphs above are not similar to the ones
predicted in QMLE results. Comparing the results, it is obvious that MARS and GAM
specifications are more flexible and show better fit of data.
Page 58
To test whether it is worth to run regressions for each individual industries, we separate
the industries into two groups, one group with R&D intensities below average (.022) and one
group above. Then we check the structural difference between two groups. And we use Wald
Test, and Likelihood Ratio Test to test the significance of difference.
The Likelihood Ratio Test Statistics is constructed as mentioned in Green (2002):
LR =
−
2(lnLR
−
lnLU]
lnLR stands for the restricted likelihood ratio, which in our model is the likelihood for
the pooled regression. lnLU is the unconstrained likelihood ratio, which is calculated as the sum
of all the likelihood ratios for individual industry regression. LR is compared with chisquared
table to check the significance of constraints.
From Table 11, we can observe that it is statistically significant that the two groups of
industries have different slopes for size and al so distinguished sets of coefficients.
TABLE 11
GROUP DIFFERENCE TESTSa
SizeT2 (SizeT2 & SizeT22) Total
Probit (Hurdle I) chi2( 1) = 22.39
Prob > chi2 = 0.0000 chi2( 11) = 442.58
Prob > chi2 = 0.0000
LogNormal (Hurdle II)
Robust Regression F(1, 3376) = 11.37
Prob > F = 0.0008 F(10, 3376) = 8.90
Prob > F = 0.0000
GLM (Logit) chi2( 2) = 8.12
Prob > chi2 = 0.0173 chi2( 12) = 453.49
Prob > chi2 = 0.0000
GLM (Logit) chi2( 2) = 14.63
Prob > chi2 = 0.0007 chi2( 12) = 471.02
Prob > chi2 = 0.0000
a Group I: Mining, Food, Tobacco, Textiles, Wood, Paper, Furniture, Plastics, Glass, Ceramics, Metals
Group II: Chemicals, Machinery, Electrical Equipment, Medical and Other Instruments, Transport Equipment
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5) Conclusion
We develop a model to investigate how a firm’s internal allocation of process and
product R&D relate to firm size. Despite the conclusions in the previous literature that larger
firms invest relatively more in process innovation and relatively less in product innovation, we
modify the model and test with nonlinear techniques and find evidence that the relationship
between product innovation and firm size to be nonlinear.
After taking into account the cannibalization due to product innovation, the comparative
advantage for larger firms in process innovation is weakened in the presence of new products.
Therefore, firm size effect on the ratio of process R&D to product R&D is predicted to be
smaller for firms engaged in both types of innovation than in the previous literature.
We also suggest the existence of a threshold firm size for product innovation to be
profitable. This insight emerges with the consideration of corner solutions. As a result, larger
firms are more likely to invest and succeed in product innovation.
New product sales ratio reflects firm’s innovation investment choice and success;
therefore it is related to firm size. Probability of new product invention increases with firm size
at the beginning due to the threshold size for product innovation. However, new product sales
ratio tends to fall with further firm size increase for those with new products and technological
opportunities for new products are reasonably high. As a result, we conclude in the model part
that the new product sales ratio should be nonlinear in firm size.
The hypothesized relationship between new product sales ratio and firm size is tested
with data from the MIP survey. In contrast to the traditional linear estimation, we adopt
nonlinear estimation techniques including Probit, Tobit, Hurdle, MARS, GAM and OLS, QMLE
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with polynomial terms. Despite the effort to fit all the industries in the same pattern, we also run
regressions for each individual industry and test the group difference.
In the pooled regression with full sample, Hurdle model estimates support our hypothesis,
with the weakness that the coefficient of firm size is not statistically significant. Results of
QMLE regressions are more statistically significant.
The fitted values of new product sales ratio show that the new product sales ratio actually
increases with firm size until firm size reaches a really large number. This is probably caused by
two factors: first, the threshold size induces the positive effect of firm size on the new product
sales ratio; second, for firms undertaking product innovations, the cannibalization effect reduces
the comparative advantage of larger firms in process innovation and hence reduces the negative
impact of firm size on new product sales ratio. The positive effect of firm size on new product
sales ratio overweighs its negative effect, which causes the size at which the size effect changes
signs to be very large and we only observe the increasing relationship between new product sales
ratio and firm size.
In the regressions for each industry, we found that the patterns of the relationship are
significantly different based on the group difference tests. Individual regression reveals more
obvious nonlinear pattern for most of the industries. The MARS and GAM technique provides a
more complicated view of the pattern of relationship between innovation choice and firm size for
each industry and showed totally 9 out of 11 industries have detected nonlinearities in size.
From estimation results of Hurdle Model and QMLE (Probit & Logit), the marginal
effects of firm size at mean level of variables are mostly positive or extremely small if negative.
For these industries with nonlinear relationships (except for Mining and Medical and Other
Instruments), the sizes at which the marginal effect switches signs are also in the large division
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of each industry, which is consistent with the regressions for constrained model (pooled
regression) with full sample and indicate the strong effect of threshold size and cannibalization.
Therefore, we conclude that larger firms excel in product innovation, both in absolute
terms and relative terms. Furthermore, linear methods might not appropriate to be used to
estimate the relationship between innovation choice and firm size.
In the future work, it is valuable to get more data of innovation, such as the process R&D
& product R&D investments with more detailed industry divisions, and industry structures. With
detailed investment data, we will be able to look more closely and more accurately about the
relationship between innovation choice of firms and scale of operation, and impact of industry
structure and other shocks.
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