Efficiency of Innovation Subsidies
Michael Hall
mjhall@uncg.edu
Abstract: The fundamental premise of this paper is to examine the efficiency of
innovation subsides. A theoretical model is presented that suggests efficient innovation subsidies
should result in marginal social benefits with respect to the subsidy that are equal across all
subsidized projects. If this marginal social benefit is not equal then the social welfare has not
been maximized. Two avenues for variations in marginal social returns are considered herein: the
first is variation in firm characteristics that affect the impacts of the innovation subsidies, and the
second is a weighting of benefits from supported projects that gives preferences to some projects
for reasons not defined here. This research will apply theoretical and econometric modeling to
data on the SBIR program to provide feedback on the efficiency of that program.
1. Introduction
Economic theory suggests that government intervention in markets can result in social
welfare gains. These interventions take many forms, including taxes and subsidies. These
interventions are ideally calibrated to perfectly eliminate market distortions and maximize social
welfare. However, this ideal may be missed due to suboptimal policy. Allcott, et al. (2014)
expressed the ability of a market intervention to be non-optimal and potentially welfare reducing,
by stating:
Corrective taxation is a common approach to addressing externalities,
internalities, and other market distortions. These distortions are often
heterogeneous: for example, some cars pollute more than others, and many
people consume alcohol “rationally” even as present biased individuals might
over-consume. Such heterogeneity raises the question of whether a corrective tax
is “well-targeted”: does it primarily affect individuals subject to relatively large
distortions? A tax set at the average level of the distortion could actually reduce
welfare if the marginal individuals were already making relatively undistorted
decisions.
The above passage expresses concern about the ability of policies to efficiently address
the market distortions that inspired their implementation. As stated, well-targeted policies
primarily affect individuals subject to relatively large distortions. Policies that are not well
targeted could “actually reduce welfare.”
This concept can be extended to consider the allocation of public monies in subsidies. In
particular, this paper examines the allocation of funds used to support technology and innovation
via the small business innovation research (SBIR) program. The question asked herein is whether
the current scheme for allocating SBIR funds results in a well-targeted subsidy. That is, are funds
directed towards firms that face larger distortions? In particular, this paper will focus on the
survival of younger and less-experienced firms, as they tend to face larger market distortions
than older and more-experienced, firms.
The remainder of this paper is structured as follows. Section two provides background
information on the SBIR program. Section three discusses the research on firm survival with an
emphasis on the relationship between innovative activity and survival. Section four presents
economic theory related to social welfare and optimal allocations of public funds as it pertains to
innovation policies. Section five empirically tests the optimality conditions derived in section
two. Section six summarizes the results and concludes the paper with policy recommendations.
2. SBIR Program
The SBIR program is “a highly competitive program that encourages domestic small
businesses to engage in Federal Research/Research and Development that has the potential for
commercialization.” (SBIR, 2015) The Small Business Innovation Development Act of 1982
(Public Law 97-219) established the SBIR program in 1982. The SBIR program requires that all
federal agencies with an extramural research budget in excess of ten billion dollars set aside 1.25
per centum of that budget to research conducted by small businesses. The Small Business
Innovation Research Program Reauthorization Act of 1992 (Public Law 102-564) increased the
required spending to 2.5 per centum of the extramural research budget, but increased the
minimum budget required to qualify to one hundred billion dollars. The SBIR program has since
been reauthorized: in 2000 as part of The Small Business Reauthorization Act of 2000 (Public
Law 106-554) and in 2012 as part of the National Defense Authorization Act of Fiscal Year 2012
(Public Law 112-81).
While each agency has some variation in how it operates the SBIR program, the general
structure of funding allocations is consistent. There are three funding phases: Phase I, Phase II,
and Phase III. Phase I awards are limited to one hundred thousand dollars and are for exploratory
research and development of a proposed technology.1 Phase II awards are limited to seven
hundred fifty thousand dollars and are for the full development of the proposed technology.
Phase III provides no funds as firms are expected to have commercialized their product or enter
1
These dollar figures reflect the current legislative guidelines.
into contracts with the agency to manufacture and produce the successfully developed
technology.
The data used herein comes from the National Research Council’s (2008) assessment of
the SBIR program. This survey was conducted in 2005 and consists of Phase I and Phase II
surveys. The survey of Phase II participants has 1916 responses. The survey of Phase I has 2746
responses.
The National Research Council asks two questions regarding firms that have won
multiple SBIR awards from the DoE: “to what extent are multiple awards made to individual
companies in the DoE SBIR program?” And “what outcomes are associated with these awards?”
The answer to the first multiple-award-winners question is detailed very well in the book. Many
awards are clustered around top-performing firms, the top 20 of which have received in excess of
100 Phase I awards. The answer to the second question is the firms that have won the highest
number of awards are associated with the largest commercialization successes. The average
revenues of firms having won more than 125 Phase I awards is nearly double that of those firms
that have won less than five Phase 1 awards.
Importantly, National Research Council (2004) notes that the DoE expressly considers
the past performance of firms in the SBIR program to be a positive determinant for funding
decisions. This is important as it may result in sub-optimal targeting of innovation subsidies.
That is, previous winners likely face smaller market distortions. As such, a systematic bias
towards previous winners may result in less than optimal social welfare. The following section
presents research on the determinants of firm survival and suggests that younger and lessexperienced firms are less likely to survive than older and more-experienced (i.e., winners of
previous awards) firms.
3. Firm Survival
Firms contribute to generation of social welfare by creating economic surplus. The ability
of a firm to create this surplus is conditioned on its survival. Extensive research on the
determinants of firm survival and the generation of economic growth
Research on the relationship between firm survival and innovation has found that
innovation can contribute to firm survival. Fernandes and Paunov (2013) examined Chilean
manufacturing firms and found that cautious innovation contributed to the survival of firms.
Cefis and Marsili (2005) examined the survival of manufacturing firms in the Netherlands and
found that innovation increase the survival probability of firms, with process innovation
providing the most significant bonus.
4. Theoretical Foundation
This section presents a theoretical model that explores the conditions required for optimal
public funding of innovative activities. These optimality conditions provide a starting point for
an empirical examination of the impact of this public funding.
The economic model herein assumes a social welfare function (W) and that there are multiple
firms denoted with the subscript i. For ease of notation it is assumed that each firm only conducts
a single innovation project. The social welfare function takes as arguments the vector of
aggregate surplus (AS) and the value of taxes. The elements of the aggregate surplus vector are
the combined value of producer and consumer surplus from the innovation from each firm (ASi).
The aggregate surplus for a given firm is assumed to be a function of a publicly funded
innovation subsidy (Subi) and a vector of firm characteristics (Xi). AS is thus expressed as:
(1)
𝑨𝑺 = [𝐴𝑆! (𝑆𝑢𝑏! , 𝑿! ), 𝐴𝑆! (𝑆𝑢𝑏! , 𝑿! ), ⋯ 𝐴𝑆! (𝑆𝑢𝑏! , 𝑿! )]
The value of the tax is defined to be the sum of all subsidies. The welfare function is defined
to be a weighted sum of the aggregate surplus from each innovation less the value of the taxes
collected to pay these subsidies. The welfare weight associated with each firm i is denoted as 𝜆!
and the vector of these weights is expressed as 𝜦:
(2)
𝜦′ = [𝜆! , 𝜆! , ⋯ 𝜆! ]
Thus, the social welfare function can be written as:
(3)
𝑊 = 𝑨𝑺𝜦 − 𝑇𝑎𝑥
The resulting optimization problem is for the government choses the subsidy for each firm to
maximize:
(4)
𝑊(𝑨𝑺(𝑆𝑢𝑏! , 𝑿! ), 𝑇𝑎𝑥) s.t.
! 𝑆𝑢𝑏!
= 𝑇ax
Optimization of this equation results in the following first order condition for a local maximum:
(5)
!"
!!"!
!!"
!"
∙ !!"#! + !"#$ = 0 ∀ 𝑖
!
As the tax used for all subsidies is drawn from the same pool, the welfare impact of the
!"
marginal tax dollar !"#$ is constant across all firms. This results in following condition:
(6)
!"
!!"!
!!"
!"
!!"
∙ !!"#! = !!" ∙ !!"#! ∀ 𝑗, 𝑘 ∈ 𝑖
!
!
!
Equation (6) means that the optimal subsidy allocation for each firm results in a marginal
effect of the subsidy on aggregate surplus from the firm inversely proportional to the impact that
firm’s surplus has on social welfare. This condition results in two potentially informative
!"
empirical tests. These tests make differing assumptions as to whether !!" varies across firms or
!
!"
!!"!
!"
is constant across firms. If !!" is assumed to vary across firms, one may use estimated
!
!!"
values of !!"#! to calculate the set of ex-post weightings under which the observed allocation of
!
!"
subsidies is optimal. Alternatively, if !!" is assumed to be constant across firms, then one may
!
!!"!
use estimates of !!"# to derive the optimal subsidy allocation and to calculate potential welfare
!
gains by changing to this new allocation paradigm.
Note that the partial derivatives expressed in this equation are potentially functions of firm
characteristics. If this is the case then the socially optimal subsidy potentially varies conditional
on these characteristics.
In addition to the first order conditions, the second order conditions for a local maximum are:
!"
(7)
!"!!
! ! !"
!! !
!! !
!!"
∙ !!"# !! + !"! !!"# ∙ !!"#! + !!"# ! < 0 ∀ 𝑖
!
!
!
!
and
!"
(8)
!"!!
!! !
!"
!!"# !
!"!!
! ! !"
!! !
!! !
!!"
!
∙ !!"# !!"#
+ !"! !!"# ∙ !!"#! + !!"# ! <
!
! ! !"
!
!
!! !
∙ !!"# !! + !"!
!
! !!"#!
!
!
!"
!"!!
! ! !"
!! !
!!"
∙ !!"# !! + !"! !!"# ∙ !!"#! +
!
!
!
!
!! !
!!"
∙ !!"#! + !!"# ! ∀ 𝑖, 𝑗.
!
An empirical test can be conducted to examine if the conditions in equations (6) and (8) hold
in practice. If these conditions do not hold, the resulting estimates can be used to guide policy
makers towards the optimal allocation of subsidy funds. Of particular interest are the impacts
!!"
that firm characteristics have on !!"#! . An understanding of these impacts might lead to policy
!
recommendations pertaining to the ideal subsidy levels conditional on firm characteristics (e.g.,
funding tiers or a schedule of subsidies conditional on observable characteristics).
5. Empirical Examination:
Note to the reader:
In short, this section will present the empirical examination of the relationships discussed in
the theoretical section above. At the moment my focus is to square up the introduction,
background, and theoretical framework sections of this paper. This section is included merely to
discuss thoughts on potential empirical work and issues that might arise.
I intend to use a multi-stage estimation routine where the first stage(s) are binary-outcome
models predicting project discontinuation/successful innovation. The final stage will examine the
surplus from the funded projects. I intend to use sales revenues as the value for these surpluses.
I’m still thinking about how to incorporate the costs into this model. Two thoughts are to netout the costs so that total surplus is estimated or to divide surpluses by costs to create a benefitto-cost ratio. The former might result in negative surpluses while the latter moves away from the
theoretical framework outlined above.
Beyond the inclusion of costs, I’m also thinking about the model specification. I would like
to use a specification that makes sense from a theoretical standpoint but also has nice properties
regarding the first and second derivatives (i.e., they exist). At the moment I am thinking a
translog specification for the final stage would be reasonable. It would have issues with the lefthand side zeros and I’m not sure how the preliminary stages would work out in those conditions.
Actual Section Start:
This section presents an empirical examination of the economic model specified above. In
particular, this examination will test whether the conditions in equations (3) and (5) hold.
Further, the examination will explore the impacts of firm characteristics on the theoretically
optimal subsidy.
The empirical examination relies on a trans-log function where the output is surplus from an
innovation (ASi) and the inputs are the subsidy received (Subi) and a vector of firm characteristics
(Xi).
(6) 𝑙𝑛 𝑇𝑆! = 𝛽! + 𝛽! 𝑙𝑛 𝑆𝑢𝑏! + 𝜷! 𝑙𝑛 𝑿! + 𝛽!! 𝑙𝑛 𝑆𝑢𝑏! 𝑙𝑛 𝑆𝑢𝑏! + 𝜷!" 𝑙𝑛 𝑆𝑢𝑏! 𝑙𝑛 𝑿! +
𝜷!! 𝑙𝑛 𝑿! 𝑙𝑛 𝑿! + 𝜀! *
It should be noted that for some firms, ASi is zero. To control for this, a two-stage estimation
procedure is used to control for potential sample selection issue. Equaition (6) will serve as the
second stage in this two-stage estimation procedure. The resulting first stage equation will then
be:
(7) first-stage probit equation that estimates ASi = 0 or > 0.
*NOTE: This specification might useful because it results in nice first/second derivatives
(http://myweb.clemson.edu/~maloney/901/22.pdf ). It also has some basis in IO/productivity
research. I’ve also considered looking at this paper further for more thoughts on specification
http://ageconsearch.umn.edu/bitstream/116231/2/sjart_st0060.pdf. However, that there might be
some issues with some of the required assumptions. Also, there will be work on some two-stage
estimation where the first stage(s) control for project failure. That is, how successful was a
project given that it was didn’t fail.
6. Conclusions
N/A
References:
Cefis, E., and Marsili, O. (2005). “A Matter of Life and Death: Innovation and Firm Survival.”
Industrial and Corporate Change. Vol 14. No. 6, 1167-1192.
Hunt, et al. (2014). “Tagging and Targeting of Energy Efficiency Subsidies.” Retrieved 01/27/15
from: https://www.aeaweb.org/aea/2015conference/program/retrieve.php?pdfid=1198
Herberger, A. (1964). “Taxation, Resource Allocation, and Welfare.” The Role of Direct and
Indirect Taxes in the Federal Reserve System. NBER/UMI. Retrieved 01/27/15 from:
http://www.nber.org/chapters/c1873.pdf
Fernandes, A. M., and Paunov, C. (2013). The Risks of Innovation: Are Innovating Firms Less
Likely to Die? OECD.
National Research Council. (2004) SBIR Program Diversity and Assessment Challenges.
National Research Council. (2008). An Assessment of the SBIR Program at the Department of
Energy.
Public Law 97-219. The Small Business Innovation Development Act of 1982.
Public Law 102-564. The Small Business Innovation Research Program Reauthorization Act of
1992.
Public Law 106-554. The Small Business Innovation Reauthorization Act of 2000.
Public Law 112-81. National Defense Authorization Act of Fiscal Year 2012.
SBIR, (2015). Frequently Asked Questions –General Questions | SBIR.gov. Accessed February
04, 2012 from: http://www.sbir.gov/faq/general