Notching R&D Investment with
Corporate Income Tax Cuts in China∗
Zhao Chen
Fudan University

Zhikuo Liu
Shanghai University of
Finance and Economics

Juan Carlos Suárez Serrato
Duke University& NBER

Daniel Yi Xu
Duke University& NBER
June 2017

Abstract
We analyze the effects of a large fiscal incentive for R&D investment in China that awards a lower
average corporate income tax rate to qualifying firms. The sharp incentives of the program generate
notches, or jumps, in firm values, and vary over time and across firm characteristics. We exploit
a novel link between survey and administrative tax data of Chinese firms to estimate investment
responses, the potential for evasion, as well as effects on productivity and tax payments. We findlarge responses of reported R&D using a cross-sectional “bunching” estimators that is new in the
R&D literature. We also find evidence that firms relabel administrative expenses as R&D to qualify
for the program, and that up to 45% of the response may be due to relabeling. These effects imply
user-cost-elasticities of 2 for the reported response, and 1.14 for the real response. Using the panel
structure of the data, we estimate that the program increased firm productivity by 2.3% for targetedfirms. Compared to the loss in tax revenue, it cost the government 4.8% of corporate tax revenue toraise productivity by 1%. These estimates are crucial ingredients for designing policies that trade-off
corporate tax revenue with productivity growth.
JEL Codes: D24, O30, H25, H26.

∗

We are very grateful for comments from Manuel Adelino, Ashish Arora, Pierre Bachas, Michael Best, Wesley Cohen,
Dhammika Dharmapala, Michael Devereux, Rebecca Diamond, Bronwyn Hall, Jim Hines, Damon Jones, Jill Popadak,Jim Poterba, Adriano Rampini, Nirupama Rao, Mark Roberts, Leslie Robinson, Stefanie Stantcheva, Daniel Wilson, andEric Zwick as well as seminar participants at ASSA, Chicago Booth, Duke (Fuqua and Econ), FRB Philadelphia, Hong
Kong University, LSE, National School of Development (PKU), NBER Development, NBER Entrepreneurship, NBER
Chinese Economy, NTA, Penn State, Stanford (SIEPR), UCSD, University of Melbourne, Warwick University, and ZEW
MaTax. Dan Garrett, Yuxuan He, and Matt Panhans provided outstanding research assistance. Suárez Serrato is gratefulfor funding from the Kauffman Foundation. All errors remain our own.

It is widely believed that economic growth is highly dependent on innovation and, in particular, on R&D
investment. For this reason, governments often encourage R&D investment through tax incentives.
As China’s development through industrialization reaches a mature stage, the country’s leaders havefocused their efforts on fostering technology-intensive industries as a source of future growth for thecountry, which has led to an explosive growth in R&D investment. Figure 1 compares this growth tothe experience of other countries and shows that China has now equalled or surpassed developed-country
levels of R&D intensity. This paper analyzes the effects of one such effort: the InnoCom program, alarge fiscal incentive for R&D investment in the form of a corporate income tax cut. We exploit a novel
link between tax return data and survey data as well as sharp and changing tax incentives to provide
new estimates of the effects of fiscal incentives on R&D investment and productivity growth.
This paper analyzes quasi-experimental variation in the InnoCom program to answer two sets ofquestions that are of both policy and economic interest. First, is R&D investment responsive to fiscal
incentives and, if so, do firms engage in evasion or manipulation of reported R&D in response to the tax
incentives? Quantifying these effects is crucial for governments to determine the cost of the marginalyuan of R&D investment in terms of foregone tax revenue. Second, what is the effect of fiscal incentives
on firm-level and aggregate productivity growth, and how much do firms value R&D investment interms of future profits? These questions are central to the decision of whether and to what degree
governments should encourage R&D investment through tax subsidies.
Answers to these questions are often confounded by the lack of large and plausibly exogenous
variation in tax incentives. Since R&D usually requires both fixed and adjustment costs, small fiscal
incentives are unlikely to have large effects on R&D investment, especially at the individual firm level.
A second concern is that, as firms with better prospects for innovation are likely to invest more heavily,
comparisons of investment and profitability across different firms yield upward biases in the valueof R&D investment to firms. In addition, an outstanding question is whether firm responses to tax
incentives for R&D investment correspond to real activity or to relabeling of expenses. In particular,
if measured R&D is contaminated by relabeling, this might result in an upwardly-biased estimate of
the user-cost-of-capital elasticity of R&D investment, and a downwardly-biased estimate of the R&D
elasticity of TFP.
We overcome these concerns by leveraging an unusual and large fiscal incentive for R&D investmentthat is embedded in the Chinese corporate income tax. Before 2008, firms with an R&D intensity (R&D
investment over revenue) above 5% qualified for a special status as high-tech firms that was accompanied
by a lower average tax rate of 15%—a large reduction from the standard rate of 33%. After 2008, thegovernment established three thresholds of 3%, 4%, and 6% for firms of different size categories. The
use of average, as opposed to marginal incentives, creates a notch in the corporate income tax thatgenerates very large incentives for firms to invest in R&D. The combination of administrative tax dataand survey data provides a new way to precisely measure a firm’s R&D investment, exposure to thefiscal incentives, as well as firm-level outcomes of interest, such as productivity. In addition, we leverage
the unusual detail in our administrative data to analyze whether firms respond to the tax incentive by
relabeling non-R&D expenses.
Overall, we find that firms are highly responsive to the tax incentives in the InnoCom program, andthat a significant fraction of the response is due to relabeling of non-R&D expenses. However, we findthe program led to large increases in productivity, and that accounting for relabeling behavior resultsin larger estimates of the effects of R&D on productivity. We use these insights to simulate alternative
policies, and show that firm selection into the program plays a crucial role in determining the effects ofthe policy on investment, relabeling, and aggregate productivity growth.
1Our analysis proceeds in four steps. We first provide descriptive evidence that the R&D notches
have significant effects on firms’ reported R&D intensity, and that part of this response may be due
to relabeling of non-R&D expenses. We show that a large number of firms choose to locate at thethreshold, and that introducing the tax cut led to a large increase in R&D investment. We use a groupof firms unaffected by the incentive prior to 2008 to show that the bunching patterns are driven by
the tax incentive, and are not a spurious feature of the data. We then analyze relabeling responses by
exploiting the fact that, under Chinese Accounting Standards, R&D is reported as a subcategory ofadministrative expenses. Our detailed tax data allows us to separate R&D from other administrative
expenses, which we use to show patterns consistent with a significant relabeling response.
Second, we develop a model of firm behavior where R&D investment and relabeling decisions depend
on tax incentives, the effect of R&D on productivity, the costs of evasion, as well as on heterogeneityin firm productivity and adjustment costs. Our analysis characterizes the profit function of the firmthat is indifferent between the level of R&D implied by the notch and a level of investment below thenotch. The model shows that as long firm productivity is smoothly distributed across the population,
the InnoCom program leads to excess bunching at the R&D notch relative to a tax system without anotch. We derive a bunching estimator that relates the bunching patterns to the percentage increase in
R&D following methods similar to those in Kleven and Waseem (2013) and Saez (2010). Our model also
predicts an increase in relabeling, and an increase in productivity that depends on the effect of R&D on
productivity, as well as on the fraction of the reported response that corresponds to real activity. We
then show that these predictions can be quantified empirically by linking our model to new methods
developed by Diamond and Persson (2016).
In our third step, we provide causal estimates of the effects of the InnoCom program on reported
R&D investment, relabeling, and productivity, as well as on other outcomes of policy interest suchas firm investment and tax revenues. We first use the bunching estimator to quantify the percentage
increase in R&D investment that is due to the tax incentive. Consistent with our descriptive evidence,
we find large increases in R&D investment of 30% for large firms, of 20% for medium firms, and of 11%
for small firms in 2011. These intent-to-treat estimates mask the behavior of complier and non-complierfirms. On average, firms that comply with the program increase investment by 46% for large firms, of
33% for medium firms, and of 29% for small firms.
We then provide causal estimates of the InnoCom program on relabeling, productivity, and tax revenues. We find estimates of intent-to-treat effects that confirm an increase in reported R&D investment
and a decrease in administrative costs. We calculate the elasticity of R&D investment to the change
in the user cost of capital that is induced by the InnoCom program, and we find an elasticity of 2 forreported R&D, and, once we account for relabeled administrative costs, an elasticity of 1.14 for real
R&D investment. Even though a significant fraction of the response is consistent with relabeling, wefind persistent and statistically significant effects of the InnoCom program on future productivity andprofitability. In particular, between 2009 and 2011, the program led to an increase of 8.6% in profitability, and 7.7% in productivity for every 100% increase in reported R&D. While the effects of the
program on profitability lessen the fiscal cost of the government, we find that raising productivity by
1% cost the government a 4.8% decrease in corporate tax revenues.
Finally, we propose a simulated method of moments approach to estimate the structural parametersof our model, including costs of evasion, the effect of R&D on TFP, and the distributions of fixed andadjustment costs. We then use these estimates to simulate the effects of counterfactual policies thatchange the current policy parameters. We find that firm selection into the program plays a crucial role indetermining the economic effects of the program. In particular, if firms have heterogeneous adjustment2

costs, the firms that participate may not be the most productive. Selection into the program generates
misallocation where low productivity firms with low adjustment costs may receive large tax benefits
that are not accrued to high productivity firms with high adjustment costs. This lowers the efficiencyof the policy and results in a lower ratio of productivity growth to tax expenditures.
The paper relates to several literatures. First, this paper is related to a large literature analyzing tax
incentives for R&D investment. Becker (2015) and Hall and Van Reenen (2000) survey evidence of R&D
tax incentives, and Hall and Van Reenen (2000) find a dollar-for-dollar effect of tax credits on R&D
investment. The recent empirical evidence so far is concentrated in OECD countries, where micro-level
data of firm innovation and/or tax records have become increasingly available.1 While earlier work
typically relied on matching and panel data methods, there is an emerging literature that explores theimpact of tax incentives on R&D incentives in a quasi-experimental setup, in particular, by exploiting
policy discontinuities. Examples include Agrawal et al. (2014), Bøler et al. (2015), Dechezlepretre et al.
(2016), Einiö (2014), Guceri and Liu (2015), and Rao (2015). To our knowledge, this is the first paper
to analyze R&D tax incentives in a large emerging economy such as China.2 It is also one of the firstfew studies that combine administrative tax data with industry survey data to study the link between
fiscal incentives, R&D investment, and firm-level productivity.
Second, a previous literature has long documented “relabeling” as an important challenge to identifying the real impact of tax incentive on R&D (see Hall and Van Reenen (2000), Eisner et al. (1984),
Mansfield and Switzer (1985)). This issue is likely more severe in a developing economy setting (Bachas
and Soto (2015), Best et al. (2015)). Our paper exploits unique data on firm expenditures to jointly
model and estimate firm’s R&D bunching and relabeling behaviors. Our policy simulations also inform
our understanding of the efficiency of different policies when firms may engage in evasion, as in Best etal. (2015). In particular, size-based policies may be preferable to investment tax credits in developing
countries if they substantially increase the cost of evasion.
Third, our paper is related to a recent literature that uses non-parametric methods to recoverestimates of behavioral responses to taxation by analyzing the effects of sharp economic incentives, suchas kinks or notches in tax schedules, on aggregate patterns of “bunching” in distributions of economic
activity.3 As detailed below, the R&D tax incentive creates a jump, or notch, in the after-tax profit
function, generating similar incentives to those in Kleven and Waseem (2013) and Best and Kleven(2015). However, in contrast to this literature, the incentive generated by the notch targets a particularaction, increasing R&D investment. We exploit this feature of our setting to estimate treatment effectsof the program on R&D investment, relabeling, tax revenues, and growth in productivity using an
estimator recently developed by Diamond and Persson (2016). Finally, we develop a simulated methodof moments estimation approach that combines the estimates of treatment effects on relabeling andproductivity with the bunching estimator to estimate structural parameters.4
1

For instance, see Agrawal et al. (2014) and Czarnitzki and Licht (2006) for Canada, Einiö (2014) for Finland, Mulkay
and Mairesse (2013) for France, Almus and Czarnitzki (2003) and Hussinger (2008) for Germany, Lach (2002) for Israel,
Bøler et al. (2015) for Norway, González and Pazó (2008) for Spain, Griffth et al. (2001), Guceri and Liu (2015), andDechezlepretre et al. (2016) for the UK, and Rao (2015) for the U.S.
2
Ding and Li (2015) provide a recent review of the effects of Chinese innovation policy.
3
These methods, pioneered by Saez (2010), have been used by researchers analyzing a wide range of behaviors. Kleven(2015) provides a recent survey. Our project is most related to a smaller literature analyzing firm-level responses (Devereux
et al. (2014), Patel et al. (2016), Liu and Lockwood (2015), Almunia and Lopez-Rodriguez (2015), Bachas and Soto (2015))
as well as to papers analyzing the effect of constraints to optimizing behavior (Kleven and Waseem (2013), Best and Kleven(2015), Gelber et al. (2014)).
4This allows us to clarify the interpretation of cross-sectional estimates by addressing issues discussed in Einav et al.
(2015).

3

The rest of the paper is organized as follows. Section 1 provides a description of the fiscal incentive
for R&D investment, and discusses the potential for relabeling of R&D expenses in China. Section 2
discusses the data, and Section 3 provides descriptive evidence of the effects of the tax incentive on
R&D investment and relabeling. Section 4 develops a model of R&D investment that links traditional
estimates of productivity with bunching estimators. Section 5 describes our results on the real andevasion responses to the InnoCom program, and how accounting for evasion affects estimates of theeffects of R&D on firm-level productivity. Section 6 culminates with the estimation of the structuralparameters of the model, and the simulation of counterfactual policies; Section 7 concludes.

1

Fiscal R&D Incentives and the Chinese Corporate Income Tax

China had a relatively stable Enterprise Income Tax (“EIT”) system in the early part of our sample
from 2000 - 2007. During that period, the EIT ran on a dual-track tax scheme with the base tax rate forall “domestic owned” enterprises (DOE) at 33% and “foreign owned” enterprises (FOE) ranging from
15% to 24%.5
Our project analyzes the “InnoCom” program, which targets qualifying “high tech” enterprises(HTE) and provides them a flat 15% income tax rate. This program is most important for DOEs,
including both state-owned and domestically private-owned enterprises, as they are not eligible formany other tax breaks. Prior to 2008, the certification process was administered by the local Ministry of
Science and Technology, which established a long list of prerequisites. The most important determinants
for certification are the following:6
1. At least 30% of the firm’s (technician) employees must have a college degree, and at least 10% of
the firm’s total employment should be devoted to R&D.
2. The firm’s R&D intensity (ratio of R&D expenditure to total sales) must be greater than or equal
to 5%. In addition, more than 60% percent of the R&D expenditure must be incurred within
China.
3. The sales of “high tech” products must account for more than 60% of the firm’s total sales.
The program thus generates a large fiscal incentive to invest more than 5% of sales on R&D, which
we model in Section 4.
5

The preferential treatment of FOEs has a long history dating to the early 1990s, when the Chinese government started
to attract foreign direct investment in the manufacturing sector. It offered all new FOEs located in the Special Economic
Zone (SEZ) and Economic and Technology Development Zone (ETDZ) a reduced EIT of 15%. It also offered a reduced
EIT of 24% for all FOEs located in urban centers of cities in the SEZs and ETDZs. The definition of “foreign owned” isquite broad: it includes enterprises owned by Hong Kong, Macau, and Taiwan investors. It also includes all joint-venturefirms which has foreign share of equity larger than 25%. The effective tax rates of FOEs are even lower since most had
tax holidays, typically tax free for the first 2 years or when the firm becomes profitable, and then half the EIT rate forthe subsequent 3 years. In addition to the special tax treatments of FOEs, the Chinese government started the first roundof the “West Development” program in 2001. Both DOEs and FOEs that are located in west China and are part ofstate-encouraged industries enjoy a preferential tax rate of 15%. West China is defined as the provinces of Chongqing,
Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Ningxia, Qinghai, Xinjiang, Inner Mongolia and Guangxi. Finally,
there is also a small and medium enterprise tax break, which is common in other countries, but the revenue threshold is
as low as $50, 000 and is effectively irrelevant for our sample.
6
The original government regulations also require that the firms operate in a number of selected state-encouraged
industries. However, due to the breadth and vagueness of these industry definitions, this requirement does not constitutea substantial hurdle.

4

Corporate Income Tax Reform of 2008
In addition to leveraging the cross-sectional implications of the InnoCom program, we also exploitchanges in tax rates across time. The Chinese government implemented a major corporate tax reformin 2008 in order to eliminate the dual-track system based on domestic/foreign ownership and established
a common rate of 25%.7 In concert with this reform, the Ministry of Science and Technology reformed
the InnoCom program by streamlining the application process, teaming-up with the Ministry of Financeand the National Tax Bureau to improve compliance, and by changing the threshold requirement of
R&D intensity as a function of firms’ sales. The post-2008 requirements are as follows:
1. Firms with sales below 50 million RMB must maintain an R&D intensity at, or above 6%.
2. Firms with sales above 50 million RMB, but below 200 million RMB must maintain an R&D
intensity at, or above 4%.
3. Firms with sales above 200 million RMB must maintain an R&D intensity at, or above 3%.
4. More than 60 percent of R&D expenditures must be incurred within China
The rest of the pre-2008 requirements remain in effect. In addition, the state authorities further requirethat firms meet all these criteria in the previous three accounting years, or from whenever the firm isregistered, in case the firm is less than three years old.
The InnoCom program has several desirable characteristics that allow us to avoid common problems
that arise when estimating the effects of fiscal incentives on R&D investment. First, researchers often
lack plausibly exogenous variation in fiscal incentives. As firms with better prospects for innovation arelikely to invest more in R&D, comparisons of investment and profitability across firms with different
levels of R&D may result in upwardly biased estimates of the value of R&D investment to firms. The
InnoCom program generates sharp counterfactual predictions for the distribution of R&D intensity
by changing firms’ average tax rate, which generates a notch in firms’ after-tax value functions. This
allows us to use cross-sectional estimation methods (e.g., Saez (2010), Kleven and Waseem (2013), andDiamond and Persson (2016)) to identify causal effects of the tax incentives on firm investment andproductivity.
A second concern is that, since R&D usually requires large fixed costs, even randomly assigned
incentives might not have the statistical power to detect meaningful responses. Since the average tax
rate of the firm can fall from 33% to 15%, the incentives implied by this program are economically very
important and may lead firms to invest in projects with substantial fixed costs.
Potential for Evasion and Relabeling
A final concern is that the reported R&D investment might not represent a real change in investment,
but instead might be a form of tax evasion. This concern is important when interpreting the reported
elasticity of R&D investment as real activity, and may loom large when measuring the effects of R&D
investment on productivity. To our knowledge, the current literature is not able to circumvent thisproblem. We now discuss features of the institutional environment that limit some forms of evasion andsuggest the that the most likely form of evasion is the mis-categorization of administrative expenses as
research expenses.
7
Some of the existing previous tax breaks for FOEs were also gradually phased-out. For instance, FOEs which previously
paid an EIT of 15% paid a tax rate of 18% in 2008, 20% in 2009, 22% in 2010, and 24% in 2011. In contrast, the “WestDevelopment” program will remain in effect until 2020.

5

The hypothesis that the entirety of the response is due to evasion is likely ruled out by the requirements of the InnoCom certification in order to obtain the preferential tax rate. First, the certification
process requires firms to maintain the required R&D intensity for a period of three years and firms
often use specialized consulting firms to ensure they satisfy the standards set by the Ministry of Scienceand Technology. Second, part of this certification includes an audit of the firm’s tax and financial
standings. In addition, the Chinese State Administration of Tax, together with the Ministry of Scienceand Technology, conducts regular auditing of the InnoCom HTE firms. These factors likely eliminate
the possibility for all-out evasion.
A second unlikely form of evasion is the reporting of “phantom expenses.” China relies on a valueadded tax (VAT) system with third-party reporting, and China’s State Administration of Tax (SAT)keeps records of transaction invoices between a given firm and its third-party business partners. As
in other settings (e.g., Kleven et al. (2011)), it is hard for companies to report expenses that are notreported by third-party vendors. For these reasons, it is very hard, if not impossible, for firms tocompletely make up “phantom” R&D expenses.
From conversations with the State Administration of Tax as well as corporate executives, we recognize that the most important source of evasion is expense mis-categorization. Specifically, in the
Chinese Accounting Standard, R&D is categorized under “Administrative Expenses,” which also includes various other expenses that are related to corporate governance.8 This raises the possibility thatfirms reallocate the non-R&D administrative expenditure into R&D in order to over-report their R&D
intensity. These type of expenses are easily shifted, and it may be hard to identify relabeling in any
given audit. In particular, since the threshold of R&D depends on sales, it might be hard for firms toperfectly forecast their expenses. A firm with unexpectedly high sales, for instance, might choose tocharacterize administrative expenses as R&D in order to meet the InnoCom requirement in any given
year. For these reasons, we choose to focus on this form of evasion since the institutional setting limits
other types of evasion.
Our empirical strategy to detect relabeling leverages these institutional features and exploits thedetailed cost reporting in our administrative tax data. In particular, our administrative tax datacontains detailed information on the breakdown of operating expenses and R&D expenses. This allows
us to test whether firms that respond to the InnoCom program change spending in categories that are
more likely to be subject to manipulation, such as administrative or clerical services.

2

Data and Summary Statistics

We connect three large firm-level databases of Chinese manufacturing firms. The first is the relatively
well-studied Chinese Annual Survey of Manufacturing (ASM), an extensive yearly survey of Chinese
manufacturing firms. The ASM is weighted towards medium and large firms, and includes all Chinese
manufacturing firms with total annual sales of more than 5 million RMB (approximately $800,000),
as well additional state-owned firms with lower sales. This survey provides detailed information onownership, location, production, and the balance sheet of manufacturing firms. This data allows us tomeasure total firm production, sales, inputs, and, for a few years, detailed skill composition of the labor
force. We supplement this data with a separate survey by the Chinese National Bureau of Statistics
that includes firms’ reported R&D. We use these data for years 2006–2007.
The second dataset we use is the administrative enterprise income tax records from Chinese State
8

Examples include administrative worker salary, business travel expenses, office equipments, etc.

6Administration of Tax (SAT). The SAT is the counterpart to the IRS in China and is in charge oftax collection and auditing. In addition, the SAT supervises various tax assistance programs suchas the InnoCom program. The SAT keeps its own firm-level records of tax payments as well otherfinancial statement information used in tax-related calculations. We have acquired these administrative
enterprise income tax records from 2008–2011, which allows us to construct detailed tax rate information
for individual manufacturing firms. We also use these data to construct residualized measures of firm
productivity.9 The scope of the SAT data is slightly different from the ASM, but there is a substantial
amount of overlap for the firms which conduct R&D. For instance, for the year of 2008, the share of
total R&D that can be matched with ASM records is close to 85%.
The third dataset we use is the list of firms that are enrolled in the InnoCom program from 2008–2014. For each of these manufacturing firms, we have the exact Chinese name, and the year it wascertified with high-tech status. This list is available from the Ministry of Science and Technology
website, and we have digitized it in order to link it to the SAT and ASM data. We use these data tocross-validate the high-tech status recorded in the SAT data.

Summary Statistics
Table 1 reports descriptive statistics of all the firms in our analysis sample. In panel A, we report thesummary statistics of our main dataset from the SAT for all surveyed manufacturing firms from 2008 to
2011. As discussed in Section 1, the 2008 tax reform creates an interesting pre- and post-test for FOEs,
as these firms did not have an incentives to obtain the high-tech certification prior to 2008. Similarly,
the change in the R&D intensity threshold across size-groups allows us to trace the response of firms
across time.
Our data are comprised of around 1.2 million observations and about 300, 000 firms in each sample
year. On average, 8% of the sample reports positive R&D. Among firms with positive R&D, the ratioof R&D to sales ratio, i.e. R&D intensity, is highly dispersed. The 25th-, 50th-, and 75th-percentile are
0.3%, 1.5%, and 4.3%, respectively. The administrative expense to sales ratio, which we use as a measureof misreporting to detect evasion, is close to 5.8% at the median. While our measure of residualized
TFP is normalized by construction, the distribution of productivity has a reasonable dispersion withan interquantile range of 1.8%.
We also report input and output variables that we used to construct measures of firm performance.
As in standard micro-level producer data, these variables are all quite dispersed and skewed, and theirmeans are much larger than their medians. For instance, the mean sales is 118.2 million RMB, while
the median firm’s sales is 10.6 million RMB. Similarly, the average number of workers is 175, while themedian is 48. The summary statistics are quite stable over the four years, which is why we only reportpooled moments.
In panel B, we report the summary statistics of Chinese manufacturing firms with R&D activity in
the Annual Survey of Manufacturing during the period 2006–2007. Since the National Statistical Officeof China stops reporting firm R&D activity after 2007, we mostly use these firms in our descriptive
evidence analysis. We have a similar sample size of around 300, 000 each year, although the firms in the
ASM sample are noticeably larger than those in the SAT sample. The difference is more pronounced
when we look at the lower quartile (i.e. 25%) of the distribution of sales, fixed assets, and the numberof workers. This is consistent with the fact that the ASM is weighted towards medium and large firms.
Interestingly, the firms in the ASM sample do not appear to invest more in R&D despite being larger.
9

We discuss the details of this procedure in Appendix A.

7

The fraction of positive R&D firms is slightly higher than 10%, however, R&D intensity ranges from
0.1% to 1.7% at the 25th and 75th percentile in this sample.

3

Descriptive Evidence of Firms’ Responses to Tax Notches

In this section, we provide descriptive evidence suggesting that R&D investment by Chinese manufacturing firms is responsive to the fiscal incentives of the InnoCom program, and that part of this
response may be due to relabeling. In particular, we document stark bunching patterns precisely above
tax notches, and we show that the ratio of administrative expenses to sales drops sharply at the notch.

3.1

Bunching Response

We first analyze data from the post-2008 period as the phasing out of the dual-track system provides
for cleaner comparisons across firms. Moreover, the multiple tax notches based on firm size generaterich variation in R&D bunching patterns.
Figure 2 plots the empirical distribution of the R&D intensity of Chinese firms in 2011. We limit
our sample to firms of R&D intensity between 1% and 15% to focus on firms with non-trivial innovation
activities. The first panel in Figure 2 shows the histogram of overall R&D intensity distribution. Thereare clear bunching patterns at 3%, 4%, and 6% of R&D intensity, which correspond to the three
thresholds where the corporate income tax cut kicks-in. This first panel provides strong prima-facie
evidence that fiscal incentives provided by the InnoCom program play an important role in firm’s R&D
investment choices.
To further validate that these R&D bunching patterns are motivated by this specific policy, theremaining panels of Figure 2 plot the histograms of R&D intensity for the three different size ranges
specified by the InnoCom program. For firms with annual sales less than 50 million RMB in sales, wefind clear bunching at 6%, and we find no evidence of bunching at other points. Similarly, for firms withannual sales between 50 million and 200 million RMB, we only find bunching at 4%, while for firms withmore than 200 million RMB annual sales, we only observe bunching at 3%. These patterns are consistent
with the size-dependent tax incentive programs laid out in the InnoCom program. Moreover, these plots
allay concerns of potential “round number problems” that might occur if firms report rounded versionsof true data and that are present in other bunching studies (e.g., Kleven and Waseem (2013)) as there
are no other significant spikes in the data.
Next, we analyze the sample of data from the pre-2008 period, and we report in Figure 3 theempirical distribution of Chinese firms’ R&D intensity during 2006–2007. Recall that the tax incentiveof the InnoCom was not size-dependent before 2008, and kicked-in uniformly at a 5% R&D intensity
level. In addition, our pre-2008 data has information of each firm’s employee education based on the
Census of Manufacturing conducted in 2004. This allows us to refine our sample to firms with more than
30% college educated workers, consistent with the requirement of InnoCom program. It is reassuring
here that we observe the R&D intensity bunching solely at 5%, and no significant spikes at 3%, 4%, and
6%. The contrast of R&D intensity bunching patterns across different time periods provides further
evidence that Chinese firms respond actively to the tax notches based on R&D intensity.
Bunching Response to the Tax Reform of 2008
The previous figures look at the cross-sectional distribution of R&D intensity and show a striking patternof bunching for both pre and post-2008 periods. We now explore some of the variation over time in the8Chinese corporate income tax system described in Section 1.
Consider first the behavior of FOEs in the large category (sales above 200 million RMB) as the
incentive to invest in R&D changes dramatically for these firms after 2008. Before 2008, most of thelarge FOEs benefited from the dual-tax system and faced an EIT rate between 15% to 24%. These firms
were not likely to obtain the HTE certification as they saw little to no tax benefits from the InnoCom
program. However, when the dual-tax system was phased-out in 2008, the InnoCom program becomesthe most important tax incentive program for large FOEs.10 In Figure 4, we compare the R&D intensity
distribution for the large FOEs before and after 2008. To make the two samples comparable, we only use
those firms that we were able to match between the SAT and ASM data. The figure illustrates clearly
that the changing EIT system has a large impact on firm behavior. Large FOEs have no clear patternof bunching before 2008, in contrast to DOEs that show a clear bunching at 5% of R&D intensity level.
This is consistent with the fact that FOEs already faced very favorable EIT treatment during that
period. In contrast, FOEs start behaving like DOEs after 2008. Their R&D intensity distribution starts
to show a very distinguishable bunching at the 3% level, which is the exact threshold required for thesefirms to qualify as HTEs.
We now consider the behavior of “small” (sales below 50 million RMB) DOEs. This is an interestinggroup of firms since it is the only category that saw an increase in the required R&D intensity thresholdfrom 5% to 6%. Figure 5 shows this adjustment process. Similar to the previous case, we restrict ouranalysis to those firms that we can match across samples over time. While there is a stable bunchingpattern at 5% for years 2006 and 2007, it almost completely disappears in 2008. However, it takes a few
additional years for this group of firms to gradually increase their R&D to generate a clear bunching
at 6%. This pattern is indicative of adjustment cost or other constraints that a firm needs to overcome
when they start to increase R&D investment.

3.2

Detecting Relabeling of R&D Investment

We now explore the degree to which the bunching response may be due to expense mis-reporting. As
mentioned above, under Chinese Accounting Standards, R&D is categorized under “Administrative
Expenses.” For this reason, we look for evidence of evasion by studying the ratio of non-R&D administrative expenses to sales. Figure 6 explores how this ratio is related to R&D intensity, and whether
this ratio changes discontinuously at the relevant notches. For each size group, this figure groups firms
into bins of R&D intensity and plots the mean non-R&D admin expense-to-sales ratio for each bin. We
report the data along with an estimated cubic regression of the expense ratio on R&D intensity withheterogeneous coefficients above and below the notches. The green dots are for large sales firms, red for
medium sales firms, and blue for small firms. For each size category, there is an obvious discontinuous
jump downward at each threshold. Once the firms get further away from the bunching threshold, there
is no systemic difference of the admin expense-to-sales ratio for firms with either low or high R&D intensities. This pattern is very consistent with the hypothesis that firms mis-categorize non-R&D expenses
into R&D when they get close to the bunching thresholds.11
In Table A1, we report the estimated jump at the notch from the series regression to further quantify
the size of the downward jump for each size group. The coefficient of structural break is highly significant
for all three groups. The large, medium, and small sales firms reduce their admin expense-to-sales ratio
10

Since most of these firms are located in coastal Special Economic Zones or in Economic and Technology Development
Zones, the Western Development program usually does not apply.
11
The existence of different thresholds across size groups also allows us to conduct a set of falsification tests. In particular,
we find that when we impose the “wrong” thresholds of the other size groups, there is no observable discontinuity.

9

by 1.4%, 1.3%, and 0.8%, respectively. Comparing the drop to the R&D intensity at the notch, we
Evasionis on average 23.3% for large sales firms, 32.9% for medium sales firms, and 26.9%
find that −β αfor small sales firms. As we discuss in Section 5.2, these estimates do not have a causal interpretation;
however, they present strong descriptive evidence that firms may respond to the InnoCom program byrelabeling non-R&D expenses.
As a robustness check, we conduct a similar set of analysis focusing on the ratio of R&D to total
administrative expenses. In this case, expense mis-categorization would result in discontinuous increases
in this ratio at the notch. This is confirmed in Table A2 and in Figure A2. We also explore the degree
to which evasion is related to firm liquidity. In Table A3, we analyze whether the jump in the non-R&D
administrative expense-to-sales ratio is larger for firms with more current assets. This table shows thatmis-reporting may be larger for firms with high current asset ratios.12
Combined, these figures provide strong qualitative evidence that firms actively respond to the incentives in the InnoCom program by increasing reported R&D investment, and by relabeling administrative
costs as R&D. Our quantitative analysis will focus on measuring the size of the change in R&D investment, analyzing the degree to which the response is due to relabeling, and studying how evasion may
influence the effect of R&D on productivity.

4

A Model of R&D Investment and Corporate Tax Notches

This section develops a model of R&D investment where firms may respond to notches in the corporate
income tax schedule in China by investing in R&D, and by relabeling non-R&D expenses. The objectiveof the model is three-fold. First, the model shows that a standard model of firm investment and evasion
may produce the patterns described in Section 3.2. Second, the model motivates a bunching estimator
for the increase in R&D investment, as in Saez (2010) and Kleven and Waseem (2013), as well as
an estimator of causal treatment effects on relabeling and productivity, as in Diamond and Persson(2016). We present estimates of these causal effects in Section 5. Finally, the model relates the extent
of bunching and the treatment effects on relabeling and productivity to structural parameters of themodel, which we estimate in Section 6.
We start with a simple model and develop extensions to allow for fixed costs of certification, adjustments costs of R&D investment, as well the possibility that the reported R&D response is partly due
to evasion. Full details of the model are presented in Appendix C.

4.1

Model Setup

Consider a firm i with a unit cost function c(φ1 , pt ) = c(pt ) exp{−φit }, where pt is the cost of inputs.13
φit is log-TFP and which follows the law of motion given by:
φi,t = ρφi,t−1 + ε ln(Di,t−1 ) + uit ,(1)

where Di,t−1 is R&D investment, and ui,t ∼ i.i.d. N (0, σ 2 ). This setup is consistent with the R&D
literature where knowledge capital is depreciated (captured by ρ) and influenced by continuous R&D
expenditure (captured by ε). In a stationary environment, it implies that the elasticity of TFP withεrespect to a permanent increase in R&D is 1−ρ.
12Appendix B provides additional analyses suggesting that a fraction of the reported R&D activity may be relabeled bycontrasting the effect of reported R&D on TFP above and below the notch.
13
Note that any homothetic production function with Hicks-neutral technical change admits this representation.

10

−1/θ

We assume the firm faces a constant elasticity demand function: pit = qit
can write expected profits as follows:. This implies that we(θ−1)εE[πit ] = E[πit |Di,t−1 = 0]Di,t−1 .
R&D Choice Under A Linear Tax
Before considering how the InnoCom program affects a firm’s R&D investment choice, we first consider
a simpler setup without such a program. In a two-period context with a linear tax, the firm’s intertemporal problem is given by:max (1 − t1 )(πi1 − Di1 ) + β(1 − t2 )E[πi2 ].
D1

The optimal choice of Di1 given by:

Di1 =

1
1 − t11(θ − 1)ε β(1 − t2 ) E[πi2 |Di1 = 0]1(θ−1)ε−1.

(2)Notice first that if the tax rate is constant across periods, the corporate income tax does not affect the
choice of R&D investment.14
This equation shows that the optimal R&D choice has a constant elasticity with respect to the netof tax rate, so thatd ln Di1
1=.
d ln(1 − t2 )1 − (θ − 1)εIn particular, this elasticity suggest that firms that have a higher valuation of R&D, that is when (θ−1)εis greater, will be more responsive to tax incentives.
The choice of R&D depends on potentially-unobserved, firm-specific factors, as they influence
E[πi2 |Di,t−1 = 0]. An important insight from this analysis is that we can recover these factors from D1i
as follows:E[πi2 |Di1 = 0] =1
1 − t11−(θ−1)εD.
(θ − 1)ε β(1 − t2 ) i1

(3)

A Notch in the Corporate Income Tax
Assume now that the tax in the second period has the following structure, modeled after the incentives
in the InnoCom program:
 LTt2
if D1 < αθπ1
t2 =
,
HT
t2
if D1 ≥ αθπ1HTwhere sales equal θπ1 , tLT
2 > t2 , and where LT /HT stands for low-tech/high-tech. Intuitively, this tax
structure induces a notch in the profit function at D1 = αθπ1 , where α is the R&D intensity required
to attain the high-tech certification. Figure 7 presents two possible scenarios following this incentive.
Panel (a) shows the situation where the firm finds it optimal to choose a level of R&D intensity below
the threshold. At this choice, the first order condition of the linear tax case holds and the optimal levelof R&D is given by Equation 2. From this panel, we can observe that a range of R&D intensity levels
below the threshold are dominated by choosing an R&D intensity that matches the threshold level α.
Panel (b) shows a situation where the firm is indifferent between the internal solution of Panel (a) and
14

This simple model eschews issues related to the source of funds, as in Auerbach (1984).

11the “bunching” solution of Panel (b). The optimal choice of R&D for this firm is characterized both by
Equation 2 and by D1 = αθπ1 .
Whether the firm finds it optimal to set R&D intensity equal to the notch threshold depends on
firm-level conditions that are summarized by E[πi2 |Di,t−1 = 0], as well as on the degree to which
R&D investment is valued by firms in terms of future profits (i.e., ε(θ − 1)). However, as long asE[πi2 |Di,t−1 = 0] is smoothly distributed around the threshold α, this incentive will lead a mass of firms
to find D1 = αθπ1 optimal and thus “bunch” at this level. Our analysis proceeds by first characterizing
the R&D intensity of the firm that is marginal between both solutions in terms of the R&D intensity,and we then use the identity of the marginal firm to define the bunching estimator.
We now characterize the firm that is indifferent between the level of R&D given by the notch and∗−a lower level of R&D investment Di1. Define Π(·|t) as the value function of the firm’s inter-temporalmaximization problem when facing tax t in period 2. A firm i is a marginal buncher if:
∗− LT
Π(Di1
|t2 ) = Π(αθπ1 |tHT
2 ),where the left-hand side is the profit from an internal solution facing the low-tech tax rate tLT
2 and theright hand side is the bunching solution when facing the high-tech tax rate tHT
.
Using
the
optimal2∗− LT
choice for an internal solution in Equation 3, we can manipulate Π(Di1 |t2 ) to obtain:
∗− LT
∗−
Π(Di1
|t2 ) = (1 − t1 )(π1 − Di1)+(1 − t1 ) ∗−D .
(θ − 1)ε i1(4)

Similarly, we manipulate Π(αθπ1 |tHT ) by substituting for the unobserved components of the firmdecision, i.e. E[πi2 |Di1 = 0], using Equation 3 to obtain:



∗− 
(1 − t1 )Di1
αθπ1 (θ−1)ε 1 − tHT2Π(αθπ1 |tHT ) = (1 − t1 )(π1 − αθπ1 ) +.
(5)∗−(θ − 1)ε1 − tLT
Di1
2
Comparing Equations 4 and 5 , we see that Equation 5 shows a larger cost of investment in the first∗−
period (since Di1< αθπ1 ) and higher profits in the second period. Profits are higher by a factor of(θ−1)ε  HT 
1−t2
αθπ1
, which combines productivity effects as well as a tax benefit.
1−tLT
D∗−
i1

2

We use Equations 4-5 and the indifference condition that defines the marginal bunching firm toobtain a relation between the R&D intensity of the marginal firm and (θ − 1)ε. Equating Π(αθπ1 |tHT
2 )
∗− LT
and Π(D1 |t2 ), dividing by (1 − t1 )αθπ1 , and manipulating we obtain: ∗− 1−(θ−1)ε




d
1
1 − tHT
d∗−
1
2
×
×
−1 =
×
−1 ,
(6)
α
(θ − 1)εα(θ − 1)ε1 − tLT
2
{z
}
|
|
{z
}
Relative Profit Not Bunching

Relative Profit Bunching∗−where we define d∗− = Dθπ1 as the R&D intensity of the marginal firm without a notch. The righthand-side of this equation describes the profit from the internal optimum, relative to the after-tax profits
in the first period. The left-hand-side describes the relative profits from bunching, which depend on
productivity gains and tax gains, but which are lower by the additional cost of investment.
To gain intuition behind Equation 6, note that the decision to bunch is influenced by firm-level
conditions that are summarized by E[πi2 |Di,t−1 = 0], as well as on the degree to which R&D investment
is valued by firms in terms of future profits (i.e., ε(θ − 1)). Our model uses Equation 3 as a sufficient
statistic of firm-level determinants of R&D investments to provide a link between the increase in theinvestment, d∗−of the to α, the profitability elasticity of R&D to the firm, (θ − 1)ε, and the magnitude

1−tHT

1−tHT

tax incentive, 1−t2LT . It can be shown that d∗− is decreasing in both (θ − 1)ε and 1−t2LT , so that a2
2
firm would experience a larger jump if it has a higher valuation of R&D, or if the tax incentive is larger.
12Fixed and Adjustment Costs
Our model provides a link between firms’ valuation of R&D and the patterns described in Section 3.
However, the simple model in the previous section also predicts patterns that are counterfactual towhat we observe in the data. First, as in common in studies of R&D investments, the distributionof R&D investment in China has large variability even conditional on firm TFP. In a world without
the InnoCom program, our model would predict a deterministic relationship between R&D and TFP.
Second, while our model predicts that all firms with R&D investment in the range (d∗− , α) would bunchat the notch, we find some firms do not obtain the InnoCom certification despite being very close to thenotch. This is consistent with the guidelines of the program discussed in Section 1, that show that agreater-than-notch R&D intensity is not a sufficient condition for participating in the program. Indeed,firms with high R&D intensity may not participate in the program due to constraints that prevent themfrom hiring the sufficient number technical employees, if they do not obtain a significant fraction of theirsales from new products, or due to compliance and registration costs. Finally, the literature on R&D
investment suggests that firms are subject to adjustment costs. If this were the case and adjustment
costs limited firms responses, the link in Equation 6 would imply a downwardly biased value of (θ − 1)ε.
We thus augment our model to allow for the possibility that firms face adjustment costs of investment
and fixed costs of certification. We assume that the fixed cost is given by: c × αθπ1i . We also allowi2hDi. Appendix C shows that for given values
for quadratic adjustment costs governed by: b × θπ21i θπ
1i
of (b, c), we obtain a similar result to Equation 6, which links the R&D intensity of the marginal firm
to the effect of R&D on profitability. In this case, however, the marginal firm depends on the values−of (b, c), which we denote d−b,c . As expected, we find that db,c is increasing (smaller response) withboth adjustment, b, and fixed, c, costs. We also allow for firms of similar pre-existing productivity tohave heterogeneous adjustment and fixed costs. We now redefine d∗− = min d−b,c as the smallest R&D
b,cintensity level for which there is a marginal firm.
Our augmented model results in a reasonable distribution of R&D intensity in the case without anotch, does not predict a “hole” in the distribution near the notch, and allows for firms with similar
productivity levels to engage in different patterns of investment depending on their fixed and adjustment
costs. As we show in the following section, the model also allows us to link the bunching response to
the increase in R&D and the parameters governing firms’ valuation for R&D, ε(θ − 1), in a manner thatis robust to the presence of adjustment costs.

4.2

Empirical Implications for Bunching on R&D

We now describe how we use the model to quantify the distributional patterns described in Section 3.
Figure 8 provides the intuition for this procedure. Panel (a) provides a counterfactual distribution of
R&D intensity under a linear tax. Denote this counterfactual density by h0 (·). Panel (a) demonstrates
the effect of the notch on the distribution of R&D intensity in a world of unconstrained firms. In
this case, there is a range of R&D intensity levels that is dominated by the threshold α, as shown by
the density of R&D intensity with a notch, h1 (d). Firms with an internal solution in this range will
opt to bunch at the notch, which generates the bunching patterns. Define the missing mass in therange (d∗− , α), relative to the counterfactual distribution, as B. To understand the empirical content
underlying this bunching prediction, it can be shown that the percentage increase in R&D intensity forfirms that may potentially respond to the incentive by bunching can be expressed as a function of the13missing mass B and the counterfactual density at the notch:15∆d ≡E[d|Notch, d ∈ (d∗− , d∗+ )] − E[d|No Notch, d ∈ (d∗− , d∗+ )]
B
≈
,
∗−
∗+
E[d|No Notch, d ∈ (d , d )]2αh0 (α)(7)

where d∗+ > α is chosen to capture the extent of bunching.
The prediction in Panel (a) of Figure 8 is quite stark in that no firms are expected to locate in
the dominated interval. As discussed above, the presence of fixed and adjustment costs may constrain
firms from responding to the incentives in the InnoCom program. For given values of (b, c), a firm will−
be constrained from responding if d < d−b,c , an event that we denote by I[d < db,c ]. The fraction of∗−
constrained firms at a given value of d in the range (d , α) is given byZ
Pr(Constrained|d) = I[d < d−b,c ]h0 (d, b, c)d(b, c) = h1 (d),b,cwhere h0 (d, b, c) is the joint density of R&D intensity, and fixed and adjustment costs, and where thesecond equality notes that we observe this fraction of firms in the data.16
Panel (b) of Figure 8 describes graphically how allowing for this degree of heterogeneity, in addition
to frictions, affects the predicted bunching pattern. In particular, the area B can now be computed asfollows:
Zα Z
B =I[d ≥ d−b,c ]h0 (d, b, c)d(b, c)dd =d∗− b,cZαZα Zd∗− b,cZα(h0 (d) − Pr(Constrained|d))dd ==(1 − I[d < d−b,c ])h0 (d, b, c)d(b, c)ddd∗−(h0 (d) − h1 (d))dd.
d∗−

As in Kleven and Waseem (2013), we can also relate the bunching patterns to the behavior of the∗−marginal firm. Defining ∆D∗ = α−das the percentage increase in R&D intensity relative to theαnotch, we have:17
B
∆D∗ ≈
.
αh0 (α)(1 − Pr(Constrained))

4.3

Real and Relabeled R&D Investment Under Tax Notch

As discussed above, one mechanism driving the large bunching responses we observe might be the manipulation of reported R&D investment. This section extends the model by allowing for firms to misreporttheir costs and shift non-RD costs to the R&D category. We show that the bunching predictions fromthe previous sections remain unaffected. However, the interpretation of the reported bunching response
is now a combination of real and relabeled activity. While relabeling obscures the link between bunching
and the firms’ valuation R&D, we show that we may uncover firms’ valuation of R&D in addition totheir costs of misreporting by analyzing the model’s implications for productivity and relabeling.
15

Appendix E contains details of this approximation. Note that in practice we may compute the left-hand-side of thisequation without an approximation evaluating the expectations using the estimated counterparts of h0 (d) and h1 (d).
16
We view this formulation as a micro-foundation for the constraints discussed in Kleven and Waseem (2013).
17
Appendix E provides details for this derivation, which relies on the assumption that Pr(Constrained) does not depend
on d.

14

Denote a firm’s reported level of R&D spending by D̃1 . The expected cost of misreporting to thefirm is given by h(D1 , D̃1 ). We assume that the cost of mis-reporting is proportional to the reported
R&D, D̃1 , and depends on the percentage of mis-reported R&D, D̃1D̃−D1 , so that:1h(D1 , D̃1 ) = D̃1 h̃ (δ) ,where δ = D̃1D̃−D1 . We also assume that h̃ satisfies h̃(0) = 0 and h̃0 (·) ≥ 0. In practice, we parametrize
1

this function with a constant elasticity: h̃(δ) = δ η /η.
Firms qualify for the lower tax whenever D̃1 ≥ αθπ1 . Notice first that if a firm decides not to bunchat the level αθπ1 , there is no incentive to misreport R&D spending as it does not affect total profits or
the tax rate. However, a firm might find it optimal to report D̃1 = αθπ1 , even if it actually invested alower level of R&D.
We characterize the firm that is indifferent between bunching and potentially misreporting, and notbunching. Figure 9 describes the intuition behind this choice. The firm that is willing to evade in orderto reach the notch now has a lower internal solution that would be preferable to the firm than bunchingif evasion were not possible. Because the firm gets positive returns from R&D investment and because
increasing actual R&D investment lowers the cost of evasion, the firm increases its real investment toD∗K , which is such that αθπ1 ≥ D∗K ≥ D∗− . At this point, the firm’s choice is characterized by three
conditions: the indifference condition, the first order condition of the internal solution, and the firstorder condition of the extent of evasion.
We now derive these conditions in our model. Define Π(D1 , D̃1 |t) as the value function of a firm’s
inter-temporal maximization problem when the firm faces tax t in period 2, invests D1 on R&D, anddeclares investment of D̃1 . A firm i is a marginal buncher if:
∗−
∗− LT
Π(Di1
, Di1
|t2 ) = Π(αθπ1 , D1∗K |tHT
2 ),where the left-hand side is the profit from an internal solution facing the low-tech tax rate tLT
, the
2
HT
right hand side is the bunching solution when facing the high-tech tax rate t2 , and where the firmchooses a real R&D level of D∗K .
As in the case without evasion, we obtain the following indifference condition:|d∗−α(1 − δ ∗ )1−(θ−1)ε1××(θ − 1)ε{z

1 − tHT2
1 − tLT2(δ ∗ )η
− 1−α(1 − δ ∗ )(1 − t1 )η
{z}} |Evasion Cost

Relative Profit from Bunching


d∗−
1
×
−
1
,
α(1 − δ ∗ )(θ − 1)ε
|
{z
}


=

(8)

Relative Profit from Not Bunchingwhere we consider the case without fixed and adjustment costs for simplicity. Appendix C shows thedetailed derivation and shows that this results is robust to including fixed and adjustment costs.
Equations 8 and 6 are very similar, and are identical in the case when δ ∗ = 0, such that there is no
evasion. When δ ∗ > 0 these equations differ by the cost of evasion. To understand the implications forbunching from this equation, note that opportunities for misreporting lower the threshold d∗− , and thatthe relevant quantity when accounting for the effects of R&D on productivity is now the real increased∗−in R&D, which is given by 1−δ∗.

15In the case when the firm decides to bunch and evade, we have the additional information that DK
is chosen optimally. The first-order-condition for evasion implies the following condition:
1−(θ−1)ε (1 − t1 ) − (δ ∗ )η−1d∗−
1 − tHT2(9)×=.
α(1 − δ ∗ )α(1 − t1 )1 − tLT
2
{z
}
|
|
{z
}
Productivity Benefit from Reducing Evasion

Investment Cost and Reduction in Evasion Cost

This equation shows that firms optimally tradeoff the productivity benefits of additional investment
with the cost of investment and the reduction in the cost of evasion. Appendix D analyzes the relation
implied by Equations 8 and 9 between the parameters of the model, the tax parameters, and the response
margins (d∗− , δ ∗ ).

4.4

Model Implications for Evasion and Productivity

In addition to the bunching predictions, our model predicts that firms that bunch may engage in
relabeling, and that their future TFP will increase to the extent that the reported R&D investment
constitutes real activity. We formalize these predictions by linking our model to the estimator for causal
treatment effects proposed by Diamond and Persson (2016). As in the case of the average increase in
the R&D of Equation 7, we study the average effect on a given outcome Y over the region (d∗− , d∗+ ):
Zd∗+
Zd∗+
E[Y |Notch, d ∈ (d∗− , d∗+ )] − E[Y |No Notch, d ∈ (d∗− , d∗+ )] =Y h1 (d)dd −Y h0 (d)dd.
d∗−

(10)

d∗−

The first thing to notice about this quantity is that E[Y |Notch, d ∈ (d∗− , d∗+ )] is directly observed in thedata. In Section 5.2 we discuss the econometric approach to estimating E[Y |No Notch, d ∈ (d∗− , d∗+ )].
To interpret this treatment effect note that the region (d∗− , d∗+ ) includes firms that do not respondto the program, as well as firms whose R&D intensity is already above the notch. Conceptually, we
can partition the firms in the region (d∗− , d∗+ ) into compliers, never-takers, and always-takers. In our
setting, the never-taker firms are firms below the notch that are constrained from responding to thepolicy. The always-taker firms are firms that are already above the notch. By assuming that there are
no defier firms, we can show that Equation 10 has the interpretation of an intent-to-treat, and that thiseffect is identified by the behavior of complier firms that respond to the incentives of the program:18

IT T

Y

Zd∗+
Zα
∗−
=
Y h1 (d)(1 − Pr(Constrained|d))I[d0 ∈ (d , α)]dd −Y h0 (d)(1 − Pr(Constrained|d))dd.
αd∗−

To see that this equation represent the behavior of the compliers, note that the first integral evaluates
the average value of Y for firms that were previously below the notch, denoted by I[d0 ∈ (d∗− , α)], andthat were not constrained in their response, and that the second integral compares this value to theaverage value for the same complier firms under the counterfactual scenario where there is no notch.
Our model for the evolution of TFP predicts a tight connection between the ITT for productivity
and the ITT for R&D. To see this, note that for a given firm we would expect to observe:
φ12 − φ02 = ρ(φ11 − φ01 ) + ε(ln d11 − ln d01 ) + (u11 − u01 ),18

In our setting, defier firms are those that would be above the notch without the InnoCom program and below thenotch in the presence of the InnoCom program. Appendix E provides details of this derivation.

16

where the superscript 1 corresponds to the notch and 0 corresponds to the no-notch case, and wheresubscripts denote time periods.19 Averaging over the firms in the excluded region we find:
IT T φ2 = εIT T ln d1 .
If complier firms respond to the InnoCom program by relabeling administrative expenses as R&D
expenses this relation is adjusted by replacing IT T ln d1 with the ITT on real investment. In this case,our model also predicts a negative ITT on administrative expenses that is informative of firms’ cost ofevasion. Section 6 discusses how we link estimated treatment effects to structural parameters even in
the case where these relations might not admit a closed-form expression.

5

Causal Effects on Investment, Relabeling, Productivity

This section presents estimates of the causal effects of the InnoCom program on investment, relabeling,
and productivity. Section 5.1 estimates the investment response from the bunching estimator. Section
5.2 presents estimates of treatment effects on relabeling, productivity, and tax revenues.

5.1

Bunching Estimates of Investment Response

We now describe how we estimate h0 (·) to recover the empirical quantities B and h0 (α). We follow
the literature (see, e.g., Kleven (2015)) by estimating a flexible polynomial on a subset of data that
excludes the area around the threshold, and by using the fitted polynomial on the excluded region as an
estimate of h0 (·). Mechanically, we first group the data into bins of R&D intensity and then estimate
the following regression:
cj =

p
X



βk · (dj )k + γj · 1 d∗− ≤ dj ≤ d∗+ + νj

k=0D

where cj is the count of firms in the bin corresponding to R&D intensity level dj = θπj11 , and where(d∗− , d∗+ ) is the region excluded in the estimation. Given the monotonically decreasing shape of the
R&D intensity, we restrict the estimated βk ’s to result in a decreasing density.
pP
An estimate for h0 (d) is now given by ĉj =β̂k · (d)k . Similarly, we obtain a counterfactual
k=0

estimate for h0 (α) and B as follows:\h0 (α) =pXβ̂k · (α)

kand B̂ =pαXXβ̂k · (dj )k .

dj =d∗− k=0

k=0

Finally, an estimate of the fraction of constrained firms relative to the counterfactual density is givenby:−)\
Pr(Constrained|αγ̂α−,a∗ (α− ) =
= p
P
−
k
h\
−
0 (α )
β̂k · (α )k=0where α− is the value of R&D such that a firm would be willing to jump to the notch even if R&D had
no effects on productivity.20
19

Note that E[φ11 − φ01 ] = E[u11 − u01 ] = 0 by construction.
This “money-burning” point is easy to compute given an estimate of θ. In this case, the tax benefit is given by(tL − tH )π1 and the cost of jumping to the notch is θπ1 (α − α− ), which implies that α− = α − (tL − tH ) × (1/θ).
20

17

Implementing the bunching estimator requires choosing the degree of the polynomial, and selecting
the excluded region. We follow Diamond and Persson (2016) in using a data-based approach to selecting
the excluded region (i.e., (d∗− , d∗+ )), and the degree of the polynomial, p. In particular, we use K-foldcross-validation (K=5) to evaluate the fit of a range of values for these three parameters. Our crossvalidation procedure searches over values of p < 7, and all possible discrete values of d∗− < α andd∗+ > α that determine the excluded region. For each value, the procedure estimates the model in
K = 5 training subsamples of the data and computes two measures of model fit on corresponding
testing subsamples of the data. First, we test the hypothesis that the excess mass (above the notch)
equals the missing mass (below the notch). Second, we compute the sum of squared errors across thetest subsamples. We select the combination of parameters that minimizes the sum of squared errors,
among the set of parameters that do not reject the test of equality between the missing and excess massat the 10% level.21 Finally, we obtain standard errors by bootstrapping the residuals from the series
regression, generating 5000 replicates of the data, and re-estimating the parameters.
Figures 10-11 display the results of the bunching estimator for the three different notches for 2009
and 2011. The red line displays the observed distribution of R&D intensity h1 (·), the vertical dashedlines display the data-driven choices of the omitted region, and the blue line displays the estimatedcounterfactual density h0 (·). Each of these graphs also reports the percentage increase in R&D intensity
for complier firms, ∆d/(1−a∗ ), the fraction of firms that are constrained below the notch point, a∗ (α− ),and the p-value of the test that the missing mass and the excess mass are of the same magnitude.22
Panel (a) of Figure 10 shows an increase in R&D intensity of 19%. This estimate corresponds to
the response of “complier” firms that are not otherwise constrained in their ability to respond to the
incentives of the InnoCom program. The specification test shows that using the missing mass or theexcess mass results in statistically indistinguishable estimates. We also find that 74% of the firms are
not able to respond to the incentive. As these are small firms, many firms may be constrained intheir ability to increase investment to a significant degree, to develop a new product, or to increase thefraction of their workforce with college degrees. In addition, a higher failure rate among small firms
implies that a long process of certification may never pay off in lower taxes.
Panels (b) and (c) show the same set of results for medium and large firms. We find similar increases
in R&D intensity of 49% and 35%, respectively. In both cases, using the missing mass and the excess
mass results in statistically indistinguishable estimates of the increases in R&D. The estimated fractionof firms that face constraints to respond to the program is now 66% and 57%, respectively. When weanalyze these firms, we find that most of these firms have low profitability, or are already benefittingfrom other tax credits. Both of these features would lower the incentive to be certified by the InnoCom
program. Figure 11 shows similar qualitative patterns for 2011, where we find that the fraction of
constrained firms is now smaller in all cases, and the average increase in R&D is greater.
Table 2 provides further detail behind these statistics. The first column of the table reports thepercentage increase in R&D intensity for all of the firms in the excluded region. This statistic is always
smaller than when we adjust for the fact that a fraction a∗ (α− ) of firms is constrained from responding
to the policy. Column (4) reports the percentage increase in R&D intensity relative to the notch for themarginal buncher. This effect represents the largest possible response for complier firms. In column (5)21Note that a common practical problem in the literature is the higher frequency in the reporting of “round numbers.”
As Figures 2 and 3 in Section 3 demonstrate, our data does not display “round-number” problems that are often present
in other applications.
22
In order to calculate the fraction of firms that is constrained, we use the average of the net profitability ratio in ourdata of 7%. This implies that firms in the range (α − .07 × (tL − tH ), α) are not able to respond to the incentives of the
InnoCom program.

18

we report the level increase in R&D intensity by multiplying by α(1 − a∗ (α− )), where we see an increaseof 1.9 percentage points for large firms in 2011. It is worth noting that these effects are estimated with ahigh degree of precision as standard errors are often an order of magnitude smaller than the estimates.
Finally, while understanding the behavior of firms of different sizes is interesting from an economic
perspective, policy makers may be interested in the aggregate increase in R&D across the economy.
Figure A1 shows that the vast majority of R&D is conducted by firms in the large sales category, so it
makes sense to focus on these firms when when mapping these estimates to the patterns in Figure 1.

5.2

Causal Estimates on Productivity, Relabeling, and Tax Collections

We now use an estimator of causal effects developed by Diamond and Persson (2016) to estimate theeffects of the InnoCom program on productivity, relabeling, and on fiscal costs. The intuition of theestimator is to compare the observed aggregate mean outcome for firms in the excluded region to asuitable counterfactual. For a given outcome Yi,t2 , the estimator is:\IT
T Yt 2∗+∗− ∗+= E[Yt2 |Notch, dt1 ∈ (d∗−t1 , dt1 )] − E[Yt2 |No Notch, dt1 ∈ (dt1 , dt1 )]
Z d∗+
X
1
Y
=
−
ĥ0 (dt1 )E[Yi,t2 |d\i,t2
t1 , No Notch]ddt1 .
N Excluded
∗−
d
∗− ∗+
di,t1 ∈(d

,d

(11)

)

The first quantity is the observed average value of a given outcome Yi,t2 over the excluded region.
The second quantity is a counterfactual average value of Yi,t2 , which is constructed by combining thecounterfactual density of R&D intensity, ĥ0 (·), estimated as part of the bunching analysis, with anestimated average value of the outcome conditional on a given value of R&D.
Since the estimator compares averages over the excluded region, which includes compliers and noncompliers, we interpret it as an intent-to-treat (ITT). Taking ratios of these estimates produce Waldestimates of treatment effects. One way to think of this counterfactual is from the point of view of thelaw of iterated expectations. As the quantity E[Y |dt\
1 , No Notch] recovers the average value of a given
outcome had there been no notch, the integral simply averages this function of dt1 over the excluded
region with respect to the counterfactual density of R&D, ĥ0 (dt1 ).
In order to implement this estimator, we estimate E[Yi,t2 |d\t1 , No Notch] as a flexible polynomial
regression of Yi,t2 on R&D intensity over the same excluded region used to estimate ĥ0 (·):
Yi,t2 =pX

|k=0

βk · (di,t1 )k{z+γ · 1 d−∗ ≤ di,t1 ≤ d+∗ + δYi,t1 + φs + νi .

}E[Yt2 |dt1 =d,No Notch]

Figure 12 presents a visual example for the case of administrative costs, where we estimate a cubic
regression of the admin expense to sales ratio on R&D intensity in 2009, and where the excluded region
corresponds to Panel (c) of Table 10. As in Figure 6, we observe a significant drop in the ratio after thenotch that is likely due to relabeling of expenses to qualify for the InnoCom program. As detailed in
our model, firms self-select into the treatment depending on whether they face fixed or adjustment costs
that prevent them from obtaining the high-tech certification. This selection prevents the econometrician
from using data just beneath the threshold as a control group for firms above the threshold.
In contrast, our procedure does not rely on such comparisons across firms, but instead relies on
the assumption that E[Yi,t2 |dt1 , No Notch] is smooth around the notch, and that it may be approximated with data outside the excluded region that, by definition, is not subject to a selection problem. As shown by Figure 12, this flexible polynomial fits the data outside of the region very well.
19Moreover, we observe from Figure 6 that small- and medium-sized firms have smooth and flat relations between administrative expenses and R&D intensity around the 3% level, which suggests that
our estimate of E[Yi,t2 |dt1 , No Notch] represents a valid counterfactual. Armed with an estimate ofE[Yi,t2 |dt1 , No Notch], we then compute an average value for firms in the excluded region by combining
this estimate with an estimate of the counterfactual density, which in this case corresponds to Panel (c)of Table 10. The resulting ITT estimate in Equation 11 thus compares the observed average outcome
over the excluded region, to a counterfactual average over the same region.23
Panel (a) of Table 3 presents estimates of ITT effects of the InnoCom program on several outcomes.
This table focuses on large firms and reports estimates of treatment effects for outcomes in 2009 and2011, given the excluded region of R&D intensity in 2009. Between 2009 and 2011, we find an increasein the profit ratio of 2.3% that is statistically significant at the 5% level. We find a similar increasein TFP as well as an increase in the investment to capital ratio of 8%. Overall, we find corporate tax
revenues decrease by 10%, which matches the size of corporate tax cut. Focusing on outcomes for 2009,
we find that R&D increased by 18.8%, and that administrative expenses decreased by 8.3%. Comparing
these two estimates, we find that about 45% of the increase in R&D intensity is due to relabeling ofadministrative expenses. Finally, we also analyze the effect of the policy on the user cost of capital, andfind a decrease of 9.2%.24
The second panel of Table 3 presents estimates of ratios of the estimates in the first panel, alongwith bootsrapped confidence intervals. The first row reports that for a doubling of R&D investment,
there is also an 8.6% increase in the profit ratio between 2009 and 2011. The interpretation of this ratio
deserves caution as it represents the effects of increasing R&D as well as other effects of the InnoCom
program, such as the tax cut.25 From the point of view of the government, it is useful, however, tocalculate the fiscal cost of encouraging R&D investment, and increasing productivity. Table 3 showsthat doubling R&D investment would cost the government 36.9% of corporate tax revenues. Similarly,
we find that increasing TFP by 1% would cost the government a reduction of 4.8% in corporate tax
revenues. Finally, we calculate a user-cost-of-capital elasticity by taking the ratio of the effect on R&D
investment to the change in the user cost. These estimates imply a user-cost-of-capital elasticity of R&D
investment of 2 for reported R&D, and of 1.14 for real R&D. These estimates are crucial ingredients for
deciding whether the InnoCom policy is too expensive, or whether externalities from R&D investment
merit further subsidies.

6

Structural Estimation and Simulation of Counterfactual Policies

While the causal estimates discussed in the previous section describe the effects of the current policy,
the evaluation of alternative policies requires a model of firm selection into the policy, as well as how
investment and relabeling decisions affect productivity. In Section 6.1, we relate the causal estimatesfrom Section 5 with the model in Section 4 to estimate structural parameters of the model including
the productivity effects of R&D, and the cost of evasion. In Section 6.2, we use the estimated model to23
In particular, this estimate does not rely on comparisons of firms that are close to the notch, as in the case of aregression discontinuity.
24
To compute the user cost of capital, we first generate an equivalent-sized tax credit by dividing the tax savings form
the policy by the R&D investment, and then use the standard Hall and Jorgenson (1967) formula as derived by Wilson(2009).
25
See Jones (2015) for a useful exposition of the economics of such restrictions. Even from the point of view of the effects
of R&D investment, this elasticity would also need to be adjusted for the fact that the program elicits persistent changes
in investment, as opposed to the static elasticities that are usually reported in the literature.

20

simulate the effects of alternative policies that vary the location of the notch, the size of the tax incentive,that may limit relabeling of R&D expenses, or that replace the current policy with an investment tax
credit.

6.1

Structural Estimation

This section proposes a method of simulated moments (MSM) framework to estimate the structuralparameters of the model in Section 4 by matching the causal estimates from Section 5 to simulated
counterparts. We then use these estimates to simulate the effects of counterfactual policies.
As different policies may elicit responses from different firms, an analysis of counterfactual policies
requires an estimation of the joint distribution of the fundamental parameters that determine firms’
selection into the program. In our case, these parameters are given by the productivity effect of R&D,
ε, the cost of evasion, η, and distributions of the set of firm fundamentals including firm productivity,
φ1 , adjustment costs, b, and fixed costs, c. We collect the set of parameters for a given firm in ω ={ε, η, φ1 , b, c}.
To implement the MSM estimator, we form the criterion function:0  B
 B
h (Ω)
h (Ω)
,
W
Q(Ω) =hIT T (Ω)
hIT T (Ω)
where W is a weighting matrix. hB (Ω) and hIT T (Ω) are moment conditions that are related to ourbunching and ITT estimators, respectively. hB (Ω) is based on our estimates of d∗− , d∗+ , and the
distribution of R&D intensity based on these cutoffs. In other words, we choose our model parameters
so that our simulated data can rationalize the bunching patterns estimated in Section 5.1.
In addition, hIT T (Ω) provides the casual impact of the InnoCom program on reported R&D, admin
expense ratio, and productivity for firms in the excluded region. To generate the simulated model
counterpart of our ITT estimates, we form moments of the form:26
Z\
hIT T (Ω) =E[Y (ω; Notch) − Y (ω; No Notch)]dFω − ITTY ,dNo Notch (ω)∈(d∗− ,d∗+ )\where ITT Y is estimated as in Section 5.2. As a simple example, consider the case where Y is next-period
productivity. Our model predicts that E[φ2 (ω; Notch)−φ2 (ω; No Notch)] = ε[ln dω,Notch −ln dω,No Notch ].
This shows that the estimated effects on firm productivity will inform the values of ε. While there isno closed-form expression for the fraction of relabeled R&D, we can form a similar moment to matchthe estimated effect on the admin expense ratio, which will inform the cost of evasion, η.
We now discuss how we parametrize the model. We begin by calibrating θ, as it is not separately
identified from the productivity distribution since we do not have physical quantity data. We set θ = 5
based on the survey by Head and Mayer (2014). Following our model of the evolution of productivity
in Equation 1, the distribution of φ1 is drawn from the stationary normal distribution implied by theAR(1) process with persistence ρ and variance σ 2 . Given θ, the persistence and volatility of log sales of
non-R&D performing firms map directly into ρ and σ 2 , a fact that we use to calibrate the values of ρand σ 2 . We assume that b and c are distributed i.i.d. across firms, that b is log-normally distributed,
so that b ∼ LN (µb , σb2 ), and that c has an exponential distribution, so that c ∼ EX P(µc ). In summary,
our simulated sample will discipline the set of parameters Ω = {ε, η, µb , σb , µc }.
26
Note that we restrict the support of firm fundamentals ω = {φ1 , b, c} by requiring the counterfactual R&D to be in
the excluded region.

21

While each of the simulated moments depends on multiple parameters, we give a heuristic descriptionof the data patterns that identify each parameter. As is clear from the previous discussion, the ITT
estimates on TFP and the admin expense ratio help to pin down ε and η. Given ε, the parameters ofthe distribution of adjustment costs, µb and σb , are identified by the counterfactual distribution of R&D
intensity below d∗− and above d∗+ . Subsequently, the bunching mass, the location of d∗− , and the ITT
on reported R&D inform parameter of the distribution of fixed costs of certification: µc .
Table 4 reports estimates of (ε, η, µb , σb , µc ) for calibrated values of ρ = 0.725 and σ = 0.385.
Panel (a) reports the parameter estimates and the standard errors. Consider the estimate for ε. The
estimate from Panel (a) then implies that double the R&D increases measured TFP by 10.3%. Since the
InnoCom program requires that firms commit to a permanent increase in R&D, the interpretation of thiscoefficient is closer to a long-run effect. The adjustment cost of R&D is quite dispersed, ranging from
1.68% to 6.82% of sales, resulting in heterogeneous behavior of investments. Panel (b) compares thesimulated moments with data moments. Overall, our model does a good job of explaining the observed
bunching pattern and the ITT estimates, and thus provides a useful micro-foundation to conduct further
counter-factual analysis.

6.2

Simulation of Counterfactual Policies

We now use our model estimates to simulate the effects of alternative R&D tax incentives, and wequantify their implications for reported R&D investment, real R&D investment, tax revenue, and productivity growth. We focus on policies that are reasonably close to the form of the InnoCom program.
In particular, we maintain the structure of an average corporate income tax cut when firm R&D intensity is above a certain threshold, and we vary the location of the threshold to explore differences inboth firm-level and aggregate responses.
Table 5 reports the results for three different levels of α = 3%, 4%, and 5%. 3% is our current
benchmark, 5% corresponds to the pre-2008 threshold faced by large firms, and 4% is the intermediatecase. The first panel of Table 5 focuses on all the firms whose counterfactual R&D intensity (in a tax
system without a notch) would be below α and above the lower limit of the excluded region, d∗− , as thisis the set of firms that may potentially respond to the policy. We report the average percentage changes
in reported R&D, real R&D, and TFP for each policy. When we push the threshold to be higher from
3% toward 5%, we find all of these changes become smaller.
These effects are analogous to our ITT estimates, in that they include the effects on complier firms,
that respond to the policy, and never-taker firms, who are constrained from participating. The main
reason we see a decline across these outcomes is that more stringent policies also lead to a reduction in
the fraction of compliers. The second panel of Table 5 shows that the fraction of compliers decreases
from 37.8% when α = 0.03, to 25.4% when α = 0.05. A reduction in compliers may not necessarily
lead to negative implications for the efficiency of the policy. In particular, if the reduction is due to adecrease in bunching from firms with lower productivity and higher adjustment costs, or from firms thatwere more likely to engage in relabeling, the reduction in participation may result in a more efficient
selection of firms into the policy.
As discussed in Section 4, a given firm’s decision to bunch depends on its pre-existing productivity,
φ1 , its adjustment costs, b, and its fixed cost, c. Interestingly, we find that complier firms under the
α = 0.05 policy are positively selected relative to the α = 0.03 policy. We report their normalized
productivity, T̄ F P, average adjustment cost, b̄, and average fixed cost, c̄. We find that the compliersin policies with larger α’s are more productive, and have with lower adjustment and fixed costs. As a22

result of this positive selection, the firms that decide to bunch have a larger increase in R&D (55.3%
vs. 43.3%), which is necessary in order to achieve the high-tech status. Accordingly, these firms see alarger increase in TFP relative to the case of α = 3%, as we show in the third panel of Table 5.
Lastly, we compare the effects of these policies on total real R&D and tax revenue. The last panelof Table 5 shows that the larger responses among the complier firms almost completely offset the dropin the fraction of bunching firms as the percentage or total real R&D remains stable across the policies
at around 13%. However, policies with higher α are accompanied by smaller revenue losses for thegovernment. We report the government’s cost of enacting each of the policies, and we find that therevenue loss decreases from 31.3%, when α = 0.03, to 25.9%, when α = 0.05. The elasticity of total real
R&D that is stimulated by the policy with respect to the total tax loss is therefore higher for policies
with larger thresholds.
Figure 13 studies the effects of changing the preferential tax rate for three values of the notch:
2%, 3%, and 6%. The first two panels analyze how the characteristics of the compliers depend on thepolicy parameters. As in Table 5, we find that higher values for the notch lead to a selection of moreproductive firms, and of firms with lower adjustment costs, on average. This graph also shows that as
we increase the tax break for high tech firms (lower preferential tax rate), the program selects firms
with lower productivity and higher adjustment costs. This implies that there are decreasing returns
from expanding the InnoCom program by increasing the tax advantage, and that larger tax break mightexacerbate misallocation of R&D. Panels (c) and (d) show that, for every level of the notch, there ismore real R&D investment for larger tax breaks, but that the fraction of the total response that is due
to evasion is also increasing in the size of the tax break.
Finally, Panel (e) plots the ratio of the change in taxes to the change in total real R&D investment.
This ratio represents the average cost to the government of increasing real R&D investment. We compute
this ratio for different values of α and tHT and plot these combinations according to the tax-to-R&D
ratio and the total increases in real R&D. This graph thus represents cost frontiers for a government thatwants to increase R&D by a given amount. The current policy of α = .03 and tHT = 0.15 corresponds
to a cost-ratio of about 2.3. The black line shows that a policy defined by α = .06 and tHT = 0.15 would
result in a similar increase in real R&D investment.27 Alternatively, a policy defined by α = .06 and alarger tax advantage tHT = 0.12 would result in a larger increase in R&D investment for a similar taxto-R&D ratio. However, as shown in Panel (d), this policy would also be accompanied by more evasion.
These graphs show how firm selection into the program depends on different policy choices that result in
non-trivial tradeoffs between encouraging R&D investment at the lowest cost to taxpayers, introducing
misallocation across firms with different adjustment costs, and incentivizing relabeling activities.

7

Conclusions

Governments around the world devote considerable tax resources to incentivize R&D investment; however, there is widespread concern that firms respond by relabeling other expenses as R&D expenditures.
This paper takes advantage of a large fiscal incentive and detailed administrative tax data to analyze
these margins in the important case of China. We provide striking graphical evidence consistent withboth large reported responses, and significant scope for relabeling. Despite the relabeling responses,
we find significant effects on firm-level productivity and profitability that are consistent with sizable
returns to R&D.
27
Note that while Panel (d) shows that complier firms do more R&D with a higher value of α, the decrease in the fractionof compliers results in small changes to the total real R&D increase, which is consistent with the results in Table 5.

23

Optimal subsidies for R&D will depend on the fiscal cost for the government and whether the
R&D investment has external effects. This paper provides a useful metric that traces the government’s
tradeoff between own-firm productivity growth and tax revenues. If R&D is believed to have positive
externalities on other-firm productivity, our estimates provide a bound on the size of the externalitythat would justify government intervention.
Finally, while we find evidence consistent with evasion, the unusual structure of the InnoCom program may limit the scope of evasion through pre-registration and auditing. In contrast, R&D investment
tax credits may be more susceptible to evasion in developing, and even developed countries. As this paper demonstrates, accounting for evasion may have large effects on the design of R&D subsidy policies,
and future research should explore the potential for relabeling in other contexts.

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27

Lokshin, Boris and Pierre Mohnen, “How effective are level-based R&D tax credits? Evidence
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28

3

Figure 1: Cross Country Comparison: R&D as Share of GDP

2.5

USA

R&D Intensity (%)
1.5
2

Canada

1

China

.5

India

1996

1999

2002

2005
Year

Source: World Bank

29

2008

2011

Figure 2: Bunching at Different Thresholds of R&D Intensity (2011)30(b) Sales<50m RMB30(a) Full Sample

6%

0

0

Density10
20

6%Density
10
20

3%4%

1%

5%
10%
R&D Intensity

15%

1%

15%

(d) Sales>200m RMB5080(c) 50m RMB<Sales<200m RMB

5%10%
R&D Intensity

Density40
60

Density
20 30 40

4%

0

0

10

20

3%

1%

5%
10%
R&D Intensity

15%

1%

5%
10%
R&D Intensity

Source: Administrative Tax Return Database. See Section 2 for details.

30

15%

40

50

Figure 3: Bunching at 5% R&D Intensity (2005-2007)

0

10

20

Density
30

5%

1%

3%

5%

7%
9%
R&D Intensity

11%

13%

Source: Annual Survey of Manufacturers. See Section 2 for details.

31

15%

Figure 4: Foreign-Owned, Large Companies.04
Histogram
.02
.03
.01
0

0

.01

Histogram
.02
.03

.04

.05

(b) Post 2008.05(a) Pre 2008

0.01 .02 .03 .04 .05 .06 .07 .08 .09
R&D Intensity.1

0.01 .02 .03 .04 .05 .06 .07 .08 .09
R&D Intensity

Source: Administrative Tax Return Database and Annual Survey of Manufacturers.
See Section 2 for details.

32.1Figure 5: Domestic-Owned, Small Companies

Pre-2008-><-Post-2008

2008
Histogram.02 .04 .06 .08 .1 .12 .14<-Post-2008

Histogram.02 .04 .06 .08 .1 .12 .14

Pre-2008->

2007

Pre-2008-><-Post-2008.01.02.03.04.05.06.07.08.09 .1
R&D Intensity.01.02.03.04.05.06.07.08.09 .1
R&D Intensity

2009

2010

2011

Pre-2008-><-Post-2008.01.02.03.04.05.06.07.08.09 .1
R&D Intensity

Pre-2008-><-Post-2008.01.02.03.04.05.06.07.08.09 .1
R&D Intensity

Histogram.02 .04 .06 .08 .1 .12 .14.01.02.03.04.05.06.07.08.09 .1
R&D Intensity

Histogram.02 .04 .06 .08 .1 .12 .14

Histogram.02 .04 .06 .08 .1 .12 .14

Histogram.02 .04 .06 .08 .1 .12 .14

2006

Pre-2008-><-Post-2008.01.02.03.04.05.06.07.08.09 .1
R&D Intensity

Source: Administrative Tax Return Database and Annual Survey of Manufacturers.
See Section 2 for details.

33

.02

Admin Expense to Sales Ratio
.04
.06
.08
.1

.12

Figure 6: Empirical Evidence of Evasion

.02

.03

.04
.05
R&D Intensity

Low (6%)

Med (4%)

.06

.07

.08

High (3%)

Source: Administrative Tax Return Database. See Section 2 for details on data sources and Section 4for details on the estimation.

34

Figure 7: Induced Notch in Profit Functions

Firm Value(a) Bunching is Sub-Optimal for Firm

0

.02

.04
R&D Intensity

.06

.08

(b) Firm is Indifferent between Internal Solution and Bunching
2 Indifference:Π(D*-|t1)=Π(αθπ1|t2)

Firm Value

1 FOC:∂Π⁄∂D*-=0

0

.02

.04
R&D Intensity.06

Notes: See Section 4 for details.

35

.08

Figure 8: Theoretical Predictions of Bunching

Density(a) Predicted Bunching

h0(α)

0

B

0

.02

.04
.06
R&D Intensity

Actual Density

.08

.1

Counterfactual Density

Density(b) Predicted Bunching with Frictions and Heterogeneity

h0(α)
B

0

a

0

.02

.04
.06
R&D Intensity

Notes: See Section 4 for details.

36

.08

.1

Figure 9: Marginal Buncher and Evasion

D*--/(θπ1)

D*K/(θπ1)αFirm Value

2 Indifference:Π(D*-,D*-|t1)=Π(D*K,αθπ1|t2)
1 FOC:∂Π⁄∂D*-=00

3 FOC:∂Π⁄∂D*K=0.02.04
R&D Intensity

No Bunching

Bunching

Notes: See Section 4 for details.

37

.06

.08
Evasion Cost

Figure 10: Estimates of Excess Mass from Bunching at Notch (2009)

Histogram.01 .02 .03 .04 .05 .06 .07 .08(a) Sales<50m RMB0

Δd/(1-a*) = 0.189***(0.046)
P-value (M=B) = 0.9763
Frictions: a* = 0.739***(0.283)

.02

.03

.04
.05
.06
R&D Intensity: D

h0(D): Density With Linear Tax

.07

.08

.09

h1(D): Density With Notch

Histogram.01 .02 .03 .04 .05 .06 .07 .08(b) 50m RMB<Sales<200m RMB0

Δd/(1-a*) = 0.391***(0.150)
P-value (M=B) = 0.9037
Frictions: a* = 0.659***(0.027)

.01

.02

.03

.04
.05
.06
R&D Intensity: D

h0(D): Density With Linear Tax

.07

.08

.09

h1(D): Density With Notch

Δd/(1-a*) = 0.347***(0.029)
P-value (M=B) = 0.7866
Frictions: a* = 0.570***(0.016)

0

Histogram.01 .02 .03 .04 .05 .06 .07 .08(c) Sales>200m RMB

.01

.02

.03

.04
.05
.06
R&D Intensity: D

h0(D): Density With Linear Tax

.07

.08

.09

h1(D): Density With Notch

Source: Administrative Tax Return Database. See Section 2 for details on data sources and Section 4for details on the bunching estimator.
38

Figure 11: Estimates of Excess Mass from Bunching at Notch (2011)

Histogram.01 .02 .03 .04 .05 .06 .07 .08(a) Sales<50m RMB0

Δd/(1-a*) = 0.289***(0.063)
P-value (M=B) = 0.9805
Frictions: a* = 0.605**(0.273)

.02

.03

.04
.05
.06
R&D Intensity: D

h0(D): Density With Linear Tax

.07

.08

.09

h1(D): Density With Notch

Histogram.01 .02 .03 .04 .05 .06 .07 .08(b) 50m RMB<Sales<200m RMB0

Δd/(1-a*) = 0.327*(0.195)
P-value (M=B) = 0.8253
Frictions: a* = 0.369***(0.072)

.01

.02

.03

.04
.05
.06
R&D Intensity: D

h0(D): Density With Linear Tax

.07

.08

.09

h1(D): Density With Notch

Δd/(1-a*) = 0.461***(0.082)
P-value (M=B) = 0.7198
Frictions: a* = 0.334***(0.032)

0

Histogram.01 .02 .03 .04 .05 .06 .07 .08(c) Sales>200m RMB

.01

.02

.03

.04
.05
.06
R&D Intensity: D

h0(D): Density With Linear Tax

.07

.08

.09

h1(D): Density With Notch

Source: Administrative Tax Return Database. See Section 2 for details on data sources and Section 4for details on the bunching estimator.
39

.01

Admin Expense to Sales Ratio
.02
.03
.04
.05
.06

.07

Figure 12: Estimates of Excess Mass from Bunching at Notch (2009) and ITT on Profit Margin

0

.01

.02

.03
R&D Intensity

Binned Data

.04

.05

.06

E[Y| d ]Source: Administrative Tax Return Database. See Section 2 for details on data sources and Section 4for details on the bunching estimator.

40

Figure 13: Simulated Effects of Counterfactual Policies
Panel (a) Mean φ1 for Compliers
Mean
30

25

Panel (b) Mean b for Compliersfor Compliers Relative to Benchmark
1

Mean b for Compliers Relative to Benchmark

120

=.02
=.03
=.06

=.02
=.03
=.06

100
80
60

Percentage Change in b

Percentage Change in 1

20

15

10

5

40
20
0
-20

0
-40
-5
-60
-10
10

12

14

16

18

20

-80
10

22

12

14

Preferential Tax Rate (%)

Panel (c) Real R&D Increase for Compliers

18

20

22

Panel (d) Fraction due to Relabeling for Compliers

Real R&D Increase for Compliers

34

16

Preferential Tax Rate (%)

Fraction due to Relabeling

65
=.02
=.03
=.06

32

=.02
=.03
=.06

60

Benchmark:=.03, t H =0.15

Benchmark:=.03, t H =0.1530Fraction due to Relabeling

Percentage Increase in R&D

55
28
26
24
22
20

50

45

40

35
18
30

16
14
10

12

14

16

18

20

25
10

22

12

14

Preferential Tax Rate (%)

16

18

20

22

Preferential Tax Rate (%)

Panel (e) Tax Revenue Cost of Increasing R&D
Tax to R&D Ratio

4.5
=.02
=.03
=.06

4

10

Benchmark:H

11=.03, t =0.15

10

12

3.5

11

Tax to R&D Ratio

13
14

3

12
13

15
2.5

16

18
19

1.5

20
21

1

21

0.5
4

20
21
6

20

13

16

14

17

18

19

11
12

15

17
2

10

14

15
17

16

18

19

8

10

12

14

16

18

20

22

Percentage Increase in Total Real R&D (%)

Source: Authors calculations using simulated data. See Section 4 for details on the structural modeland the simulation.
41

Table 1: Descriptive Statistics
Panel A: State Administration of Tax Data 2008 - 2011
Mean
Std
p25
p50
p75
Sales (mil RMB)
118.263 1394.828 2.579 10.608 42.056
Fixed Asset (mil RMB)
32.912390.406
0.402
2.089
10.743# of Workers
175.402 852.494 17.000 48.000 136.000
R&D or not (%)
0.081
0.273
0.000
0.000
0.000
R&D/Sales (%, if>0)
3.560
7.019
0.337
1.544
4.296
Adm Expense/Sales (%)
9.417
11.8862.809
5.814
11.103
TFP (%)
2.058
0.522
1.638
2.007
2.434

Panel B: Annual Survey of Manufacturing 2006 - 2007
Mean
Std
p25
p50
p75
Sales (mil RMB)
110.801 1066.080 10.760 23.750 59.513
Fixed Asset (mil RMB)
42.517701.282
1.630
4.492
13.370# of Workers
238.379 1170.327 50.000 95.000 200.000
R&D or not (%)
0.102
0.303
0.000
0.000
0.000
R&D/Sales (%, if>0)
1.631
3.184
0.118
0.461
1.736
Notes: Various sources, see Section 2 for details.

42# of Obs.
1202257
1139038
12134971219630
98258
1171365
1100845# of Obs.
63866863866863866863866865267

Table 2: Bunching Estimates of Reported R&D Investment

Sales
Group
Small
Medium
Large

Sales
Group
Small
MediumLarge(1)Perc. Inc. in d∆d
0.056
(0.093)0.133**(0.067)0.149***(0.019)(1)
Perc. Inc. in d∆d0.114*(0.061)0.207***(0.035)0.307***(0.078)(a) R&D Investment in 2009
(2 )
(3)
(4)
Fraction Constrained Perc. Inc. in d Marginal Buncher
For Compliers
Response∆da∗ (α− )∆D∗
1−a∗ (α− )0.739***
0.189***
0.378***(0.283)(0.046)(0.092)0.659***
0.391***
0.782***(0.027)(0.150)(0.299)0.570***
0.347***
0.694***(0.016)(0.029)(0.058)(5)
R&D Intensity of
Marginal Buncherα(1 − a∗ (α− ))∆D∗
0.556(0.748)1.087**(0.541)0.897***(0.108)(a) R&D Investment in 2011
(2 )
(3)
(4)
Fraction Constrained Perc. Inc. in d Marginal Buncher
For Compliers
Response∆d∗−∆D∗a (α )
1−a∗ (α− )0.605**
0.289***
0.577***(0.273)(0.063)(0.125)0.369***
0.327*
0.655*(0.072)(0.195)(0.390)0.334***
0.461***
0.921***(0.032)(0.082)(0.165)(5)
R&D Intensity of
Marginal Buncherα(1 − a∗ (α− ))∆D∗
1.368**(0.664)
1.549***(0.373)1.856***(0.448)Source: Administrative Tax Return Database. See Section 2 for details on data sources and Section 5 for details on theestimation. Standard errors in parentheses.
∗p < .1, ∗∗ p < .05, ∗∗∗ p < .01

43

Table 3: Estimates of Treatment Effects(a) Estimates of Intent-to-Treat (ITT) Effects
Bootstrap
5th Perc. 95th Perc.

ITT

SE

T-Stat2011
Profit Ratio

0.023

0.008

2.868

0.009

0.036

Investment to Capital Ratio

0.081

0.029

2.764

0.028

0.124

TFP

0.021

0.008

2.567

0.007

0.033

Tax

-0.1000.032-3.101-0.154-0.048

R& D

0.272

0.028

9.729

0.228

0.319

2009
R& D

0.188

0.059

3.212

0.088

0.282

Admin Costs-0.0830.045-1.836-0.156-0.006

User Cost of Capital-0.0920.040-2.284-0.159-0.023(b) Wald Estimates of Treatment Effects
Bootstrap
Wald Estimate 5th Perc. 95th Perc.
2011
Profit Ratio to R&D

0.086

0.034

0.139

TFP to R&D

0.077

0.024

0.127

Tax to R&D-0.369-0.589-0.173

Tax to TFP (1%)-0.048-0.143-0.0192009
Reported R&D to User Cost

-2.040-6.319-0.695

Real R&D to User Cost

-1.136-4.0880.381

Source: Administrative Tax Return Database. See Section 2 for details on data sources
and Section 5 for details on the estimation. Standard errors obtained via bootstrap.

IT T =

1
N Excluded

X

Z D∗+
Yi −

i∈(D∗− ,D∗+ )

44

D∗−

\
ĥ0 (r)E[Y |rd,
No Notch]dr

Table 4: Structural Estimates

Estimate
SE(a) Point Estimates
ε
η
µb
σb
0.1025 0.1106 5.1221 1.275
0.0416 0.1979 0.2019 0.1494

µc
0.575
0.2357(b) Simulated vs. Data Moments
Simulated
Data
Prob Mass < D−∗
0.105
0.138
Excess bunching mass
3.492
2.611
Prob Mass above D+∗
0.157
0.142
Bunching Point D−∗
0.68%
0.88%
ITT reported R&D
0.158
0.188
ITT TFP
0.016
0.021
ITT admin-0.48%-0.43%The simulation is based on 30, 000 firms.

45

Table 5: Counterfactual Policy Experiments
Different thresholdsα∆R&D All Firms∆R&D real All Firms∆TFP All Firms
Frac. of Compliers
T F¯ P of Compliersb̄ of Compliersc̄ of Compliers∆R&D Compliers∆R&D real Compliers∆TFP Compliers∆Total Real R&D∆Total Tax

3%
0.169
0.097
0.010
0.378
0.150
-116.4-0.322
0.433
0.243
0.025
0.136
-0.313

46

4%
0.150
0.084
0.009
0.296
0.219
-134.7-0.359
0.493
0.270
0.028
0.137
-0.287

5%
0.143
0.077
0.008
0.254
0.292
-145.6-0.387
0.553
0.293
0.030
0.135
-0.259Online Appendix: Not For Publication
This appendix contains multiple additional analyses. Appendix A discusses the estimation of ourmeasure of residualized log-TFP. Appendix B provides additional analyses suggesting that a fraction of
the reported R&D activity may be relabeled by contrasting the effect of reported R&D on TFP aboveand below the notch. Appendix C provides a detailed derivation of the model. Finally, Appendix E
provides approximations of bunching implications.

A

Estimation of Residual Productivity

This appendix describes how we construct an empirical measure of firm-level productivity φˆit . First,
we use the structure in our model of constant elasticity demand to write firm revenue (value-added) as:
θ−1[κ ln kit + (1 − κ) ln lit + φit ],ln rit =θwhere lit is the labor input which we assume may be chosen each period. Second, we obtain the following
relation from the first order condition of cost minimization for the variable input lit :





wlit
θ−1
l
ln sit ≡ ln
+ vit ,= ln (1 − κ)rit
θwhere vit ∼ iid, and E[vit ] = 0 is measurement error or a transitive shock in factor prices. Third, we
obtain a consistent estimate of (1 − κ)( θ−1θ ) for each 3-digit manufacturing sector. Finally, given ourbenchmark value of θ = 5, we construct a residual measure of log TFP as follows:φˆit =

Bθ
ln rit − κ̂ ln kit − (1 − κ̂) ln lit .
θ−1Inferring Relabelling from Productivity Effect of R&D

We now investigate the implications of firm bunching and evasion behavior for measured productivity.
Our benchmark model assumes the following relationship between R&D and the firm productivity:
φi,t = ρφi,t−1 + ε ln(Di,t−1 ) + uit .
Our evasion analysis indicates that firms have incentives to over-report their R&D in order to obtainthe HTE status.
This measurement problem can result in attenuation bias in the estimated effectiveness of R&D on
firm productivity. We overcome this challenge by borrowing from the model intuition that firms do not
misreport if they decide to have an R&D intensity below the qualifying threshold. Thus, our empirical
specification allows the elasticity of log TFP with respect to log reported R&D, i.e. ε, to depend onwhether or not the firm is below or above the respective HTE threshold.
φit = ρφit−1 + β1 I[Above] × ln RDi,t−1 + β2 I[Below] × ln RDi,t−1 + uit .
Table A4 reports the results of this regression analysis. All specifications include industry-year
fixed effects and the standard errors are clustered at the industry level. Overall, the coefficients on

47

lagged log R&D are always highly significant. Column (1) shows that doubling R&D increases firmlevel productivity by 2.8%. Comparing columns (1) and (2), we find that separately estimating the
R&D elasticity based on a firm’s position relative to the notch produces results consistent with thepresence of evasion. When a firm’s R&D intensity is below the notch, doubling R&D spending improves
productivity by 2.8%. However, when a firm’s R&D intensity is above the notch, this magnitude is
reduced to 2.5%, around ten percent lower than the “no evasion” group. The last row of the tableshows that this difference is statistically significant at the 1% level.
Columns (3)-(5) report similar estimates when we estimate this equation separately for small,medium, and large firms. The magnitude of the R&D elasticity varies across these groups, with theeffectiveness of R&D improving when firm size is larger. Doubling R&D improves the productivity ofa small firm by 1% but improves the productivity of a large firm by 4.4%. We also find evidence ofsmaller effects of R&D on productivity for firms that are above the notch, and likely misreporting. Thisdifference also grows with firm size and is statistically significant in all cases. The attenuation in theeffect of R&D on productivity suggests a second measure of relabeling given by: 1 − ββ12 . This measureis reported in the last row of the table and is overall lower than that reported in the previous section. A
potential concern with this measure is that it represent decreasing returns to scale in R&D investment.
Table A5 assuages this concern by showing that we do not obtain the same pattern of results when we
replicate this table at a fake notch that is above the true notch.

C

Detailed Model Derivation

C.1

Model Setup

Consider a firm i with a constant returns to scale production function given by:
qit = exp{φit }F (Kit , · · · , Vit ),where Kit , · · · , Vit are static inputs with prices pit , and where φit is log-TFP which follows the law of
motion given by:
φi,t = ρφi,t−1 + ε ln(Di,t−1 ) + uit
where Di,t−1 is R&D investment, and ui,t ∼ i.i.d. N (0, σ 2 ). This setup is consistent with the R&D
literature where knowledge capital is depreciated (captured by ρ) and influenced by continuous R&D
expenditure (captured by ). In a stationary environment, it implies that the elasticity of TFP withεrespect to a permanent increase in R&D is 1−ρ.
The cost function for this familiar problem is given by:C(q; φit , pit ) = qc(φit , pit ) = qc(pit ),
exp{φit }c(pit )
where c(φit , pit ) = exp{φis the unit cost function. The firm faces a constant elasticity demand function
it }given by:−1/θ
pit = qit ,1−1/θ

where θ > 1. Revenue for the firm is given by qit

1−1/θ

max qitqit. In a given period, the firm chooses qit to− qc(φit , pit ).

48

The profit-maximizing qit is given by:
∗
qit
=



1
θ−1
θ c(φit , pit )θ.

Revenue is then given by:
Revenueit =1θθ − 1 c(φit , pit )

θ−1
=

θ ∗
q c(φit , pit )θ − 1 itθ
. Head and Mayer (2014)
That is, revenues equal production costs multiplied by a gross-markup θ−1survey estimates of θ from the trade literature. While there is a broad range of estimates, the central
estimate is close to a value of 4, which implies a gross-markup around 1.33. Per-period profits are thengiven by:1 ∗(θ − 1)θ−1
πit =qit c(φit , pit ) =c(φit , pit )1−θ .
θ−1θθUncertainty and R&D investment enter per-period profits through the realization of log-TFP φit . We
can write expected profits as follows:(θ − 1)θ−1c(ρφi,t−1 + ε ln(Di,t−1 ) + (θ − 1)σ 2 /2, pit )1−θθθ(θ−1)ε= E[πit |Di,t−1 = 0]Di,t−1 ,E[πit ] =where E[πit |Di,t−1 = 0] is the expected profit without any R&D investment.
We follow the investment literature and model this cost with a quadratic form that is proportional
to revenue θπi1 and depends on the parameter b:bθπi1 Di1 2
g(Di1 , θπi1 ) =.
2
θπi1
We also allow for the possibility that firms incur a fixed cost of attaining the InnoCom certification. To
model this, we assumer that if firms decide to pursue the certification, they incur a cost of: c × Di1 .

C.2

R&D Choice Under Linear Tax

Before considering how the InnoCom program affects a firm’s R&D investment choice, we first consider
a simpler setup without such a program. In a two-period context with a linear tax, the firm’s intertemporal problem is given by:max (1 − t1 ) (πi1 − Di1 − g(Di1 , θπi1 )) + β(1 − t2 )E[πi2 ],D1where the firm faces and adjustment cost of R&D investment given by g(Di1 , θπi1 ). This problem has
the following first-order condition:



Di1
(θ−1)ε−1
F OC : −(1 − t1 ) 1 + b+ β(1 − t2 )ε(θ − 1)Di1
E[πi2 |Di1 = 0] = 0.
(12)
θπi1
Notice first that if the tax rate is constant across periods, the corporate income tax does not affect the
choice of R&D investment.28 In the special case of no adjustment costs (i.e., b = 0), the optimal choiceof Di1 is given by: 1(θ−1)ε−1
1 − t1
1
1
Di1 =
.
(13)
(θ − 1)ε β(1 − t2 ) E[πi2 |Di1 = 0]28This simple model eschews issues related to source of funds, as in Auerbach (1984).

49

This equation shows that the optimal R&D choice has a constant elasticity with respect to the net oftax rate, so thatd ln Di1
1=.
d ln(1 − t2 )1 − (θ − 1)εIn particular, this elasticity suggest that firms that have a higher valuation of R&D, that is when (θ−1)εis greater, the firm will be more responsive to tax incentives.
Even in the general case (unrestricted b), we also observe that the choice of R&D depends on
potentially-unobserved, firm-specific factors including Ki and φi1 that influence E[πi2 |Di,t−1 = 0]. An
important insight for the proceeding analysis is that we can recover these factors from D1i as follows:1−(θ−1)ε (1 − t1 )Di1
E[πi2 |Di1 = 0] =β(1 − t2 )ε(θ − 1)



Di1
1+b
θπi1


.

Second Order Condition
This problem may feature multiple solutions. To ensure our model results in sensible solutions, we
confirm the second order condition at the estimated values. The SOC is given by: 1(θ−1)ε−2
SOC : −(1 − t1 ) b+ β(1 − t2 )ε(θ − 1)((θ − 1)ε − 1)Di1
E[πi2 |Di1 = 0] < 0.
θπi1
Using the expression for E[πi2 |Di1 = 0] above, we can re-express this condition for the marginal buncheras: ∗−  ∗− 
(1 − t1 )D
D
SOC 0 :
((θ
−
1)ε
−
1)
1
+
b
−
b
< 0.
D∗−
θπi1
θπi1
1)
> 0 we focus on the term in the brackets and use the definition of ∆D∗ to obtain:
Since (1−tD∗−

SOC 00 : ((θ − 1)ε − 1) (1 + αb(1 − ∆D∗ )) − αb(1 − ∆D∗ ) < 0,which holds whenever:C.3(θ − 1)ε − 11<b2 − (θ − 1)ε α(1 − ∆D∗ )A Notch in the Corporate Income Tax

Assume now that the tax in the second period has the following structure that mirrors the incentives
in the InnoCom program:
 LTt2
if D1 < αθπ1
t2 =
,
HT
t2
if D1 ≥ αθπ1sales equal θπ1 , tLT> tHT
and where LT /HT stands for low-tech/high-tech. Intuitively, this tax
2
2
structure induces a notch in the profit function at D1 = αθπ1 , where α is the R&D intensity required
to attain the high-tech certification. Figure 7 presents two possible scenarios following this incentive.
Panel (a) shows the situation where the firm finds it optimal to choose a level of R&D intensity below
the threshold. At this choice, the first order condition of the linear tax case holds and the optimal levelof R&D is given by Equation 12. From this panel, we can observe that a range of R&D intensity levels
below the threshold are dominated by choosing an R&D intensity that matches the threshold level α.
Panel (b) shows a situation where the firm that is indifferent between the internal solution of Panel (a)and the “bunching” solution of Panel (b). The optimal choice of R&D for this firm is characterizedboth by Equation 12 and by D1 = αθπ1 .
50

Which of the two scenarios holds depends on determinants of the R&D investment decision that
may vary at the firm level and are summarized by E[πi2 |Di,t−1 = 0], as well as on the degree to which
R&D investment is valued by firms in terms of future profits (i.e. ε(θ − 1)). However, as long asE[πi2 |Di,t−1 = 0] is smoothly distributed around the threshold α, this incentive will lead a mass of firms
to find D1 = αθπ1 optimal and thus “bunch” at this level. Our analysis proceeds by first identifying
the firm that is marginal between both solutions in terms of the R&D intensity and then by using theidentity of the marginal firm to relate the amount of bunching at the notch to the firm’s valuation of
R&D investment ε(θ − 1).
We start by characterizing the firm that is indifferent between level of R&D given by the notch and∗−a lower level of R&D investment Di1. Define Π(·|t) as the value function of the firm’s inter-temporalmaximization problem when facing tax t in period 2. A firm i is a marginal buncher if:
∗− LT
Π(Di1
|t2 ) = Π(αθπ1 |tHT
2 ),where the left-hand side is the profit from an internal solution facing the low-tech tax rate tLT
2 and theright hand side is the bunching solution when facing the high-tech tax rate tHT
.
Using
the
optimal2∗− LT
choice for an internal solution in Equation 12, we can manipulate Π(Di1 |t2 ) to obtain: ∗− 2 !
Di1
bθπ
i1
∗− LT
∗−
∗− (θ−1)εΠ(Di1|t2 ) = (1 − t1 ) πi1 − Di1−+ β(1 − tLT
E[πi2 |Di1 = 0]
2 )(Di1 )
2
θπi1


  ∗− 2 !

Di1
1
1
1
∗−
+ bθπi1− 1 Di1−,(14)= (1 − t1 ) πi1 +ε(θ − 1)ε(θ − 1) 2
θπi1
where we substitute for E[πi2 |Di1 = 0] using the optimality condition above.
Similarly, we manipulate Π(αθπ1 |tHT ) by substituting for the unobserved components of the firmdecision, i.e. E[πi2 |Di1 = 0], using Equation 12 to obtain: !
bθπi1 αθπi1 2HT(θ−1)εΠ(απ1 |t2 ) = (1 − t1 ) πi1 − αθπi1 (1 + c) −+ β(1 − tHT
E[πi2 |Di1 = 0]
2 )(αθπi1 )2θπi1α2 bθπi1= (1 − t1 ) πi1 − αθπi1 (1 + c) −2!
(θ−1)ε  ∗− 
HT
Di1
αθπi1
(1 − t2 )
∗−
+
1+b
Di1
.
(15)
∗−
θπ
ε(θ − 1)(1 − tLT
)
D
i1
2
i1
We then use Equations 14 and 15 and the indifference condition that defines the marginal bunching firm
to obtain a relation between the percentage difference in R&D intensity and the parameters of interest:51

∗− LT(θ − 1)ε. Subtracting Π(αθπ1 |tHT2 ) from Π(D1 |t2 ) and manipulating we obtain:  ∗− 2


Di1
1
1
α2 bθπi11∗−+ αθπi1 (1 + c) +− 1 Di1 + bθπi1−ε(θ − 1)ε(θ − 1) 2
θπi12(θ−1)ε  ∗− HTDi1(1 − t2 )
αθπi1
∗−
1+b
Di1
∗−
LT
θπi1
ε(θ − 1)(1 − t2 ) Di1
  ∗− 2
 ∗−
Di1
Di1
1
1
1
αb
+ αb
−1
−
+1+c+
ε(θ − 1)αθπ1ε(θ − 1) 2
αθπi1
2

(θ−1)ε−1  ∗− 
HT
Di1
αθπi1
(1 − t2 )1 + αb∗−LTαθπi1ε(θ − 1)(1 − t2 ) Di1




αb
1
1
1
∗
(1 − ∆D∗ )2 + 1 + c +− 1 (1 − ∆D ) + αb−ε(θ − 1)ε(θ − 1) 2
2


0 =
−
0 =
−
0 =
−

(1 − tHT(1 − ∆D∗ )1−(θ−1)ε2 )×(1 + αb(1 − ∆D∗ )) ,ε(θ−1)(1 − tLT)
2(16)

where the first line ignores the common term (1 − t1 ) in both equations, the second line divides by∗−
1 −D
αθπ1 , and the third line defines ∆D∗ = αθπαθπ
as the percentage increase in R&D spending due
1
to the notch. Given an estimate of b, c, Equation 16 is an implicit function for (θ − 1)ε. Thus, given∗
observable tax parameters tHT
and tLT22 and the empirical quantity ∆D , which can be estimated fromthe bunching patterns described in Section 3, it is possible to recover an estimate of the parameters(θ − 1)ε, b, and c from multiple groups of firms with similar structural parameters.

C.4

R&D Choice Under Tax Notch with Evasion

Assume now that firms may misreport their costs and shift non-RD costs to the R&D category. Following
conversations with CFOs of large Chinese companies, we model evasion as a choice to misreport expenses
across R&D and non-RD categories. Misreporting expenses or revenues overall is likely not feasible asfirms are subject to third party reporting (see, e.g., Kleven et al. (2011) and Pomeranz (2015)).
Denote a firm’s reported level of R&D spending by D̃1 . The expected cost of misreporting to thefirm is given by h(D1 , D̃1 ). We assume that the cost of mis-reporting is proportional to the reported
R&D, D̃1 , and depends on the percentage of mis-reported R&D, D̃1D̃−D1 , so that:1h(D1 , D̃1 ) = D̃1 h̃

D̃1 − D1
D̃1!
.

We also assume that h̃ satisfies h̃(0) = 0 and h̃0 (·) ≥ 0.
The effects of the InnoCom program are now as follows: LTt2
if D̃1 < αθπ1
t2 =
,
HT
t2
if D̃1 ≥ αθπ1
Notice first that if a firm decides not to bunch at the level αθπ1 , there is no incentive to misreport
R&D spending as it does not affect total profits and does not affect the tax rate. However, a firm mightfind it optimal to report D̃1 = αθπ1 even if the actual level of R&D is lower. We characterize the firmthat is indifferent between bunching, and potentially misreporting, and not bunching.

52

We start by characterizing the firm that is indifferent between level of R&D given by the notch∗−
and a lower level of R&D investment Di1. Define Π(D1 , D̃1 |t) as the value function of the firm’s intertemporal maximization problem when facing tax t in period 2 that spends D1 on R&D but that declaresD̃1 . A firm i is a marginal buncher if:
∗−
∗− LT
Π(Di1
, Di1
|t2 ) = Π(αθπ1 , D1∗K |tHT
2 ),where the left-hand side is the profit from an internal solution facing the low-tech tax rate tLT, the2right hand side is the bunching solution when facing the high-tech tax rate tHT
,
and
where
the
firm
2
∗K
chooses a real R&D level of D .
∗−∗− LT
We first consider Π(Di1, Di1|t2 ). Since the firm need not mis-report in this case, Equation 14
still describes the profit in this case.
∗−We now we manipulate Π(αθπ1 , D1∗K |tHT ) using the FOC for Di1
to obtain: ∗K 2 !
Di1
bθπ
i1
∗K HT
∗K
Π(αθπi1 , Di1|t2 ) = (1 − t1 ) πi1 − Di1− αθπi1 c −2θπi1∗K (θ−1)εE[πi2 |Di1 = 0] − h(D1∗K , αθπ1 )+β(1 − tHT
2 )(Di1 ) ∗K 2 !
bθπi1 Di1
∗K
= (1 − t1 ) πi1 − Di1 − αθπi1 c −− h(D1∗K , αθπ1 )2
θπi1
 ∗K (θ−1)ε  ∗− 
Di1
Di1(1 − t1 )(1 − tHT
∗−
2 )
Di1
+
1+b
∗−
LT
θπi1
ε(θ − 1)(1 − t2 ) Di1(17)

We then use Equations 14 and 17 and the indifference condition that defines the marginal bunching firm
to obtain a relation between the percentage difference in R&D intensity and the parameters of interest:∗−∗− LT(θ − 1)ε. Subtracting Π(αθπ1 , D1∗K |tHT2 ) from Π(Di1 , Di1 |t2 ) and manipulating we obtain:  ∗− 2 ∗K 2Di1
111bθπi1 Di1∗−∗K
− 1 Di1+ bθπi1−+ Di1+ αθπi1 c +ε(θ − 1)ε(θ − 1) 2
θπi1
2
θπi1





(θ−1)ε∗−∗K
Di1(1 − tHT
Di1
h(D1∗K , αθπ1 )
∗−
2 )
−
1
+
b
D
+
i1
∗−
θπi1
(1 − t1 )ε(θ − 1)(1 − tLT
Di1
2 )

 ∗−

  ∗− 2 ∗K 2
Di1
Di1
1
1
1
D∗K
αb Di1
0 =
−1
+ αb
−
+ i1 + c +ε(θ − 1)αθπ1ε(θ − 1) 2
αθπi1
αθπi1
2 αθπi1





∗−
∗K
∗K (θ−1)ε−1Di1(1 − tHT
Di1
Di1
h̃(D1∗K , αθπ1 )
2 )
−
1
+
αb
+
,
∗−
αθπi1
αθπi1
(1 − t1 )ε(θ − 1)(1 − tLT
Di1
2 )


0 =

where the first line ignores the common term (1 − t1 ) and the second line divides by αθπ1 . We now∗−
1 −D
use the definitions ∆D∗ = αθπαθπ
as the percentage increase in R&D spending due to the notch1and δ = D̃1D̃−D1 as the percentage of misreporting relative to the reported value. We also consider
1

1+η

a particular function for h̃(δ) given by δ1+η . These definitions and assumptions yield the following
condition:

 




c
αb
1 − ∆D∗1
1
1∗∗
0 = 1++(1 − δ ) +− 1 + αb−(1 − ∆D )1 − δ∗
2
1 − δ∗ε(θ − 1)ε(θ − 1) 2
(1 − tHT
1 − ∆D∗ 1−(θ−1)ε 1 + αb(1 − ∆D∗ )(δ ∗ )η+1 (1 − δ ∗ )−1
2 )
−
+
(18)
1 − δ∗ε(θ − 1)(1 − t1 )(η + 1)
(1 − tLT
2 )53

Notice that in the special case with no evasion, when δ ∗ = 0, Equation 18 is identical to Equation 16.
In the case when the firm decides to bunch and evade, we have the additional information that DK
is chosen optimally. From Equation 17, the firm solves the following problem: ∗K 2 !
η+1αθπ1 − DK1bθπi1 Di1∗K
− αθπ1max(1 − t1 ) πi1 − Di1 − αθπi1 c −
2
θπi1
αθπ1
η+1
D1K
 ∗K (θ−1)ε  ∗− 
Di1(1 − t1 )(1 − tHT
Di1
∗−
2 )
+
Di1
1+b
∗−
LT
θπ
ε(θ − 1)(1 − t2 ) Di1
i1,
with the following FOC:  ∗K (θ−1)ε−1  ∗K  ∗− 
Di1
Di1
1 − tHTDi1
2=
1 + αb
1+b
∗−
LT
αθπi1
θπi1
1 − t2Di1
ηK
αθπ1 − D1+αθπ1
1 − t1
Notice that this equation is equivalent to:

1 − δ∗
1 − ∆D∗(θ−1)ε−1∗ η)
1 + αb(1 − δ ∗ ) − (δ1−t1
=  HT 
1−t2(1 + αb(1 − ∆D∗ ))
1−tLT

(19)

2

Equation 19 along with Equation 18 now form a system of two equations that are implicit functions forthe parameters η and (θ − 1)ε.
C.4.1

Second Order Conditions

Consider again the FOC for the evasion problem:
DK∗
F OC : −(1 − t1 ) 1 + b
θπi1







+ (1 − t1 )1 − tHT2
1 − tLT
2



∗K
Di1
∗−
Di1

(θ−1)ε−1  ∗− 
Di1
1+b
θπi1

η−1
αθπ1 − DK+αθπ1

The SOC is given by:  ∗K (θ−1)ε−2  ∗− 
Di1
1((θ − 1)ε − 1)
1 − tHTDi1
2+(1 − t1 )−(1 − t1 )b
1+b
∗−
∗−
LT
θπi1
θπi1
1 − t2
Di1
Di1


η−2
αθπ1 − DK1−(η − 1)
<0
αθπ1
αθπ1


Collecting terms and substituting for δ ∗ and ∆D∗ we can rewrite this as:((1 − t1 )(1 − ∆D∗ )((θ − 1)ε − 1)
(1 − ∆D∗ )

1 − tHT2
1 − tLT2

1 − δ∗
1 − ∆D∗(θ−1)ε−2(η − 1) ∗ η−2(1 + αb(1 − ∆D∗ )) − αb −(δ )(1 − t1 )

)

<0

54

D

Relation Between (d∗− , δ ∗ ) and Model Parameters

D.1

Simple Model

Consider first the model without evasion, adjustment, or fixed costs. In this case, Equation 16 defined
an implicit function of (θ −1)ε as a function of ∆D∗ . While there is no closed-form equation for (θ −1)ε,there is an intuitive relation between ∆D∗ and (θ − 1)ε. As more firms choose to bunch at the notch,
this would imply that the effect of R&D on profits is larger. It follows that (θ − 1)ε is increasing in∆D∗ . Figure A3 provides the implied value of Equation 16 for a range of values of ∆D∗ and confirms
this intuition.

D.2

Model With Evasion

While there are no closed-form expressions for η and (θ − 1)ε, using Equations 18 and 19 we can finda closed-form solution for the effect of R&D on profits as a function of η and b. Solving for (θ − 1)ε in
Equation 19 yields: HT 
∗ )η
1−t2
∗ ))
ln 1 + αb(1 − δ ∗ ) − (δ
(1
+
αb(1
−
∆D
−
ln
LT
1−t1
1−t2


ε(θ − 1) = 1 +
(20)
1−δ ∗
ln 1−∆D∗
Similarly, we can substitute Equation 19 into 18 to obtain the following expression:

 




1 − ∆D∗
1
1
1
αb
∗
∗
(1 − δ ) +− 1 + αb−(1 − ∆D )0 = 1+c+2
1 − δ∗ε(θ − 1)ε(θ − 1) 2
∗ η

−

)
1 + αb(1 − δ ∗ ) − (δ1−t1ε(θ − 1)+(δ ∗ )η+1 (1 − δ ∗ )−1,(1 − t1 )(η + 1)

which is linear in (θ − 1)ε. Solving for (θ − 1)ε, we obtain:


∗ )η
1−∆D∗
(1 + αb(1 − ∆D∗ )) − 1 − αb(1 − δ ∗ ) + (δ
∗
1−δ
1−t1

.
ε(θ − 1) = (δ ∗ )η+1 (1−δ ∗ )−1
1−∆D∗
c
αb
∗
∗
1 + αb1−δ ∗2 (1 − ∆D ) − 1 − 1−δ ∗ − 2 (1 − δ ) −(1−t1 )(η+1)(21)

Figure A4 plots the non-linear relations between η and (θ − 1)ε that are implied by Equations 20
and 21 while holding b, c = 0. Panel (a) explores Equation 20 and shows that for reasonable values ofη, (θ − 1)ε is positive. This figure also shows that, given values of ∆D∗ and δ ∗ , as evasion become morecostly (larger η), the value of R&D to the firm also increases. Figure A4 panel (b) explores Equation
21 and shows that, for a given cost and amount of evasion, i.e., η and δ ∗ , a larger response in terms ofreported R&D corresponds to larger values of (θ − 1)ε. This figure plots this relation for different valuesof η and thus shows how the reduced-form moments δ ∗ and ∆D∗ influence the estimates in the model.
For a given set of empirical estimates ∆D∗ and δ ∗ and values b and c, the structural parameters ηand (θ − 1)ε are identified by the intersection of the graphs in both panels. This intersection will varyas a function of b and c and will generate a set of structural parameters that are compatible with thedata. Figure A5 shows the intersection of these functions for multiple values of b, while holding c = 0.
Th red line represent the locus of parameters that is compatible with a given set of data ∆D∗ and δ ∗ .
The parameters η, (θ − 1)ε, b, and c are identified through cross-group restrictions that use data on ∆D∗and δ ∗ for the three groups of firms.

55

E

Bunching Approximations

This appendix details derivations of expressions that approximate changes in the R&D investment withthe estimated density.

E.1

Percentage Increase in R&D Intensity of Marginal Firm

As in previous papers, (e.g., Kleven and Waseem (2013)), we can use similar approximations to relate
the quantities B and h0 (α) to the behavior of the marginal firm. We first consider the special casewithout frictions, and note that
Zα
B =


α − d∗−
h0 (u) du ≈ h0 (α) α − d∗− = h0 (α)α
.
α }
|
{z
∗−

d

(22)

∆D∗

The first part of Equation 24 makes the point that the excess mass B will equal the fraction of the
population of firms that would have located in the dominated region. This quantity is defined by the
integral of the counterfactual distribution h0 (·) over the dominated interval, which is given by (d∗− , α) .
The second part of Equation 24 approximates this integral by multiplying the length on this intervalby the value of the density at α. Simplifying this expression and solving for ∆D∗ we obtain:
∆D∗ ≈

B
.
h0 (α)α(23)

Thus, in order to estimate ∆D∗ , it suffices to have an estimate of the counterfactual density h0 (·), andto use this to recover the quantities B and h0 (α). Note that while ∆D∗ is the percentage increase
relative to the notch, the percentage increase relative to the initial point of the marginal firm is given
∆D∗
α−d∗−
by: 1−∆D.
∗ =d∗−In the case of heterogeneous frictions, we may obtain a similar approximation if we assume that theprobability of being constrained does not depend on d. This may happen, for instance, if a constantfraction of firms are constrained regardless of d. While this may be a strong assumption, it provides auseful approximation for B. To see this, note that
Zα Z
B =d∗− b,cZα Z=

I[d ≥ d−b,c ]h0 (d, b, c)d(b, c)ddI[d ≥ d−b,c ]h0 (b, c|d)d(b, c)h0 (d)ddd∗− b,cZα(1 − Pr(Constrained|d))h0 (d)dd,=
d∗−where the second line uses the definition of conditional probability, and the third line integrates over(b, c). Using the assumption that Pr(Constrained|d) does not depend on d and using the same approx-

56

imation as in Equation 24, we obtain:
Zα
B = (1 − Pr(Constrained))h0 (d)ddd∗−≈ (1 − Pr(Constrained))h0 (α)αα − d∗−
.
α }
| {z
∆D∗

The formula for ∆D∗ now becomes:B.
h0 (α)α(1 − Pr(Constrained))

∆D∗ ≈

E.2

Average Percentage Increase in R&D Intensity

We now derive an approximation of the average percentage increase in R&D due to the notch. We begin
by writing the average R&D intensities in both situations as:
Zα
Zd∗+
Zd∗+
∗+
∗−
d −α
α−d
h0 (d)dd +h0 (d)dd
E[d|No Notch, d ∈ (d∗− , d∗+ )] = dh0 (d)dd ≈
2
2 }
|
{z
}
|
{z
∗−
∗−
α
d

d

d

d∗+

E[d|Notch, d ∈ (d∗− , d∗+ )] =Zd∗−

α − d∗−
dh1 (d)dd ≈
2 }
| {z

d¯

Zα

d∗−

d

(24)

Zd∗+
h1 (d)ddd∗+ − αh1 (d)dd +
2 }
| {z

(25)

α

d¯

We can then write the change in R&D intensity as:∗−

E[d|Notch, d ∈ (d

∗+

,d

∗−

)] − E[d|No Notch, d ∈ (d∗+,d)] ≈ d¯

Z d∗+
|α
Z α

+ d
d∗−

|

(h1 (d) − h0 (d))dd
{z
}

(26)

(h1 (d) − h0 (d))dd
{z
}

(27)

B

−B

= B(d¯ − d),(28)where we use the fact that the excess mass above the notch is equal to the missing mass below thenotch.
Now, taking the following approximation of E[d|No Notch, d ∈ (d∗− , d∗+ )]:∗−E[d|No Notch, d ∈ (d

∗+

,d

Z d∗+
)] =
d∗−

Z d∗+
dh0 (d)dd ≈d∗−αh0 (α)dd= αh0 (α)(d∗+ − d∗− ) = 2αh0 (α)(d¯ − d),we obtain:

E[d|Notch, d ∈ (d∗− , d∗+ )] − E[d|No Notch, d ∈ (d∗− , d∗+ )]
B
=
.
∗−
∗+
E[d|No Notch, d ∈ (d , d )]2αh0 (α)(29)

Note that while these derivations do not explicitly include the role of heterogeneous frictions, these
expressions are not affected by the presence of heterogeneous frictions.
57

E.3

Identification of Intent-to-Treat Effect

The ITT estimates are identified by firms that “comply” with the tax incentive. To see this, note:∗−

E[Y |No Notch, d ∈ (d

∗+

,d

Zα
Y h0 (d) × Pr(Constrained|d)dd

)] =

(30)

d∗−

{z

|

}

Never Takers

Zα
+

Zd∗+
Y h0 (d) × (1 − Pr(Constrained|d))dd +Y h0 (d)dd

d∗−

{z

|

}

Compliers

|α

{z

}

Always Takers

Similarly, we can write∗−

E[Y |Notch, d ∈ (d

∗+

,d

Zα
)] =

Y h1 (d)dd

(31)

d∗−

|
+

{z

Never Takers}

Zd∗+
Y h1 (d) × (1 − Pr(Constrained|d)) × I[d0 ∈ (d∗− , α)]dd
|α

+

{z

Compliers}Zd∗+
Y h1 (d)I[d0 ∈ (α, d∗+ )]dd,
|α

{z

}

Always Takers

where we assume that there are no defier firms that would be above the notch without the InnoCom program, but would be below the notch with the InnoCom program. Noting that h0 (d) ×
Pr(Constrained|d) = h1 (d), and that h1 (d) × I[d0 ∈ (α, d∗+ )] = h0 (d), we can write the IT T Y as:

IT T

Y

Zd∗+
Zα
∗−
=
Y h1 (d)(1 − Pr(Constrained|d))I[d0 ∈ (d , α)]dd −Y h0 (d)(1 − Pr(Constrained|d))dd,
α

d∗−

(32)
which is just the change in the average of firms in the excluded region that is driven by the compliers.
Approximation of Intent-to-Treat EffectFinally, we can obtain more intuition behind the ITT estimates by noting that:
Zd∗+
Zα
∗−
h0 (d)(1 − Pr(Constrained|d))dd.
B=h1 (d)(1 − Pr(Constrained|d))I[d0 ∈ (d , α)]dd =αd∗−Using this fact, the following expression is an approximation of Equation 32:
IT T Y ≈ B(Ȳ − Y )
58

(33)

where Ȳ = E[Y |d ∈ (α, d∗+ )] and Y = E[Y |d ∈ (d∗− , α)]. This equation gives a discrete treatment effectinterpretation to the ITT by showing that the ITT is driven by the amount of switching of compliers
between the “below notch” and “above notch” regions, given by B, and the change in the outcome
associated from being in the “above notch” region. Combining this equation with Equation 28 we
obtain the Wald estimator as follows:
W aldY =Ȳ − YIT T Y
≈ ¯
,
d
IT T
d−d

which gives the interpretation of the increase in Y for a given unit increase in d. Note that thisinterpretation carries the implication that there are no other effects from being certified as an InnoCom
firm on Y beyond the effect on d.

59

Appendix Graphs

0

Share of Total R&D By Firm Group
20
40
60
80

100

Figure A1: Aggregate Implications

2009

2010
Year
Low Sales

Med Sales60

2011High Sales

.2

R&D to Admin Expense Ratio
.3
.4
.5
.6

.7

Figure A2: Alternative Empirical Evidence of Evasion

.02

.03

.04
.05
R&D Intensity

Low (6%).06

Med (4%).07
High (3%)01(θ-1) ε2

3

4Figure A3: Relation Between 1 − ∆D∗ and (θ − 1)ε Without Evasion.

.2

.4

.6
1-ΔD*

Note: tHT = .25, tLT = .15

61

.8

1

.08

Figure A4: Identification When Evasion is Possible(b) Relation Between (θ − 1)ε and 1 − ∆D∗for different values of η
1
0

.2

.2

.4

(θ-1) ε.6(θ-1) ε
.4
.6

.8

.8

1

(a) Relation Between (θ − 1)ε and η

0

.2

.4

.6

.8

0

1-ΔD*
0

1

2
η

3

4

η = .5

Note: tHT = .15, tLT = .25, δ=.25, ΔD* = .5

η = 1.5

Note: tHT = .15, tLT = .25, δ=.45

Figure A5: Identification in Full Structural Model

1.5

Identification in Model with Adjustment Costs
Locus varying b
b=2000, AC=2.7% of 3:
b=3000, AC=4.0% of 3:
b=4000, AC=5.4% of 3:

1.4

1.3

1.2

0(3-1)

1.1

1

0.9

0.8

0.7

0.6

0.5
0.1

0.12

0.14

0.16

0.18

2

62

0.2

0.22

0.24

η = 2.5

1

Appendix Tables
Table A1: Estimates of Mis-categorized R&D
(1)
(2)
Small
Medium
Structural Break-0.014∗∗ -0.013∗∗∗(0.007)(0.004)
Observations
5,016
8,336
Percentage Misreported Relative to Notch α.233∗∗.329∗∗∗(SE)(.111)(.093)(3)Large-0.008∗∗∗(0.003)8,794.269∗∗∗(.095)

Source: Administrative Tax Return Database. See Section 2 fordetails on data sources and Section 5 for details on the estimation.
Standard errors in parentheses.
∗p < .1, ∗∗ p < .05, ∗∗∗ p < .01

Table A2: Alternative Estimates of Mis-categorized R&D
(1)
(2)
(3)
Low Sales Medium Sales High Sales
Structural Break
0.02
0.03∗∗
0.05∗∗(0.02)(0.01)(0.01)
N
4028
6461
7222
Mean Ratio Above α
0.47
0.45
0.51
Fraction Constrained: a∗
0.87
0.47
0.41
∗
Percentage Evasion: δ
0.25
0.15
0.16
Standard errors in parentheses* p < 0.10, ** p < 0.05, *** p < 0.01

63

Table A3: Estimates of Mis-categorized R&D by Current Asset Ratio
(1)
(2)
(3)
Low
MediumLarge(a) Low Current Asset Ratio
Structural Break-0.017∗∗ -0.013∗∗∗-0.004(0.007)(0.004)(0.002)
Percentage Misreported.278∗∗.326∗∗∗.117(SE)(.111)(.088)(.081)(b) High Current Asset Ratio
Structural Break-0.020∗-0.013∗-0.011∗∗(0.011)(0.007)(0.005)∗∗Percentage Misreported
.328
.318
.375∗∗(SE)(.181)(.171)(.166)
Standard errors in parentheses∗

p < .1, ∗∗ p < .05, ∗∗∗ p < .01

Lagged Log TFPTable A4: Effects of R&D on Log TFP
(1)
(2)
(3)
(4)
All
All
Small
Medium0.735∗∗∗ 0.735∗∗∗ 0.724∗∗∗ 0.713∗∗∗(0.009)(0.009)(0.015)(0.014)

100 X Log R&D

(5)
Large
0.738∗∗∗(0.014)2.779∗∗∗(0.260)100 X Log R&D X Above Notch

2.510∗∗∗(0.232)0.968∗∗∗(0.355)1.503∗∗∗(0.320)3.767∗∗∗(0.397)

100 X Log R&D X Below Notch

2.809∗∗∗(0.263)21,052.107∗∗∗(.008)

1.017∗∗(0.408)6,030.048(.041)

1.681∗∗∗(0.373)7,662.106∗∗∗(.027)

4.364∗∗∗(0.454)
7,360.137∗∗∗(.017)

Observations
Implied δ ∗ = 1 − ββ12

21,052

Source: Administrative Tax Return Database. See Section 2 for details on data sources and Section 5 fordetails on the estimation. Industry X Year FE, standard errors in parentheses, clustered at Industry level.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

ˆ + β1 I[Above] × ln RDt−1 + β2 I[Below] × ln RDt−1 + uit
φˆit = ρφit−164

Table A5: Effects of R&D on Log TFP: Placebo with Fake Notch
(1)
(2)
(3)
(4)
(5)
All
All
Small
MediumLarge
Lagged Log TFP
0.716∗∗∗ 0.717∗∗∗ 0.705∗∗∗ 0.688∗∗∗ 0.726∗∗∗(0.014)(0.014)(0.027)(0.021)(0.017)
100 X Log R&D

3.319∗∗∗(0.449)100 X Log R&D X Above Notch

3.280∗∗∗(0.433)1.514∗(0.827)3.518∗∗∗(0.591)5.391∗∗∗(0.579)100 X Log R&D X Below Notch

3.315∗∗∗(0.444)9,223.011(.016)

1.370∗(0.793)
3,203
-.105
(.08)

3.779∗∗∗(0.687)3,528.069∗(.041)

5.324∗∗∗(0.656)
2,492
-.013
(.03)

Observations
Implied δ ∗ = 1 − ββ21

9,223

Source: Administrative Tax Return Database. See Section 2 for details on data
sources and Section 5 for details on the estimation. Industry X Year FE, standard
errors in parentheses, clustered at Industry level.
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

ˆ + β1 I[Above] × ln RDt−1 + β2 I[Below] × ln RDt−1 + uit
φˆit = ρφit−165