Corporate income tax, IP boxes and the location of R&D

We discuss corporate tax effects on multinationals’ R&D. Theoretically, we find that a host country’s tax increase may boost local R&D expenditure: while R&D becomes deductible at a higher rate, this higher rate may not apply to all R&D returns. First, as R&D creates a public good within the MNE, some R&D returns are taxed at other countries’ tax rates. Second, some of the R&D returns are taxed at a lower IP regime tax rate. The positive tax rate effect is empirically supported by country-by-country R&D data of U.S.-owned subsidiaries for countries that have an IP regime.


Introduction
The taxation of income from intellectual property (IP) has received considerable research interest in recent years. Much of this interest has been stirred by new tax legislation and the political debate connected to it. In the last twenty years, many countries have moved to schedular taxation by introducing a special tax rate on intellectual property income that is below the standard corporate tax rate. Schemes that introduce such a schedularization of business taxation have been labelled as patent boxes, innovation boxes, IP boxes, or IP regimes (OECD, 2015; OECD, 2017).
Intangible assets are increasingly perceived to be important value-drivers within multinational enterprises (MNEs). From the perspective of an MNE, locating these assets in low-tax affiliates is an attractive tax-saving strategy. There is a large body of literature, more extensively reviewed in the next section, that indicates that IP boxes and taxes on income from intellectual property affect the location of patents. For example, Griffith et al. (2014) and Alstadsaeter et al. (2018) provide evidence that a lower tax on IP income increases the number of patents that are registered in the respective jurisdiction.
While there is ample evidence that low tax rates attract the location of patents, empirical evidence on the effects of taxes on the location of actual research and development (R&D) activity is all but missing. An exception is Alstadsaeter et al. (2018) who find that the tax advantage of IP boxes in a panel sample of large research-intensive multinationals is negatively rather than positively correlated with a variable designed to measure the shift of inventors to IP box countries.
One difficulty of identifying tax effects on the location of R&D activity is that country-level data on R&D expenditures of multinational companies is scarce. Most existing studies on IP boxes work with patent registration data. At the same time, the location of patent registration provides limited evidence on where the actual R&D activities takes place and, in particular, on the size of local R&D expenditures. When it comes to patent registration data, evidence on the distinction of patent registration and the location of real R&D activity can only be derived from a gap between the country of registration and the residence country of the inventor. This leaves a potentially important research gap since the technological spillover effects of foreign direct investment and foreign know-how are expected to result from the size of real research activity, not so much from the mere registration of patents or the residence of single individuals. Within an MNE, the registration of patents may be influenced by the wish to shift profit into low-tax jurisdictions, without much connection to the location of research activity.
While corporate groups report aggregate R&D expenditures, the distribution across different subsidiaries is difficult to obtain in data bases that are readily available for researchers. The present paper adds empirical evidence on real R&D activity by looking at R&D expenditures of U.S. majority-owned subsidiaries abroad, data that is available on the country-year level from the Bureau of Economic Analysis (BEA).
Our empirical analysis is guided by a model of optimal R&D decisions. Within our model MNE, the benefits of R&D derive both from royalty income and from increased productivity of the MNE as a whole. Since the increased productivity is not confined to the subsidiary that undertakes the R&D, research expenditures contribute towards a public good within the MNE. 1 This can have interesting and counter-intuitive implications for the role of corporate taxes if one country exogenously increases its corporate tax. An increase in the corporate tax of one country means that the value of the cost deductibility of R&D expenditures increases in this country. At the same time, due to the public goods characteristics, the additional benefits of a marginal unit of R&D occurs in other countries as well. As the tax rates of these other countries are constant, the average tax rate on R&D benefits across subsidiaries increases by less than the tax rate for the deduction of R&D expenditures. As a result, a corporate tax increase can increase local R&D of foreign subsidiaries. This cost shifting is a tax efficient reaction if, as it is assumed in the model, the subsidiary that increases its R&D costs reports positive taxable profits, which implies that transfer pricing strategies and other strategies of tax avoidance are insufficient to wipe out all taxable profits.
Thus, in our study, we propound the possibly counter-intuitive idea that a higher statutory corporate income tax rate may have positive effects on the local R&D expenditures by MNEs.
The positive effect of the corporate tax on R&D expenditures may even be amplified by the existence of an IP regime. In this case, if the R&D in the tax-reform country increases, not only the profitability gains of affiliated subsidiaries in other countries are sheltered from the corporate tax increase. In addition, the IP regime allows to spare from the tax rise qualified IP income in the country that introduces the corporate tax increase.
A priory, the role of IP regime for the way in which the corporate tax rate affects R&D expenditures, however, is not unambiguous. While it is true that a lower IP tax rate leaves more of the benefits of R&D to an innovating firm, the existence of an IP box may also reduce the tax rate 1 See for instance Bilir and Morales (2020) for evidence on the fact that gains from corporate R&D partly accrue abroad in MNEs. This study documents that the spatial concentration of innovation is higher than that of production within multinational firms, consistent with the idea that knowledge is shared across locations within the firms (Arrow 1975) and with recent results emphasizing the transfer of intangible inputs within firm boundaries as a key motive for plant integration (Atalay et al., 2014). applicable when a subsidiary deducts its R&D expenditures. De jure, most international IP regimes are following the net income approach. In a net income approach, the preferential IP rate applies not only to the revenues earned on the IP. It should also be applied when deducting the cost incurred to produce the IP. If this approach is followed through, an increase in the headline corporate tax rate may not increase the value of the cost deductibility of R&D expenditures and their overall size. In practice, however, it should be difficult to tell apart all those cost from normal business expenses. In this case, for tax purposes, firms have a strong incentive to declare that facilities and most of the personnel are used for non-R&D related purposes.
A further reason why an IP box may not prevent that R&D expenditures are deducted against the standard corporate tax rate changes is the application of the gross income approach: a few countries officially allow all R&D costs to be deductible at the higher standard rate, while IP revenues still benefit from the preferential IP rate.
In the end, the question of whether an increase in the corporate tax rate has a higher or lower R&D effect in countries with an IP box is an empirical one. Our empirical analysis of R&D by U.S.-owned MNEs shows that the headline corporate tax has a positive, though insignificant, effect on R&D if there is no IP regime. The effect of a corporate tax increase on R&D expenditures is larger and significant in IP regime countries. This is compatible with the expectation that tax incentives are active and a large share of R&D deductions for tax purposes is channeled into the standard basket of deductions. We find no significant differences of corporate tax changes depending on whether an IP regime uses the gross or a net income approach.
The empirical result that a higher corporate tax rate tends to have a positive effect on R&D expenditures may not only come as a surprise to many policy makers, but, as to our best knowledge, is new to the literature on taxes and R&D.
When it comes to the effect of an IP regime, we find that given an IP regime is in place, a lower preferential rate on IP income significantly increases R&D expenditures. This suggests a positive effect of the tax preference on the attractiveness for R&D, while Alstadsaeter et al. (2018, p. 165) found that, in their sample, the size of the tax advantage of patent boxes led to a surprising negative effect on the probability of moving inventors to the patent box country. At the same time, in our study, the introduction of an IP regime has only a small effect on R&D.
The remainder of the paper is as follows. Section 2 provides a literature review of previous studies that look at how taxes affect the international location of patents. Section 3 introduces a simple model of an MNE's R&D decisions. Section 4 presents our data, Section 5 discusses the empirical derived from U.S. MNE expenditures. Section 6 concludes. Evers et al., (2015) and Bradley et al., (2015) among a rank of objectives that may motivate governments' decisions to introduce Intellectual Property regimes, 2 focus on the reduction of the tax base erosion. These papers suggest that the governments' objective to reduce tax base erosion, which occurs when IP is shifted to tax havens or other tax law jurisdictions, is associated with the introduction of IP regimes.

Literature review
Against the background of our own study, the main interest is in existing papers that evaluate the link between taxes, IP regimes and the amount and location of R&D output. While most papers focus on the effect of patent boxes on mobile income, i.e., patent location, -though some important exceptions are Alstadsaeter et al., (2018) and Schwab and Todtenhaupt (2017), -our paper looks at the impact of patent boxes on R&D investment. Furthermore, the focus of our paper on the statutory corporate income tax rate, relates it closely to Akcigit et al., (2021), which estimates a negative effect of tax rate on R&D. However, Akcigit et al., (2021), -in line with most papers, which look at the at the effect of taxes on aggregate R&D or pool micro data on MNEs and national enterprises, -focuses on the impact of personal and corporate income taxes on individual inventors (the micro level) and on states (the macro level). Hence, although some exceptions exist, i.e., Knoll et al., (2021) 3 , the focus on multinational firms is another contribution of our own study.
Prior studies have measured R&D output in terms of patents and suggest that low and preferential tax rates on IP income lead to more local R&D output. At the same time, the tax induced increase in patent applications seems associated with a significant increase of the share of patents whose inventors are located abroad. This leaves open whether an IP regime is able to attract also the underlying R&D activity. Ernst and Spengel (2011) estimate that decrease of the corporate income tax rate increases the average count of patent applications, the effect being 120% larger for inventions developed by 2 Other objectives that may motivate governments' decisions to introduce Intellectual Property regimes might be: to foster domestic innovation and the creation of high-value jobs; to incentivize firms to increase investment in innovative activities; to attract or retain mobile investments that may be associated with high-skilled jobs and knowledge creation Bradley et al., 2015). 3 This study however, looks at the input-related R&D tax incentives such as tax credits, accelerated depreciation or super-deductions, suggesting a negative effect of B-Index on R&D activity, and claiming that MNEs respond to R&D tax incentives by relocating R&D activity across groups locations rather than by increasing their aggregate R&D investments. foreign inventors. Griffith et al. (2011) and Griffith et al., (2014) confirm that lowering a country's corporate tax increases the probability that a patent is registered for a firm in that jurisdiction. In addition, Griffith et al. (2011) document that the introduction of IP regimes in Benelux countries increased newly created patents in Benelux countries, but a fall elsewhere. Bradley et al., (2015) suggest roughly a 3% increase in new patent applications for every one percentage point decrease in the tax rate on patent income. Unlike in Griffith et al. (2011), this effect appears to be confined to patents for which the inventors and patent owners are located in the same host country; there seemed no measurable impact on the number of patents owned and invented in different countries.
Bornemann et al., (2020) document an increase in innovative activity, including patent applications, grants and high-skilled employment, following the enactment of an IP regime, at the expense of patent quality. Authors claim that the financial benefits following an IP regime are greater for MNEs that do not have an incentive to shift income out of the IP regime implementing country than for MNEs with income shifting opportunities, and even greater than for domestic firms. When it comes to real activity, the tax advantage linked to IP boxes is associated negatively with the annual growth in the number of inventors and also negatively with the probability that a MNE moves inventors from other affiliates to an affiliate in a patent box country.
As intellectual property is firm-specific in nature, arm's length prices are difficult to obtain. This creates opportunities for MNEs to shift income to low-tax countries by mispricing intra-firm royalties and license fees. Papers looking for evidence on such profit shifting are part of a closely related strand of the literature. Dischinger and Riedel (2011) find that the lower a subsidiary's corporate tax rate compared to all other affiliates of the same multinational group, including also the parent, the higher is its probability of holding intangible assets there. Karkinsky and Riedel (2012) show that the number of patent applications filed by multinational affiliates strongly responds to changes in corporate tax rate. The estimated semi-elasticity ranges between -3.5% and correlation between a country's patent income tax rate and its fraction of foreign-invented patents, suggesting that the propensity to locate patent ownership in foreign tax haven economies increases in the inventor country's patent income tax rate.

A Model of R&D location within an MNE
This section studies the decision making on R&D expenditures in a simply model, in which an MNE consists of two subsidiaries in two different countries, labelled 1, 2. The main objective of the exercise is to show that the size of the standard corporate tax rate may have a positive effect on local R&D if (i) R&D cost are deductible against this standard rate and (ii) the benefits of R&D are partly taxed at some other rate, either at a foreign one or at a rate deriving from a preferential IP regime.
In our framework, R&D expenditures of one subsidiary increase the productivity of both subsidiaries. A further effect of R&D and the production of IP is that leads to royalties for the subsidiary that carries out the respective R&D, leading to an extra benefit for the R&D-conducting subsidiary. We distinguish two tax rates in both countries. denotes the standard corporate tax rate in country = 1,2; is the rate on royalty income in country , that may benefit from an IP regime, such that this rate may or may not fall short of .
The IP labelled , within the MNE derives from the sum of IP of both subsidiaries, = 1 + 2 .
Each subsidiary produces IP using a strictly concave research function, such that = ( ), > 0, Royalty incomes for the subsidiaries in country 1 and 2 are simply modelled as 1 ( 1 ) and 2 ( 2 ), where may be thought of as the share of IP that cannot only be used to increase MNE productivity but can also be sold on the market. Net of tax, the global MNE profit derives as: The Lagrangian of the profit maximization problem can be written as = Π + 1 1 + 2 2 , where 1 and 2 represent Kuhn-Tucker multipliers for the non-negativity constraints on local research expenditures. The two first-order conditions for a profit maximum are: Consider a special case, in which is particularly easy to analyze, is where just one subsidiary, say in country 1, conducts research ( 1 = 0; 1 > 0) and the other subsidiary is in a corner solution with ( 2 > 0; 2 = 0). In this case, a marginal change d or d 1 leaves constant 2 . This, in the following, will be assumed for ease of presentation.
A change in the corporate tax rate of country 1, may have different effects, depending on whether an IP regime is in place or not. The effect of a corporate tax rate change in the presence of an IP regime can be derived by marginally changing 1 , but leaving the rate on IP income (royalties) constant (d 1 = 0). By total differentiation of the first-order condition we receive for d 2 = 0: If country 1 changes its corporate tax rate without having an IP regime in place, the effect on 1 needs modification as d 1 = d 1 and the effect of a corporate tax increase derives as: With 1 = 1 , the numerator (as the denominator) continues to be negative, but the positive term 1 1 tends to dampen the positive effect of an increase in 1 . Evaluating equation (3) and (4) for the same set of initial tax rates yields Next, consider a marginal change in 1 assuming an IP regime is present and d 1 = 0. From differentiating the first-order condition, we now get This leads to the formulation of the following hypotheses, which are empirically testable.
H1. An increase in the corporate tax rate of a country increases the local R&D expenditures of MNEs.

H2. The increase in local R&D expenditures of MNEs upon an increase in the corporate tax rate is higher if IP income in the respective country is subject to a separate tax rate (IP regime) than if this is not the case.
H3. If there is an IP regime in place, an increase of the local tax rate on IP income will decrease local R&D.
Clearly, the above model introduced a very simple framework. Several limitations come to mind and may or may not be important factors in practice.
The corporate tax modeled above resembles a pure profits tax, as all costs are tax deductible. Real world corporate taxes differ and usually disallow deduction of some cost, for example, the opportunity cost of equity. Therefore, high real-world taxes, unlike the corporate tax in the above model, may induce the MNE to exit a country or enter a different one. This would have a negative effect on R&D in high-tax countries, possibly negatively affecting the empirical support for H1 and H2. Despite this possibility, the mechanism described above would work against such a reduction of R&D and cushion the effect of a corporate tax increase.
Another caveat applies to the implicit assumption of the model that tax rates indeed are relevant as all subsidiaries have positive taxable profits. In so far, as some real-world MNEs have sufficiently powerful tax avoidance instruments that already wipe out taxes, the above mechanisms would have reduced predictive power.
Another possible concern is that the model does not explicitly allow for contract R&D. Within an MNE, a low-tax subsidiary could pay a high-tax subsidiary to conduct R&D services on behalf of the low-tax subsidiary (Griffith et al., 2014, p.14). While this has not been explicitly modelled, the possibility of such schemes should reinforce the expectation that the cost deductibility of R&D expenditures is an argument to conduct real R&D activity in high-tax countries, given that the MNE wishes to be present in those countries.

Data
The empirical part of the paper uses aggregated data, although the above model discussed the decision problem of a single MNE. Unfortunately, company accounts data does not typically distinguish the geographical location of firm's R&D activities and multinationals report R&D expenditures at consolidated level. Therefore, we use data on R&D expenditures of majorityowned foreign affiliates of U.S. MNEs, reported at country level. We obtain the data from the Bureau of Economic Analysis (BEA) homepage. To the best of our knowledge, this is the first study using the BEA's direct investment data for investigating tax policy effects on real research activity.
The BEA database contains the R&D expenditures of U.S. majority-owned foreign affiliates as performed by the relevant foreign affiliates. Should one affiliate pay a second affiliate within the same MNE to conduct R&D, then the R&D expenditure would be attributed to that second affiliate; no R&D cost are recorded for the first, merely contracting U.S. affiliate. 4 This accounting convention is adequate for our purpose, as our main interest is in where the actual research activities take place and how these activities are affected by taxation. 5 Our sample includes seventy-five countries where U.S. multinationals have reported R&D expenditures for at least one year during the period under analysis, 2009-2017. 6 In total, the sample includes 621 country-year observations, resulting in a slightly unbalanced panel with only 54 missing country-year entries.
The presence of an IP regime in the host country in a certain year constitutes the first variable of interest in our empirical analysis. Finally, we add control variables on non-tax country characteristics. We refer to prior literature  8 We include LN (GDP) to control for market size, which measures the log of GDP in purchasing power parities. Since tax rates and country sizes have been found to be systematically correlated, inclusion of this size measure prevents the tax rate from picking up size effects (Weichenrieder, 2005;Ruf and Weichenrieder, 2012). In order to control for the country's degree of development and living standards, the logarithm of GDP per capita is included. In line with Dischinger and Riedel (2012), as a proxy for the country's economic situation, we include the unemployment rate. The Corruption Perception Index (CPI) represents the Transparency International corruption index, which is constructed with higher values of the index indicating lower corruption, in order to capture perceptions of the public sector corruption, the quality of public services, the quality of policy formulation and implementation and the credibility of the governments' commitment to such policies. Table A1 in Appendix A reports summary statistics of all variables used. China, that enacted an IP regime in 2008 and France, which has an IP regime since 1971, have the highest preferential tax rate (15%) among the rest of the six countries that run an IP regime. The United Kingdom, after the 2013 enactment of an IP box introduced a preferential tax rate of 10%.
In the year of IP box enactment, the tax advantage was about 13%. It decreased to 9% after a year-by-year decrease of the statutory corporate income tax rate (19% in 2017).
A country with frequent changes is Israel. Its statutory corporate income tax rate ranges between 24% and 26% and its preferential tax rate within the period changes from 10% to 7%, then again to 9% and in the last two years 2016, 2017 it decreases to 6%. Ireland, which provided the lowest tax rate on IP income, 2.5% for 2009 and 2010, abolished its IP regime in 2010 and re-introduced it in 2016 with a preferential tax rate of 6.5%. 9 In 2011, the Canton of Nidwalden in Switzerland introduced a License Box Regime, which provided exemption at the cantonal level, but not at the federal level, equal to 80% of eligible income. Given that the tax advantage was not given at the federal level, in the regressions below, Switzerland is considered as a country without IP regime (Guenther, 2017, p.9). Switzerland recently introduced a patent box regime going into effect in 2020, which covers all of Switzerland. The regime will provide a maximum tax base reduction of 90% on income from patents and similar rights developed in Switzerland. Cantons can opt for a lower reduction. Figure 2, for each of the 22 countries with IP regimes, compares the mean corporate tax rate and the mean preferential IP rate across the years when an IP-regime was in place. The largest difference between the two mean rates is in Uruguay, Colombia and Macau, the smallest difference applies to the Republic of Korea.    Keen (2001) and others have argued that preferential tax regimes may allow for higher standard corporate tax rates since, with such a special regime, parts of the most mobile tax base are taken out of the high-taxed base. We checked whether this is reflected in our sample. 12 out of 22 IPregime countries had the regime in place during all of our sample years; 10 countries had years with and without IP regimes. For these 10 countries, the mean statutory corporate tax rate in years without an IP regime (24.6%) is almost identical to the average rate in years with an IP regime (23.2%). Controlling for country and time-fixed effects, we found an insignificant negative correlation between an IP regime dummy and the rate of the statutory corporate tax rate. This finding does not support the idea that countries introduce a preferential regime to be able to increase their rates on the remaining tax base.
The missing correlation is also interesting for another reason. If one suspects that the selection into having an IP regime is based on the political perception of the need to correct for a low level of R&D and may therefore be endogenous, then the absence of a correlation between the corporate tax rate and an IP regime dummy suggests that the corporate tax rate can be taken as exogenous.
Among the 22 countries, Ireland, Israel, Netherlands, Portugal, Hungary, Italy, Korea and Spain had different rates of the preferential tax rate on IP across the years in which a regime had been in place. For the rest, the tax rate on IP income did not change.

Estimations
In this section, we exploit our panel-data to regress country-level R&D expenditures of US-owned subsidiaries on country characteristics that capture R&D-friendliness from a tax and non-tax perspective. Based on the model in Section 3, our main interest is in the corporate tax rate, the availability of a preferred patent box regime, and the interaction between tax rates and regimes.
This leads us to the following empirical model.
Our left-hand variable, LN (R&D)it, represents the natural log of R&D expenditures by U.S. majority-owned subsidiaries in country i in year t. 10 In each country there are two, possibly distinct,

Empirical Results
Columns (1) and (2) in Table 1 report on OLS fixed effects model estimations, columns (3) and (4) report on the NB model. The NB estimations contain the same set of regressors as the OLS regression in column (1) and column (2). While the left-hand side is now measured in level rather than its logarithm, the coefficients of tax rates in the negative binomial model can be interpreted as semi-elasticities. To account for heteroscedasticity and possible serial correlations, we cluster all estimates in Table 1 at the country level. 13 We first focus on the interpretation of column (2), where the full set of control variables in an OLS regression is included to discuss the hypotheses H1 -H3 of Section 3. As discussed in that section, a change in the statutory corporate tax rate may be different depending on whether the variation happens with an IP regime in place or not.
In the absence of an IP regime, a change in Stat_CIT, by construction, goes along with a change in τIP_it, as the standard corporate tax then also applies to IP income. This means that, in this case, a one percentage point increase in the CIT leads to an increase in R&D expenditures by some 0.9% (= -0.0279 + 0.0364). This, however, is not statistically significant according to line (i) and lends 12 Although this suggestion may have an incidental parameter problem, Allison and Waterman (2002) and Greene (2004) suggest that the resultant incidental parameters bias is not disturbing due to moderately small time dimension (Cameron and Trivedi, 2013, p.357). 13 Presence of heteroscedasticity is suggested by scatterplots of fitted, predicted and residual values, Breusch-Pagan test, White test and a modified Wald statistic for group-wise heteroscedasticity in the residuals of a fixed-effect regression model. no particular support to H1. Section 3 discussed potential reasons, why effects outside our model could actually lead to a negative effect of the corporate tax rate on R&D. Against this background, it is an interesting observation that a higher tax rate does not seem to have a negative effect on R&D.
Compared to when an IP regime is not in place, H2 expresses the expectation that an increase of The observation that a marginal change in the corporate tax rate has a larger effect if an IP regime is in place is in line with our expectation (H2). In countries without a preferential tax rate regime on IP income, a higher corporate tax makes the deductibility of R&D cost more valuable, but also increases the tax on R&D returns. This is different in IP regime countries, where the income generated from IP is sheltered by the IP regime.
The positive and strongly significant effect of the statutory CIT on R&D expenditures in these countries is compatible with the view that subsidiaries manage to deduct a large share of the cost of R&D at the higher statutory corporate tax rate, while the returns of R&D investments benefit from the lower IP rate. Although formally, this is only allowed under the gross income approach, it could be that countries are lenient under the net income approach and effectively there is always a de facto gross approach in place. With R&D costs largely consisting of labor costs, firms might easily report R&D costs as normal costs in order to get their deductibility under the normal statutory corporate income tax rate, while maintaining returns from R&D taxed at the lower (preferential) corporate income tax rate.
The coefficient of IP Regime (dummy), is not statistically significant across columns. This in itself would indicate no significant increase of R&D expenditures if a host country introduces such a regime; the coefficient is even negative. At the same time, such a regime allows for a reduced rate on intellectual property income. The effect of an IP Regime derives from both the IP Regime (dummy) and the reduced tax rate on IP income (τIP_it). The significantly negative coefficient of this latter variable indicates that (given an IP regime is in place) a lower tax rate on IP income (keeping the corporate income tax constant) indeed is associated with higher R&D expenditures: a reduction of the rate on IP income by one percentage point increases local R&D expenditure by some 2.8%. 14 Again, the results are closely comparable across columns and models (OLS/NB), providing support for H3. As noted, to evaluate whether the introduction of an IP regime has a stimulating effect on R&D, a look at the coefficient of iprit is insufficient, as an IP regime also comes with a reduced tax. Assuming that the introduction of an IP regime reduces the applicable rate from the average of the corporate income tax rate (24.1%) rate to the average rate of IP regimes in the sample (8.0%), from column (2) (1) and (2) represent coefficients rather than odds ratios. The unit of observation is country-year. The alpha parameter informs about the degree of dispersion, if alpha is significantly greater than zero the data are over dispersed and are better estimated using a negative binomial model than a Poisson model.

Gross income approach
The results in Table 1 are based on a pooling of countries that apply IP regimes with a gross or a net approach. This reflected the expectation that, for tax purposes, it is difficult to tell apart R&D  LN (R&D Expn.)it = α0 + β1 iprit + β2τIP_it + β3 Stat_CITit + + δ1 Stat_CITit * iprit+ β4 Gross_approachit + δ2 Gross_approachit * Stat_CITit + + δ3 Gross_approachit * τIP_it +β5Xit + φi + γt + uit (7) Table 2 reports the results for equation (7). The four columns again report on OLS and NB regressions. The full set of controls is included in columns (2) and (4), while in columns (1) and (3) only the main variables of interest are included.
We first concentrate on the results for OLS in column (2). As in Table 1, the preferential tax rate on IP income enters significantly negative for R&D expenditures, resulting in a semi-elasticity of some -3.4%. As we have added an additional interaction of this rate with the gross approach dummy, the value of 3.4% is estimated for net approach regimes. The interaction with the gross approach dummy enters surprisingly with a positive sign that is statistically significant in columns (2) and (4), although not in (1) and (3).
Again, the statutory corporate income tax rate increases R&D expenditures only insignificantly in countries that do not offer a preferential tax rate on IP income, while it exerts a positive effect of some 2.6%, significant at the 5% significance level in countries that have an IP regime (net income approach) in place.
The heterogeneity we are interested in when estimating equation (7) concerns the new variables that indicate the application of the gross income approach. A significantly positive coefficient of Gross_approach*Stat_CIT would suggest that IP regimes with a gross approach help better to cushion the effects of a corporate tax increase than those with net approach. The fact that we observe only an insignificant positive coefficient is in line with the view that de facto, all IP boxes tend to be used as if they were following the gross income approach. This said, we should also keep in mind the limited observations that identify the size of the interaction effect and that limits statistical power.
If we concentrate on IP-regime countries with a gross approach in place, the coefficient representing the marginal effect of the statutory corporate income tax rate on the log of R&D expenditures is hardly changed (2.68%) compared to net approach countries, but is not significant according to the test in line (iv) of Table 2.
Somewhat less expected, the coefficient on the interaction Gross_approach*τIP , turns out positive and statistically significant at the 1% significance level in columns (2) and (4). It suggests that there is a difference on the effect of the preferential tax rate depending on whether a change in the tax rate happens in a gross or net IP regime approach. Lowering the preferential rate in a gross approach, which should be the more generous approach, seems to be less stimulating for R&D.
Again, the fact that the estimation is based on tax rate change in only a few (here three) countries adds an important caveat.

Conclusions
A growing literature indicates that high corporate taxes are detrimental to the number of patent applications by MNEs in these high-tax countries. Conversely, the question of whether high corporate taxes also reduce R&D expenditures and real research activity has received much less attention, but is the focus of the present paper. We hope that this paper may trigger a larger discussion on taxes and the location of real R&D activities. While the location of patents may be informative on tax planning activities of MNEs, in the end, we expect that it is the location of real R&D activity that is decisive when it comes to international spillover effects in knowledge.
Using a model of R&D decisions by MNEs, we identified mechanisms that could induce more R&D expenditures when the tax rate increases. An intuition for this somewhat counter-intuitive tax effect is that R&D costs are tax deductible and the value of this deduction tends to be the highest where the corporate tax is the highest. Given that R&D expenditures are tax deductible against the high corporate taxes, the possible positive R&D effect reflects a tax asymmetry: not all R&D returns are subject to the higher tax. First, since R&D creates a public good within the MNE, some of the R&D benefit is taxed at other countries' tax rates that are not subject to the tax increase. Second, some of the R&D benefits are taxed at a lower IP regime tax rate. Therefore, a higher corporate tax, which increases value of the cost deductibility of R&D, may foster R&D.
This expectation is empirically supported by country-by-country R&D data of U.S.-owned subsidiaries for countries that do have an IP regime. When it comes to the effect of IP regimes, we find a small overall impact on R&D expenditures, which results insignificant.
Several caveats and opportunities for future research remain. One issue is that our theoretical model is tailored to MNEs. It does not necessarily allow similar conclusions for national firms that conduct R&D. On the empirical side, one possible problem is that, as in the vast majority of papers evaluating the tax effects on patent behavior, we have taken changes in tax characteristics of countries as exogenous variations. While countries' corporate tax rate decisions, much more than IP regimes, may be set with a focus on a broad set of goals, we cannot rule out that corporate taxes are set also with an eye to attracting R&D. At the same time, we did not find evidence that countries that introduced an IP regime systematically changed their headline corporate tax.
Our empirical estimations are based on the R&D expenditures of U.S. wholly -owned subsidiaries, aggregated at the country-year level. Although the U.S. reports R&D for up to 75 different countries, confirming our results with confidential BEA firm-level data would be a worthwhile project, but would have to occur from within the BEA. Although subsidiary-level R&D expenditures are difficult to attain, using data from non-U.S. MNEs would also be a useful endeavor.   Gross income approach takes on the value one if the country that has an IP regime in place applies an asymmetric treatment of IP income and IP expenses and as long as the taxpayer has sufficient ordinarily taxed non-IP income from which to deduct the IP expenses, this can produce substantial tax advantage. Thus, this variable takes on the value one if the current expenses are deductible from non-IP income, which is taxed at the regular corporate tax rate, and zero otherwise. Unemployment Unemployment refers to the share of the labor force that is without work but available for and seeking employment, thus it is expressed as the total % of total labor force).

Source: World Bank Database
Corruption Perception Index (CPI) Transparency International corruption index, which is constructed with higher values of the index indicating lower level of corruption.

Source: Transparency International
Property Rights Index A subcomponent of the Index of Economic Freedom, the property rights index measures the degree to which a country laws protect private property rights, and the degree to which its government enforces those laws. The more certain the legal protection of property, the higher a country's score; similarly, the greater the chances of government expropriation of property, the lower a country's score.
Countries that fall between two categories may receive an intermediate score.   (1) and (2) (1) and (2) using an Inverse Hyperbolic Sine Transformation.
Note: This table reports results of the estimation of equation (1) and (2) while using an Inverse Hyperbolic Sine Transformation of the dependent variable. Differently from the simple logarithmic transformation we used in table 1 and 2, here HIS transformation allows us not to loose 33 observations which have a zero value of R&D expenditures of U.S. majority-owned subsidiaries. The levels of significance are reported as *** p<0.01, ** p<0.05, * p<0.1. Coefficients are robust to both heteroscedasticity and serial correlation using the cluster estimator, clustered at country level. In column (2), all the coefficients on the main variables of interest preserve their sign, as well as their significance level, while they result to be higher compared to those reported in column (2) in Table (1), where the simple logarithmic transformation is used. In addition, using the HIS, the marginal effect of the statutory corporate income tax rate on R&D expenditures also in countries without an IP regime in place becomes marginally significant. It remains positive and statistically significant at the 1% significance level in countries with an IP regime in place, although economically higher then the one using the logarithmic transformation.  Table B3. Controlling for input-related R&D tax incentives.
Note: This robustness check controls for the presence of input-related tax incentives per country and year (although in the previous estimations, the inclusion of fixed-effects counts for them). We introduce a dummy variable, which equals one if country c in year t offers at least one of the four R&D related tax incentives, i.e., tax credits, tax allowance, accelerated depreciation and/or super deductions, and 0 otherwise. Qualitative information for the quantitative construction of the Inputrelated tax incentives dummy variable is obtained from (i) Ernst   incentives seem to exert no impact on R&D expenditures of U.S. majority-owned subsidiaries, which is somehow in line with Knoll et al., (2021), i.e., firms hardly raise their R&D activities due to generous input-related R&D tax incentives. However, we are aware of the fact that our dummy variable cancels out the heterogeneity of input-related R&D tax incentives across countries, leading us to a very naï ve and facile result.
In table B3, we report results of the estimation of equation (1) in column 1 and 2 and of the estimation of equation (2) in columns 3 and 4. The levels of significance are reported as *** p<0.01, ** p<0.05, * p<0.1. Coefficients are robust to both heteroscedasticity and serial correlation using the cluster estimator, clustered at country level. All estimations include countryfixed effects and time-fixed effects and countries are observed during the period 2009-2017 (unbalanced sample). The unit of observation is country-year. The model is estimated via OLS estimation method in regressions (1) and (3), and via a negative binomial model in regressions (2) and (4).The alpha parameter informs about the degree of dispersion, if alpha is significantly greater than zero the data are over dispersed and are better estimated using a negative binomial model than a Poisson model.