Effectiveness of R&D tax incentives in small and large enterprises in Québec

It should be noted that fiscal measures to support innovative activities other than R&D have also been implemented in Quebec. This is the case for the measures set up with respect to information technology development centres (ITDCs) and marketplaces for the new economy (MNEs) and other measures related to the knowledge-based economy such as the refundable tax credit for E-commerce solutions and the refundable tax credit for technological adaptation services. This study, however, focuses only on R&D fiscal measures, and we present below the fiscal measures that took place in Quebec in the last 3 decades, that is to say, the SR&DE refundable tax credit, the super-deductions for R&D and the refundable tax credit based on the increase in R&D expenditures.²

Table 1 summarizes the estimated cost of the various fiscal measures in support of R&D that are in order:

The dataset used in this study results from the matching of three different microdata files: the survey on Research and Development in Canadian Industry (RDCI), the Annual Survey of Manufactures (ASM) and administrative data from Revenu Québec.

The RDCI survey is a firm-level survey conducted on an annual basis by Statistics Canada. Its sampling frame comprises all Canadian firms known or believed to perform or fund R&D. Since 1997, only firms performing or funding more than $1 million in R&D are surveyed. For all the other firms, the data are extracted from administrative data from Canada Revenue Agency (CRA).⁷ The Annual Survey of Manufactures (ASM)⁸ is an annual survey conducted by Statistics Canada that collects data on employment, wages, total cost of materials, total sales of manufactured products, inventories, value added by manufacturing and capital expenditures. It also provides other principal industrial statistics such as energy consumption and information on commodities consumed, produced and shipped. Contrarily to the RDCI survey described above that collects and reports data at the company or enterprise level, the reporting unit in the case of the ASM survey is the establishment. More specifically, the universe of this survey consists of all establishments primarily engaged in manufacturing activities, that is, all establishments classified in sectors 31, 32 and 33 under the North American Industry Classification System (NAICS). Two methods are used to collect data, the data collected directly from firms’ respondents by questionnaires and the data obtained from administrative files from Canada Revenue Agency. Administrative data from Revenu Québec (ADRQ) comprises records of the amounts of SR&ED or other fiscal incentives to R&D effectively received by R&D performers located in Quebec or having had R&D conducted on their behalf in Quebec. This is a slight difference compared to the target population of Statistics Canada RDCI survey described above, which does not include firms that contract out their R&D activities. However, Statistics Canada and Revenu Quebec both use the same definition for SR&ED. The reporting unit in the present dataset is the provincial-enterprise, which is the same as in the case of the RCDI survey data of Statistics Canada.

Matching was performed at the level of provincial-enterprises.⁹ The three files contained only firms located in Quebec. Matching proceeded in two steps: the RDCI data from Statistics Canada was matched to the fiscal data from Revenu Québec, and the resulting file was then matched to the ASM data from Statistics Canada. Another difficulty was due to the fact that the data correspond to different levels of aggregation. While the RCDI-ADRQ matched data are at the provincial–enterprise level, the ASM data are at the establishment level. To solve this problem, we grouped the establishments in the ASM data file by provincial-enterprises prior to performing the matching in the cases of multi-establishments enterprises. We decided to discard all cases of mergers and acquisitions. The data on the fiscal support received from the Federal government were constructed by using the official statutory rates.¹⁰

Breaking R&D performers by size class in the manufacturing sector between 1997 and 2003, data show that most of the R&D tax credit applications come from small firms but that the large firms get the greater part of the amount of attributed tax credits. As shown in Table 2, more than 65.3% of all tax claimants are small firms (0 to 50 employees) making up 28.5% of the total value of attributed tax credits. However, large firms that represent only 3.6% of tax claimants get more than 37.5% of the total amount of attributed tax credits. The tax credit for salaries of researchers was the most important program accounting for at least 75% of the total attributed tax credits. The tax credit for university research shows no significant differences across size classes. Tax credit for pre-competitive research was used more often by small and medium-sized firms (less than 500 employees). The reason is that because of limited capacity of funding a research project, firms enter into partnership contracts for pre-competitive research projects (or to have the project done on their behalf). This tax credit and the credit for university research, however, represented only 0.9 and 0.6%, respectively, of the total attributed tax credit over the sample period. Concerning the tax credit for dues or contributions paid by corporations to a research consortium, data show that the majority of beneficiaries were firms with more than 500 employees.

Table 2 also shows the non-negligible use of other fiscal incentives such as the super-deductions for R&D and the tax credit based on the increase in R&D expenditures. Even though these fiscal measures lasted only 1 and 5 years respectively, corresponding claims totaled 4.0 and 4.5%, respectively, of the total attributed tax credits over the sample period.

The model from which we estimate the elasticity of R&D with respect to its user cost is the same as the one used in Lokshin and Mohnen (2007). In a nutshell, we start from a CES approximation to the true production function for firm i at time t (as in Chirinko et al. 1999; Hall and van Reenen 2000; Mairesse and Mulkay 2004):where Q _it is the output, K _it is the end of period R&D stock, X _it is the other inputs, and γ (a scale factor), β (the distribution parameter), ν (a measure of the returns to scale) are parameters to be estimated that characterize the technology, as well as ρ that enters the expression for the elasticity of substitution (σ) between R&D stock and the other inputs and is given by \( \sigma = 1/\left( {1 + \rho } \right) \ge 0. \) In a static model of profit maximization, the optimal amount of R&D capital in logarithms would be given by¹¹ where u _R,it is the logarithm of the user cost of R&D and p _Q,it the unobservable output price. Following Klette and Griliches (1996), we assume a price elasticity of ε > 0 in absolute value of the demand for the output of firm i relative to industry demand:where q _It is the industry demand and p _It the industry price in period t. Substituting (3) into (2) yields the long-run relationshipwhere \( \phi = \sigma + \mu \left( {1 - \sigma } \right)/\nu \), and \( \gamma = \left( {1 - \mu } \right)\left( {1 - \sigma } \right)/v \), and v _it is the nominal output deflated by the industry output price deflator.

Investment is composed of a replacement investment (\( R_{it}^{r} \)) and a net investment (\( R_{it}^{n} \)). The former is proportional to the R&D stock at the beginning of the period: \( R_{it}^{r} = \delta K_{i,t - 1} \). The latter represents the change in the R&D stock: \( R_{it}^{n} = K_{it} - K_{i,t - 1} . \) Hence, we can write

We approximate the discrete growth rate in the R&D stock by a log difference and assume that the growth rate in the R&D stock follows a partial adjustment mechanismwhich after substitutions can be rewritten asChanges in the R&D stock are therefore expressed as a weighted sum of changes in the desired R&D stocks in the past. We can now rewrite (5) asor asWe have appended a random error term in (9) to account for random unobserved disturbances. Any individual effect present in (4) is removed by the first-differencing. The error term follows a MA(1) process. Because of the simultaneity between the user cost and the amount of R&D we have to instrument for the contemporaneous change in the user cost of R&D. The short-run elasticity of R&D stock with respect to the user cost of R&D is given by −σλ. The long-run elasticity is given by −σ.

Table 3 gives the magnitude of the variables appearing in the final estimating Eq. 9. The R&D stock has been constructed by the perpetual inventory method, the starting value being obtained by dividing the initial R&D flow by the sum of the R&D depreciation rate (taken to be 15%) and the growth rate of R&D flow during the sample period. The R&D stock is on average five times bigger than the R&D flow. All nominal values are converted in 2002 prices by the appropriate deflators. The R&D deflator is computed as the average of the GDP deflator and the monthly wage index of the manufacturing sector in Quebec (Statistics Canada, Cansim, Table 281-0039). The industry price and quantity used to eliminate the firm output in Eq. 3 is from the NAICS 3-digit industry in which the firm has its major activity.

In Table 4 we present the GMM estimates for all firms in our sample, and separately for the large firms (with more than 250 employees) and the small firms (with less than 250 employees). As we can see, most of the firms in our sample are small, benefiting from favourable R&D tax credits. We have relatively few large firms in our sample. Two explanatory variables have to be instrumented: the user cost of R&D, which may vary with the amount of R&D, and the lagged dependent variable, which is correlated with the MA(1) error term. Without instrumenting, i.e. estimating Eq. 9 by ordinary least squares, yields a short-run price elasticity −σλ of −0.01 (non-significant). We then turn to the GMM estimations. As instrumental variables we use the one-period lagged level of the user cost of R&D (in log), the two-period lagged level of the dependent variable, and the contemporaneous R&D deflator, interest rate and tax credit on researchers’ salaries in Quebec.

The rank test of underidentification rejects the null hypothesis that the matrix of reduced form coefficients has less than full rank, and hence points to the relevance of the instruments and to the identification of the model with those instruments. Regarding the weakness of the instruments, the F-test based on Shea’s partial R ² is greater than 10 for the first-stage significance of the exogenous variables in explaining the user cost of R&D, but less than 10 in explaining the lagged dependent variable. However, in the presence of two endogenous variables we should rather use the Cragg-Donald statistic (the minimum eigenvalue of the first stage F-statistic matrix) and the Stock and Yogo (2005) critical values for testing whether the instruments are weak (1) in terms of relative bias, i.e. whether the maximum relative squared bias of the IV estimator relative to the OLS estimator is at least some value b, and (2) in terms of bias in the Wald test size, i.e. whether the actual size of the test is at least some value b above the nominal level of the test. At the 5% level, we reject the null hypothesis that the instruments bias the IV estimate relative to the OLS estimate by more than 30%, and we cannot reject the null that the bias in the size of the Wald test exceeds 25%. With our instruments the Sargan test of overidentifying restrictions is accepted. We have explored with different additional instruments (the lagged value of sales in logarithms, the Federal incremental tax credit rate, the ratio of log assets over log employees and the ratio of growth in output over growth in employment). In each case the test of overidentifying restrictions was rejected. We thus conclude that our instruments are rather weak, but that at least they fulfill the overidentifying restrictions.

The speed of adjustment in the desired R&D stock λ is equal to 0.74 for small firms and 0.57 for large firms, although statistically speaking they are not significantly different from each other. The short-run price elasticity of R&D is −0.14 for small firms and not significantly different from zero for large firms. It may be that large firms are not very price responsive, but it may also be that our sample size is too small for large firms to yield significant coefficients. For the whole sample, however, the short-run price elasticity is significantly different from zero and lower than for the subsample of small firms. Small firms do hence seem to be somewhat more price responsive than large firms. The long-run price elasticity σ is equal to −0.19 for small firms and −0.14 for the whole sample. The long-run output price elasticity is equal to 0.03 for small firms and 0.07 for large firms. From the constant term in the regression we can recover the estimated R&D depreciation rate, which turns out to be between 17 and 27%, thus not far away from our ad hoc choice of 15%.

We have also experimented with an alternative modeling of the dynamics in the R&D investment by specifying an error-correction model with an autoregressive distributed lag specification ADL(1, 1) following Mairesse and Mulkay (2004). This specification does not assume a particular type of adjustment as we do in the above model. However, the alternative model did not yield a significant price elasticity of R&D. Maybe a higher order lagged specification would be required, but our short time interval did not allow us to do this. Finally, we could think of estimating a different sensitivity to R&D tax credits between small and large firms by exploiting a regression discontinuity design, in the sense that the user cost of R&D would be lower for small firms that benefit from more generous R&D tax credits. The number of firms falling in a close neighbourhood of the discontinuity in the R&D tax credit schedule, some falling just above and some just below $2 ML of R&D wages, was too small to find good matches to compare the treatment effect of both types of firm.

To evaluate the effectiveness of the whole R&D tax incentive program, we compare the present situation with a fictive scenario where the government changes part of the R&D tax incentive scheme. In the absence of a proper cost–benefit calculation, including all indirect costs and benefits related to such a program (administration costs, opportunity costs and externalities), the usual way to assess the effectiveness of R&D tax incentives consists in computing the so-called “bang for the buck” (BFTB). By that is meant how much private R&D increases per dollar of R&D tax receipts foregone. If it is greater than 1, R&D tax incentives are considered to be effective in stimulating additional R&D; a value smaller than 1 means that part of the money received from tax incentives substitutes for private financing.

We start from an old scenario where firms invest in R&D every year to keep the R&D stock constant and/or to expand that stock. In the new scenario the government decides to increase the tax incentives, which leads to a decrease in the user cost of R&D and to increases in the R&D stock of knowledge until a new desired R&D stock is reached. As firms invest more in R&D, government needs to spend more on R&D tax incentives. In Table 5 we describe the evolution of the flows and stocks of R&D before and after the change in R&D tax credits (the stocks and flows in the new scenario are denoted by ~). In principle, given our assumed partial adjustment process, it takes until infinity to reach the new steady state, but in practice the new optimal stock is reached after 15 to 20 years.

To find out how much R&D arises from an R&D tax incentive scheme, we have to compute the differences in R&D flows (or expenditures) from period 1 onwards till infinity between the two scenarios, where the flows of each additional year are discounted by 1/(1 + r) vis-à-vis the previous year. This in our particular model is equal to¹² wherewhere −σλ is the estimated short-run user cost elasticity of R&D stock in the first period, λ is the estimated partial adjustment coefficient, δ is the depreciation rate of the R&D stock, taken to be 15%, r is the risk-free interest rate, taken to be on average 3%, and where the user cost elasticity, common to all firms of a given size class and constant over time, is converted to a marginal effect for period t using the optimal R&D stock and the user cost of R&D of period t.

For every dollar of private R&D expenditure, the government supports a fraction of it by giving tax incentives in proportion to the wage and salary costs for researchers, the fraction of R&D carried out by a public research centre, the fraction carried out in a research consortium, the fraction of pre-competitive research or the increments of R&D with respect to a base year. Let us denote the fraction of the private R&D so supported by the tax incentive program for firm i at year t by \( \gamma_{1} R_{it}^{{}} + \gamma_{2} \Updelta R_{it}^{{}} \), where γ₁ is the R&D tax credit rate in proportion of the level of R&D and γ₂ the rate in proportion of the increase in R&D. Appendix A explains in detail the various rates that apply in Quebec. Table 6 lists for every year the average user cost of R&D, the B-index and its components, and what the user cost of R&D would be without the R&D tax credit.

The total cost to the government to support the R&D tax credit program is given by

The BFTB is given by the ratio of (10) and (12). In other words, we compute the ratio of the increases in R&D for all the firms along the entire trajectories towards their new steady states to the saving in government costs to support R&D along those trajectories, both appropriately discounted.¹³

In our computation of the BFTB, we use size-class specific short and long-run estimated price elasticities reported in Sect. 4. We use two size classes: small firms with fewer than 250 employees, and large firms with 250 and more employees. We report each time the BFTB computed for all firms with the specificities in the tax scheme that pertain to them and with their own price elasticities. We also report the BFTB separately for small and large firms.

We run the following two experiments. In the first we increase the level-based provincial tax incentives (γ₁) by 10% (all rates appearing in PL and PO are increased by 10%), in the other we increase the increment-based provincial R&D tax credit (γ₂) by 10%. The result of the first experiment is plotted in Fig. 1. For small firms the BFTB, i.e. the ratio of cumulative additional R&D to cumulative government expenses to support R&D, starts at a value much higher than 1 and slowly drops to a value that stays above 1 even after 20 years. Hence, for small firms it is beneficial to support R&D by tax incentives. More R&D gets created than it costs the government to support it even after 20 years. For large firms, however, the BFTB starts at 3, but falls below 1. Already after 7 years the cumulative additional R&D no longer covers the cumulative government costs to support this R&D. If we take all the firms in our sample, the BFTB falls below the bar of 1 after 13 periods. Thus, if we consider the whole adjustment towards a new steady state, the level-based R&D tax incentives do not come out as very effective. The reason for this ineffectiveness is that level-based tax incentives contain a deadweight loss, namely the tax support on the R&D that would be done in the absence of all support. The importance of the deadweight can be computed by rewriting (12) as

The second term represents the deadweight loss connected to a change in the level-based R&D tax credit. In percentage of the total, the deadweight loss converges to 68% for small firms and to 82% for large firms.

In the second experiment we increase only the incremental-based R&D tax credit by 10%, i.e. the rate appearing in PI. In this case, there can also be a deadweight loss, the fourth term in (13), to the extent that we do not start from an initial steady state, but that some R&D investment was already planned before the tax change. However, this deadweight loss is likely to be small. By simulating the effect of the tax change on R&D and government support for R&D for a period of 20 years, we find that the bang for the buck is about 2.98 for small firms and 2.79 for large firms. The incremental R&D tax credit is much more effective than the level based tax credit, and its effectiveness does not vary much by firm size.