Responsiveness of taxable income to changes in the corporate income tax rate of small businesses

Summary

Corporations, like individuals, are responsive to changes in their tax rate. An increase in the corporate tax rate might not increase tax revenue by the same magnitude. Indeed, corporations might reduce their taxable income in response to tax increases. This response is generally referred to in the economic literature as the corporate elasticity of taxable income (CETI) where the elasticity is a measure of how sensitive taxable income is to taxation.

The aim of this report is to estimate the magnitude of changes to Canadian-controlled private corporations’ taxable income in response to changes in the CIT rate. This report relies on the bunching approach to estimate the CETI. It uses administrative firm-level data reported on T2 Corporate Income Tax returns from 2008 to 2019. This empirical method uses changes to incentives created by discrete changes in the tax system at a specific point, called the kink point. This report uses the change in the marginal tax rate faced by CCPCs eligible to the small business deduction at $500,000 as the kink point.

We find that estimates of the CETI for Canadian-controlled private corporations range from 0.26 in New Brunswick to 1.43 in Alberta. Summary Table 1 presents the results of our elasticity estimates by province as well as a 95% confidence interval.

This report also provides an illustrative example of applying the estimated elasticities to a revenue estimation of an increase in the small business tax rate using 2019 tax data. Considering the behavioural response of CCPCs following a one percentage point increase in the federal small business tax rate reduces the federal revenue estimate by 7.6 per cent compared to the estimate where no behavioural changes are incorporated. In other words, not considering the behavioural response overestimates the federal revenue increase by 8.2 per cent.

Introduction

Corporations, like individuals, are responsive to changes in their tax rate. An increase in the corporate tax rate might not increase tax revenue by the same magnitude. Indeed, corporations might reduce the taxable income they will report either through a reduction in real economic activity (for example by relocating some of its productive activities in another jurisdiction), or through more “cosmetic” changes that have an impact on how income is reported for tax purposes (for example using non-capital losses from previous years that can be carried forward). This response is generally referred to in the economic literature as the corporate elasticity of taxable income (CETI) where the elasticity is a measure of how sensitive taxable income is to taxation.

There are several estimates in the literature of the elasticity of taxable income with respect to changes in the corporate income tax (CIT) rate.[^1] These estimates vary widely depending on the country studied, and the data and method used. To our knowledge, there exists only two papers published in peer-reviewed journals that have attempted to estimate the corporate elasticity of taxable income in the Canadian context.[^2] However, these two papers focus on differences in provincial CIT rates and the ensuing interprovincial income shifting.

The aim of this report is to estimate the magnitude of changes to Canadian-controlled private corporations’ taxable income in response to changes in the CIT rate. This elasticity is a critical piece of information in evaluating revenue implications of proposed changes to the CIT rate. This report relies on the bunching approach to estimate the CETI. The approach uses administrative firm-level data, obtained from the Canada Revenue Agency as reported on T2 Corporate Income Tax returns, and features of the Canadian tax system to elicit behavioural responses.

The obtained estimates, which rely on the combined federal-provincial statutory tax rate, can be readily used in evaluating changes to the Federal small business tax rate. We find that estimates of the CETI for Canadian-controlled private corporations range from 0.26 in New Brunswick to 1.43 in Alberta.

The rest of the report proceeds as follows. The next section briefly explains the methodology while section 2 presents the data used for the estimation. Section 3 summarizes the key results and section 4 presents an application of our elasticity estimates to the revenue estimation of a change in the Federal CIT rate for small businesses. Finally, section 5 concludes.

1. Methodology

This report relies on the bunching approach. This empirical method developed by Saez (2010) and Chetty et al. (2011) uses changes to incentives created by discrete changes in the tax and transfer system at a specific point. Here, the change of interest is a discrete change to the marginal tax rate on taxable income faced by Canadian-controlled private corporations (CCPCs). The point where there is a change in the marginal tax rate is called the kink point. For example, CCPCs will usually face a change in the corporate tax rate at $500,000 of taxable income (the limit of the small business deduction (SBD)) where income above the threshold will be taxed at a higher rate than the income below the same threshold.  

The presence of a kink point in the tax schedule will lead some firms to choose not to increase their income slightly above the threshold because it would not be worth the marginal cost of obtaining the extra income. Thus, theoretically, we would expect to observe more firms earning exactly the amount of income at the threshold than we would observe in the absence of this discrete change in the marginal tax rate and less firms just after the kink. In other words, corporations will “bunch” at the kink point.

This theoretical prediction can be observed in the Canadian corporate tax data. Figure 1 shows the empirical distribution of taxable income of CCPCs eligible to the SBD in Ontario from 2012 to 2015 around the $500,000 kink point. There is a large mass of corporations at and around this specific kink point. Without this point, we would expect a flatter profile to the figure, as can be seen further away from the kink where there are no discrete changes to the corporate tax rate. We call “bunching mass” the mass of firms that locate at the kink point in excess of the number of firms we would observe in the counterfactual scenario without the kink.

T2 Administrative data;

Statistics Canada.

T2 Administrative data;

Statistics Canada.

The key insight of the bunching approach is that the more corporations “bunch” by reducing income to the kink point the more they are sensitive to changes in the tax rate, i.e. the larger the elasticity of taxable income is the larger the bunching mass will be.

To motivate this approach where there is a link between the bunching mass and the elasticity parameter, we use a neoclassical model of the firm where it seeks to maximise its value to shareholders. Further details of the model can be found in Appendix C.

To estimate the corporate elasticity of taxable income from this bunching mass, we use the methodology from Bertanha, McCallum and Seegert (2022).[^3] This method relies on the fact that bunching can be reframed as a censored regression model. More specifically it uses a mid-censored Tobit model to identify the elasticity using data truncated in an interval around the kink point.

Finally, the theoretical prediction that every bunching corporation will choose the exact taxable income of the kink point is very strong. As can be seen in Figure 1, there is extra mass around the $500,000 kink point and not just specifically at the kink. In practice, this can be caused by many things such as optimizing frictions like adjustment costs which would prevent corporations to perfectly choose the level of taxable income. It can also be measurement errors and other distortions. Conceptually, these firms are attempting to bunch and should therefore be counted in the bunching mass on which the estimate of the elasticity relies upon. To handle this issue, we use a filtering method that fits a polynomial to the empirical distribution of taxable income, excluding observations in a specified window around the kink, to create a counterfactual distribution in the excluded interval. Using this distribution, we obtain a “filtered” taxable income for each observation of the data from which we can proceed in estimating the corporate elasticity of taxable income.[^4]

2. Data

We use CORTAX data which is a dataset of the universe of all T2 Corporate Tax Returns and their schedules filed by Canadian corporations from 2000 onwards. It contains an average of about 2 million tax filings per year. This database is generated by the Canada Revenue Agency and shared with Statistics Canada. PBO researchers accessed an anonymized version of the microdata through Statistics Canada’s Canadian Centre for Data Development and Economic Research (CDER).

We constructed multiple samples where for each sample we kept together corporations facing the same combined federal-provincial statutory tax rate, before and after the kink throughout a given tax year. A table of CIT rates by year and province is presented in Appendix A and the full list of subsamples and their characteristics is detailed in Appendix B.

Corporations eligible for the small business deduction (SBD) face a lower tax rate on their first $500,000 of taxable income (called the business limit). Taxable income in excess of $500,000 will then be taxed at the general CIT rate. For example, sample 16 contains corporations in Ontario with a tax year beginning on or after January 1, 2012, and ending on or before December 31, 2015. These corporations faced a combined rate of 15.5% (federal rate of 11% and provincial rate of 4.5%) on their first $500,000 of taxable income and then a combined rate of 26.5% (federal rate of 15% and provincial rate of 11.5%) after the kink.

In some situations, the business limit of a CCPC can be lower than $500,000.[^5] Corporations with a different business limit would not face the kink at the same value of taxable income and thus would have an incentive to bunch at that different value. To avoid having these corporations “contaminate” the distribution around the $500,000 kink, we have excluded them from all samples used.[^6] We also excluded inactive corporations.[^7]

Canadian-controlled private corporations (CCPC) that are considered “small”, that is they have a total taxable capital of less than $10 million, are eligible for the small business deduction. The SBD allows for a corporation to pay a lower rate of tax both at the federal and provincial level on the first $500,000 of taxable income (known as the business limit). The business limit is gradually reduced if the CCPC earns between $50,000 and $150,000 of passive investment income or if it has a total taxable capital between $10 million and $50 million. Corporations that are not CCPCs (publicly traded corporations and other private corporations) face the general CIT rate on all their taxable income.

3. Estimation Results

Table 1 presents the results of our elasticity estimates by province as well as a 95% confidence interval.[^8] As can be seen in Appendix B, some provinces were represented in more than one sample. For these provinces, the elasticity presented in the table is an inverse-variance weighted average of the different samples.[^9]

The estimates range from 0.26 in New Brunswick to 1.43 in Alberta. CCPCs in provinces with significant oil & gas revenue (Newfoundland and Labrador, Saskatchewan, and Alberta) tend to have higher elasticity estimates, which could suggest industry specific differences. Unfortunately, the North American Industry Classification System (NAICS) codes available with the tax data are self-reported, and are missing for about 20% of the CCPCs, and therefore do not allow for a robust estimation by industry.

These estimates are slightly above what is found in the literature, e.g. Gruber and Rauh (2007), but in line with the estimates from Coles et al. (2022). The authors also found that small private corporations in the U.S. were more sensitive to a change in the tax rate than public corporations as they could rely more on earnings management techniques to reduce their taxable income. It is reasonable to believe that Canadian private corporations also have more flexibility in their financial reporting, which could very well explain the higher elasticities obtained in our analysis.

4. Illustrative Application

The PBO has designed a microsimulation model which is used to estimate changes in federal government revenue brought about by modifications to the corporate income tax system.[^10] The model computes mechanically the revenue impacts of a tax change. For example, if a corporation has a taxable income of $100,000 and is facing the small business CIT rate of 9% at the federal level, under the baseline scenario (that is the current system) it will pay $9,000 in tax ($100,000 * 9%). If we wanted to measure the change in tax revenue from increasing the rate by one percentage point to 10%, our model would now calculate tax payable as $100,000 * 10% which would yield a federal tax payable of $10,000. Hence, the revenue impact from that increase in the tax rate would be $1,000 ($10,000 - $9,000).

The behavioural impact can be measured by the following formula

$$dTI=\ -e\ast TI\ast d\tau/(1-\tau)$$

where: $dTI$ is the change in taxable income reported, $e$ is the corporate elasticity of taxable income (CETI), TI is taxable income reported by the corporation prior to the increase in the tax rate, $d\tau$ is the change in the tax rate and d\tau is the combined federal and provincial tax rate prior to the increase.

If we assume a CETI of 0.5 and a provincial tax rate of 3% for small businesses, we can substitute these values with those from the previous example in the equation above and obtain a change in taxable income reported of -$568.18. Therefore, in response to the one percentage point increase in the federal CIT rate, the corporation would now only report $99,431.82 of taxable income. When multiplying this amount by the increased rate of 10%, we obtain a new federal tax revenue of $9,943.18. Thus, when accounting for the behavioural effect we see that the increase in federal revenue was only $943.18 rather than the $1,000 we estimated from the mechanical calculation, which is a reduction of $56.82 (-5.7%) from our mechanical estimate. If we assume a CETI of 1.0, the reduction would be equal to $113.64 (-11.4%).

Using the elasticity estimates reported in section 3, Table 2 presents the impact on federal revenue of a 1 percentage point increase in the small business rate (which corresponds to a 1 percentage point reduction in the small business deduction rate). The revenue increases are calculated using our microsimulation model.[^11]

In the mechanical estimate, the increase translates into additional federal revenue of $1,100.4 million. However, when we account for the behavioural component, the increase in federal revenue is estimated to be of $1,017.1 million. Therefore, not considering the behavioural response of CCPCs following an increase in the tax rate overestimates the federal revenue increase by 8.2 per cent.[^12]

5. Concluding Remarks

The estimates presented in this report are derived from the responses of small CCPCs and may not be representative of the responses to taxation of larger corporations. Future work could be done to estimate the elasticity of large businesses facing the general CIT rate. However, the bunching methodology requires a discrete change in the tax schedule faced by the firms. For these large corporations the only kink in the tax schedule is at a taxable income of zero. Indeed, negative income is not taxed (facing a rate of 0%) but above zero the corporation starts facing a CIT rate of 15% at the federal level plus the provincial CIT rate in effect. Estimating the CETI using the bunching methodology requires some modifications to the approach used in this report as in Agostini et al. (2022) or requires a different method as in Coles et al. (2022).

Furthermore, as mentioned in the introduction, the behavioural response of corporations may encompass many different behaviours. Although the theoretical model used to motivate the approach implies a real response through the choice of capital, it does not imply that what we measure is due entirely to real responses. Further work could be done to try and disentangle real earnings versus earnings management responses. In addition, the elasticities presented in this report capture responses along the intensive margin, i.e. changes in the level of taxable income, but do not capture changes along the extensive margin such has the decision to operate or perhaps to relocate to another jurisdiction.

Federal and Provincial Tax Rates

Data Samples

Model

To derive a parametric relationship between bunching at a kink point in the tax schedule and the elasticity of taxable income with respect to the net-of- corporate tax rate, we use the following two-period neoclassical model of firms.[^13]

Consider firms with heterogeneous productivity, captured by $A_i$, that exist for two periods. Each firm is owned by a single shareholder. In the first period, firm $i$ begins with retained earnings $K_1$ and it must choose the amount of dividend payments ( $D\geq0$ ) to distribute and the amount of equity ( $E\geq0$ ) to issue. The choices implicitly determine the amount of capital the firm has in the second period, i.e. $K_2=K_1+E-D$.

$$Y\left(K_2\right)=\frac{1+e}{e}{A_i^{\frac{1}{1+e}}K}_2^{\frac{e}{1+e}},$$

where $e$ is the elasticity of taxable income with respect to net-of-tax rate. Shareholders can also hold government bonds which yield a tax-exempt rate of return $r>0$. Finally, at the end of period 2, all firms liquidate implying that all principal and profits are returned to the shareholders. Firms face a piecewise linear tax system where the marginal tax rate on taxable income is $t_0$ for $Y_i\le\kappa$ and $t_1$ for $Y_i>\kappa$. The firm’s problem of maximizing the present value of the firm to the shareholder is

$$\begin{aligned}\max_{\mathcal{K}_2}V=&K_1-\frac{r}{1+r}K_2+\frac{\mathbb{I}(Y(K_2)\leq\kappa)(1-t_0)Y(K_2)}{1+r}\&+\frac{\mathbb{I}(Y(K_2)>\kappa){(1-t_0)\kappa+(1-t_1)[Y(K_2)-\kappa]}}{1+r},\end{aligned}$$

where $\mathbb{I}$ is the indicator function. [^14] The solution to the choice of capital in the second period leads to the following piecewise linear function for taxable income:

$$Y_i=\begin{cases}\frac{1+e}er^{-e}(1-t_0)^eA_i,\quad A_i\leq\underline{A}\\kappa,\quad\underline{A}<A_i<\overline{A}\\frac{1+e}er^{-e}(1-t_1)^eA_i,\quad A_i\geq\overline{A},&\end{cases}$$

where thresholds $\underline{A}$ and $\overline{A}$ are

$$\underline{A}=\frac{\kappa}{\frac{1+e}{e}r^{-e}\left(1-t_0\right)^e}\ \ \ and \ \ \ \overline{A}=\frac{\kappa}{\frac{1+e}{e}r^{-e}\left(1-t_1\right)^e}$$

Firms with productivity $A_i$, such that $\underline{A}<A_i<\ \overline{A}$, have a non-interior solution and bunch at the kink. Notice that the solution has a similar form to the ones found in the bunching literature in different context e.g. Saez (2010) and conforms to the framework found in Berthanta, McCallum and Seegert (2022) where the natural logarithm of taxable income is used.

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