# Analytical Studies Branch Research Paper SeriesMarket Behaviour Versus Tax Planning Responses to Changes in Marginal Income Tax Rates Among Older Couples

by Derek Messacar
Social Analysis and Modelling Division, Statistics Canada

Release date: November 19, 2018

## Abstract

The standard model of labour supply predicts that individuals’ taxable incomes will bunch at convex kink points in the budget set created by government tax and transfer systems. However, empirical evidence of such behaviour is scarce. Using administrative tax data from Canada, this paper estimates bunching responses in taxable income among older individuals at discontinuities in marginal tax rates created by federal and provincial and territorial systems, from 2001 to 2012. The results show that bunching is prevalent across the income distribution, but this is mostly driven by married individuals from 2007 onward. Further analysis reveals this occurs predominantly because pensioners split some of their pension income with their spouses who tend to have lower marginal tax rates. Pensioners do this pursuant to the introduction of this tax planning program in the 2007 federal budget. These findings offer credible evidence of significant intra-household tax planning behaviour that depends on the availability of deductions.

Keywords: pension income; elasticity of taxable income; tax planning; income splitting; bunching; empirical density design

## Executive summary

This paper investigates the extent to which older Canadian taxfilers, aged 60 to 69, respond to predictable changes in marginal tax rates created by the tax and transfer system by exhibiting sorting behaviour in taxable income. More precisely, the prediction from the standard model of labour supply that individuals’ taxable incomes bunch at convex kink points in their budget sets is tested, in an empirical density design.

Using administrative tax data for the years from 2001 to 2012, the analysis assesses how individuals respond to changes in marginal tax rates created at the lower bounds of the second, third and fourth federal tax brackets; the lower bounds of the second and third provincial and territorial tax brackets; and the thresholds at which the Old Age Security and Employment Insurance benefits start being clawed back through recovery taxes. The results indicate the following.

1. Taxable income is responsive to the changes in tax rates at the thresholds analyzed. Bunching is observed at every threshold. Hence, individuals are sorting in their taxable incomes in response to the tax and transfer system, as expected.
2. Bunching appears the most prevalent among married (either legally married or in a common-law relationship) individuals from 2007 onward.

However, a closer inspection shows the following:

1. Bunching is driven primarily by individuals who are married and who used the pension income splitting provision of the tax code, pursuant to the introduction of this program in the 2007 federal budget.
2. In contrast, the bunching responses to changes in income tax rates appear to be negligible among
1. unmarried individuals
2. married individuals before 2007
3. married couples who do not have at least one spouse receiving private pension income and are ineligible for pension income splitting.

These findings offer credible evidence of intra-household tax planning behaviour that depends on the availability of deductions. Effectively, couples are not only using the pension income splitting program to reduce their own tax liabilities but also taking into account the marginal tax rates of their spouses to minimize household tax liabilities, as expected.

## 1 Introduction

Income taxes are often found to have small effects on individuals’ labour supply decisions and other economic behaviour (e.g., investment decisions) and large effects on individuals’ tax planning responses (Saez, Slemrod and Giertz 2012). Individuals can delay or avoid paying higher income taxes in many ways, such as by making tax-deductible charitable donations or contributions to retirement savings vehicles (Stiglitz 1985; Auten, Sieg and Clotfelter 2002; Bakija and Heim 2008). Shifting income from the personal to the corporate tax base is also a potential tax planning channel among business owners (Goolsbee 2000; Gordon and Slemrod 2000; Kreiner, Leth-Petersen and Skov 2014). Evidence suggests that the elasticity of taxable income (ETI) with respect to the marginal tax rate—a measure once viewed as a sufficient statistic for the efficiency cost of taxation (Feldstein 1995, 1999; Slemrod and Yitzhaki 2002)—depends on the availability of deductions and, therefore, can be manipulated by policy makers (Kopczuk 2005).

In general, the ETI is an incomplete measure of the deadweight loss from taxation when some burden of sheltering income is incurred as a resource or transfer cost (Chetty 2009). If the unit of taxation is the individual, sheltering can occur within households when family members split income—provided that resources are not shared, as in the unitary model of the household (Kornhauser 1993; Cantillon and Nolan 1998; Freiler, Stairs and Kitchen 2001; Gelber 2014). Consequently, a better understanding of the extent to which older couples reduce personal income tax liabilities through splitting warrants investigation.

The goal of this study is to assess the extent to which income taxes induce changes in market behaviour (sometimes called “real” responses) versus changes in tax planning strategies. The paper focuses particularly on income splitting between spouses as the channel through which tax avoidance may occur. Market response refers to a change in actual economic activity by individuals—such as a change in employment income through an adjustment in the number of hours worked. Tax planning response refers to the use of allowances, credits and deductions to reduce tax liabilities while holding constant economic behaviour.

The paper makes two key contributions. The first contribution is to use administrative data on a 20% nationally representative sample of Canadian taxfilers, for the years from 2001 to 2012, to estimate, in an empirical density design, the effects of changes in marginal tax rates on the taxable incomes of older individuals aged 60 to 69 (Saez 2010; Chetty et al. 2011). The standard model of labour supply predicts that individuals will bunch at convex kink points in their budget sets created by government tax and transfer systems, but evidence of such behaviour is scarce (Saez, Slemrod and Giertz 2012). This study finds significant bunching at various convex kink points along the income distribution associated with the lower bounds of the federal and provincial and territorial tax brackets, where marginal tax rates increase discontinuously as a result of tax progressivity. In addition, bunching is observed at two convex kink points where effective marginal tax rates change, namely the income thresholds where Employment Insurance (EI) and Old Age Security (OAS) benefits start being clawed back through recovery taxes. In these cases, responses are observed only among EI recipients and OAS-eligible individuals.

The second contribution of this paper is to estimate how much of this bunching is the result of intra-household tax planning. In theory, the magnitude of tax avoidance or evasion should be proportional to the expected costs of such behaviour, including costs from administration, effort or detection (Allingham and Sandmo 1972; Stiglitz 1985; Slemrod and Yitzhaki 2002). Pension income splitting in Canada is both legal and notional in the sense that it does not require a transfer of income or division of asset ownership. Pension income splitting is a no-cost tax avoidance channel for older couples; consequently, take-up is predicted to be high.Note 1 To separately identify the effect of splitting from other types of market behaviour or tax planning responses, the analysis exploits exogenous variation in individuals’ eligibility to split pension income by marital status and around the introduction of this program.Note 2 Moreover, the data provide information on whether individuals and their spouses are pension income recipients and the actual amounts of income they elect to split. This facilitates a direct comparison of bunching between couples who could have used or did use this tax provision and those who did not use it.

The results of this analysis show that bunching is only weakly observed before pension income splitting was introduced, as well as among unmarried individuals and couples who were ineligible for splitting after the reform was introduced. In contrast, the magnitude of bunching, after pension income splitting was introduced, among individuals collecting a private pension income or whose spouses do so is substantial. Further analysis conditional on whether splitting actually occurs shows that the bunching stems mostly from the use of this program. Within couples, bunching occurs from one of two possible behaviours:

1. an individual, who is a pensioner, sends enough income to a spouse to reduce taxable income to a lower tax bracket; or
2. an individual, whose spouse is a pensioner, receives income only up to the point where taxable income would otherwise enter a higher tax bracket.

Hence, pensioners are not only using this tax planning tool to lower their own tax liabilities but also to lower household tax liabilities, taking into account the marginal tax rates of their spouses. These findings offer credible evidence of intra-household tax planning behaviour that depends on the availability of deductions.

This paper contributes to a growing literature that seeks to disentangle market behaviour from tax planning responses to personal income taxation. Prior research shows that income shifting, both intertemporally and across tax bases, is substantial among high-income earners and the self-employed who have the most access to tax planning technologies (Gordon and Slemrod 2000; Goolsbee 2000; Chetty et al. 2011; le Maire and Schjerning 2013; Kreiner, Leth-Petersen and Skov 2014, 2016; Harju and Matikka 2016). However, few studies consider the extent to which families coordinate to reduce combined tax liabilities. This is likely because many studies that estimate the ETI are carried out using data from the United States, where the unit of taxation is the household. Other studies look at countries where the unit of taxation is the individual, but where household-level tax return data or the policy variation needed for proper identification are not available. A notable exception is Stephens and Ward-Batts (2004), who showed that the 1990 reform from joint to individual taxation in the United Kingdom led to an increase in the sharing of assets claimed by spouses with lower marginal tax rates. Wolfson and Legree (2015) used data from Canada on business owners and their families who work for the business and live in the same household. They posited that business owners make labour and dividend payments strategically to reduce household tax liabilities.Note 3 This paper is among the first to assess how, following the introduction of a mechanism that was explicitly designed to facilitate tax planning at the household level, taxable income responds to marginal tax rates within couples. It also relates more broadly to the work of Gugl (2009), who analyzed intra-household equity considerations of pension income splitting.

Since this paper centres on the responsiveness of older couples to income taxation, it relates to a large literature on the labour supply decisions of the elderly. Many studies investigate how pension receipt or retirement decisions are influenced by the design of public pension plans (Baker and Benjamin 1999; Feldstein and Liebman 2002; Baker, Gruber and Milligan 2003; French and Jones 2012). However, few studies consider the extent to which the tax code is a viable policy instrument for influencing the labour supply decisions of older workers (Schmidt and Sevak 2009; Alpert and Powell 2014; Messacar 2017). Lastly, this paper adds to a developing literature that estimates income responses to taxation using the empirical density design (Saez 2010; Chetty et al. 2011; le Maire and Schjerning 2013; Bastani and Selin 2014; Harju and Matikka 2015).

This paper proceeds as follows. The next section, Section 2, gives an overview of the standard model of labour supply and derives the bunching prediction; it includes a brief discussion of the empirical density approach for estimating excess mass. Section 3 summarizes features of the Canadian income tax system of relevance to the empirical analysis. Section 4 discusses the data and sample selection used in this study. Section 5 presents the baseline results, the analysis of the pension income splitting reform, two placebo checks, and tests of heterogeneous responses. Section 6 concludes.

## 2 Background

This section presents an overview of the theory of labour supply prediction that individuals bunch at convex kink points in their budget sets. Then, the method for estimating this bunching behaviour is briefly discussed. In particular, the theoretical and methodological contributions of Saez (2010) and Chetty et al. (2011), which are of direct relevance herein, are provided. The reader is encouraged to refer to those papers directly, as well as to the wide-spanning ETI literature discussed in Saez, Slemrod and Giertz (2012), for more information.

### 2.1 Theory

Saez (2010) considered the standard model of labour supply, in which an agent $i$ ’s utility depends positively on after-tax income, ${c}_{i}$, and negatively on before-tax income, ${z}_{i}$. The agent prefers to consume more but is hindered by the effort cost of supplying labour to earn more. The utility function is given by ${u}_{i}\left({c}_{i},{z}_{i}\right)$ and satisfies several conditions: (1) $\partial {u}_{i}/\partial {c}_{i}>0$ ; (2) $\partial {u}^{2}/\partial {c}^{2}<0$ ; (3) $\partial u/\partial z<0$ ; and (4) $\partial {u}^{2}/\partial {z}^{2}<0$.

To begin, suppose an agent faces a linear budget set with a constant marginal tax rate $t$, so that after-tax income is $c=z\left(1-t\right)$. A graphical depiction of the solution to this optimization problem is shown in Panel A of Figure 1. The agent will provide effort and earn income up to the point where the marginal benefit of consumption equals the marginal disutility of effort. For agent $i$, this results in the optimal levels of before-tax income, ${z}_{i}^{\star }$, and after-tax income, ${c}_{i}^{\star }$. The assumption that agents are heterogeneous in before-tax income because of underlying differences in preferences or ability is captured by heterogeneity in the utility function. The figure shows how the solution to this optimization problem varies across agents.

Description for figure 1

The title of Figure 1 is “Theoretical prediction of agents’ bunching responses to a convex kink in the budget set as a result of tax progressivity.” Figure 1 consists of three charts: “Panel A — Constant tax rate; “Panel B — Progressive tax rate”; and “Panel C — Bunching.” In Panels A and B, the y axis title is “Consumption, c,” and in Panel C, “Density distribution.” The x-axis title for the three charts is “Before-tax income, z.” The explanation for each panel is given in the explanatory note below, which appears at the bottom of the figure.

Note: Panel A shows the optimal levels of before-tax and after-tax incomes for an agent with preferences given by the indifference curve shown, facing tax rate $t$. Panel B shows how agent $k$, who would optimally consume ${z}_{k}^{\star }$ given a constant tax rate, chooses ${z}_{i}^{\star }$ in the presence of the convex kink changing the marginal tax rate to $t+dt$. This puts agent $k$ on a lower indifference curve (thick solid purple line) than under a constant tax rate (dashed purple line). Agents $i$ and $j$ optimally choose before-tax incomes at or below the convex kink point, and are therefore unaffected by it. Panel C shows the effect of the convex kink on the distribution of before-tax income. The distribution under a constant tax rate is smooth around the kink point (solid blue line). As a result of the kink, agents with before-tax incomes from ${z}_{i}^{\star }$ to ${z}_{i}^{\star }+d{z}_{i}^{\star }$ bunch at ${z}_{i}^{\star }$, creating a spike in the distribution under progressivity (dashed orange line), and the density above ${z}_{i}^{\star }+d{z}_{i}^{\star }$ shifts to ${z}_{i}^{\star }$.

The source for this figure is Statistics Canada, based on the model and bunching prediction of E. Saez, 2010, “Do taxpayers bunch at kink points?”, p. 184.

That the response in taxable income occurs through the labour supply adjustment is referred to as a market behaviour response. In other words, the actual behaviour of economic agents is being affected by income taxation in a standard manner as predicted by economic theory. To understand how workers are expected to respond, suppose that a convex kink were introduced in the budget set at income $\stackrel{˜}{z}$ by increasing the marginal tax rate from $t$ to $t+dt$ on income earned above this tax threshold. Panel B of Figure 1 shows that, in this case, workers with earnings below the tax threshold (agents $i$ and $j$ in the figure) remain unaffected and continue to consume their initial amounts. However, an agent earning from $\stackrel{˜}{z}$ to $\stackrel{˜}{z}+d\stackrel{˜}{z}$ (agent $k$ in the figure), who initially consumed ${c}_{k}^{\star }$ under the scenario of a constant tax rate, now finds it optimal to consume ${c}_{i}^{\star }$. Hence, the convex kink in the budget set results in an excess of agents who optimally bunch at the convex kink point in before-tax income. Panel C of Figure 1 shows how the density distribution of before-tax (taxable) income is expected to look—within the context of the theory—under the scenarios of a constant or progressive piecewise-linear tax system. In contrast, a “tax planning” response refers to the use of allowances, credits or deductions to modify taxable income so that bunching occurs but without any change in actual economic behaviour.

The standard prediction from the economic model assumes labour income (or another type of income that requires effort) is the primary income source. Especially among older workers, adjustments may be prevalent—compared with young and middle-aged workers—through transitions into flex-time, part-time (e.g., partial retirement) or bridge employment. If an individual’s main source of income requires no effort to collect, such as pensions, the size of the response is unclear. The response may be smaller because collecting income beyond a particular tax threshold has no effort cost. However, pensioners face an intertemporal trade-off between receiving an extra dollar at a higher marginal tax rate and delaying the receipt of that dollar until the following year, at a lower marginal tax rate. Bunching may be especially prevalent because the amount of pension income received can be manipulated. This issue is especially important in the context of this study, because only approximately one-third of taxfilers have employment earnings.

In addition, labour supply may not respond as predicted by the stylized model for many reasons. For example, many workers may have strict preferences to work a fixed number of hours per week. Similarly, employers may offer contracts with hours constraints. Search costs of changing jobs can significantly reduce the extent to which bunching at discontinuities in the marginal tax schedule occurs—this issue is explored in detail by Chetty et al. (2011). On balance, common labour frictions that are not always well represented in canonical models can significantly affect actual responses. The findings from this study, which centre on the introduction of pension income splitting, serve to credibly identify the effect of this tax planning tool on the ETI, which is analogous to that of a difference-in-differences approach.

### 2.2 Estimation

The approach developed by Saez (2010) and extended by Chetty et al. (2011) for estimating bunching in an empirical density design is used. To that end, the “bunch_count” Stata module (an “.ado” file) written by Olsen (2011) is employed in the analysis. This empirical procedure is briefly described here, with a discussion of how to interpret the results.

The approach begins by normalizing taxable income relative to the convex kink point analyzed; for example, having relative taxable income equal to zero in the reference year means taxable income was exactly equal to the tax threshold. Using this normalized taxable income variable, the study groups individuals with incomes within $10,000 on either side of the tax threshold into bins of width$250 (e.g., from -$10,000 to -$9,751, from -$9,750 to -$9,501, from -$9,500 to -$9,251), and bin counts (frequencies) are computed.

Then, a counterfactual density distribution is estimated. This gives a prediction of what the distribution would have looked like under a constant tax rate over the relevant range of taxable income. The counterfactual is estimated by fitting a polynomial to the bin counts, excluding data near the kink, where actual bunching would influence these results. The procedure adjusts for the fact that individuals at the convex kink point must come from other points to the right of this kink. The estimate of bunching is the excess mass around the convex kink point relative to the average density of the counterfactual earnings distribution within a range of income close to the convex kink point.Note 4

For a bunching estimate $b$ obtained from this procedure, the point estimate indicates that the excess mass around the convex kink point is $b$ % of the height of the counterfactual distribution within the range of income close to the convex kink point. A parametric bootstrap procedure is used to compute standard errors for $b$.

## 3 Institutional details

Personal income tax in Canada is based on a measure of taxable income minus any permitted deductions; then credits are applied to determine the net amount payable. The unit of taxation in Canada is the individual. However the income tax system recognizes that individuals may have reduced abilities to pay income taxes when they have dependent spouses or relatives. This is provided for in the form of additional credits and of transfers of certain dependents’ unused credits to the taxpayer.

Income taxes are determined at both federal and provincial and territorial levels. Each government applies its own tax rates to a uniform measure of taxable income and offers its own credits to determine the net amount of income taxes owed. In 2012, federal taxable income was divided into four brackets. The tax rate was 15% for the first bracket ($42,707 or less), 22% for the second bracket (from$42,708 to $85,414), 26% for the third bracket (from$85,415 to $132,406), and 29% for the fourth bracket ($132,407 or more). This tax progressivity creates the convex kink points in individuals’ budget sets that are expected to induce bunching responses. The federal basic exemption in 2012 was $10,822, such that the marginal tax rate applied to taxable income below this threshold was 0%.Note 5 At the provincial and territorial levels, the income tax structures and rates are significantly heterogeneous. For example, Alberta imposed a flat tax rate of 10% in 2012 on taxable income above a basic personal exemption of$17,282. The provinces that had only two tax brackets in 2012 were Newfoundland and Labrador, Prince Edward Island, Quebec, Ontario, Manitoba and Saskatchewan. The provinces and territories with three tax brackets in 2012 were New Brunswick, Northwest Territories, Yukon and Nunavut. The provinces with four tax brackets in 2012 were Nova Scotia and British Columbia. In general, provinces and territories set thresholds for their tax brackets that fall within the federal tax brackets. For example, in 2012, the lower bounds of the second and third brackets were the following: $32,893 and$65,785 in Newfoundland and Labrador; $39,020 and$78,043 in Ontario; and $37,013 and$74,028 in British Columbia. The differences between federal and provincial and territorial brackets are useful for the empirical analysis to separately identify bunching at these various convex kink points.

In addition to estimating bunching at these federal and provincial and territorial tax thresholds, this study also considers the extent to which individuals respond to clawback provisions in the OAS and EI programs. First, the OAS pension is a demogrant for individuals starting at age 65 (Baker, Gruber and Milligan 2003) based on Canadian legal status and residence requirements; the maximum annual OAS pension was $6,540 in 2012. However, if annual net world income exceeds a pre-specified amount, recipients must repay part or all of their pension benefits. In 2012, the threshold was$69,562, and the recovery tax rate was 15%.

### 5.2 Bunching analysis

Graphical inspections of bunching at the tax thresholds are shown in Charts 2-1 and 2-2. Chart 2-1 looks at data from the pre-reform period, and Chart 2-2 looks at the post-reform period. Each panel shows the distribution of taxable income relative to the relevant tax threshold over an interval spanning $10,000 on either side of that threshold. Each dot shows the percentage of individuals in the sample with taxable incomes within a bin of width$250.Note 9 In addition, each panel shows the estimated counterfactual distribution based on the procedure of Chetty et al. (2011).Note 10 This analysis appears to show that individuals are somewhat responsive to the discontinuous increases in their marginal tax rates in both periods, where spikes in the distributions of taxable income are observed at most tax thresholds.

Data table for Chart 2-1
Data table for Chart 2-1
Table summary
This table displays the results of Data table for Chart 2-1. The information is grouped by Bin (appearing as row headers), Panel A — Second federal tax, Panel B — Second provincial/territorial tax, Panel C — Third federal tax, Panel D — Third provincial/territorial tax, Panel E — Fourth federal tax, Panel F —Old Age Security recovery tax, Panel G — Employment Insurance recovery tax, Actual and Predicted, calculated using percent units of measure (appearing as column headers).
Bin Panel A — Second federal tax Panel B — Second provincial/territorial tax Panel C — Third federal tax Panel D — Third provincial/territorial tax Panel E — Fourth federal tax Panel F —Old Age Security recovery tax Panel G — Employment Insurance recovery tax
Actual Predicted Actual Predicted Actual Predicted Actual Predicted Actual Predicted Actual Predicted Actual Predicted
percent
-10,000 1.546 1.524 1.487 1.476 2.022 2.031 2.062 2.095 1.587 1.654 2.023 1.987 2.111 2.157
-9,750 1.512 1.525 1.464 1.477 2.001 2.020 2.114 2.074 1.715 1.628 1.991 1.968 2.040 2.083
-9,500 1.502 1.525 1.474 1.477 2.043 2.006 2.077 2.053 1.574 1.607 1.919 1.946 2.167 2.025
-9,250 1.516 1.523 1.473 1.475 2.018 1.991 2.067 2.031 1.653 1.591 1.873 1.921 2.004 1.979
-9,000 1.532 1.520 1.477 1.473 1.975 1.973 1.940 2.008 1.623 1.579 1.905 1.895 1.847 1.941
-8,750 1.514 1.517 1.475 1.470 1.946 1.954 1.956 1.984 1.397 1.568 1.835 1.867 1.949 1.911
-8,500 1.530 1.513 1.474 1.466 1.929 1.934 1.958 1.960 1.631 1.560 1.812 1.838 1.878 1.885
-8,250 1.509 1.509 1.458 1.461 1.865 1.913 1.940 1.935 1.680 1.553 1.772 1.809 2.004 1.862
-8,000 1.497 1.504 1.445 1.456 1.904 1.890 1.900 1.910 1.494 1.547 1.791 1.781 1.756 1.841
-7,750 1.517 1.499 1.435 1.451 1.800 1.867 1.902 1.884 1.490 1.540 1.815 1.752 1.756 1.821
-7,500 1.470 1.494 1.452 1.446 1.885 1.844 1.871 1.858 1.415 1.534 1.732 1.725 1.746 1.801
-7,250 1.490 1.489 1.450 1.441 1.861 1.820 1.864 1.831 1.521 1.527 1.699 1.698 1.730 1.780
-7,000 1.504 1.484 1.419 1.436 1.779 1.795 1.823 1.804 1.525 1.520 1.689 1.672 1.822 1.759
-6,750 1.476 1.480 1.452 1.431 1.743 1.771 1.725 1.777 1.525 1.512 1.659 1.648 1.725 1.737
-6,500 1.476 1.475 1.431 1.426 1.737 1.746 1.761 1.750 1.583 1.503 1.706 1.625 1.675 1.714
-6,250 1.457 1.470 1.420 1.421 1.742 1.721 1.739 1.723 1.485 1.494 1.603 1.603 1.725 1.689
-6,000 1.477 1.465 1.431 1.417 1.768 1.696 1.672 1.696 1.565 1.483 1.552 1.582 1.527 1.664
-5,750 1.452 1.461 1.417 1.412 1.680 1.672 1.677 1.669 1.450 1.472 1.573 1.563 1.766 1.639
-5,500 1.434 1.456 1.399 1.408 1.634 1.647 1.653 1.643 1.371 1.460 1.493 1.545 1.690 1.612
-5,250 1.472 1.451 1.387 1.404 1.634 1.623 1.591 1.616 1.614 1.447 1.513 1.528 1.649 1.586
-5,000 1.447 1.446 1.416 1.400 1.601 1.598 1.538 1.590 1.472 1.434 1.584 1.512 1.502 1.560
-4,750 1.474 1.441 1.397 1.397 1.602 1.574 1.612 1.565 1.415 1.420 1.575 1.497 1.507 1.534
-4,500 1.432 1.436 1.402 1.393 1.510 1.550 1.582 1.539 1.260 1.406 1.440 1.483 1.502 1.509
-4,250 1.433 1.430 1.388 1.390 1.516 1.527 1.560 1.515 1.313 1.391 1.395 1.470 1.467 1.485
-4,000 1.415 1.424 1.380 1.386 1.472 1.503 1.434 1.490 1.393 1.376 1.443 1.457 1.538 1.461
-3,750 1.412 1.418 1.384 1.383 1.429 1.480 1.415 1.467 1.357 1.362 1.393 1.445 1.441 1.440
-3,500 1.371 1.412 1.385 1.379 1.444 1.457 1.431 1.444 1.397 1.347 1.416 1.434 1.467 1.419
-3,250 1.405 1.405 1.363 1.376 1.422 1.435 1.426 1.421 1.260 1.333 1.391 1.422 1.426 1.401
-3,000 1.402 1.398 1.352 1.372 1.421 1.412 1.433 1.399 1.317 1.318 1.332 1.411 1.426 1.384
-2,750 1.369 1.390 1.381 1.368 1.435 1.390 1.437 1.378 1.371 1.304 1.417 1.401 1.365 1.368
-2,500 1.379 1.382 1.354 1.363 1.402 1.368 1.351 1.357 1.309 1.291 1.446 1.390 1.289 1.355
-2,250 1.385 1.373 1.351 1.359 1.370 1.347 1.311 1.337 1.260 1.278 1.394 1.379 1.294 1.343
-2,000 1.356 1.364 1.351 1.354 1.315 1.325 1.312 1.317 1.335 1.265 1.382 1.368 1.253 1.332
-1,750 1.391 1.355 1.356 1.349 1.274 1.304 1.314 1.298 1.300 1.254 1.416 1.357 1.238 1.323
-1,500 1.349 1.345 1.344 1.343 1.308 1.284 1.242 1.279 1.141 1.242 1.310 1.345 1.411 1.315
-1,250 1.346 1.334 1.341 1.337 1.247 1.263 1.241 1.260 1.238 1.232 1.340 1.333 1.208 1.309
-1,000 1.337 1.323 1.344 1.330 1.279 1.243 1.242 1.242 1.322 1.222 1.377 1.321 1.421 1.303
-750 1.352 1.312 1.347 1.323 1.243 1.223 1.276 1.225 1.340 1.213 1.365 1.308 1.071 1.297
-500 1.343 1.301 1.355 1.315 1.266 1.203 1.207 1.208 1.278 1.204 1.355 1.294 1.208 1.292
-250 1.465 1.289 1.369 1.307 1.290 1.184 1.168 1.190 1.331 1.196 1.579 1.280 1.264 1.287
0 1.336 1.276 1.322 1.298 1.217 1.165 1.143 1.174 1.388 1.189 1.377 1.266 1.548 1.282
250 1.264 1.264 1.297 1.289 1.172 1.146 1.164 1.157 1.172 1.182 1.377 1.251 1.512 1.276
500 1.250 1.251 1.289 1.279 1.109 1.127 1.141 1.140 1.132 1.176 1.269 1.235 1.426 1.269
750 1.232 1.238 1.277 1.268 1.093 1.109 1.163 1.124 1.172 1.170 1.306 1.219 1.380 1.261
1,000 1.211 1.225 1.245 1.257 1.079 1.091 1.136 1.108 1.070 1.164 1.229 1.202 1.208 1.251
1,250 1.198 1.211 1.257 1.246 1.049 1.073 1.100 1.091 1.132 1.159 1.157 1.184 1.314 1.241
1,500 1.192 1.198 1.256 1.234 1.077 1.056 1.073 1.075 1.163 1.154 1.115 1.166 1.208 1.228
1,750 1.168 1.185 1.182 1.222 1.018 1.039 1.028 1.059 1.203 1.149 1.037 1.148 1.274 1.213
2,000 1.133 1.171 1.201 1.209 1.035 1.022 1.022 1.042 1.176 1.144 1.097 1.129 1.106 1.196
2,250 1.156 1.158 1.174 1.196 0.980 1.006 1.032 1.026 1.167 1.139 1.072 1.110 1.101 1.177
2,500 1.134 1.145 1.201 1.183 0.987 0.989 0.980 1.009 1.074 1.134 1.063 1.090 1.116 1.156
2,750 1.127 1.132 1.160 1.170 0.946 0.973 0.968 0.993 0.964 1.128 0.983 1.070 1.091 1.133
3,000 1.112 1.119 1.148 1.156 0.951 0.958 1.028 0.976 1.203 1.123 1.055 1.050 1.111 1.107
3,250 1.079 1.106 1.153 1.143 0.939 0.943 0.986 0.959 0.986 1.117 0.966 1.030 0.908 1.080
3,500 1.067 1.094 1.108 1.129 0.897 0.927 0.921 0.942 1.030 1.111 0.997 1.010 1.076 1.051
3,750 1.080 1.082 1.101 1.116 0.939 0.913 0.887 0.925 1.048 1.105 0.898 0.990 1.005 1.020
4,000 1.063 1.070 1.076 1.103 0.890 0.898 0.898 0.908 1.074 1.098 0.904 0.969 0.913 0.987
4,250 1.044 1.059 1.076 1.090 0.861 0.884 0.907 0.891 1.172 1.091 0.972 0.949 0.939 0.954
4,500 1.052 1.048 1.074 1.077 0.857 0.870 0.873 0.874 1.220 1.083 0.863 0.929 0.974 0.919
4,750 1.027 1.037 1.061 1.064 0.841 0.857 0.872 0.858 1.070 1.075 0.905 0.909 0.812 0.885
5,000 1.022 1.026 1.039 1.053 0.813 0.843 0.833 0.841 0.933 1.066 0.900 0.890 0.898 0.850
5,250 1.000 1.016 1.039 1.041 0.858 0.830 0.795 0.825 1.127 1.057 0.844 0.871 0.822 0.816
5,500 1.020 1.006 1.013 1.030 0.797 0.817 0.811 0.808 1.039 1.048 0.846 0.852 0.721 0.783
5,750 0.985 0.997 1.028 1.020 0.789 0.805 0.798 0.793 0.955 1.039 0.862 0.833 0.670 0.752
6,000 0.979 0.987 1.018 1.010 0.773 0.793 0.798 0.777 0.990 1.029 0.777 0.816 0.746 0.722
6,250 0.978 0.978 0.973 1.000 0.758 0.781 0.765 0.762 1.074 1.019 0.794 0.798 0.710 0.695
6,500 0.960 0.969 0.995 0.992 0.780 0.769 0.767 0.748 1.119 1.009 0.808 0.781 0.675 0.670
6,750 0.942 0.960 0.994 0.983 0.732 0.758 0.722 0.734 0.844 0.999 0.695 0.765 0.579 0.648
7,000 0.945 0.952 0.975 0.976 0.742 0.747 0.714 0.721 0.858 0.989 0.708 0.750 0.634 0.629
7,250 0.934 0.943 0.962 0.968 0.773 0.736 0.718 0.708 0.893 0.979 0.721 0.735 0.650 0.614
7,500 0.905 0.933 0.958 0.961 0.698 0.726 0.682 0.696 1.017 0.969 0.690 0.721 0.655 0.601
7,750 0.912 0.924 0.954 0.954 0.722 0.716 0.684 0.685 1.026 0.960 0.698 0.707 0.604 0.592
8,000 0.907 0.915 0.963 0.947 0.702 0.706 0.661 0.675 0.911 0.952 0.698 0.694 0.411 0.585
8,250 0.902 0.904 0.919 0.940 0.698 0.697 0.672 0.665 0.915 0.944 0.686 0.682 0.609 0.580
8,500 0.879 0.894 0.903 0.932 0.714 0.689 0.655 0.656 0.937 0.937 0.665 0.670 0.594 0.576
8,750 0.877 0.883 0.926 0.923 0.645 0.681 0.634 0.648 1.008 0.930 0.618 0.660 0.497 0.571
9,000 0.866 0.871 0.904 0.914 0.655 0.674 0.655 0.640 0.800 0.925 0.621 0.649 0.604 0.565
9,250 0.852 0.858 0.885 0.902 0.639 0.667 0.616 0.633 0.928 0.920 0.595 0.640 0.523 0.555
9,500 0.850 0.844 0.888 0.889 0.648 0.662 0.644 0.627 0.911 0.917 0.581 0.631 0.563 0.539
9,750 0.816 0.830 0.870 0.873 0.647 0.657 0.624 0.620 0.915 0.914 0.611 0.623 0.462 0.515
10,000 0.802 0.814 0.855 0.854 0.668 0.654 0.605 0.613 0.880 0.913 0.638 0.616 0.487 0.477

Data table for Chart 2-2
Data table for Chart 2-2
Table summary
This table displays the results of Data table for Chart 2-2. The information is grouped by Bin (appearing as row headers), Panel A — Second federal tax, Panel B — Second provincial/territorial tax, Panel C — Third federal tax, Panel D — Third provincial/territorial tax, Panel E — Fourth federal tax, Panel F —Old Age Security recovery tax, Panel G — Employment Insurance recovery tax, Actual and Predicted, calculated using percent units of measure (appearing as column headers).
Bin Panel A — Second federal tax Panel B — Second provincial/territorial tax Panel C — Third federal tax Panel D — Third provincial/territorial tax Panel E — Fourth federal tax Panel F —Old Age Security recovery tax Panel G — Employment Insurance recovery tax
Actual Predicted Actual Predicted Actual Predicted Actual Predicted Actual Predicted Actual Predicted Actual Predicted
percent
-10,000 1.460 1.445 1.281 1.329 2.027 2.010 1.905 1.736 1.531 1.496 1.675 1.688 2.051 2.056
-9,750 1.465 1.491 1.276 1.276 1.935 1.920 1.817 1.833 1.451 1.477 1.681 1.683 2.051 2.015
-9,500 1.444 1.526 1.266 1.245 1.891 1.847 1.782 1.901 1.484 1.462 1.720 1.674 1.993 1.980
-9,250 1.441 1.550 1.260 1.229 1.715 1.789 1.839 1.943 1.386 1.448 1.678 1.661 2.001 1.950
-9,000 1.700 1.566 1.255 1.226 1.695 1.743 1.804 1.966 1.451 1.437 1.577 1.644 1.830 1.924
-8,750 1.792 1.575 1.268 1.232 1.675 1.706 1.908 1.971 1.392 1.427 1.657 1.625 1.766 1.899
-8,500 1.872 1.578 1.249 1.244 1.627 1.678 2.008 1.962 1.442 1.418 1.627 1.605 1.862 1.876
-8,250 1.431 1.577 1.266 1.260 1.647 1.656 1.964 1.943 1.481 1.411 1.574 1.584 1.937 1.854
-8,000 1.417 1.573 1.303 1.278 1.675 1.639 2.044 1.916 1.274 1.404 1.519 1.563 1.905 1.831
-7,750 1.427 1.566 1.261 1.296 1.777 1.625 1.931 1.882 1.469 1.397 1.560 1.542 1.798 1.809
-7,500 1.432 1.557 1.266 1.314 1.725 1.614 2.321 1.844 1.427 1.391 1.478 1.521 1.878 1.785
-7,250 1.424 1.546 1.266 1.330 1.575 1.604 1.690 1.802 1.339 1.385 1.445 1.501 1.731 1.762
-7,000 1.466 1.534 1.265 1.344 1.580 1.596 1.691 1.760 1.478 1.379 1.485 1.482 1.651 1.737
-6,750 1.615 1.522 1.274 1.356 1.571 1.587 1.622 1.717 1.365 1.374 1.503 1.464 1.702 1.712
-6,500 1.625 1.510 1.291 1.365 1.523 1.579 1.617 1.674 1.324 1.369 1.472 1.448 1.779 1.686
-6,250 1.451 1.497 1.804 1.371 1.571 1.571 1.781 1.632 1.377 1.364 1.424 1.434 1.726 1.661
-6,000 1.418 1.485 1.368 1.375 1.517 1.562 1.489 1.592 1.289 1.359 1.470 1.421 1.510 1.634
-5,750 1.638 1.473 1.290 1.377 1.493 1.552 1.440 1.553 1.339 1.354 1.437 1.409 1.584 1.608
-5,500 1.457 1.461 1.282 1.376 1.516 1.541 1.449 1.517 1.419 1.350 1.414 1.400 1.523 1.583
-5,250 1.557 1.450 1.328 1.374 1.533 1.529 1.451 1.484 1.286 1.345 1.421 1.392 1.619 1.557
-5,000 1.593 1.439 1.367 1.370 1.511 1.516 1.384 1.452 1.448 1.341 1.404 1.385 1.587 1.532
-4,750 1.506 1.429 1.475 1.365 1.462 1.502 1.450 1.424 1.327 1.338 1.378 1.380 1.462 1.509
-4,500 1.384 1.419 1.371 1.359 1.507 1.488 1.351 1.397 1.318 1.334 1.376 1.376 1.518 1.486
-4,250 1.353 1.409 1.302 1.354 1.452 1.473 1.327 1.373 1.374 1.331 1.343 1.373 1.462 1.464
-4,000 1.471 1.400 1.289 1.348 1.684 1.457 1.393 1.351 1.268 1.328 1.332 1.371 1.382 1.444
-3,750 1.364 1.391 1.297 1.342 1.419 1.440 1.500 1.332 1.389 1.325 1.380 1.370 1.467 1.425
-3,500 1.281 1.382 1.359 1.338 1.447 1.424 1.234 1.314 1.289 1.323 1.358 1.370 1.419 1.407
-3,250 1.294 1.373 1.515 1.334 1.367 1.407 1.269 1.297 1.232 1.321 1.361 1.370 1.491 1.391
-3,000 1.329 1.364 1.321 1.331 1.361 1.389 1.256 1.282 1.294 1.319 1.382 1.370 1.283 1.376
-2,750 1.236 1.356 1.286 1.330 1.390 1.372 1.270 1.269 1.271 1.318 1.332 1.371 1.443 1.362
-2,500 1.238 1.347 1.290 1.329 1.405 1.355 1.282 1.256 1.294 1.316 1.367 1.372 1.384 1.350
-2,250 1.286 1.339 1.268 1.331 1.318 1.338 1.378 1.244 1.362 1.315 1.363 1.372 1.368 1.339
-2,000 1.520 1.330 1.471 1.333 1.286 1.321 1.269 1.233 1.321 1.313 1.343 1.373 1.251 1.329
-1,750 1.335 1.321 1.286 1.337 1.214 1.305 1.321 1.223 1.345 1.312 1.366 1.373 1.259 1.320
-1,500 1.260 1.312 1.321 1.342 1.290 1.288 1.190 1.212 1.371 1.310 1.319 1.372 1.187 1.311
-1,250 1.334 1.303 1.497 1.348 1.254 1.273 1.132 1.202 1.303 1.308 1.388 1.371 1.256 1.303
-1,000 1.284 1.294 1.437 1.354 1.316 1.257 1.168 1.193 1.250 1.306 1.388 1.368 1.251 1.296
-750 1.317 1.285 1.313 1.362 1.280 1.243 1.222 1.183 1.433 1.304 1.634 1.365 1.208 1.288
-500 1.461 1.275 1.344 1.369 1.409 1.228 1.290 1.173 1.507 1.301 2.026 1.361 1.416 1.280
-250 4.773 1.266 2.230 1.377 2.162 1.214 1.792 1.163 2.004 1.298 5.262 1.356 2.283 1.272
0 2.556 1.256 1.652 1.384 1.727 1.201 1.416 1.154 1.625 1.294 2.435 1.349 1.614 1.264
250 1.403 1.246 1.535 1.391 1.286 1.187 1.139 1.144 1.422 1.290 1.414 1.342 1.382 1.255
500 1.195 1.236 1.372 1.396 1.193 1.174 1.152 1.134 1.371 1.285 1.275 1.333 1.307 1.244
750 1.142 1.226 1.195 1.401 1.149 1.162 1.143 1.124 1.265 1.279 1.216 1.323 1.240 1.233
1,000 1.125 1.217 1.159 1.404 1.101 1.149 1.062 1.114 1.241 1.273 1.176 1.312 1.328 1.220
1,250 1.069 1.207 1.184 1.405 1.098 1.137 1.032 1.103 1.294 1.266 1.146 1.299 1.166 1.206
1,500 1.042 1.197 1.341 1.404 1.104 1.125 1.033 1.093 1.150 1.258 1.070 1.285 1.142 1.191
1,750 1.021 1.187 1.325 1.401 1.026 1.113 0.992 1.083 1.209 1.249 1.072 1.271 1.168 1.174
2,000 1.009 1.177 1.194 1.396 1.083 1.101 1.008 1.073 1.188 1.240 1.066 1.255 0.990 1.155
2,250 0.986 1.167 2.102 1.388 1.017 1.089 1.027 1.063 1.088 1.230 1.091 1.238 1.131 1.135
2,500 0.982 1.158 1.550 1.377 0.994 1.076 1.010 1.053 1.206 1.219 0.953 1.220 1.118 1.113
2,750 0.981 1.148 1.258 1.363 0.990 1.064 1.013 1.043 1.126 1.207 0.915 1.201 0.998 1.090
3,000 0.970 1.138 1.116 1.347 1.014 1.051 0.991 1.034 1.138 1.195 0.900 1.182 1.003 1.065
3,250 0.970 1.128 1.098 1.328 0.948 1.039 0.974 1.024 1.093 1.182 0.915 1.162 0.912 1.039
3,500 0.936 1.119 1.357 1.307 0.942 1.026 0.958 1.015 1.064 1.169 0.918 1.141 0.920 1.013
3,750 0.957 1.109 1.723 1.283 0.938 1.013 0.952 1.006 1.179 1.156 0.900 1.121 0.814 0.985
4,000 0.922 1.098 1.126 1.257 0.957 1.000 0.975 0.997 1.132 1.143 0.922 1.100 0.862 0.958
4,250 0.902 1.088 1.078 1.229 0.920 0.987 0.974 0.988 1.120 1.129 0.974 1.078 0.843 0.929
4,500 0.897 1.078 1.056 1.200 0.914 0.974 1.054 0.979 1.073 1.116 0.911 1.057 0.888 0.902
4,750 0.923 1.067 1.028 1.170 0.904 0.961 1.130 0.970 1.088 1.102 0.858 1.036 0.816 0.874
5,000 0.935 1.055 1.166 1.139 0.899 0.948 1.053 0.960 1.067 1.090 0.864 1.015 0.779 0.848
5,250 0.937 1.044 1.090 1.108 0.882 0.936 0.913 0.951 1.049 1.077 0.948 0.995 0.784 0.822
5,500 0.857 1.031 1.066 1.078 0.907 0.923 0.863 0.941 1.046 1.066 0.857 0.975 0.840 0.798
5,750 0.850 1.019 0.956 1.048 0.846 0.912 0.853 0.930 0.978 1.055 0.737 0.956 0.806 0.776
6,000 0.852 1.005 0.946 1.020 0.819 0.900 0.808 0.919 0.955 1.045 0.752 0.937 0.678 0.756
6,250 0.927 0.991 0.923 0.993 0.830 0.889 0.853 0.908 1.070 1.035 0.735 0.920 0.747 0.739
6,500 0.853 0.977 0.916 0.969 0.870 0.879 0.801 0.895 0.931 1.027 0.747 0.902 0.715 0.724
6,750 0.850 0.962 0.904 0.948 0.868 0.869 0.839 0.882 0.934 1.021 0.733 0.886 0.646 0.711
7,000 0.911 0.947 0.906 0.930 0.830 0.860 0.827 0.868 1.067 1.015 0.772 0.871 0.662 0.701
7,250 0.830 0.931 0.922 0.916 0.809 0.852 0.851 0.854 1.005 1.010 0.813 0.856 0.630 0.694
7,500 0.742 0.916 0.917 0.905 0.788 0.844 0.854 0.839 0.958 1.006 0.692 0.841 0.688 0.689
7,750 0.750 0.900 0.985 0.897 0.770 0.838 0.825 0.823 0.898 1.004 0.647 0.827 0.667 0.685
8,000 0.742 0.885 0.868 0.892 0.795 0.831 0.776 0.807 0.984 1.001 0.670 0.814 0.691 0.683
8,250 0.738 0.871 0.875 0.890 0.778 0.825 0.762 0.791 1.005 1.000 0.713 0.801 0.694 0.681
8,500 0.745 0.858 0.869 0.890 0.779 0.818 0.727 0.775 0.866 0.998 0.607 0.787 0.568 0.678
8,750 0.719 0.847 0.918 0.891 0.751 0.812 0.758 0.760 1.034 0.996 0.659 0.773 0.595 0.673
9,000 0.714 0.838 0.818 0.892 0.740 0.804 0.749 0.746 0.895 0.992 0.611 0.758 0.573 0.664
9,250 0.724 0.833 0.800 0.890 0.734 0.795 0.716 0.735 0.937 0.987 0.597 0.742 0.613 0.649
9,500 0.714 0.832 0.846 0.884 0.736 0.783 0.702 0.727 1.023 0.980 0.617 0.724 0.584 0.626
9,750 0.724 0.837 0.849 0.871 0.769 0.769 0.723 0.723 0.925 0.969 0.611 0.703 0.608 0.591
10,000 0.746 0.848 0.854 0.847 0.699 0.750 0.681 0.725 0.898 0.953 0.572 0.679 0.520 0.542

The distributions of taxable income appear noisier as sample sizes decrease. For example, compare the results at the third federal tax bracket to those at the fourth bracket: the sample size is larger in the former than the latter. The distributions around the provincial and territorial tax thresholds are confounded by the fact that these thresholds vary by province and territory and are fairly close to other convex kink points that could also induce bunching. For this reason, the results of bunching at provincial and territorial tax thresholds should be interpreted a bit more cautiously than the other results. However, the bunching responses are substantial in all cases, despite the potential for these factors to have confounded the analysis.

A comparison of the results across periods reveals that the majority of bunching occurs in the post-reform period. From 2001 to 2006, before pension income splitting was introduced, only a small amount of bunching is observed at most convex kink points. This greatly contrasts with the extent of bunching observed from 2007 to 2012, where the spikes in the distributions are very apparent.

To better quantify the extent of bunching observed in these charts, Table 3 uses the empirical density estimator from Chetty et al. (2011) (see Footnote 8) to estimate the magnitude of excess mass at each tax threshold. These results confirm that bunching is more prevalent from 2007 to 2012 than from 2001 to 2006. For example, the amount of bunching following the reform is 15.8 times larger than it was before pension income splitting was introduced at the lower bound of the second federal tax bracket, 6.4 times larger for the third and 2.4 times larger for the fourth. The results by year are slightly noisier given that the sample sizes are smaller. This results in taxable income distributions that are estimated less precisely. Nevertheless, in these cases, bunching continues to be more prevalent in the post-reform years. This is especially apparent when the results are compared over time at the second and third federal tax brackets, as well as the OAS recovery tax threshold, where sample sizes are still comparatively large.

### 5.3 The effect of pension income splitting

The previous results show that income responses to taxation changed fundamentally from 2006 to 2007. This coincides with the introduction of pension income splitting. To further assess the extent to which the results are driven by splitting, this section delineates the analysis along several margins of variation that affected individuals’ eligibility to split pension income.

Table 4 repeats the previous analysis across individuals by marital status and whether they, or their spouses if married, are collecting private pension income. The effects of the convex kink points on effective marginal tax rates are reported in Panel A, and the subsequent bunching responses are reported in Panels B. The results show, first, that the effective marginal tax rate changes at each tax threshold are quite uniform across groups. This is not surprising given that the unit of taxation is the individual. The tax thresholds apply to everyone equally irrespective of marital status. Moreover, the tax code treats most types of income identically, so that whether the income derives from private pensions or other sources should not affect these results.Note 11

Unmarried Married No pension income Has pension income Either No pension income Has pension income 6.843Note *** 6.117Note *** 6.394Note *** 6.838Note *** 4.707Note *** 3.375Note *** 4.261Note *** 2.149Note *** 3.073Note *** 2.546Note *** 2.710Note *** 3.105Note *** 3.244Note *** 3.198Note *** 3.895Note *** 3.709Note *** 3.809Note *** 3.750Note *** 3.368Note *** 3.688Note *** 3.592Note *** 3.837Note *** 3.167Note *** 3.479Note *** 3.244Note *** 1.781Note *** 1.406Note ** 1.883Note *** 3.925Note *** 1.594 2.942Note *** 2.925Note *** 2.321Note *** 2.061Note *** 2.280Note *** 8.168Note *** 9.404Note *** 8.997Note *** 8.066Note *** 7.699Note *** 6.898Note *** 7.416Note *** 18.250Note *** 19.020Note *** 18.620Note *** 19.010Note *** 17.440Note *** 15.060Note *** 16.660Note *** 0.072 0.025 0.045 0.346Note *** 7.327Note *** 8.299Note *** 7.077Note *** 0.124 0.021 0.065 0.093Table 4 Note † 1.596Note * 1.351Note * 1.461Note ** -0.148 0.200 0.014 0.282Note * 3.884Note *** 4.282Note *** 3.505Note *** 0.505Note ** 0.132 0.306Note ** 0.034 1.880Note *** 2.120Note *** 1.804Note *** 0.249 -0.328 -0.009 0.311Table 4 Note † 2.913Note *** 3.143Note *** 2.784Note *** 0.848Note ** 0.331Table 4 Note † 0.472Note ** 1.086Note *** 7.195Note *** 8.661Note *** 7.056Note *** 0.615 0.672Table 4 Note † 0.639Note * -0.196 2.493Note *** 3.629Note *** 2.849Note *** Note * significantly different from reference category (p < 0.05) Return to note * referrer Note ** significantly different from reference category (p < 0.01) Return to note ** referrer Note *** significantly different from reference category (p < 0.001) Return to note *** referrer Note † significantly different from reference category (p < 0.10) Return to note † referrer Note: This table presents the regression discontinuity estimates of the changes in marginal tax rates and the empirical density estimates of bunching. The analysis is conditional on the post-reform period and delineates according to marital status and whether the individual (if unmarried) or couple (if married) has private pension income. Each tax threshold refers to the lower bound of the relevant tax bracket. Source: Statistics Canada, Longitudinal Administrative Databank.

Despite the uniformity of treatment, the bunching responses vary significantly across groups. Among unmarried individuals, the responses are all small in magnitude and generally insignificant except in a few cases, notably at the OAS and EI thresholds and the lower bound of the third provincial or territorial tax bracket. Similarly, married individuals without a pensioner in the couple, who are unable to split income, exhibit bunching at most thresholds, but the magnitudes of the responses are comparatively small. These results could differ from those of the unmarried non-pensioners for several reasons, including differences in market behaviour responses to taxation or access to other tax planning technologies related to marital status. In addition, the results may simply be more precisely estimated among married individuals given that 72.3% of the individuals in the sample are legally married or in common-law relationships, as shown in Table 1. This analysis also shows that the bunching responses of married individuals in a couple with at least one person receiving private pension income are both relatively large in magnitude and statistically significant at every tax threshold. Being a pensioner appears to be a precursor to responding actively to the changes in marginal tax rates in a manner predicted by the standard model, described earlier. This is consistent with expectations regarding the role of pension income splitting in driving the results.

To further explore the role of splitting, Table 5 conditions on married individuals in the post-reform period and on whether and how the pension income splitting program is actually used. On balance, the effects of the tax rate increases on effective marginal tax rates are quite uniform across groups, as shown in Panel A. The only notable exceptions are among transferees, who receive pension income from their spouses, at the lower bounds of the third provincial and territorial brackets and the fourth federal tax bracket threshold. However, most higher-income earners tend to send income to their spouses rather than receive income from them, and the imprecision of these estimates is partly the result of small sample sizes. However, as Panel B shows, the bunching responses at every tax threshold are almost entirely driven by individuals who utilize the pension income splitting program.

Interestingly, these responses are qualitatively similar across individuals who send and receive pension income. This suggests bunching is the result of two types of tax planning responses. First, individuals who are pensioners are sending enough income to spouses that their taxable incomes are reduced to lower tax brackets, at which point they stop because the marginal tax rates of individuals and spouses have presumably equalized. Second, individuals with spouses who are pensioners receive income up to the point where their taxable incomes would otherwise enter higher tax brackets, and at the margin they would end up paying taxes equal to or greater than those already being paid by their spouses. Hence, couples appear to be effectively coordinating to reduce joint tax liabilities.

A final check of the importance of the pension income splitting program in driving these results is shown in Chart 3. Specifically, this chart plots the probability of sending or receiving pension income relative to each tax threshold analyzed, among married individuals in the post-reform period who are eligible for this program. The results show large spikes in the probability distributions around each threshold. This is consistent with expectations.

Data table for Chart 3
Data table for Chart 3
Table summary
This table displays the results of Data table for Chart 3. The information is grouped by Bin (appearing as row headers), Panel A — Second federal tax, Panel B — Second provincial/territorial tax, Panel C — Third federal tax, Panel D — Third provincial/territorial tax, Panel E — Fourth federal tax, Panel F — Old Age Security recovery tax, Panel G — Employment Insurance recovery tax, Send, Receive and Either, calculated using percent units of measure (appearing as column headers).
Bin Panel A — Second federal tax Panel B — Second provincial/territorial tax Panel C — Third federal tax Panel D — Third provincial/territorial tax Panel E — Fourth federal tax Panel F — Old Age Security recovery tax Panel G — Employment Insurance recovery tax
percent
-10,000 27.139 24.537 51.676 22.857 23.440 46.296 23.620 21.613 45.234 23.036 16.410 39.446 18.676 11.348 30.024 29.155 15.233 44.388 21.843 9.556 31.399
-9,750 27.809 22.890 50.700 23.627 23.597 47.224 22.322 15.699 38.021 22.700 15.370 38.070 14.975 9.898 24.873 29.035 16.282 45.317 23.167 11.667 34.833
-9,500 27.681 22.169 49.850 23.119 23.967 47.086 23.510 18.578 42.088 21.217 16.485 37.702 17.207 7.731 24.938 27.108 16.376 43.484 24.156 13.321 37.478
-9,250 28.073 23.289 51.362 24.657 22.987 47.645 22.154 11.812 33.966 23.863 15.024 38.887 17.962 9.383 27.346 27.037 16.366 43.403 24.035 11.053 35.088
-9,000 34.889 25.725 60.615 24.245 24.009 48.254 20.163 11.542 31.705 24.084 17.559 41.642 21.094 9.635 30.729 29.059 15.789 44.848 18.618 11.900 30.518
-8,750 35.388 25.881 61.269 24.463 22.932 47.395 21.446 12.373 33.819 25.436 19.692 45.128 17.367 7.283 24.650 30.846 14.778 45.624 23.154 7.984 31.138
-8,500 36.284 27.827 64.111 24.751 22.575 47.326 21.983 12.168 34.151 27.333 23.333 50.667 19.363 8.824 28.186 27.917 17.356 45.273 24.953 9.263 34.215
-8,250 28.036 23.113 51.149 24.969 22.943 47.912 21.326 11.307 32.634 27.368 17.929 45.297 17.500 8.250 25.750 29.697 13.636 43.333 23.757 9.945 33.702
-8,000 27.939 21.974 49.914 25.458 23.722 49.181 23.002 11.524 34.526 29.769 22.280 52.049 17.683 7.927 25.610 28.450 17.039 45.490 24.194 7.527 31.720
-7,750 28.030 22.835 50.864 25.162 23.491 48.653 22.753 13.502 36.255 29.087 20.190 49.278 17.829 11.111 28.941 27.372 17.263 44.635 26.411 12.903 39.315
-7,500 28.566 22.600 51.167 24.309 24.218 48.526 21.017 15.933 36.950 31.283 24.973 56.257 23.698 6.510 30.208 26.298 16.900 43.199 23.698 12.029 35.727
-7,250 27.937 22.802 50.739 25.259 23.048 48.307 21.026 12.777 33.803 24.640 17.373 42.013 18.667 6.400 25.067 26.987 17.964 44.950 26.016 11.585 37.602
-7,000 29.586 23.396 52.983 25.707 23.135 48.842 19.031 12.587 31.618 25.331 15.525 40.856 19.347 7.286 26.633 27.135 15.164 42.298 24.000 10.105 34.105
-6,750 33.224 25.199 58.424 25.648 23.378 49.026 20.110 10.883 30.993 23.713 17.065 40.778 18.254 6.614 24.868 27.389 19.108 46.497 23.493 9.148 32.640
-6,500 34.409 25.017 59.426 27.068 23.459 50.527 21.958 11.844 33.802 24.132 17.232 41.364 20.166 12.155 32.320 27.773 17.247 45.020 24.225 10.465 34.690
-6,250 29.424 24.954 54.378 40.329 26.865 67.194 21.501 13.142 34.642 25.745 22.837 48.582 21.622 9.730 31.351 26.718 17.133 43.851 28.571 14.677 43.249
-6,000 29.400 22.480 51.880 28.892 23.437 52.329 22.701 13.766 36.468 23.206 14.623 37.829 19.118 7.647 26.765 27.478 17.325 44.803 21.292 11.962 33.254
-5,750 34.958 23.780 58.738 26.252 23.235 49.487 21.230 13.505 34.735 24.860 13.106 37.966 23.077 7.692 30.769 29.024 17.805 46.829 26.667 6.237 32.903
-5,500 31.792 23.036 54.828 26.263 23.480 49.743 20.706 13.752 34.458 23.225 15.346 38.571 17.949 8.974 26.923 26.432 18.576 45.008 24.658 8.904 33.562
-5,250 33.763 23.602 57.365 29.067 24.239 53.306 20.074 13.471 33.545 23.456 15.346 38.802 17.302 6.745 24.047 26.131 15.159 41.290 25.966 7.082 33.047
-5,000 35.154 24.011 59.166 29.891 23.871 53.762 19.409 13.186 32.595 23.230 15.179 38.409 19.338 8.397 27.735 25.688 15.680 41.368 26.316 14.035 40.351
-4,750 33.693 23.060 56.753 32.373 25.472 57.845 22.373 12.466 34.839 23.425 15.723 39.148 17.989 9.259 27.249 25.217 19.913 45.130 27.027 6.143 33.170
-4,500 29.121 21.614 50.735 29.508 25.571 55.080 20.272 12.539 32.811 23.656 15.005 38.661 23.851 10.632 34.483 28.398 18.528 46.926 23.666 9.513 33.179
-4,250 29.022 21.795 50.818 27.783 23.431 51.214 22.601 16.791 39.392 22.064 16.218 38.282 18.919 6.486 25.405 25.953 20.145 46.098 26.379 8.633 35.012
-4,000 32.552 23.374 55.926 28.780 23.711 52.490 23.936 22.473 46.410 23.979 14.672 38.651 17.681 7.826 25.507 27.353 19.716 47.069 29.412 7.673 37.084
-3,750 28.773 22.251 51.024 28.514 23.320 51.834 22.485 14.671 37.156 26.492 20.694 47.186 18.063 9.424 27.487 28.856 19.237 48.094 27.830 8.255 36.085
-3,500 27.819 21.253 49.072 31.233 24.995 56.228 20.631 17.202 37.833 20.776 13.833 34.609 17.287 7.979 25.266 27.810 19.817 47.627 26.098 13.415 39.512
-3,250 28.113 21.025 49.139 34.088 26.552 60.640 20.207 14.162 34.370 22.770 14.376 37.146 18.541 11.550 30.091 27.730 18.977 46.707 30.324 8.102 38.426
-3,000 29.129 21.883 51.012 29.349 23.841 53.190 20.163 13.829 33.992 20.429 13.673 34.102 22.571 9.429 32.000 27.595 19.110 46.705 27.441 11.082 38.522
-2,750 28.173 20.770 48.943 28.563 22.596 51.159 20.857 13.980 34.837 25.158 13.924 39.082 20.760 8.772 29.532 29.649 18.852 48.500 27.336 7.710 35.047
-2,500 28.069 20.809 48.879 28.721 22.525 51.246 21.614 15.920 37.535 23.649 17.464 41.112 16.905 10.888 27.794 29.145 18.803 47.949 29.250 9.750 39.000
-2,250 28.861 20.385 49.246 28.703 22.208 50.911 23.960 11.474 35.434 23.869 21.725 45.594 17.112 8.556 25.668 28.318 18.343 46.661 28.606 11.058 39.663
-2,000 36.275 22.301 58.575 35.107 23.422 58.529 19.600 12.257 31.857 22.459 15.041 37.500 21.788 8.659 30.447 26.778 18.410 45.188 25.000 6.720 31.720
-1,750 29.962 20.623 50.585 29.095 22.673 51.767 20.364 12.622 32.986 23.745 19.454 43.198 17.819 8.511 26.330 29.427 18.634 48.061 20.844 8.707 29.551
-1,500 28.455 20.825 49.280 31.627 22.671 54.298 20.304 12.340 32.644 22.524 13.299 35.823 21.237 8.065 29.301 27.517 22.396 49.913 30.548 5.764 36.311
-1,250 31.078 21.461 52.539 36.025 24.662 60.688 21.623 11.604 33.228 23.363 13.097 36.460 18.539 8.146 26.685 27.265 20.366 47.631 20.216 9.434 29.650
-1,000 29.070 21.616 50.687 35.861 23.533 59.394 21.708 13.108 34.816 23.489 14.220 37.709 21.972 10.141 32.113 28.447 21.632 50.079 29.121 10.440 39.560
-750 30.236 22.205 52.441 31.170 22.763 53.933 23.706 12.274 35.981 24.464 13.519 37.983 21.228 8.440 29.668 32.095 25.597 57.692 30.028 8.499 38.527
-500 34.062 23.355 57.417 33.050 22.301 55.351 29.910 14.664 44.574 27.452 17.792 45.244 27.700 11.502 39.202 38.590 28.803 67.394 34.562 10.138 44.700
-250 47.327 40.529 87.856 46.664 28.590 75.254 38.155 26.262 64.417 33.900 28.633 62.533 32.594 18.771 51.365 40.952 43.916 84.868 41.248 28.358 69.607
0 42.701 35.270 77.971 39.570 25.856 65.426 27.133 27.549 54.682 27.768 23.694 51.461 19.140 27.957 47.097 39.463 30.124 69.587 32.158 11.618 43.776
250 28.143 30.329 58.471 37.671 25.845 63.516 20.343 20.284 40.627 21.006 17.145 38.151 14.734 19.324 34.058 29.545 22.414 51.959 32.234 5.838 38.071
500 28.089 21.782 49.871 31.812 24.866 56.678 20.858 15.140 35.997 22.081 16.185 38.266 14.961 17.848 32.808 31.303 17.713 49.016 32.329 3.836 36.164
750 27.018 20.593 47.610 27.760 22.558 50.318 20.394 13.392 33.787 22.854 17.112 39.966 17.101 13.913 31.014 31.107 16.889 47.996 31.953 3.254 35.207
1,000 27.332 18.942 46.274 28.024 22.009 50.033 20.259 13.003 33.261 22.276 15.315 37.591 14.970 13.473 28.443 32.232 15.115 47.347 29.024 5.277 34.301
1,250 26.997 18.996 45.993 28.383 22.894 51.277 20.346 10.750 31.097 21.816 11.300 33.116 15.946 12.973 28.919 28.384 15.455 43.838 28.779 3.779 32.558
1,500 26.196 18.019 44.215 30.058 28.173 58.230 20.088 11.921 32.009 22.898 14.036 36.934 17.925 11.321 29.245 31.305 14.159 45.465 31.487 5.831 37.318
1,750 26.990 17.907 44.897 29.200 28.183 57.383 20.340 10.054 30.394 19.690 12.205 31.895 17.771 9.036 26.807 32.075 12.875 44.950 29.769 4.046 33.815
2,000 27.369 16.612 43.981 31.222 20.959 52.181 21.901 9.354 31.255 21.733 12.607 34.340 14.970 11.677 26.647 31.444 14.778 46.222 26.545 4.000 30.545
2,250 25.509 16.944 42.453 47.050 29.188 76.238 21.384 11.557 32.940 20.296 12.113 32.410 18.430 13.311 31.741 31.149 18.690 49.839 33.227 3.195 36.422
2,500 26.268 17.331 43.599 39.119 27.816 66.935 22.301 9.220 31.521 21.607 12.582 34.190 16.258 10.429 26.687 30.201 13.033 43.233 30.960 4.644 35.604
2,750 26.410 16.687 43.097 30.592 27.276 57.868 21.872 9.685 31.558 20.403 13.645 34.048 17.799 8.738 26.537 30.931 10.223 41.153 28.618 4.934 33.553
3,000 26.146 16.664 42.810 29.040 22.312 51.352 21.210 8.327 29.537 21.739 12.516 34.256 18.671 9.810 28.481 29.818 11.719 41.536 25.532 3.901 29.433
3,250 25.548 16.338 41.885 28.666 20.739 49.405 19.698 10.813 30.511 21.948 14.877 36.825 16.129 6.129 22.258 29.521 10.904 40.426 29.134 5.118 34.252
3,500 26.381 15.939 42.320 35.046 26.457 61.503 18.992 11.681 30.672 22.578 14.529 37.108 16.000 9.333 25.333 28.225 13.155 41.379 29.317 4.418 33.735
3,750 25.843 15.349 41.192 37.226 33.634 70.861 21.296 8.838 30.135 21.248 15.708 36.957 20.767 6.390 27.157 33.680 13.264 46.944 33.621 3.448 37.069
4,000 25.612 16.044 41.656 28.127 25.253 53.380 20.698 7.711 28.409 21.881 15.744 37.625 15.858 8.414 24.272 29.315 15.228 44.543 33.193 4.202 37.395
4,250 25.604 15.656 41.260 28.784 22.910 51.694 20.952 6.840 27.792 23.077 15.516 38.593 18.241 9.121 27.362 30.445 19.438 49.883 24.017 5.240 29.258
4,500 26.097 16.278 42.375 29.041 21.784 50.824 19.449 10.757 30.207 27.636 15.030 42.667 18.596 7.719 26.316 30.068 14.150 44.218 32.922 4.115 37.037
4,750 25.875 15.663 41.538 28.463 20.352 48.816 19.718 9.331 29.049 29.644 19.671 49.315 18.707 4.762 23.469 28.155 16.227 44.383 32.377 4.918 37.295
5,000 26.587 16.891 43.478 31.589 25.224 56.813 20.726 10.363 31.089 25.644 19.053 44.697 18.118 8.362 26.481 32.373 15.912 48.285 34.862 3.670 38.532
5,250 27.568 18.879 46.448 29.757 23.799 53.556 20.618 9.083 29.700 24.012 15.007 39.019 19.113 9.898 29.010 30.244 18.293 48.537 31.674 4.525 36.199
5,500 24.499 14.778 39.277 30.244 23.717 53.961 21.581 8.970 30.551 24.252 12.663 36.915 19.231 6.993 26.224 30.261 18.294 48.556 29.362 4.681 34.043
5,750 25.162 15.371 40.533 26.909 19.741 46.650 20.825 7.198 28.023 21.273 12.422 33.696 18.868 9.811 28.679 32.588 10.703 43.291 28.899 6.881 35.780
6,000 26.912 15.500 42.413 26.393 18.801 45.193 18.443 10.843 29.286 22.259 11.866 34.124 14.599 8.394 22.993 31.940 13.545 45.485 24.468 2.660 27.128
6,250 28.801 18.448 47.249 27.586 18.043 45.629 20.020 8.832 28.852 19.152 13.265 32.418 19.795 8.532 28.328 31.164 9.418 40.582 34.234 3.604 37.838
6,500 26.193 14.290 40.484 27.044 18.611 45.655 21.174 7.918 29.093 22.399 11.326 33.725 16.732 5.058 21.790 31.360 11.200 42.560 36.232 3.382 39.614
6,750 28.556 15.909 44.465 27.161 17.559 44.720 22.344 8.516 30.861 20.331 12.372 32.703 18.251 7.985 26.236 29.969 13.509 43.478 31.361 5.917 37.278
7,000 29.315 18.148 47.463 27.040 17.777 44.818 19.105 8.574 27.679 22.133 12.109 34.242 19.588 6.529 26.117 30.792 14.200 44.993 35.859 5.051 40.909
7,250 25.503 16.374 41.877 28.060 18.646 46.707 18.578 10.142 28.720 24.656 16.031 40.687 13.483 7.116 20.599 32.675 18.314 50.988 28.655 7.018 35.673
7,500 23.197 13.079 36.276 28.795 18.778 47.573 17.946 8.375 26.321 22.935 17.920 40.855 17.530 9.562 27.092 30.598 9.402 40.000 35.450 7.407 42.857
7,750 23.049 12.801 35.850 30.669 21.853 52.521 19.028 8.401 27.429 20.424 15.947 36.371 18.443 8.197 26.639 25.735 12.316 38.051 30.208 7.292 37.500
8,000 23.196 12.449 35.646 26.737 18.569 45.306 18.533 9.713 28.246 22.442 14.026 36.469 19.444 8.333 27.778 28.546 11.208 39.755 33.668 7.538 41.206
8,250 22.846 13.146 35.993 27.624 18.006 45.630 19.517 8.652 28.169 22.716 13.920 36.635 21.739 8.333 30.072 30.408 16.144 46.552 25.641 8.718 34.359
8,500 22.077 13.397 35.474 28.286 17.681 45.967 20.804 8.040 28.844 22.171 11.224 33.395 19.502 6.639 26.141 29.905 11.238 41.143 32.278 9.494 41.772
8,750 22.014 13.813 35.828 30.202 20.656 50.857 20.795 9.786 30.581 20.796 13.186 33.982 17.376 5.674 23.050 28.136 8.961 37.097 29.714 6.857 36.571
9,000 23.278 13.058 36.336 25.836 17.112 42.948 20.106 8.617 28.723 21.048 11.092 32.140 19.835 7.025 26.860 27.533 9.751 37.285 30.128 8.974 39.103
9,250 23.880 13.402 37.282 25.707 16.714 42.420 20.878 7.709 28.587 21.811 9.932 31.743 15.663 5.221 20.884 24.752 11.287 36.040 35.632 7.471 43.103
9,500 23.828 12.842 36.670 28.958 19.160 48.119 18.036 7.791 25.827 18.515 10.993 29.508 18.794 10.638 29.433 27.048 13.143 40.190 31.410 8.333 39.744
9,750 24.981 14.341 39.323 29.473 18.318 47.792 22.256 7.654 29.909 21.019 11.296 32.315 16.016 10.156 26.172 31.504 10.569 42.073 26.471 5.882 32.353
10,000 26.797 16.649 43.446 29.721 20.272 49.993 18.800 7.382 26.182 20.626 12.317 32.942 20.717 8.367 29.084 25.103 14.198 39.300 37.500 5.263 42.763

### 5.4 Placebo checks

The validity of the estimator and robustness of the results in studies that use quasi-experimental methods in cross-sectional settings can be tested several ways. For example, Ganong and Jäger (2017) proposed a permutation test for the regression kink (RK) design that involves repeating the RK estimation at points along the running variable localized around the true kink to assess how the significances vary. Another approach is to repeat the analysis on a running variable or sample known not to be treated (Landais 2015; Messacar 2015). This approach is used here to assess how individuals known not to be affected by the OAS and EI recover tax thresholds behave around these points in the income distribution.

Prior to July 2013, individuals could not delay claiming OAS benefits to receive higher monthly payments upon receipt. This means the majority of taxfilers began collecting OAS when they became eligible, at age 65, since delaying provided no benefit. As a result of this exogenous variation in eligibility, a potentially valid control group at this tax threshold is individuals aged 60 to 64 who are unaffected by the recovery tax.Note 12 The analysis delineated by age is presented in Table 6, shown separately for individuals by marital status, private pension income receipt, and whether pension income splitting is observed. Panel A indicates that individuals’ effective marginal tax rates are unaffected by the recovery tax until they turn age 65. This supports this placebo test approach. Bunching responses are robustly observed only among married individuals who had pension income or used the pension income splitting program, as indicated in Panel B. This is consistent with the previous findings. This behaviour is driven predominantly by individuals aged 65 to 69 who are affected by the recovery tax.

Unmarried Married No pension income Has pension income Pension income Pension income splitting 0.122 0.157 -0.339 0.551 -0.254 0.766 -0.191 1.705 -0.376 -0.448 -0.345 -0.545 0.001 0.524 0.404 0.687 -0.011 1.220Note * 0.437 -0.565 -0.205 0.313 0.079 0.242 -0.673 0.928 0.119 -0.345 -0.051 -0.460 8.440Note *** 9.716Note *** 6.622Note *** 7.919Note *** 6.595Note *** 8.348Note *** 8.314Note *** 9.447Note *** 7.573Note *** 7.046Note *** 8.190Note *** 6.590Note *** 7.779Note *** 9.574Note *** 8.986Note *** 7.020Note *** 9.036Note *** 6.492Note *** 8.380Note *** 9.090Note *** 10.740Note *** 7.152Note *** 9.554Note *** 6.920Note *** 7.213Note *** 9.015Note *** 8.160Note *** 7.986Note *** 10.020Note *** 7.327Note *** 0.312 -0.135 0.078 0.891Note ** 0.179 1.102Note ** -0.046 -0.436 -0.259 0.410 -0.167 0.600 0.273 -0.437 0.260 0.249 0.100 0.527 0.188 -0.076 0.050 0.476 -0.028 0.828Table 6 Note † 0.095 -0.117 -0.260 0.488 -0.300 0.943Table 6 Note † -0.525 0.684 1.138Note ** 5.456Note *** 1.093Note *** 7.827Note *** 0.709 -0.099 1.048Note *** 6.916Note *** 0.928Note *** 9.722Note *** 1.279 0.553 0.966Note ** 6.930Note *** 0.938Note *** 9.657Note *** 2.398Note ** 0.602 1.197Note ** 8.033Note *** 1.187Note *** 10.980Note *** 3.099Note ** -0.153 1.095Note * 8.314Note *** 0.956Note *** 11.620Note *** Note * significantly different from reference category (p < 0.05) Return to note * referrer Note ** significantly different from reference category (p < 0.01) Return to note ** referrer Note *** significantly different from reference category (p < 0.001) Return to note *** referrer Note † significantly different from reference category (p < 0.10) Return to note † referrer Note: This table presents the regression discontinuity estimates of the changes in marginal tax rates and the empirical density estimates of bunching at the Old Age Security recovery tax threshold, in the post-reform period. The analysis delineates according to marital status, whether the individual (if unmarried) or couple (if married) has private pension income, whether pension income splitting is observed, and age. Source: Statistics Canada, Longitudinal Administrative Databank.

The primary analysis of bunching around the EI recovery tax threshold conditions on individuals who received these benefits, since those who did not are untreated. In Table 7, EI non-recipients are used as a placebo group to test how effective marginal tax rates and the distributions of taxable income would have otherwise evolved around this convex kink point in the post-reform period. As before, the analysis delineates individuals by marital status, private pension income receipt, and whether pension income splitting is observed. The results show that changes in effective marginal tax rates are meaningful only for those individuals receiving EI, as expected. The small discontinuities in the tax rates for those not receiving EI that in some cases appear significant may be attributed to the size of the dataset and the fact that tax rates generally increase with income. However, the magnitudes of the estimates in these cases are not economically relevant. The bunching responses are observed only among those individuals who both received EI and were eligible to split pension income, as expected.

Unmarried Married No pension income Has pension income Pension income Pension income splitting 18.250Note *** 19.020Note *** 19.010Note *** 16.660Note *** 18.830Note *** 17.540Note *** 0.350 0.696Note ** 0.174 0.243Note * 0.207 0.245Note ** 0.615 0.672 -0.196 2.849Note *** -0.048 3.946Note *** -0.057 0.063 -0.098 0.002 -0.115Note * 0.108 Note * significantly different from reference category (p < 0.05) Return to note * referrer Note ** significantly different from reference category (p < 0.01) Return to note ** referrer Note *** significantly different from reference category (p < 0.001) Return to note *** referrer Note: This table presents the regression discontinuity estimates of the changes in marginal tax rates and the empirical density estimates of bunching at the Employment Insurance recovery tax threshold, in the post-reform period. The analysis delineates according to marital status, whether the individual (if unmarried) or couple (if married) has private pension income, whether pension income splitting is observed, and Employment Insurance receipt. Source: Statistics Canada, Longitudinal Administrative Databank.

### 5.5 Heterogeneous responses

Briefly considering how the primary results of this study vary across different personal characteristics is instructive. Much of the literature cited earlier found responses to income taxes are larger among women, the self-employed and individuals working in sectors with more flexible labour markets (Saez, Slemrod and Giertz 2012). On this basis, this section considers how effective marginal tax rates change and bunching responses vary by sex, type of income and sector of employment for unmarried (Table 8-1) and married individuals (Table 8-2).

First, Table 8-1 indicates that the effects of the tax thresholds on effective marginal tax rates are both consistent with the previous findings and uniform across groups, as shown in Panel A. This means that any differences in bunching across groups are not likely to be the result of differences in treatment. However, Panel B shows that no meaningful bunching responses to tax rate changes appear among unmarried individuals across groups, notwithstanding a few cases that appear weakly significant. For example, the self-employed are not much more likely to respond to changes in taxes by bunching than other workers. Second, Table 8-2 shows that, among married individuals, the results are qualitatively similar. The effects of the tax rate changes are uniform across groups, and no meaningful differences appear in the corresponding bunching responses.

## 6 Conclusion

The standard model of labour supply predicts bunching responses in taxable income to convex kink points in budget sets created by the tax and transfer system. This paper assesses the extent to which older Canadian taxfilers, aged 60 to 69, exhibit such responses. Bunching was detected at various points along the income distribution coinciding with the lower bounds of the second, third, and fourth federal tax brackets and of the second and third provincial or territorial tax brackets; as well as with the recovery tax thresholds for Old Age Security and Employment Insurance benefits. This is consistent with expectations. Such behaviour is apparent from graphical inspections of the distributions of taxable income around these tax thresholds and is credibly estimated in an empirical density design. However, a closer inspection of this result finds that bunching occurs primarily because of pension income splitting between married individuals and their spouses in order to reduce joint tax liabilities. This finding offers novel evidence of intra-household tax planning behaviour that depends on the availability of tax deductions.

When a tax planning technology is introduced in a salient manner and very low costs—in terms of administration, effort and implementation—are associated with using the technology, individuals can be expected to proactively use the technology to reduce tax liabilities. As stated earlier, income sharing is also permissible for income drawn from the Canada Pension Plan and the Quebec Pension Plan. However, this transfer is not strictly notional, and more administrative procedures control the use of this tax planning provision. This suggests that the procedures associated with using a tax planning technology can significantly affect the level of responsiveness to income taxation. Another interesting finding from this study is that such behaviour occurs at the household level. This implies coordination that is to some extent consistent with the unitary model (Messacar 2017). However, in the absence of such a technology, taxable income—from labour, pensions and otherwise—is relatively non-responsive to changes in marginal income tax rates. This finding is consistent with the related literature on the elasticity of taxable income.

Several studies have found recently that individuals sometimes struggle to understand the true marginal costs of their actions at the time of making economic decisions. For example, Ito (2014) showed, using administrative data from the United States that household consumption of electricity often varies more with the average, rather than the marginal, price. Consumers do not always understand complex nonlinear electricity pricing schedules. Such behaviour has been coined “schmeduling” behaviour (Liebman and Zeckhauser 2004) in that economic agents are responding to a price “schmedule” rather than the true price schedule. In a related study, Messacar (2017) assessed the effects of the introduction of pension income splitting on the labour supply decisions of older Canadian taxfilers. That study found that individuals are more responsive to their average, rather than marginal, income tax rates at the time of making labour supply decisions at the household level. The finding from this paper that individuals bunch at convex kink points in their budget sets indicates that they are sensitive to marginal tax rates. However, this occurs ex post, at the time of filing taxes and depends on whether a tax planning technology exists to facilitate such behaviour.

Individuals do respond to marginal tax rates at the time of filing their taxes, but the underlying mechanism for this behaviour cannot be discerned from the data. For example, are taxfilers sufficiently tax code savvy and aware of how to use pension income splitting to minimize tax liabilities, or do they rely on the assistance of software or tax professionals? A better understanding of this issue would contribute to a large literature on tax literacy (Feldman and Katuščák 2006; Chetty, Looney and Kroft 2009; Finkelstein 2009; Chetty and Saez 2013; Taubinsky and Rees-Jones 2015; Feldman, Katuščák and Kawano 2016) and remains an important issue for future research.

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