Bertrand Garbinti
email: bertrand.garbinti@ensae.fr

Jonathan Goupille-Lebret
email: jonathan.goupille-lebret@ens-lyon.fr

Mathilde Muñoz
email: mathildemunoz@berkeley.edu

Stefanie Stantcheva
email: sstantcheva@fas.harvard.edu

Gabriel Zucman
email: zucman@berkeley.edu

TAX DESIGN, INFORMATION, AND ELASTICITIES: EVIDENCE FROM THE FRENCH WEALTH TAX

We study a French wealth tax reform that starkly reduced the information some taxpayers must report to the tax authority. Using a new dynamic bunching approach we estimate the average response to the reform, the share of compliers, and the local average treatment effect. The annual wealth growth rate of treated taxpayers falls by 0.5 percentage points after the reform. This decline is likely due to increased evasion, as suggested by the sharp responses in self-reported wealth but not in third-party-reported incomes. The wealth tax base becomes more elastic post reform, illustrating the key role of information policy choices for tax base elasticities.

Introduction

Over the last decades, there has been extensive research on the behavioral responses to taxes.

Following the work of Feldstein (1995) and Gruber and Saez (2002), a rich literature has estimated the elasticity of taxable income. Recent work has focused on the elasticity of taxable wealth (e.g., Seim, 2017; Duran-Cabré et al., 2019; Jakobsen et al., 2020; Agrawal et al., 2020; Brülhart et al., 2021; Londoño-Vélez and Avila-Mahecha, 2022). These estimates are critical for formulating empirically-grounded statements about optimal tax policy and informing the public debate on core policy issues, such as the feasibility and desirability of taxing wealth.

A key difficulty in using empirical tax elasticities for policy is that tax base elasticities are not structural parameters: they can be affected by tax design. Policy choices such as the stringency of reporting requirements and enforcement can make tax bases more or less elastic (Slemrod and Kopczuk, 2002; Keen and Slemrod, 2017). 1 Because these tax design features vary over time and across countries, it is challenging to generalize elasticities estimated in specific contexts to others.

To address this limitation, isolating the causal effect on behaviors of key features of tax design would be valuable, but this task is difficult for several reasons. First, sharp or fundamental changes in tax design occur less frequently than changes in tax rates. Second, when they do occur, they are often paired with tax rate changes, complicating the identification of causal effects. Third, when it comes to the design of wealth taxation, only few countries tax wealth and collect individual-level administrative wealth data. This paper tackles these challenges and provides evidence on the effects of changes in information reporting requirements-a key dimension of tax design-on taxpayer behavior. We study an unusual reform of the French wealth tax that considerably scaled back reporting requirements for some taxpayers. Until 2011, all taxpayers had to report their detailed asset composition on their wealth tax return. A reform introduced simplified reporting requirements in 2011, allowing taxpayers with less than e3 million in wealth (changed to less than e2.57 million in 2013) to file a simplified return reporting only total gross and net taxable wealth, with no breakdown by components. This reform drastically reduced the amount of information reported to the tax authority.

It allows us to estimate the causal effects of changing information reporting requirements while keeping most other features of the tax schedule constant. More specifically, the French institutional setting and reforms make it possible to disentangle behavioral responses to marginal tax rates (kinks), exemption thresholds, and information reporting requirements (keeping other features of the tax system and tax rates constant). To do so we leverage new, exhaustive longitudinal data on the universe of French wealth taxpayers matched to their income tax returns. 2 Our contribution is also methodological. We develop a new method of dynamic bunching. This method relies on studying discontinuities in the distribution of (appropriately normalized) wealth growth rates for different groups, and differences in the distributions of these growth rates relative to counterfactual distributions. The counterfactual distributions are derived from a control group of similar but unaffected taxpayers. Our method does not require imputing a counterfactual distribution using a smooth polynomial or another fitting method, and we do not need to assume similar preferences in our treatment and control groups, thus avoiding the concerns raised by Blomquist et al. (2021). Our method can be more generally used to study the responses of variables for which growth rate distributions can be computed in panel data.

Our approach offers advantages over the classic static and standard difference-in-differences bunching approach. By using longitudinal data, we can improve on the classic static bunching approach (Saez, 2010; Kleven and Waseem, 2013), as already shown by Marx (2018). Our dynamic bunching method maps in a straightforward manner to the causal identification framework of Angrist et al. (1996). 3 We can thus identify compliers (i.e., "bunchers") who took advantage of the reform within the bunching segment. In turn, this enables us to estimate the local average treatment effect of reducing reporting requirements and the intent-to-treat effects. 4 Furthermore, by studying the entire distribution of (normalized) growth rates instead of the distribution of taxable wealth, we can quantify heterogeneous responses among different groups defined by taxable wealth levels and show responses along the full wealth distribution, even far below the threshold. Relative to a simple difference-in-differences analysis, our approach yields more precise estimates and lets us directly estimate the share of compliers and the LATE.

Our main findings can be summarized as follows. First, we illustrate the first-order role of information requirements on the wealth tax base by showing sharp bunching responses at information discontinuities. By contrast, we cannot detect any bunching at any pure tax kink. When marginal tax rate kinks become associated with changes in reporting requirements (exemption and simplification thresholds), we find large, sharp, and persistent bunching responses. The absence of bunching at thresholds where only tax rates change but substantial bunching at information discontinuity thresholds suggests that reporting requirements are crucial in driving behavioral responses to the wealth tax.

Second, we use our dynamic bunching method to estimate micro-level dynamic responses to changes in reporting requirements. We focus on the introduction of the simplified return below e2.57 million in 2013 and estimate the heterogeneous effects of this reform depending on the prereform distance to the threshold. We use the group of taxpayers located very far above the threshold in 2012, which we show is not affected by the reform, to build a counterfactual distribution of wealth growth rates. We then compare this counterfactual distribution of wealth growth rates to that of taxpayers below and above (but not too far above) the threshold. The reform led to substantial reductions in the growth of wealth reported by treated taxpayers. The estimated average annual growth rate reduction equals 0.5 percentage points, equivalent to 20% of the control group's wealth growth rate in 2012. These responses are driven by a minority of compliers (around 15% of taxpayers previously just below the threshold) who reduce their growth rates substantially (by 3 or more percentage points).

Behavioral responses are more pronounced among individuals with taxable pre-reform wealth just below the information discontinuity threshold than among those further below. However, the responses of taxpayers far below the threshold are also significant: their wealth growth rates are systematically lower in the low-information regime. Our results thus highlight that not all responses take the form of sharp bunching. Furthermore, there is a strong asymmetry whereby taxpayers who were already above the threshold (and, as such, would have to report negative growth rates to locate below the threshold) exhibit much smaller responses to the reform, likely because they worry about reporting negative wealth growth rates. The reductions in growth rates below the threshold, the sharp bunching, and the rapid adjustment to changes in the simplification threshold all support the hypothesis that behavioral responses to the reform appear to be driven by evasion rather than actual changes in savings or investment.

Our methodology allows us to document the dynamic longer-term effects of low information reporting. We show that the bunching at the simplification threshold is highly persistent within taxpayers over time and remains sharp and large even four years after the reform. This persistence reveals that the reform's effect is cumulative over time: taxpayers under-report a growing fraction of their wealth year after year to stay in the low-information regime, implying that the change in tax design has growing revenue costs. In addition, responses appear to increase and spread further down the wealth distribution over time.

Third, we explore the channels through which taxpayers react to the reduced reporting requirements by using our comprehensive administrative dataset linking wealth taxpayers to their income tax returns. We show that taxpayers who react to the reform by reporting lower wealth growth do not experience any corresponding change in their (third-party) reported labor and capital income. This provides further evidence in favor of tax evasion and misreporting of wealth. Thanks to data on the asset composition of taxpayers, we show that taxpayers who bunch below the simplification threshold end up crossing it after they experience large positive shocks to their financial assets. These findings suggest that taxpayers are pushed into the detailed reporting regime once they experience shocks that become "too hard to hide." 5 Our results are consistent with a simple model of taxpayers' behavior with dynamic misreporting. In this model, taxpayers value being in the simplified regime and try to remain in it by misreporting their wealth. Misreporting is costly, and the cost increases in the amount of misreporting and decreases in the reported growth rate from year to year. Because wealth is a stock, the tax authority can compare reported amounts in different years. Low wealth growth rates-especially negative growth rates-can raise a flag for the tax authority. This feature makes wealth misreporting an inter-temporal choice for the taxpayer. Forward-looking taxpayers anticipate how their future ease of misreporting is affected by their current misreporting of wealth, leading to "misre-porting smoothing." This smoothing motive explains why even taxpayers far below the threshold may engage in misreporting in anticipation.

There are several reasons taxpayers may value being in the simplified regime, for instance, lower hassle costs or reduced privacy concerns. Suppose the simplified reporting reduced the burden of filing wealth taxes or the associated privacy concern. In that case, some taxpayers who would otherwise have remained below the wealth exemption threshold should be enticed to cross it after the reform. We find no support for this mechanism. Instead, misreporting around the exemption threshold remained substantial and similar to that under the previous detailed reporting regime. Thus, our findings indicate that the ease of misreporting may be the most important reason taxpayers value the simplified regime. When taxpayers do not need to report a detailed breakdown of their portfolio, they may feel it is easier to hide specific assets or to report incorrect amounts, which leads to persistently higher under-reporting of wealth in the low-information regime.

One of our contributions is the ability to study very wealthy taxpayers (around the 99.5 th percentile of the wealth distribution in France). While there is a large literature on tax enforcement and tax evasion (e.g., Kleven et al., 2011; Almunia and Lopez-Rodriguez, 2018; Pomeranz, 2015; Bachas and Soto, 2021; Harju et al., 2019; Brockmeyer et al., 2021), there is more scarce evidence on tax evasion responses by wealthy taxpayers, which matter substantially for tax revenues. A notable exception is Johannesen et al. (2020) who document reductions in US tax evasion following improvements in information reporting of offshore accounts. Alstadsaeter et al. (2019) highlight substantial offshore wealth tax evasion in Scandinavia (Alstadsaeter et al. (2019)), and Guyton et al. (2021) shed new light on evasion at the top of the US income distribution. Studies of simplified tax regimes mostly focus on low-income taxpayers, for whom such regimes were made available. 6 Our findings confirm that tax design choices can have immediate implications for tax compliance and enforcement and that these effects may be significant and persistent. Lower information environments (such as the simplified reporting in our setting) can lead to a growing erosion of the tax base, cumulative over multiple years, since wealth not reported in one year continues to be unreported by taxpayers in future years. By contrast, responses around changes in wealth tax rates appear minimal in our context, highlighting that tax base elasticities are substantially affected by tax design. The variation of tax design across countries and time can rationalize the wide range of elasticities found in different countries and periods (e.g., Scheuer and Slemrod, 2021). For instance, while exemption thresholds have been widely used to analyze the impacts of wealth taxation on reported wealth, these thresholds are usually (by construction) associated with changes in reporting requirements, too, complicating the interpretation of estimated elasticities and their implications for optimal policy. The rest of this paper proceeds as follows. In Section 2 we describe the institutional framework and the administrative tax data we use. Section 3 provides graphical evidence of the effect of information reporting requirements vs. tax rates on reported wealth. We then present our dynamic bunching method and results in Section 4 before studying mechanisms in Section 5. Section 6 concludes.

2 Institutional Setting and Data

Wealth Taxation in France

The impôt sur la fortune (ISF) was an annual progressive wealth tax implemented in France from 1989 to 2017. 7 It applied to French tax residents with net taxable wealth above an exemption threshold. This exemption threshold varied over time, as we discuss below, but it was always located above the 97 th percentile of the household wealth distribution during our period of study.

Appendix B provides a detailed description of the features of the French wealth tax. We summarize here the key elements needed for our analysis.

Tax base. The base of the ISF was net wealth above an exemption threshold. Net wealth was defined as financial plus non-financial assets minus debts and was assessed as of January 1 st of year t for fiscal year t. Thus, in calendar year t, taxpayers filled out income tax returns and paid income tax for income earned in t -1, but filled out wealth tax returns and paid tax on wealth as of January 1 st of year t. For French tax residents, the base included assets held worldwide. 8 7 The first progressive annual wealth tax in France was implemented in 1982 and called the impôt sur les grandes fortunes. It was abolished in 1986 after the election of a new government. In 2018, the ISF was abolished and replaced by a progressive tax on real estate wealth, called the impôt sur la fortune immobilière.

8 Non-residents could be liable for the wealth tax under certain conditions, as detailed in Appendix B. Non-residents represent 3% of our estimation sample. We exclude them from our benchmark analysis; results are unchanged if we

The exemption threshold ranged from around e800,000 in 2010 (roughly the top 2% of the wealth distribution) to e1.3 million after 2011 (roughly the top 1% of the wealth distribution).

Several major exemptions reduced the tax base. First and most importantly, the business wealth of owner-managers was exempt. Owner-managers were defined as sole proprietors and individuals owning 25% or more of the stock of a company, including listed firms. In addition, groups of individuals (e.g., family members or business partners) who collectively owned significant stakes in a company (of at least 20% or 34% depending on the business) could exclude three-quarters of the corresponding assets from their net wealth. Thus in practice, the vast majority of private business wealth and large stakes in public companies were exempt. Second, 30% of the value of a household's primary residence could be deducted from the tax base. Third, artwork was exempt. 9

Tax schedule. The ISF had a progressive tax schedule, with five to six tax brackets over our study period (see Panel B of Figure 1). Marginal tax rates ranged from 0.5% for the first bracket to 1.5% for the top bracket in 2013.

Reporting requirements. Wealth was self-reported by households and there was no third-party reporting of any asset. However, the tax administration provided detailed guidelines for taxpayers to properly estimate the value of their assets; the general principle was to use prevailing market prices.

If noncompliance was uncovered upon audit, taxpayers could be required to file amended returns for up to 10 preceding years. 10 Taxpayers above the exemption threshold had (until the simplification reform we study in this paper) to file a wealth tax return listing the value of each component of their net taxable wealth such as primary residence, other real estate, stocks, and bank deposits (listed in Appendix Table B.3). When filling the detailed wealth tax return, taxpayers must send detailed appendices listing all of their assets' characteristics and must attach additional proofs. 11 include them.

9 Tax credits for the wealth tax are also explained in Appendix B but are not relevant for the analysis in this paper. They concern investments in small and medium enterprises, charitable giving, and a tax ceiling mechanism capping the amount of wealth tax owed by taxpayers as a fraction of their taxable income.

10 Based on data provided by the French tax administration, in 2014, noncompliance upon audits was uncovered for 5% of all wealth taxpayers that year. We do not have information on the total number of audits performed that same year.

11 For real estate, taxpayers must list the number of rooms, the size of the land and the exact address of each of their properties. For financial assets, taxpayers must list each of their financial assets with details on the asset and the methodology used to assess the reported market value. Taxpayers must also send proofs to benefit from some wealth tax exemptions and deductions. For instance, they must send proofs for each debt or liability they wish to deduct from their wealth tax base.

Although we do not know whether taxpayers are filing wealth tax returns themselves or using tax preparers, the industry of tax preparers is less developed in France than in the U.S., because most of the components of income tax returns are pre-populated. Note also that tax preparers are not responsible for the veracity of information reported in the wealth tax returns, and must only fill returns based on the information they received from their clients. Thus, evasion is still possible when using tax preparers.

Wealth Tax Reforms Studied in This Paper

Changes to reporting requirements. In June 2011, a simplified wealth tax return for taxpayers with taxable wealth below a threshold, called the "simplification threshold," was introduced.12 In the simplified return, taxpayers only report total net and gross taxable wealth, as well as three specific tax credits (charitable giving, direct and indirect investment in small and medium-size enterprises). Figure A.1 shows the detailed and the simplified wealth tax returns. Appendix Table B.3 summarizes the changes in reporting requirements item by item. 13 The simplification threshold was initially set at e3 million. After the election of a new president, a second reform was passed in July 2012, which lowered the simplification threshold from e3 million to e2.57 million, effective in 2013. The 2013 reduction of the simplification threshold is particularly helpful for estimating the effects of reporting requirements because there is no other policy change occurring around this specific wealth level in the years after 2013. Panel A of Figure 1 summarizes the changes in information reporting requirements over time.

Exemption threshold and tax bracket changes. Panel B of Figure 1 summarizes changes in the tax brackets and schedule. The 2011 reform also increased the wealth tax exemption threshold from e0.8 million to e1.3 million, which reduced the number of households subject to the tax by a factor of about two. Furthermore, the e1.3 million threshold is interesting because it was a pure tax kink before 2011 and, in 2010, the marginal tax rate jumps from 0.55% to 0.75% at this kink. In 2011, the marginal tax rate at this kink increases again but the e1.3 million threshold simultaneously becomes the exemption threshold. The policy variations around the e1.3 million threshold thus allow us to contrast behavioral responses at a pure marginal rate discontinuity in 2010 and those at a marginal rate plus information discontinuity in 2011.

To summarize, although several changes to wealth taxation happened between 2007 and 2017, we focus in this paper on two salient reforms: the reduction of the simplification threshold from e3 million to e2.57 million in 2013; the increase of the exemption threshold to e1.3 million in 2011.

Administrative Tax Data and Summary Statistics

Our analysis builds on a new administrative longitudinal dataset from the French tax administration (Direction Générale des Finances Publiques or DGFIP), containing the universe of wealth tax returns matched to income tax returns from 2006 to 2017. For taxpayers subject to the wealth tax, the tax returns include all the information required in either the detailed or simplified tax returns (see Appendix Table B.3). The income tax returns include information on all taxable capital and labor incomes, and basic demographics.

Columns 1 and 2 of Table 1 report summary statistics for taxpayers liable to the wealth tax in 2010 and 2012. The lower number of taxpayers in the second column stems from the increase in the exemption threshold in 2011. Wealthy taxpayers are on average 66 years old. About 67% of them are retirees and around 70% are landlords. Their taxable income is on average e90,000 in 2010 and (following the increase in the exemption threshold) e120,000 in 2012. Their average wealth is e1.8 million in 2010 and e2.7 million in 2012. Figure A.3 plots the composition of gross taxable wealth by net wealth level (in the e790,000 to e3 million range) in 2010, the year before the simplification reform. Assets can be divided into financial assets, primary residence, and other real estate. Financial assets are always the largest category, but their importance increases from less than 40% for taxpayers with e790,000 in wealth to 60% for taxpayers with e3 million in net taxable wealth. Real estate assets excluding the primary residence account for a roughly constant share (30%) of taxable wealth. The value of the primary residence is around 30% at the lowest wealth levels and decreases to just 10% for taxpayers with e3 million in net taxable wealth.

Graphical Evidence on Wealth Responses to Tax Rates and Reporting Requirements

This section presents graphical evidence of behavioral responses to three types of discontinuities in the wealth tax schedule: tax brackets, the exemption threshold, and the simplification threshold.

Bunching at Marginal Tax Rate Discontinuities

Tax brackets introduce changes in marginal wealth tax rates, so-called "kinks" in the budget set of taxpayers. Figure 2 shows the responses to the kinks in the wealth tax schedule in 2010 associated with a tax bracket threshold. The figure reveals that the distribution of taxpayers below and above all tax kinks is smooth. Figure A.10 shows that the distribution of growth rates around the tax brackets is also smooth. Similar results hold for all years and across all tax brackets (see Figures

A.5-A.7).
The lack of significant bunching at the kinks suggests that households do not sharply manipulate their reported taxable wealth to stay below tax kinks. This finding is somewhat surprising given the low level of wealth tax enforcement and lack of third-party reporting, but is consistent with the findings in Denmark of Jakobsen et al. (2020). Of course, evasion and avoidance may still be prevalent but not visible at the kinks: the whole distributions may be shifted to the left relative to a counterfactual of lower tax rates.

Bunching at the Exemption Threshold

Next, we study behavioral responses at the exemption threshold.

Panel A of Figure 3 shows the distribution of taxable wealth above the exemption threshold for 2006-2010 (we do not observe wealth below). The shape suggests a missing mass just above the exemption threshold and indicates that many taxpayers who have wealth a little above the threshold level choose to "bunch" below and do not file a wealth tax return. The distribution of taxpayers is distorted above the exemption threshold in all years and this distortion increases over time.

To bolster the identification of the behavioral responses to the exemption threshold, we also exploit the 2011 increase in the exemption threshold to e1.3 million. Before this reform, in 2009 and 2010, the e1.3 million threshold was a pure tax kink. Panel B of Figure 3 shows that, consistent with the findings from Figure 2, there is no discontinuity in the wealth distribution at that wealth level in 2009 and 2010. In Panel C, we plot the distribution in year 2011. There is a clear drop in the number of taxpayers just above e1.3 million as compared to 2010, suggestive of a substantial share of households attempting to remain just below the exemption threshold. The distortion in the distribution of taxpayers is persistent and grows over time (see Panel D).

Therefore, we detect no response at e1.3 million when it was a pure tax kink but we see a clear and growing response when it becomes the exemption threshold. An exemption threshold is a combination of a tax kink and a reporting discontinuity since taxpayers below it do not report any information to the tax authority. This finding suggests that discontinuities in information disclosure play a key role in behavioral responses to the wealth tax.

Behavioral Responses to the Simplification Threshold

Last, we provide graphical evidence of behavioral responses at the simplification threshold.

Bunching in wealth at the simplification thresholds. To quantify the responses at the simplification threshold, we implement a standard static bunching approach following Kleven (2016), described in detail in Appendix C and with results reported in Table B.4. The excess mass around the e2.57 million threshold increases from 8% of the counterfactual distribution at the kink in 2010 to 2.7 times the counterfactual in 2013. It reaches 4.50 times the counterfactual in 2017.

Because there was no excess mass below e2.57 million before 2013 (when there was only a discontinuity in marginal tax rates at that wealth level, but not in information reporting requirements), bunching responses after 2013 appear to be entirely due to the change in reporting requirements. Our findings also suggest that wealthy taxpayers quickly learn about and adjust to wealth tax design changes, which stands in contrast to other types of taxpayers such as small business entrepreneurs (Aghion et al., 2022).

Average growth rates below and above the simplification thresholds. Figure 5 reports changes in average reported wealth growth rates around the simplification threshold for three sub-periods:

2006-2010 (before the simplification reform), 2011-2012, and 2013-2017 (post-reform). Before the introduction of the simplification threshold in 2011, growth rates were roughly constant across wealth levels (Panel A). 15 Panel B shows that, after the introduction of the simplified returns in 2011, there is an immediate distortion in growth rates around the e3.0 million simplification threshold. For taxpayers with e2.0 to e3.0 million in wealth, growth rates decrease as we move closer to e3.0 million. For taxpayers with e3.0 to e3.5 million in wealth, growth rates are constant and similar to those of taxpayers located far below the threshold. When the simplification threshold is reduced to e2.57 million in 2013, the discontinuity in wealth growth rates moves to that new threshold (Panel C). 16 Furthermore, the wealth growth rates are reduced for a large segment below the simplification threshold. Distribution of growth rates above and below the threshold. Next, we study heterogeneity in growth rates at each taxable wealth level. Figure A.13 reports the share of taxpayers by quartiles of wealth growth, where quartiles are defined based on the sample of households with taxable wealth between e3.0 and e3.5 million. The proportion of taxpayers with low growth rates (in the bottom quartile) increases right below the threshold and then falls above the threshold. On the contrary, the share of taxpayers with high growth rates (third or top quartile) sharply declines before the threshold. Figure A.14 shows the share of taxpayers with zero or negligible growth (growth rates between 0% and 0.1%). Whether in the cross-section (Panel A) or for cohorts defined in the years 2012-2016 (Panels B to F), there is a significant spike in the share reporting a zero growth rate right below the threshold.

Summary of the graphical evidence. To summarize, we find no bunching at thresholds where only tax rates change (pure tax thresholds), but substantial bunching at information discontinuity thresholds (exemption and simplification thresholds). Furthermore, we find clear reductions in wealth growth rates for a large segment below the simplification threshold. The immediate and sharp responses to changes in reporting requirements are suggestive of avoidance and misreporting rather than real (savings or investment) changes. Overall, these facts suggest that reporting requirements play a key role in driving behavioral responses to the wealth tax.

Dynamic Responses to Changes in Reporting Requirements

In this section, we exploit the panel dimension of our dataset to study the dynamic effects of reporting discontinuities. We focus on the lowering of the simplification threshold to e2.57 million in 2013, a clean variation in reporting requirements that kept tax liabilities unchanged.

To study the effect of this reform, we keep households for which we can observe growth rates at least once before and once after the reform (this reduces sample size by 9%). Second, we drop households who experience a change in family status such as a death, divorce, or marriage (10.4% of the initial sample). Last, we exclude observations with extreme wealth growth rates (above the 99th or below the first percentile of each annual growth rate distribution, another 2% of the sample). In total, we drop 19.8% of the raw sample. Table 1 summarizes the characteristics of the full raw sample and of our analysis sample for the pre-reform years 2010 and 2012. Demographic characteristics, income composition, wealth tax payments and tax rates are similar in the two samples.

Motivation for a Dynamic Bunching Approach

Even absent behavioral responses, we would expect wealth to grow because of saving and valuation effects. A "classic" difference-in-differences bunching approach that considers the levels of wealth from year to year may therefore be misleading, unless it accounts for some normal growth rate. To address this issue, we study changes in the distribution of wealth growth rates.

We define groups of taxpayers based on their pre-reform distance to the simplification threshold of e2,570K. These groups are depicted in the diagram below. All households with taxable wealth close to the e2,570K threshold in 2012 are potentially treated by the change in reporting requirements in 2013. To capture potential heterogeneity in the responses, we split the treated group with taxable wealth in the [e2360K, e2710K[ range into five treated groups by bins of e70K euros of taxable wealth. 17 We select as our control group taxpayers with wealth between e2,710K and e2,850K in 2012. These taxpayers are simultaneously far enough above the e2,570K threshold and below the previous simplification threshold of e3,000K so that they are not affected by any of the reforms. Panel C of Figure 5 confirms that the wealth growth rates for these taxpayers exhibit no discontinuity. 18 Figure 6 plots the distribution of growth rates in our treatment and control groups, before and after the change in reporting requirements in 2013. Panel A shows that before the reform, all treated and control groups had similar distributions of growth rates (from 2011 to 2012). Panel B reveals that the distribution of wealth growth rates in the treatment group experienced a substantial change after the reform. For households located just below the simplification threshold in 2012, a spike in wealth growth rates appears around zero, mirrored by a missing mass of taxpayers with small positive wealth growth rates (between 1% and 5%). This is consistent with the intuition that taxpayers located very close to the simplification threshold in 2012 and who want to remain below the simplification threshold need to report a wealth level in 2013 that is almost identical to their wealth level in 2012, i.e., a wealth growth rate close to zero. The wealth of these taxpayers would otherwise potentially have grown at 1%-5% that year.

For treated taxpayers located further below the simplification threshold in 2012, the figure also reveals a substantial spike in wealth growth rates compared to the pre-reform year. The spike in wealth growth rate is, however, not centered around zero, but rather around small positive wealth growth rates. This suggests that households further away below the simplification threshold can report small positive wealth growth rates and still manage to remain right below the simplification threshold. This spike in the distribution of wealth growth rates induces a corresponding missing mass in the number of taxpayers with positive wealth growth rates that are between 5% and 10%.

Conversely, for treated taxpayers located just above the threshold in 2012, there is a spike in growth rates centered around small negative rates. These taxpayers must report negative wealth growth rates if they wish to locate below the simplification threshold. For this group of taxpayers, the wealth growth rate distribution after the reform features a corresponding missing mass around zero and small positive growth rates.

Figure 6 further sheds light on the nature of behavioral responses. We do not see a uniform downward shift in the distribution of growth rates for all households below the simplification threshold nor a spike at zero growth rates for all these groups. The different shapes of the growth rate distributions mean that we cannot directly compare across groups, unless we find a proper way to "normalize" these distributions, which is at the core of our dynamic bunching approach.

Dynamic Bunching Method

We develop an original dynamic bunching approach based on a causal effect framework as in Angrist et al. (1996). This method allows us to estimate: i) the growth rate reduction to study the effects of the simplification threshold at the group level (an intent-to-treat or ITT effect); ii) the proportion of bunchers, i.e., the share of taxpayers who react to the 2,570K simplification threshold (the compliers); iii) the growth rate reduction among the bunchers (a local average treatment effect or LATE).

We proceed in three steps. First, we define and compute "normalized growth rates" around the simplification threshold for treated groups. Second, we use the control group to estimate an appropriate counterfactual distribution of normalized growth rates. Third, we present a causal effect framework based on the comparison of the observed and counterfactual distributions to estimate the ITT, the share of compliers, and the LATE.

Normalized growth rates

For taxpayers affected by the simplification threshold, we define the normalized growth rate as the growth rate in excess of the growth rate that would make individuals cross the simplification threshold:

gi,t,2570 = W i,t+1 -W i,t W i,t actual growth rate - 2570K -W i,t W i,t
growth rate needed to be at threshold

= W i,t+1 -2570K W i,t (1)
If gi,t,2570 is zero, individual i locates exactly at the simplification threshold. When gi,t,2570 is negative, this means that i locates below the 2,570K threshold. For instance, gi,t,2570 = -0.015 means that the individual reported a wealth growth rate 1.5 percentage points lower than the growth rate that would have allowed her to locate exactly at the simplification threshold. Henceforth, for the sake of simplicity, we abstract for the subscript t and label the normalized growth rate as gi,2570 . To generalize our notation, we denote gi,S the normalized growth rate defined relative to the threshold S for individual i with taxable wealth W i,t in year t. We define f (g i,S ) as the distribution of gi,S and f T j (g i,S ) as the distribution of gi,S for taxpayers belonging to one of our treated group T j .

Figure 7 illustrates why the concept of a normalized growth rate allows us to resolve the issues highlighted above in Figure 6. Panel A depicts the distributions of normalized growth rates in 2013 for all the groups below the threshold. While the growth rate distributions have different means and shapes, the normalized growth rate distributions are directly comparable to one another.

They exhibit clear excess mass just below 0 and missing mass right above zero (taxpayers with these small positive growth rates would end up just above the simplification threshold in 2013).

There is excess mass just below the zero normalized growth rates, and bunching decreases with distance to the threshold. For instance, the group "very far below" seems only barely affected by the threshold. Panel B focuses on the groups above the threshold. The normalized growth rate distributions are now shifted toward positive values with excess mass exactly at the wealth growth rates that would push these groups below the simplification threshold. The size of bunching appears to be much less important for group located above than for groups located below the threshold prereform. The control groups' normalized growth rate distribution appears unaffected and exhibits no discontinuity.

Counterfactual distribution and placebo threshold

In a second step, we use the control group to derive a counterfactual distribution for each treated group. We construct the difference between the observed growth rate of the control group and the growth rate that would make taxpayers in the control group locate at a placebo threshold. The placebo threshold needs to be at the same distance-according to some metric-from the control group as the actual simplification threshold is for each treated group. Therefore, this placebo threshold differs for each treated group considered. For any treated group T j = [a j , b j [, the normalized growth rate of the control group C (taxpayers with wealth in the [2710K,2780K[ interval in 2012) is defined as:

gi,c j = W i,t+1 -c j W i,t with c j = 2780K × (2570K/b j ) (2)
where c j is the placebo threshold defined relative to each treated group T j for individuals in the control group C. Under our benchmark assumption, the distance between the placebo threshold and the control group is the same as the difference between the treated group and the simplification threshold in percent terms.

Alternatively, the placebo threshold can be such that the distance between that threshold and the control group is the same (in level) as the difference between the treated and control group.

This amounts to using the additive form:

c j = 2780K + 2570K -b j (3)
For instance, imagine we consider households in the treated group located with wealth in the threshold. This confirms that the 2011 reform around 3,000K did not shift the distribution of wealth growth rates for the control group we will use in our main analysis. Finally, our control group is also not affected by the simplification threshold around 2,570K in 2013, as already showed in Panel B of Figure 7.

Conceptual Framework

We now provide a causal effect framework as in Angrist et al. (1996) to estimate the effects of the simplification threshold. In Appendix F we provide more details on the mapping of our dynamic bunching approach with the causal effect framework, and we formally derive and discuss our identifying assumptions. 19 For each treated group T j (defined by an interval of wealth in 2012), we observe the distribution of normalized growth rates f T j (g i,2570 ). We call bunching area or excluded range, denoted by [a L , a U ], the interval affected by the simplification threshold and where the distributions of the control and treated groups diverge. We explain how we compute the (unobserved) bounds a L and a U below. In the bunching area below the threshold, [a L , 0], there is an excess mass, mirrored by a corresponding missing mass in the bunching area above the threshold [0, a U ]. We first want to measure the impact of the 2,570K simplification threshold on the distribution f T j in the interval

[a L , 0].
We define B j as the share of bunchers in each treated group T j :

B j = 0 a L [ f T j (g i,2570 ) -f counterf actual T j (g i,2570 ) ]dg i,2570 (4)
where

f counterf actual T j (g i,2570
) is the counterfactual distribution of the normalized growth rate in the treated group, i..e, the distribution that would arise absent the treatment. It cannot be observed directly in the data. To recover this counterfactual distribution, we use the control group's normalized growth rate distribution relative to the placebo threshold:

f counterf actual T j (g i,2570 ) = f C (g i,c j ),
with c j the placebo cut-off adapted to the treated group T j . The share of bunchers can then be rewritten as:

B j = 0 a L f T j (g i,2570 )dg i,2570 - 0 a L f C (g i,c j )dg i,c j (5)
We can approximate this share of bunchers using the data by bins. Let P Z (a) be the proportion of the group Z population in a given bin a of gi,S . The share of bunchers is estimated as:

B j = 0 ∑ a=a L [P T j (a) -P C (a)] (6)
Figure 8 shows the application of our dynamic bunching framework for the group just below the threshold in 2012. The distribution of normalized growth rate is plotted in blue for the treated group and in red for the control group, and the difference between the two distributions in the interval [a L , 0] identifies B j .

Bunching range. To compute the lower and upper bounds of our bunching range, we first set the lower bound a L visually by noting the point at which the distributions f C (g i,c j ) and f T j (g i,S ) begin to diverge. In our benchmark case, a L = -0.045. The upper bound a U is then chosen such that the bunching mass (blue area in Figure 8) equals the missing mass (green area in Figure 8), i.e., such that:

0 ∑ a=a L [P T j (a) -P C (a)] = - a U ∑ a=0 [P T j (a) -P C (a)] (7)
This leads us to set a U = 0.1 and our bunching interval is therefore [-0.045, 0.1].

Growth rate reduction in the treated group. We compute the average growth rate reduction at the group level ∆E j (g) using the formula:

∆E j (g) = E(g|T j ) -E(g|C) = a U ∑ a=a L [P T j (a) × g T j (a) -P C (a) × g C (a)] (8)
where g Z (a) stands for the average growth rate for the group Z population in a given bin a. ∆E j (g) is akin to an ITT effect. We compute it over the bunching range [a L , a U ] because the distributions are assumed to be identical (by definition of the counterfactual) outside of this range and this is verified empirically.

Growth rate reduction amongst bunchers We also compute the growth rate reduction among the bunchers ∆E j (g) B , which can be interpreted as the LATE of the simplification threshold. We scale the average effect ∆E j (g) by the share of bunchers:

∆E j (g) B = ∆E j (g)/B j (9)
We obtain standard errors using a bootstrap procedure.

Results

We now present our results using this methodology in Figure 10. Each panel displays our treatment (blue lines) and control (red lines) series, for four different treated groups ("Just below" in Panel A, "Far Below" in Panel B; "Just above" in Panel C; and "Far above" in Panel D). In each panel, we report our three key statistics of interest: the average growth rate response in the treated group (ITT), the share of bunchers, and the average growth rate response amongst bunchers (LATE).

There are four main findings.

First, Figure 10 shows that lowering reporting requirements substantially distorted wealth growth rates in a broad segment of the wealth distribution, not only for groups located right below the threshold. Groups further below or just above the threshold are also significantly affected.

Second, the average responses to the simplification threshold are smaller for groups located further away from it. The average reductions in growth rates (ITT) range from 0.47 p.p for the group Just Below and 0.44 for the group Far Below to 0.18 p.p for the group Just above, which can be compared to the average growth rate of 2.3% for the control group. These ITT estimates are similar to the ones estimated with a simple difference-in-differences strategy, as we show in Section 4.4.

Third, these responses of different groups (defined by their levels of wealth) to the simplification threshold are driven by a small subset of taxpayers. We can compute the share of taxpayers who react to the simplification threshold in each group, i.e., the share of bunchers. These shares are 14.7% taxpayers in the group Just below, 8.4% for the group Far below, 3.9% for the group Just above, and 1.4% for the group Far above. The share of bunchers thus decreases as we move away from the simplification threshold.

Among bunchers in each group, the growth rate reductions are much larger than for the average taxpayer in the group. For the group Just below, the wealth growth rate is 3.2 percentage points lower, relative to a counterfactual growth rate of 4.8%. For the group Far below, the growth rate reduction is 5.2 p.p relative to a counterfactual growth rate of 7.8%. In the group above, the reduction in the growth rate is 4.8 p.p, even though the counterfactual suggests these groups should have grown at 1.6% (they essentially report negative wealth growth).

Our analysis therefore shows that the ITT effects that would be estimated through the lens of a standard difference-in-differences approach are actually driven by a small share of taxpayers who significantly reduce their wealth growth rates to benefit from low information requirements when filling for the wealth tax.

Fourth, our findings indicate that the proportion of bunchers in the group located just above the wealth threshold in 2012, which stands at 3.9%, is significantly lower than for those located just below the threshold in the same year (14.7%). Similarly, the average growth rate reduction in the group just above the threshold is smaller than for the one below. What explains this asymmetry?

Taxpayers above the threshold in 2012 must report a decrease in their net worth to qualify for the simplified reporting regime, whereas those below the threshold only need to report a lower (weakly positive) growth rate. Taxpayers may worry that reporting lower taxable wealth relative to the previous year could raise suspicions from the administration and make it more likely to be audited. 20 We explore issues related to the costs of evasion and avoidance in Section 5.3.

Growing responses to the threshold over time. We apply our dynamic bunching approach to subsequent cohorts, namely those defined in 2013 and 2016 (Figures A.20 and A.21). The results are similar to those for our benchmark 2012 cohort. However, the estimated average growth reduction (ITT) is increasing over time: for taxpayers just below the threshold, the ITT almost doubles from 20% of the control group's growth rate in 2012 to 40% in 2016. The share of bunchers in each treated group is also significantly larger for later cohorts. For instance, among taxpayers just below the threshold, the share of bunchers increases from 15% for the 2012 cohort to 24% for the 2016 cohort.

Related to our result regarding the asymmetric response of taxpayers above and below the thresholds, we can see some form of "reverse bunching" among taxpayers in the Just above groups in the 2013 and 2016 cohorts (Panels C in Figures A.20 and A.21). Relative to the control group, there is some excess mass at small positive normalized growth rates for the group Just above, as these taxpayers are reluctant to report negative enough growth rates (even if those are legitimate)

to push them below the threshold out of fear of raising suspicion.

Persistence within taxpayers. How does a given taxpayer adjust to the simplification threshold over time? Figure 11 Consider taxpayers in the treated group with a normalized growth rate between -2% and 0%.

These are taxpayers who located right below the simplification threshold in 2013. Following our earlier analysis, there is a substantial share of bunchers in this group, i.e, individuals who intentionally adjust their growth rate to remain below the threshold. By contrast, taxpayers in the control group with a normalized growth rate between -2% and 0% are locating at the same relative distance from their placebo threshold and there are, by construction, no bunchers in this group.

These taxpayers from the control group serve as a counterfactual for the expected probability to cross an equivalent threshold after one or three years, absent a behavioral bunching response to the simplification.

In line with our findings of substantial and persistent misreporting behavior around the 2,570K threshold, the probability that taxpayers with normalized growth rates between -2% and 0% in 2013 end up above the 2,570K threshold in 2014 (one year after the reform) is 32% in the treated group against almost 60% in the control group. Panel B shows that this effect persists over time.

In 2016, three years after the reform, the probability that taxpayers in 2013 end up above the 2,570K threshold is 43% in the treated group against more than 60% in the control group. More generally, we see that taxpayers in the treated group with negative normalized growth rates in 2013 (i.e, who remain below the threshold in 2013) systematically have a lower probability of crossing the threshold than taxpayers in the control group with the same normalized growth rates. This discrepancy persists even three years later.

Robustness check around another simplification threshold. As a robustness check, we apply our dynamic bunching analysis to the introduction of a simplified return for taxpayers below the 3,000K threshold in 2011 and 2012. We define treatment and control groups following the same methodology as before except that we focus on 3,000K instead of 2,570K as our information discontinuity. We present dynamic bunching estimates of responses to the 3,000K threshold in is consistent with the dynamic responses by cohorts around the 2,570K threshold that we previously described in Figure 11. For both simplification thresholds, we find that responses grow over time for a given group, and those responses progressively spread-out below the threshold over the years. This confirms that our estimates do capture behavioral responses to information discontinuities rather than responses to other potentially unobserved discontinuities that would be associated with the 2,570K threshold after 2013.

In Figure A.24, we can also show that the response around the 3,000K threshold disappears in 2013, when the simplification threshold is reduced to 2,570K. Once the information discontinuity is removed in 2013, the distribution of normalized growth rates for taxpayers located just below the 3,000K threshold in 2012 aligns with the control group.

Difference-in-Differences Strategy

We now present results from a simple difference-in-differences strategy in which we track taxpayers' wealth growth rates in control versus treated groups before and after the change in reporting requirements. This allows us to compare the results from a difference-in-differences approach to our dynamic bunching method. Furthermore, by tracking taxpayers over several years, we can study persistent responses to the lower reporting requirements. We estimate the following model:

g i,t = W i,t -W i,t-1 W i,t-1 = ∑ j 2017 ∑ k=2008 k̸ =2012 β jk • 1{i ∈ T j } × 1{t = k} + α i + λ t + ε i,t (10)
where α i is an individual fixed effect, λ t is a year fixed effect, 1{i ∈ T j } is a dummy equal to one if the individual belongs to the treated group T j and 1{t = k} is a dummy equal to one if year is year k. We set β j,2012 = 0 and λ 2012 = 0 such that all estimates can be interpreted as the difference in wealth growth rates between treated and control taxpayers in year k relative to 2012. The sequence of estimates β jk captures the differential evolution of wealth growth rates for households in the treated group j compared to the control group over time. They represent an intent-to-treat effect of lowering information requirements because they capture the responses of all taxpayers in the treatment group, regardless of whether they effectively react to the reform.

Results and comparison to the dynamic bunching method. We report our estimates for all treated groups in Table B.2 and plot the estimated effects for the groups closest to the threshold in Figure 13, distinguishing between treated taxpayers located just below the threshold in 2012 (panel A), and those located just above (panel B). The growth rates follow the same evolution in each of the treated groups and the control group for the four years preceding the policy change. This lends support to our identifying assumption that households located far above the 2,570K threshold provide a credible counterfactual for the evolution of wealth growth rate of households located closer to the threshold. The figure shows significant and persistent reductions in growth rates or treated taxpayers located just below the 2,570K threshold in 2012 (equal to 0.6-0.8 percentage points in each of the four years following the 2013 reform). This magnitude is equivalent to 25-30% of the control group growth rate. For households located just above the 2,570K threshold in 2012, we find a much lower and non statistically significant effect. Consistent with our dynamic bunching approach, the bulk of the response to the change in reporting requirements comes from households located below the simplification threshold.

Table 2 compares the estimates of the ITT effects in the dynamic bunching approach and the standard difference-in-differences for the year 2013. The estimated ITT effects are consistent and not statistically significantly different. However, the standard errors are four times smaller when using the dynamic bunching approach. We find significant effects for all treated groups with the dynamic bunching approach but only for the group Just below using the difference-in-difference approach.21

Mechanisms and Discussion

In this section, we study the mechanisms through which taxpayers substantially and persistently reduce their wealth growth rates following the lowering of reporting requirements.

Pre-Reform Differences Between Treated and Control Groups

We first seek to understand whether bunchers (i.e., compliers) differ from other taxpayers in terms of assets, occupation, and income composition. However, we do not know whether any given individual taxpayer is a buncher. As Figure 8 showed, taxpayers in the treated group and taxpayers in the control group have different distributions of normalized growth rates. The treated group is made of "always takers," i.e., taxpayers who would have a given normalized growth rate even absent the simplification threshold and compliers (taxpayers who only exhibit a given wealth growth because of the threshold). "Always takers" correspond to taxpayers who would have been below

the threshold irrespective of the reform, and "compliers" to taxpayers who would have been above

the threshold absent the reform but, due to the reform, locate themselves below the threshold.

Among taxpayers in the treated group in the bunching area below the threshold, there is a larger share of bunchers. For instance, at normalized growth rates between -2% and 0%, the share of bunchers in the treated group is 40%. Therefore, we compare the characteristics of treated taxpayers with normalized growth rates in 2013 of, say, between -2% and 0%, to the characteristics of control group taxpayers with that same normalized growth rate in 2013. Under the assumption that taxpayers who are always-takers in the treated group have the same characteristics as taxpayers in the control group with the same normalized growth rate, any differences between the treated and control group at a given normalized growth rate can be attributed to the compliers.

We start by comparing the pre-reform characteristics (in 2010) of the treated and control groups. In for the treated and control group, by bins of 2013 normalized growth rates. If bunchers were different in terms of asset composition and had, say, a higher share of a given asset in 2010, we would expect to see higher shares of that asset in the treated group around normalized growth rates ranging from -2% to 0%. We may also expect to see a corresponding lower share of those assets for treated taxpayers with normalized growth rates between 0% and 2%. We do not detect any such differences between the treated and control groups.

We repeat the same analysis as in .27). We find that before the reform, treated taxpayers with normalized growth rates around -1% had similar occupations, received the same type of income, and claimed similar levels of tax credits, compared to taxpayers in the control group at these normalized growth rates. Bunchers do not significantly differ along these characteristics.

Post-reform Differences Between Treated and Control Groups

Are responses to low reporting requirements associated with lower income after the reform?

A key benefit of the link between the wealth tax data and income tax returns is that we can investigate whether the effective change in reported taxable wealth following the 2013 reform goes hand in hand with a change in labor and capital income. If the lower reported taxable wealth is driven by real effects, we would expect to see a corresponding fall in capital income and/or labor income (through savings). However, Figure 14, shows that this is not the case. The figure

shows the evolution between 2010 and 2017 of different types of incomes and tax rates for the subsample of the control group and the treated group "Just Below" (as defined in 2012) who have a normalized growth rate just below zero (]-2%,0%[), i.e., who are in the bunching area below the threshold. Recall that, in the treated group, there is a large share of bunchers at these normalized growth rates. The figure shows that taxable income and the shares of financial income, real estate income, and self-employed income all evolved similarly for these two groups, before and after the change in reporting requirements. Thus, while taxpayers who respond to the reporting requirements significantly reduce their reported taxable wealth, we do not see any corresponding change in their capital and labor incomes. Furthermore, Panels E and F show that there is no difference in the effective tax rates paid by these groups, either before or after tax credits. This suggests that behavioral responses to low reporting requirements capture avoidance or misreporting rather than real responses.

Are responses to low reporting requirements driven by misreporting of specific assets?

We then try to identify the categories of taxable wealth which are adjusted by taxpayers after the change in reporting requirements by studying the portfolio compositions of different groups after the implementation of the simplified tax returns.

The main challenge is that taxpayers below the simplification threshold after 2013 do not report detailed asset compositions. Our strategy is therefore to focus on taxpayers who cross the simplification threshold at some point during the 2014 to 2017 period (as highlighted in Figure 12).

To understand what is driving taxpayers out of the simplified regime, we then decompose wealth growth rate by assets type for the treated group taxpayers that cross the threshold one year after the reform and for the control group taxpayers who cross the placebo threshold. Like before, we compare the treated and control group of taxpayers "Just Below" (as defined in 2012) by level of normalized growth rate from 2012 to 2013. Treated taxpayers with a normalized growth rate just below zero (]-2%,0%[) are in the bunching area below the simplification threshold.

In Figure 15, we show that conditional on crossing the threshold, there are large differences between treated and control taxpayers in terms of financial assets growth after the reform. Treated taxpayers in the bunching area experienced a 3.5 percentage point higher growth rate in their financial assets between 2010 and 2014, compared to their counterparts in the control group. In contrast, those in the treated group who did not react to the simplification reform experienced the exact same growth in terms of financial assets compared to taxpayers in the control group with similar normalized growth rates in 2013. The results are similar when looking at bunchers who cross the threshold in 2016 (Figure A.28). Treated taxpayers experienced a 2.5 percentage point higher growth rate in their financial assets between 2010 and 2016, compared to their counterparts in the control group.

This analysis highlights that bunchers end up crossing the threshold after they experience large positive shocks to their financial assets. One way to interpret this finding is that shocks in financial assets are hard to hide and therefore force bunchers into filing the detailed wealth tax return again.22

Discussion

Summary of key behavioral responses. What can we learn about the underlying reasons and mechanisms for taxpayers' behaviors from the previous analyses? The findings to inform a potential model of taxpayer behavior are as follows:

1. There is sharp bunching of taxpayers at the simplification threshold.

2. Several groups of taxpayers below the threshold respond to it, not only those directly below, even though responses are strongest for groups closer to the threshold.

3. Taxpayers above the threshold (who would have to report negative growth rates in order to locate below the threshold) exhibit much lower bunching.

4. Growth rates are systematically lower for taxpayers below the simplification threshold than for taxpayers above.

5. Responses to the simplification threshold are persistent, with taxpayers attempting to remain below the threshold for multiple years, as long as possible and being "pushed out" of the simplified regime once significant financial asset shocks occur.

6. We cannot detect any change in labor or capital income that could justify the changes in reported wealth.

7. There is no discernible response at pure tax kinks in the detailed reporting regime.23 8. There is significant bunching at the exemption threshold.

A model of wealth tax misreporting. The second and fifth findings point to reporting and avoidance responses rather than real saving responses, because the true value of taxable wealth is not easily controllable by taxpayers since it depends on asset prices. This hypothesis is bolstered by the finding that there is no corresponding change in labor or capital income that could justify changes in taxable wealth. In Appendix E, we suggest a simple model to rationalize these findings. Taxpayers value being in the simplified regime so that the simplification threshold generates a substantial notch in the payoff. They therefore misreport their wealth in order to stay below the simplification threshold. Misreporting is costly and the cost is increasing in the amount of misreporting and decreasing in the reported growth rate from year to year. The latter assumption explains why forward-looking taxpayers further below the threshold will report lower wealth and growth rates as well, to facilitate anticipated misreporting in future years.

There are no discernible bunching at pure tax kinks in the detailed regime for two potential reasons (which can both be applicable): because the underlying misreporting elasticities are small (but would still generate significant bunching at a large notch in payoffs such as the simplification threshold or the exemption threshold) and/or because the simplified regime makes misreporting easier. The bunching at the exemption threshold can be rationalized with a fixed cost from filing any wealth tax return.

Why do taxpayers want to remain in the simplified regime? There are three potential, nonexclusive reasons why taxpayers may want to remain in the simplified regime. First, taxpayers may value the lower hassle cost of reporting taxes with a simplified return. Second, they may have privacy concerns and be averse to reporting information to the government. Finally, it may be easier to misreport wealth in the simplified reporting regime. When taxpayers only need to report total wealth, instead of detailed a breakdown, they may feel that it is easier to hide specific assets or report incorrect amounts.

Although each of these channels may play some role, it is unlikely that there is a big hassle cost difference between the detailed and the simplified tax form. The tax administration requires that taxpayers keep records in case of audits, so the information needs to be recorded and stored regardless of the type of form filled out. Furthermore, the affected taxpayers are wealthy (in the top 1% the wealth distribution) likely use some professional help for accounting and tax purposes (even if the overall tax preparer industry is less developed than in the US).

The extent of privacy concerns is also unclear because the government already has access to a lot of information on real estate (through property tax filing), financial wealth (through bank and brokerage accounts), and other sources of capital income (through income tax returns). 24 Although this information does not currently appear to be used explicitly for the wealth tax administration, taxpayers should be aware that most of it is already in the hands of the tax administration.

All in all, the ease of misreporting may be the most important reason why taxpayers value the simplified regime. In fact, if the simplified reporting reduced the burden of filing wealth taxes or the privacy concern associated with it, we might expect that some taxpayers who would otherwise have remained below the exemption threshold are now enticed to cross it. However, the data does not support this view, as we show next.

Are more people willing to cross the wealth tax exemption threshold? In Appendix D, we quantify the number of missing taxpayers around the exemption threshold. Our baseline methodology exploits Pareto parameters computed in the unaffected segment of the wealth distribution, that we then use to extrapolate the distribution of taxpayers around the exemption threshold. 25 Table B.5 shows substantial missing mass just above the exemption threshold, both pre-2011 when the exemption threshold was around e790,000, and after 2011 when the exemption threshold was 24 There is no automatic third-party reporting of bank accounts value, only taxable capital income flows from those accounts are third-party reported by banks. However, the government has access to information on all "assurances vie" (of more than e7,500) which the most important financial asset owned by French households, see Goupille-Lebret and Infante (2018) for more details. 25 Our identifying assumption when conducting this analysis is that Pareto parameters should be constant over the [1,300K-4,000K] interval. Fortunately, data on pre-reform distributions allows us to gauge the plausibility of this assumption. Figure A.30 shows that this assumption is validated in the data. moved to 1,300K. The share of missing taxpayers around the exemption threshold after 2011 is increasing, as behaviors slowly adjust to the newly implemented simplification threshold. In 2017, around 30% of taxpayers are missing around the exemption threshold. This share is close to and, if anything, slightly lower than the 37% of missing taxpayers in 2010, before any simplified return was implemented. This suggests that allowing taxpayers to fill a simple tax return did not induce more taxpayers to enter the wealth tax reporting and did not reduce bunching below the exemption threshold after 2013.

Summing up. The reason why people value the simplified regime relates to the normative question of whether it should be extended or eliminated. Clearly, the threshold itself is generating a behavioral effect and distortion, so we may ask whether it should be expanded to everyone (or more taxpayers) or rather eliminated altogether. Based on the preceding arguments, it is likely that taxpayers value the ease of misreporting and that the loss of information leads to persistently higher under-reporting of wealth. It also does not appear that the simplified regime enticed more taxpayers to file a wealth tax return in the first place.

Conclusion

In the debate on the desirability of wealth taxes, several papers have studied the experience of various countries with wealth taxes. Estimated elasticities, however, vary widely. We find zero bunching responses to changes in the wealth tax rates alone (kinks) in France, but substantial responses to information notches introduced by the exemption and simplification thresholds. Most papers in the literature focus on exemption thresholds. In Sweden, Seim (2017) finds substantial behavioral responses to the exemption threshold in the context of wealth tax in Sweden, with implied elasticities between 0.1 and 0.3. In Denmark, Jakobsen et al. (2020) find substantial responses to the exemption threshold, with long-run elasticities of taxable wealth around 1. In Colombia, where enforcement is lower than in Sweden, Londoño-Vélez and Avila-Mahecha (2022) find large behavioral responses to the wealth tax, in particular at the salient exemption notch. Like in France, taxpayers in Colombia face additional reporting requirements when they become subject to the wealth tax. 26 Londoño-Vélez and Avila-Mahecha (2022) estimate an elasticity with respect to the net-of-tax rate between 0.3 and 4.4 at the exemption notch. Our results show that behavioral responses to the exemption notch are likely to capture responses to changes in reporting requirements rather than to changes in tax rates. In our context, bunching responses to the wealth tax only arise when discontinuities in marginal tax rates are associated with changes in reporting requirements, corroborating that information avoidance is the main channel explaining bunching responses to the wealth tax.

Our results imply that poor tax design choices can have immediate implications for tax enforcement, and that these effects may be large and persistent. Taxpayers in lower reporting environments (such as those below the simplification threshold in our setting) persistently under-report their wealth, which in turn can lead to deterioration in the information and, hence, enforcement capacities of the tax authorities. A one-off collection of information may not be enough and it may take a long time to recoup the lost enforcement capacities.

If specific design choices can contribute to increasing tax elasticities, other choices can contribute to reducing them, such as mandating pre-populated returns, collecting and using information automatically transmitted by domestic and foreign third parties, or taxing non-residents.

A full cost-benefit analysis of different elasticity-reducing design features of income and wealth taxes constitutes a fruitful avenue for future research. Notes: This figure shows the distribution of taxpayers by net taxable wealth around the simplification threshold (dashed vertical line) implemented for taxpayers with net taxable wealth below 3,000K in 2011 and that was moved at 2,570K in 2013. We group households into bins of e10,000 of taxable wealth and plot the bin counts around the threshold each year. We also plot the threshold for the third tax bracket, which was 2,520K in 2009, 2,530K in 2010, and 2,570K in 2013 (solid vertical line). The discontinuity in MTR associated with passing the third bracket threshold was stable: 0.25 percentage points before 2013, and 0.30 percentage points after 2013. From 2007 to 2012, the third bracket MTR threshold was associated with a change in marginal tax rate (a tax kink) but not with a change in reporting requirements. In 2013, the third bracket and the simplification threshold coincide at 2,570K. In each figure, we group households into bins of e10,000 and plot the bin counts around the simplification threshold. Panel A shows the distribution of taxpayers in 2011, when the simplification threshold is newly created at 3,000K, as compared to the distribution in 2010; Panel B plots the distribution of taxpayers in 2011 and 2012, after the simplification threshold at 3,000K has been in place for one year already. Panel C plots the distribution in 2013 when the simplification threshold is moved to 2,570K and starts to coincide with the third bracket and compares it to the distribution in 2012. Panel D plots the distribution of taxpayers for 2013, 2015, and 2017, years for which the simplification threshold remained stable at 2,570K and compares it to the distribution in 2011. Notes: This figure shows the distribution of yearly wealth growth rates by wealth bins, pooled for different periods, around the simplification threshold (vertical solid line). In each figure, we group household into bins of e20,000 of reported taxable wealth. We plot the average wealth growth rate by bin and fit linear models (one below and one above the cut-off), depicted by the dashed black lines. Panel A pools all observations for the period before the simplified reporting was introduced (2006-2010), Panel B pools all observations for the period during which the simplification threshold was at 3,000K (2011-2012) and Panel C pools all years for the period during which the simplification threshold was 2,570K (2013-2017). The shaded areas depict 95% confidence intervals.

Figures and Tables

  Figure 4 starts by showing the distribution of taxable wealth around discontinuities in reporting requirements. Panel A shows that the distribution of taxpayers around e3.0 million was smooth in 2010, but an excess mass appears in 2011 when this wealth level becomes the simplification threshold. Panel B shows that the discontinuity is even larger in 2012. 14 In 2013, the simplification threshold was reduced to e2.57 million. The distribution of taxpayers around e2.57 million is smooth in 2012 but exhibits significant bunching in 2013 (Panel C), which persists and grows over time (Panel D). Meanwhile, bunching at the old e3.0 million simplification threshold disappears.

[

  2430K,2500K[ range in 2012. The distance between the upper bound b = 2, 500K of this interval and the simplification threshold is 70K (= 2, 570K -b). To pick a placebo threshold for the control group [2710K,2780K[ that is at the same distance, we need to choose c j = 2, 780K + 70K.

Figure A. 15

 15 Figure A.15 shows that the additive approach yields similar results.

  tracks the same taxpayers over time. In Panel A, left figure, we follow the cohort of taxpayers who are in the Just below group in 2012 and plot their normalized growth rate distributions in the subsequent four years(2013-2016). In Panel B, we repeat this with the cohort in the Just below group in 2014; in Panel C in 2016. The first two panels show that the bunching in normalized growth rates is highly persistent within taxpayers over time. Although it is strongest in the first year (e.g., 2013 for the 2012 cohort and 2015 for the 2014 cohort) it remains sharp and large even after four years. The right figure in Panel A considers taxpayers at a given level of taxable wealth in 2012 and plots their reduction in growth rates relative to the growth rate of taxpayers above 3,000K for the subsequent four years. The normalization by the growth rate of taxpayers further above the threshold is to account for the different growth rates of the economy in different years. Panel B repeats this analysis for the cohort defined in 2014; Panel C for the cohort defined in 2016. There is a persistently lower growth rate for taxpayers below the threshold that is attenuated over time. Together these results suggest a high persistence in the reduction of growth rates for taxpayers below the simplification threshold. Taxpayers persistently report lower wealth and pay less taxes than they would have absent the simplification threshold.

Figure 11

 11 Figure11suggests that, although bunching is highly persistent within taxpayers over time, some taxpayers do end up crossing the threshold. Panel A of Figure12shows the share of taxpayers in the treatment and control groups (as defined based on their pre-reform taxable wealth in 2012) who cross the simplification threshold in 2014 as a function of their normalized growth rate from 2012 to 2013. Panel B shows the same three years later in 2016. For the control group, this share is defined relative to the placebo threshold.

Figure A. 22

 22 Figure A.22 for year 2011, and in Figure A.23 for year 2012. Our analysis of the 3,000K threshold

  Figure A.25, we plot the 2010 share of housing wealth (Panel A), financial assets (Panel B), liabilities (Panel C), and primary residence (Panel D) in taxpayers' total taxable wealth,

  Figure A.25, focusing on differences in occupations (Figure A.26) and income composition (Figure A

Figure 1 :

 1 Figure 1: Wealth Tax Schedule and Reporting Requirements in France, 2007-2017 A. Reporting Requirements

Figure 2 :

 2 Figure 2: Absence of Bunching at Kinks in the Tax Schedule (Marginal Tax Rate Changes)

Figure 4 :

 4 Figure 4: Bunching at Simplification Thresholds

Figure

  Figure 5: Behavioral Responses to Simplification Thresholds: Wealth Growth Rates

  5: Behavioral Responses to Simplification Thresholds: Wealth Growth Rates A. No Simplification Threshold in 2006-2010 B. Simplification Threshold is 3,000K in 2011-2012

		.03
									.03
	Wealth Growth Rate	.01 .02						Wealth Growth Rate	.01 .02
		0		Average growth rate	Linear fit			0		Average growth rate	Linear fit
		2000	2250	2500	2750	3000	3250	3500	2000	2250	2500	2750	3000	3250	3500
				Taxable Wealth (EUR 000s)					Taxable Wealth (EUR 000s)
	C. Simplification threshold is 2,570K in 2013-2017
		.03
	Wealth Growth Rate	.01 .02
		0		Average growth rate	Linear fit
		2000	2250	2500	2750	3000	3250	3500
				Taxable Wealth (EUR 000s)

  Figure 14: Evolution of Reported Income, Income Composition, and Income Taxes A. Taxable Income B. Share of Financial Income Notes: This figure shows differences in taxable income (Panel A), income composition (Panels B, C, and D) and income tax rates (Panels E and F) over time for the treated group just below ([2500-2570[) and the control group([2710-2780[) with a normalized growth rate between -2% and 0% in 2013. 114,447 184,104 161,437 180,884 160,928 168,699

		160		Groups defined in 2012 with a 2013					.3		Groups defined in 2012 with a 2013
				normalized growth rate in ]-0.02;0[:							normalized growth rate in ]-0.02;0[:
					Treated Group Just Below									Treated Group Just Below
	Fiscal income (in EUR 000s)	120 140			Control Group					Share of financial income	.1 .2				Control Group
		100										0
		2010	2011	2012	2013	2014	2015	2016	2017		2010	2011	2012		2013	2014	2015	2016
					Year											Year
			C. Share of Real Estate Income				D. Share of Self-Employment Income
		.5		Groups defined in 2012 with a 2013					.3		Groups defined in 2012 with a 2013
				normalized growth rate in ]-0.02;0[:							normalized growth rate in ]-0.02;0[:
					Treated Group Just Below									Treated Group Just Below
	.1 .2 .3 .4 Pension benefits (%) Share of rental income Control Group Wages (%) Self-employment income (%) Rental income (%) Financial income (%)		23 28 13 17 18		17 23 11 15 22	Share of self-employed income	.1 .2	18 28 14 19 20		18 25 13 17 20	Control Group	18 27 15 19 19	20 25 14 19 20
	Other (incl. Capital gains) (%)		1		11			1		6	1	2
	0 Income Tax				0 17,099 29,086 26,941	30,416	26,973 28,976
	2010 Income tax rate (% gross income) 2011 2012 2013 2014 Year	2015	2016 15		16		2010	2011 17	2012	17	2013	Year	2014 17	2015	2016 17
	Wealth & wealth tax
	E. Effective Tax Rate Before Tax Credits Taxable wealth ('000) 1,747 Housing assets (%) 46	2,656	2,371 F. Effective Tax Rate After Tax Credits 2,585 2,380 2,584 46 45
	.3 incl. Primary Residence (%) Groups defined in 2012 with a 2013	17				.3	15	Groups defined in 2012 with a 2013 15
	.1 .2 Financial assets (%) Treated Group Just Below normalized growth rate in ]-0.02;0[: Average tax rate before tax credits Control Group Liabilities (%) Wealth tax Wealth tax rate (%) Wealth tax (total, billion) Tax units 590,031 289,119 26,677 62 62 .1 .2 8 8 6,094 16,919 7,944 0.3 0.6 0.3 3,6 4.9 0.21 Average tax rate after tax credits	normalized growth rate in ]-0.02;0[: 63 Treated Group Just Below Control Group 8 12,537 7,925 0.5 0.3 0.36 0.17 28,872 21,243 22,331 12,533 0.5 0.28
		0										0
		2010	2011	2012	2013	2014	2015	2016				2010	2011	2012		2013	2014	2015	2016
					Year											Year

For instance,[START_REF] Fack | The effect of tax enforcement on tax elasticities: Evidence from charitable contributions in France[END_REF] find that tightening reporting requirements for charitable giving deductions for the income tax in France decreased the elasticity of reported contributions.[START_REF] Kopczuk | Tax bases, tax rates and the elasticity of reported income[END_REF] shows that US income tax elasticities depend on the availability of deductions.[START_REF] Basri | Tax administration versus tax rates: evidence from corporate taxation in Indonesia[END_REF] show that stronger monitoring in Indonesia reduces corporate income tax elasticities.

These data are used in contemporaneous papers to study the effects of the French wealth tax on entrepreneurs' investment behaviors[START_REF] Bach | Escape or play again? How retiring entrepreneurs respond to the wealth tax[END_REF], charitable giving[START_REF] Cage | Is charitable giving political? New evidence from wealth and income tax returns[END_REF], and redistribution[START_REF] Bozio | Predistribution vs. Redistribution: Evidence from France and the U.S[END_REF].

The standard bunching method has been applied to many settings (see[START_REF] Kleven | Bunching[END_REF] for a review).[START_REF] Pollinger | Kinks Know More: Policy Evaluation Beyond Bunching with an Application to Solar Subsidies[END_REF] shows that static bunching can capture participation and intensive margin response, and develops an alternative bunching estimator to measure these responses.[START_REF] Jakobsen | Wealth taxation and wealth accumulation: Theory and evidence from Denmark[END_REF] also argue that static bunching estimates may capture short-term responses, frictions, and avoidance as opposed to true, long-term responses to taxes.

Closely related to our contribution,[START_REF] Diamond | The long-term consequences of teacher discretion in grading of high-stakes tests[END_REF] and[START_REF] Chen | Notching RD investment with corporate income tax cuts in China[END_REF] also estimate the ITT and LATE but must rely on parametric assumptions for their counterfactuals.

We find no such effect for real estate assets, the valuation of which is less clear-cut and which are likely easier for taxpayers to misvalue and misreport.

[START_REF] Aghion | Tax Simplicity or Simplicity of Evasion? Evidence from Self-Employment Taxes in France*[END_REF] study how French self-employed individuals react to tax simplicity and find that entrepreneurs bunch at the threshold to benefit from simplified income tax regimes. Other recent studies include[START_REF] Benzarti | How taxing is tax filing? using revealed preferences to estimate compliance costs[END_REF],[START_REF] Zwick | Figure 3: Bunching at the Exemption Thresholds A. Exemption Threshold in 2006-2010 B. 1,300K is[END_REF],[START_REF] Colombo | Tax Differentiation, Lobbying, and Welfare[END_REF][START_REF] Neve | How to improve tax compliance? Evidence from population-wide experiments in Belgium[END_REF] and[START_REF] Blesse | Do people really want a simple tax system? Evidence on preferences towards income tax simplification[END_REF].

Because the reform was passed in June, the deadline for filing a 2011 wealth tax return was postponed from June to the end of September.

Although households below the simplification threshold did not have to send any justification of their self-assessed wealth to the tax authority, they were required to keep all information and intermediary steps used to estimate their net wealth. Starting in 2012, the simplified form could also be filed as part of the income tax return.

The larger response in 2012 could be due to the fact that the simplification reform was only announced in May 2011. Many taxpayers had already submitted their 2011 wealth tax returns prior to the reform.

While wealth growth rates tend to increase with the level of wealth across broad ranges of wealth (for instance, when comparing households in the top 10% and those in the top 1%), the taxpayers depicted in this figure are in the same percentile of the wealth distribution (between P99.7 and P99.8)

For the distribution of growth rates around the simplification threshold year by year, see Figure A.12. Figure A.11 reproduces Figure 5 by adding year fixed effects. The results are unchanged.

We pick this bin size to allow for sufficiently many treated groups (five), but also not slice the data too thinly and introduce excessive noise.

We investigate this issue carefully in Section 4.2.2 and show that the whole distribution of wealth growth rates for this group is not affected by those reforms.

In particular, we show that standard assumptions (exclusion restriction, monotonicity, and independance) allow to identify the ITT and the LATE estimates.

This fear may be accentuated by the fact that the tax authority sends taxpayers a default empty tax form to fill out, based on their wealth in the previous year.

The higher precision of the dynamic bunching approach can be explained as follows. Outside the excluded range, average growth rates by bins are similar between control and treated groups. However, these growth rates have wide variation. By focusing only on observations in the excluded range for the estimation, the dynamic bunching estimates the same ITT as the difference-in-differences approach but with less noise.

Assessment is likely easier to enforce for financial assets than for real estate assets. The net worth of financial assets must be assessed at market value for stocks in listed companies. Upon audits, the tax authorities can thus detect misreporting based on the public value of the stock market, and can then impose large penalties if fraud is detected (e.g a 40% increase in wealth tax payments). For real estate, the assessment of market value is less clear, as taxpayers must use information on recent properties sales in the same ZIP code, but can adjust it for differences in properties quality or other specific characteristics of their house.

This means that there is no bunching at any tax kink before the simplification reform, when everyone files a detailed tax form and there is no bunching at tax kinks above the simplification threshold after it was introduced. There are no pure tax kinks inside the simplified region to be able to assess what happens there.

More specifically, households below the exemption cut-off must declare their assets in a very aggregate way. If they are above the exemption cut-off, they file an additional wealth tax statement that requires to disclose detailed information on their taxable wealth to the government.

for helpful comments and reactions. We owe a special thanks to Xavier d'Haultfoeuille and Peter Hull for their insightful and constructive comments. We thank the French ministry of finance-DGFiP for providing access to the data, and Christophe Bellégo and Gerard Forgeot for their great help with fiscal data. We acknowledge financial support from the French National Research Agency (References: ANR-19-CE41-0011-01, "Investissements d'Avenir": LabEx Ecodec/ANR-11-LABX-0047). Zucman acknowledges financial support from the Stone Foundation, the Carnegie Foundation, and the European Research Council. Access to confidential data has been made possible within a secure environment offered by CASD (Ref. ANR-10-EQPX-17). The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed

Notes: This figure plots the distribution of wealth growth rates for households with different levels of taxable wealth in 2012. Notes: This figure investigates whether the distribution of normalized growth rates in the control group (taxpayers located in [2710K,2850K[ in 2012) is comparable to the distribution of normalized growth rates for taxpayers "Just Below". We define our control and treated group by level of wealth in 2011, and plot their 2012 normalized growth rates as explained in Sections 4.2.1. Panel B investigates whether the control group has been affected by the introduction and the repeal of the simplification threshold at 3,000K (see Figure 1, Panel A for details on the timing of reforms). It compares the distributions of normalized growth rate at 3000K in the control group ([2710K,2850K[) with the group of individuals far above the 3,000K threshold ("Control Group 3,000K" in [3150K,3225K]). Notes: This figure plots the distributions of 2013 normalized growth rates as defined in Section 4.2 for the control group and for one treated group ("Just below" in Panel A; 'Far below" in Panel B; "Just above" in Panel C; and "Far Above" in Panel D), where groups are defined in 2012. Each panel summarizes our estimates of the impact of the simplification reform on wealth growth rates, using our dynamic bunching analysis described in Section 4.2.3. Each panel reports the average growth rate reduction between the treated and control group (ITT); the average growth rate in the control group; the proportion of the treated group that bunches ("bunchers"); the reduction in growth rates among bunchers (LATE); and the counterfactual growth rate of bunchers in the absence of the simplification threshold. [2500K,2570K[ [2430K,2500K[ [2360K,2430K[ [2570K,2640K[ [2640K,2710K[ Diff-in- Notes: This table summarizes our estimates using dynamic bunching or standard difference-in-differences designs for the year 2013. More details are provided in the text.