The accuracy of bunching method under optimization frictions: Students' constraints

Transcription

1 The accuracy of bunching method under optimization frictions: Students' constraints Tuomas Kosonen and Tuomas Matikka November 6, 2015 Abstract This paper studies how accurately we can estimate the elasticity of taxable income under the presence of optimization frictions. We especially focus on the bunching estimator and develop a novel method to investigate to what extent the local bunching estimator underestimates the global behavioral responses under optimization frictions. We are able to estimate this by utilizing income thresholds applied to a study subsidy, which all higher education students are eligible for in Finland. The income thresholds create the notches in the income tax schedule. We are able to detect the more global eects from the income taxation by utilizing a reform to the study subsidy rules. We nd that students do respond to incentives induced by the notches, but at the same time a large fraction of students make sub-optimal choices by exceeding the income threshold by a small amount. This is a strong evidence of optimization frictions. By utilizing a reform to study subsidy rules, we nd that income incentives can aect income in substantial income range. Although it seems that students in general are aware of the system, we also nd evidence supporting that optimization errors would explain partially the sub-optimal choices by taxpayers. Keywords: income taxation, study subsidy, bunching estimator, frictions JEL Classication Codes: H21, H24, H30 Government Institute for Economic Research and CESifo, tuomas.kosonen@vatt. Government Institute for Economic Research, tuomas.matikka@vatt. 1

2 1 Introduction An increasingly active literature utilizes the bunching method to estimate behavioral responses to various tax incentives, following Saez (2010). Kinks in tax schedule sometimes alter behavior of taxpayers by creating excess bunches in income distributions, and sometimes do not (Bastani and Selin 2014). The modest estimates for the elasticity of taxable income derived by utilizing the bunching method have been explained by the presence of optimization frictions (Chetty et al. 2011). These optimization frictions are collectively all factors that prevent taxpayers from fully responding to tax incentives according to standard labor-leisure preferences (Chetty 2012, Kleven and Waseem 2013). Especially job search costs and other labor market frictions that prevent taxpayers from controlling their income very precisely could lead to no local behavioral responses to some incentives (Chetty et al. 2011). Other kind of frictions are, for example, insucient knowledge about tax rules and inattention potentially caused by salience of tax regulations (Chetty et al. 2013, Chetty and Saez 2013, Chetty et al. 2009). The bunching method is very local in nature in that it derives the estimate of behavioral response to tax incentives from local excess mass below or around the discontinuity in incentives. When the incentives are strong enough, such as in the case of notches (jumps in average tax rates), some behavioral responses are bound to occur. In these cases the bunching method is capable of answering to the qualitative question, do tax incentives matter or not. However, the bunching estimator could create biased answer in the presence of optimization frictions for quantitative question, to what extent tax incentives matter (i.e. elasticity). This bias occurs from the local nature of the estimator. Kleven and Waseem (2013) developed a correction for local optimization frictions when calculating the elasticities by taking into account the mass of individuals in dominated regions, who surely are located there due to optimization frictions. Even this correction cannot capture the potential global eects of income taxation that aect the income distribution from wider area than around the discontinuous tax incentive. To calculate the elasticity of taxable income correctly, all behavioral responses due to taxation should be taken into account. In this paper we utilize a study subsidy in Finland, which all university students can apply for (approx. 500 euros/month). We examine the impact of income thresholds in the study subsidy on income distribution. These income thresholds create notches, since exceeding an income threshold results in losing one month of study subsidy. The region above the notch is called the dominated region, and under standard labor-leisure preferences no one would want to locate themselves there. Thus, the share of individuals in this dominated region is informative about optimization frictions. We are able to contribute to the literature in number of ways. First, by utilizing the local bunching response to income thresholds in the study subsidy, we are able to 2

3 investigate whether or not taxpayers respond to tax incentives, and by utilizing the share in dominated region we are able to investigate whether or not this response is attenuated by optimization frictions. Second, we explore the global nature of responses to income thresholds by utilizing a reform that shifted out the income thresholds by about 30%. If the income distribution shifts out with the income thresholds, the total behavioral response is wider than just the visible bunch and mass in dominated region. Importantly, the responses beyond these local measures represent the downward bias in standard bunching estimator when calculating the elasticity of taxable income. These shifts in income distribution are also informative about overall labor market frictions that hinder all labor responses to policy shocks. Third, we utilize divided sample results according to factors that are correlated with optimization abilities in order to separate out their role in attenuating optimization behavior. This latter analysis is augmented by utilizing domestic help tax credit, which features a maximum threshold to the credit and rules that taxpayers potentially misunderstand. We use register-based panel data on all Finnish taxpayers from The data include detailed tax and transfer variables originating from tax- and social administrations. The excellent quality of Nordic administrative data combined with large number of observations allow us to accurately analyze bunching behavior associated with dierent kinks and notches, and separate potential bunching behavior from other irregularities in the income distribution. Our results shows that taxpayers do respond to tax incentives evident in a visible bunching behavior below the notch. At the same time it is evident that frictions play an important role in explaining taxpayer responses to tax incentives. We nd that many students are located in the dominated region just above the notch. This is compelling evidence in favor of notable optimization frictions (Kleven and Waseem 2013). We next turn to understanding the wider scope of income responses to the study subsidy. We rst investigate how the shape of the income distribution develops over the years when there is not change in nominal income thresholds. This analysis reveals that the income distribution for students is rather stable over the years. We then plot the income distribution for students in two years immediately after the reform. Especially for students that have the default nine months of study subsidy, the income distribution shifts out starting from income levels that are far below the income threshold. This establishes our main result. The behavioral responses to local changes in income tax incentives turned out to be global in nature. In fact it seems that greater amount of mass shifted out from bottom part of income distribution than the mass that was bunching wright below the income distribution. Thus, ignoring total behavioral responses lead to a severe bias when estimating the elasticity of taxable income by utilizing the local bunching estimator. We also nd that although many students increased their income when the income 3

4 thresholds shifted out in the reform, some also went over the new threshold into the dominated region. This nding supports the notion that taxpayers do not have precise control over their income. It seems that students responded to the reform by increasing their income (by a substantial amount), but could not stop earning at the threshold, and consequently went over the new income threshold. Furthermore we nd that the bunch below the previous bunch disappears (and reappears below the new threshold). Thus it seems that students are in general aware of the fact that the study subsidy eligibility rules have income thresholds. Despite of this general awareness, it could be that some of the mass in the dominated region could be explained by optimization errors. One source of error is knowledge about precisely what income concept is used in calculating the income threshold (annual gross income), and knowledge about which items are considered as income (e.g. holiday bonuses). We attempted to gain insight into this type of optimization frictions by dividing students into groups according to how much they have received study credits within the year. This should be an indication of their abilities to pass exams, or how hard-working students they are, which both potentially would be positively correlated with how good they are in understanding details of the rules etc. Interestingly, the results reveal that the amount of study credits per year is positively correlated with the amount of bunching and negatively with being in the dominated region. Finally, we looked into domestic help tax credit utilization to nd support for the optimization errors result explained above. The domestic help tax credit enables to deduct certain share (45% or 60% depending on year) of costs of domestic help services (cleaning and house repairing) up to a maximum amount. A source for optimization errors is that the guidelines for domestic help credit (from the Tax Administration) highlight the maximum amount of tax credit, but what needs to be lled in to the tax declaration is the amount paid for the service. We investigated the share of optimization errors by plotting the distribution of the declared service use by all taxpayers applying for the credit. The result shows a clear excess mass around the correct upper limit of service costs that are deductible, as well as a clear excess mass at the value of maximum tax credit. This latter excess mass cannot be explained by anything else than the taxpayers mistook the maximum amount of credit highlighted in the rules to be the maximum amount of service deductible. In addition to optimization frictions, this study contributes to the literature on observed responses to kinks and notches (Saez 2010, Bastani and Selin 2014 and Chetty et al. 2011). Kleven and Waseem (2013) show that wage earners bunch actively at income tax notches in Pakistan. We add to this study by estimating responses to income notches in a developed country where the tax system is strongly enforced, and thus the responses are more related to labor supply decisions as opposed to reporting behavior. Other existing evidence on responses to notches comes from a range of dierent institutions, for 4

5 example, the medicaid notch in the US (Yelowitz 1995), eligibility for in-work benets in the UK (Blundell and Hoynes 2004 and Blundell and Shepard 2012), social security and nancial incentives in retirement rules (Gruber and Wise 1999 and Manoli and Weber 2011), and car taxes aecting the fuel economy of cars (Sallee and Slemrod 2012). This paper proceeds by presenting the relevant institutions in Section 2. In Section 3 we present the conceptual background on responding to kinks and notches, and discuss the role of dierent behavioral frictions. We then present the empirical methodology and data in Section 4. Section 5 presents the results. Section 6 discusses the implications and concludes the study. 2 Institutions 2.1 Income taxation and marginal tax rate kink points We briey study the marginal tax rate (MTR) kink points created by the earned income tax schedule to be able to compare to other studies on the bunching behavior at kink points (Saez 2010, Chetty et al and Bastani and Selin 2014). The MTR schedule is nationwide in Finland, and the other local tax schedules are proportional and thus do not aect the location of kink points. 1 Small amounts of earned income are not taxed in the nationwide schedule, and thus the rst kink appears at a point where the rst tax rate applies. After this the tax schedule increases in a stepwise manner, which results in 4-6 kink points in MTR, depending on the year in question. Dierent kink points are associated with MTR increases between 4-11 percentage points. At the rst income threshold, there is a clear increase in the MTR varying between 6-14 in percentage points, which relates to a 22-53% decrease in the overall net-of-tax rate (1-MTR). The last kink involves the most salient and distinctive increase in the MTR, associated with a 6-9 percentage points increase in the MTR, and 9-16% decrease in the overall net-of-tax rate. As an example, Figure 1 presents the marginal income tax rate schedule for the year The Figure illustrates the discontinuous changes in the income tax rate at dierent levels of taxable income. 1 The Finnish income tax system comprises of three components: progressive central government income taxes, proportional municipal taxes and mandatory social security contributions. The average municipal income tax rate is 18.3, and the average social security contribution rate is 5.1 (in ). In general, municipal income taxation and social security contributions do not induce kink points since they are proportional. 5

6 Marginal income tax rate schedule Year 2007 Marginal tax rate Taxable income Note: Marginal tax rates include the average flat municipal tax rate and average social security contributions Figure 1: Marginal income tax rate schedule (year 2007) 2.2 Study subsidy This study focuses on studying discontinuous incentives created by the study subsidy. In Finland, all students that are enrolled in a university or polytechnic can apply for a monthly-based study subsidy. 2 The maximum amount of the subsidy is 461 per month in the academic year 2006/ Students can apply for the subsidy for a limited number of months per degree (max. 55 months). Students typically rst apply for the study subsidy when they are accepted to a higher education program. The default number of study subsidy months per academic year is 9 (fall + spring semester), which most students also receive. The study subsidy eligibility depends on academic progress 4, and on not having too high the yearly gross income (earned income + capital income). The discontinuous incentives are created by income thresholds: if gross income is higher than the threshold, the study subsidy of one month is reclaimed by the Social Insurance Institution. Additional month of the subsidy is reclaimed for an additional 2 The study subsidy is intended to enhance equal opportunities to acquire higher education, and to provide income support for students who often have low disposable income. In Finland, university education is publicly provided, and consequently there are no tuition fees. A large proportion of individuals receive higher education in Finland (ca. 40% of individuals aged have a degree), and the study subsidy program is widely used among students. 3 The full study subsidy includes a study grant and housing benet. The standard study grant is 259 /month and the maximum housing benet is 202 /month (in 2006/2007). In addition to the study subsidy, students can apply for repayable student loans which are secured by the central government. 4 The academic progress criteria requires that a student completes a certain number of credit points per academic year in order to be eligible for the subsidy. 6

7 1,010 of gross income over the threshold. With the typical 9 months of the subsidy per calendar year, the annual gross income limit is 9,260 (in 2006/2007). Students can alter the number of subsidy months by making an application, or by returning already granted subsidies by the end of March in the next calendar year. Having more study subsidy months decreases the income limit. 5 Students face large local incentives not to exceed the income limit. Since earning just a little over the limit results in losing one study subsidy month, this results in an implied marginal tax rate of over 100% just above the notch. Thus the study subsidy notch induces a strictly dominated region above the notch where students can earn more disposable income by decreasing their gross income level. Disposable income, euros Disposable income around the study subsidy notch 9 months of study subsidy, year Gross income relative to notch point Disposable income, euros Disposable income around the 1st MTR kink Gross earned income relative to kink point Figure 2: Disposable income around the study subsidy notch (left-hand side) and the rst MTR kink point (right-hand side), year 2007 The left-hand side of Figure 2 illustrates the eect of the study subsidy notch on disposable income with the standard case of 9 study subsidy months (in 2007). In the gure, the vertical axis denotes disposable income including the subsidy, and the horizontal axis denotes gross income relative to the notch point (9,260 ). The Figure shows that once the gross income limit is exceeded, reclaiming of the study subsidy causes a dip in disposable income. The right-hand side of Figure 2 illustrates the eect of the rst marginal income tax rate kink point on disposable income. Earning income after the kink point results in less disposable income than before the kink. For example, 100 euros of gross income above the kink results in 9 euros less disposable income than below the kink. Figure 2 highlights that the dierence between the study subsidy notch and the MTR kink points is notable. The study subsidy program was reformed in The main outcome of the reform was that the income limits were increased by approximately 30%. The default income limit for 9 study subsidy months increased from 9,260 to 12,070 6 In addition, the 5 The formula for the annual gross income limit is the following: 505 per study subsidy month plus a xed amount of 170, and 1,515 per month without the study subsidy (in 2006/2007). 6 After 2008, the gross income limits are 660 (before 505 ) per study subsidy month plus a xed 7

8 monthly study subsidy was increased from 461 to 500 per month. In general, other details of the system were not changed, including the academic criteria and the loss of the subsidy of one month if the income limit is exceeded. 7 Finally, Table 2 in the Appendix shows the income limits for dierent number of study subsidy months, and the relative loss incurring when the income limit is exceeded both before and after the reform. 3 Conceptual framework We analyze taxpayer responses to kinks and notches in the tax schedule in the lines of Saez (2010) and Kleven and Waseem (2013). We are in particular focusing on understanding the role and type of optimization frictions, and thus focus on analyzing the responses to notch point created by the study subsidy. In general both kinks and notches could create behavioral responses, kinks typically smaller than notches, in the form of some individuals bunching at or below the discontinuous point in the tax schedule. The distinction between these is that notches create a dominated region where it is clearly not optimal to locate, and if taxpayers still locate there, it is a sign of optimization frictions. Kinks do not have that feature. We follow the bunching literature in utilizing discontinuous incentives in tax schedules and analyzing their eects from excess mass around these discontinuities. In the literature more excess mass relative to some counterfactual means larger behavioral responses which in turn, given the size of change in incentives, leads to a larger elasticity estimate. Comparative statics are then possible by comparing the relative sizes of excess masses across dierent subgroups. However, for the elasticity calculation the optimization frictions create complications, because they potentially aect the counterfactual distribution. Kleven and Waseem (2013) correct for the optimization frictions by adding to the excess mass the share in the dominated region. This correction is only possible for notches, and it is local in nature. If some frictions aect the shape of the income distribution more generally, this correction still underestimates the extent of behavioral responses, and thus the size of the elasticity of earned income (since the size of incentives is known, and thus xed). We attempt to utilize dierent reference groups and the reform in 2008 to build more global counterfactual for the shape of the income distribution without the study subsidy income thresholds. In the analysis, we decompose behavioral frictions into two broadly dened components: inability to respond to tax incentives and optimization errors. The former category is thought to arise from frictions in the labor markets, and in that sense not directly under amount of 220 (170 ), and 1,970 (1,515 ) per month when no study subsidies are collected. 7 After 2008, additional month of the subsidy is reclaimed for an additional 1,310 of gross income over the threshold, compared to 1,010 before

9 the control of the individual. The latter category is to some extent under the control of the taxpayers, in that they could pay more attention to understanding tax incentives. The inability to respond covers a range of reasons why taxpayers are not able to exibly respond to tax incentives. The inability to respond might stem from constraints to optimization. For example, due to non continuous wage-hour employment contracts, wage earners might not be able to alter their working hours easily. Especially those working part-time (including university students) may receive work oers for December that they could not predict, and declining them would lead to losing the whole job contract. Due to the large incentives created by the notch in the study subsidy, students may decide not to work at all during the winter for the reason that they expect this extra part time work resulting in the going over the income threshold and consequently losing subsidies. Also, it might be costly to search for a new job that provides more suitable working hours and wage rates in terms of tax incentives (see e.g. Chetty et al and Chetty 2012). Optimization errors include complete unawareness of tax rules, errors in understanding all relevant income and tax concepts (i.e. confusing marginal and average tax rates) and ability to calculate an optimal response to incentives (see e.g. Chetty and Saez 2013, and Liebmann and Zeckhauser 2004). Students are likely to be, at least at some level, aware of the income thresholds in the study subsidy, since they are clearly stated in the application form and guidelines describing the system. However, it could be possible that students don't always understand the exact income denition (gross earned plus capital income) used to dene the income threshold in the study subsidy, or which income items are taken into consideration. One example are the (completely predictable and deterministic part of wage income) holiday bonus salaries, that students may forget to include when calculating their annual gross income. We attempt to shed light on the signicance of ability to control income by examining the behavioral responses to the reform that changed shifted the income threshold out. The reform to study subsidy helps us to discover whether or not the responses to taxation are limited to the local responses. We can measure the total mass of taxpayers that increase their income in response to shifting out of the earnings thresholds. If the income distribution shifts out due to the reform, it indicates that the total responses are greater than those measured by the bunching behavior. We can also build alternative counterfactual distributions from subgroups that resemble students in their labor market behavior, but are not applying for the study subsidy, and thus not subject to the income incentives it creates. Whenever we nd that study subsidy aects the global shape of income distribution, it reveals that ability to control income inuences behavior. This is because the optimization errors type of frictions should lead to more local attenuation, like exceeding the income threshold by a small amount, whereas ability to control income potentially aect income in a large income span. 9

10 We also investigate if the optimization errors by a role in attenuation optimization behavior by studying the share of individuals in the dominated region across subgroups and to what extent people are aware of the shifting out of the income thresholds. It would be especially revealing if some students would continue bunching at the old thresholds, and if not, would indicate that they are at least aware of the overall system. For subsamples we look at factors that are potentially correlated with optimization ability. One such factor are study credits, basically how many courses were passed during the year. Low number of study credits could be correlated with low ability and vice versa. Thus dividing results into high and low study credits allow us to look at how optimization errors are correlated with optimization behavior. Other things correlated with ability could be majors in universities where it is more dicult to get in versus easy to get into places. As a supplementary results supporting the optimization errors mechanisms we look at the domestic help tax credit utilization and to what extent that reects taxpayers not fully understanding the rules of the tax credit. Another division of results related to understanding how to optimize within the study subsidy system is how long a student has been a student. If bunching is greater for students that have been longer time in the system, it indicates that learning how to optimize played a role in behavioral responses. On the other hand, if time spent in the system has no eect to the results, it would indicate that learning or any diculty to understand the optimization of income plays no role. Similarly, if time spent in the study subsidy system has any correlation for the share of students in the dominated region, optimization frictions could arise partly because students at rst did not know how to optimize and avoid the dominated region, and learned that later on. 4 Data We use panel data on all working-aged individuals (15-70 years) living in Finland in The data set is based on the Finnish Longitudinal Employer-Employee Data (FLEED). To this data we have linked a variety of essential register-based variables, such as detailed tax register data from , and information on students and the study subsidy program from With this data we can reliably and accurately analyze local changes in incentives among various subgroups of taxpayers. To analyze self-employed individuals, we use panel data on all main owners of Finnish businesses from , provided by the Finnish Tax Administration. Table 3 in the Appendix presents the key summary statistics for all taxpayers. Table 4 shows the summary statistics for students. The average gross income excluding the study subsidy among students is 7,600 euros per year. This implies that many students have part-time or full-time jobs during their studies and breaks between semesters, which is very typical among Finnish university students. Finally, Table 5 presents the summary 10

11 statistics for the self-employed individuals, including the key rm-level characteristics. 5 Results 5.1 Baseline results This section presents the overall results on bunching at MTR kink points and the study subsidy notch. We characterize the role and signicance of frictions in the following sections. Marginal tax rate kink points First, we present taxable income distributions around dierent MTR kink points for all taxpayers. The gures plot the observed income distributions and counterfactual distributions relative to each MTR kink point in bins of 100 in the range of +/ from the kink. The gures denote the excess mass estimates (with standard errors), and the implied elasticity estimates based on observed excess bunching. In each graph, the kink point is marked with a dashed vertical line. The excluded counterfactual region (the bunching window) is marked with solid vertical lines. In each graph, the bunching window is +/- 7 bins from the kink. The counterfactual density is estimated using a 7th-order polynomial function. Our results are not sensitive to the choice of the bunching window and the order of the polynomial. Figure 3 presents the income distributions around dierent kink points of the MTR schedule for all taxpayers. The gure illustrates bunching at the rst, second, third and last kink point using pooled data for the years As shown in Table 1 in the Appendix, the number of kink points have decreased from 6 to 4 in the period we study. Throughout the study, the rst MTR kink point always includes the threshold where the national income tax rate rst applies. The other kink points in Figure 3 correspond to the kink points still existing after The Figure shows that there is no bunching at the marginal tax rate kink points in Finland. The only conceivable exception might be the second kink. However, the second kink is likely to produce upward-biased excess bunching because of the locally hollow shape of the income distribution around the kink. Consequently, the elasticity estimates are zero or very close to zero at all MTR kink points. The result of no bunching at MTR kink points in gure 3 indicates that marginal tax rates do not induce local behavioral responses. This could be explained by both the low underlying (local) tax elasticity and various behavioral frictions. Small elasticities would mean that the relatively small changes in incentives do not induce behavioral responses, even in the absence of frictions and even modest optimization frictions would prevent taxpayers to react to kink points even if they would want to do so. Unfortunately, with 11

12 First MTR kink, all taxpayers Excess mass: (.076), Elasticity: -.003(.005) Distance from the kink Observed Counterfactual Second MTR kink, all taxpayers Excess mass:.095 (.035), Elasticity:.004(.001) Distance from the kink Observed Counterfactual Third MTR kink, all taxpayers Excess mass:.01 (.023), Elasticity: 0(.001) Distance from the kink Observed Counterfactual Last MTR kink, all taxpayers Excess mass:.005 (.065), Elasticity: 0(.001) Distance from the kink Observed Counterfactual Figure 3: Income distributions around MTR kink points, the no bunching anywhere results we cannot separate whether it is about elasticities or frictions, and if the latter, what kind of frictions. Thus we turn to analyzing the study subsidy notches, since they create larger incentives and allow to gauge into the existence and source of optimization frictions. Study subsidy notch Next, we study behavioral responses around the notch points of the study subsidy system among Finnish university students. Figure 4 shows the gross income distribution around the notch point (relative to the notch in bins of 100 in the range of +/ from the notch). The gure presents the distribution of all students (left-hand side) and students with the default number of 9 study subsidy months (right-hand side) in In the gure, the dashed vertical line denotes the notch point above which a student loses one month of the subsidy. The solid vertical lines denote the excluded range (see Section 4 for details on dening the upper limit of the excluded range). The dash-point vertical line above the notch shows the upper limit for the dominated region. The gure also includes the estimates and standard errors for the excess mass at the notch, the share of individuals in the dominated region, and the upper limit of the counterfactual and z. In each gure the counterfactual density is estimated using 12

13 a 7th-order polynomial function. Our main conclusions are not very sensitive to this choice, although the point estimates vary somewhat with dierent choices on the degree of polynomial Study subsidy notch, all students Excess mass: (.227), Share in the dominated region:.906 (.032) Upper limit: 26 (4.613) Distance from the notch Observed Counterfactual Study subsidy notch, students with default subsidy (9 months) Excess mass: (.269), Share in the dominated region:.881 (.039) Upper limit: 23 (3.24) Distance from the notch Observed Counterfactual Figure 4: Bunching at the study subsidy notch, Figure 4 indicates a clear and statistically signicant excess mass on the left of the notch for both all students (1.8) and students with the default subsidy (2.0). This indicates that students are both aware of the notch and respond to the strong incentives created by it. However, these responses are not large compared to the large incentives. To have some understanding on the size of elasticities, we calculated them using Kleven and Waseem (2013) reduced form method (not taking optimization frictions into account). The implied earnings elasticities are (0.019) for all students and (0.007) for students with 9 subsidy months (standard errors in parenthesis). 8 Thus even though excess bunching is evident and notable earnings responses occur ( z is around 15% of disposable income at the notch), the observed elasticities are still small. This stems from the fact the changes in incentives are also very distinctive, as notches induce very high implicit marginal tax rates above the income limit. 9 Figure 4 implies that students are aware of the incentives and respond to the notch created by the income limit of the study subsidy program. However, the gure also shows clear evidence on the existence of optimization frictions. There is an economically and statistically signicant mass of students at the strictly dominated region above the notch where students can increase their net income by lowering their gross income. It should 8 Earnings elasticity for all students is calculated using the average number of study subsidy months (7). All elasticities at study subsidy notches are calculated using the SISU microsimulation model and the average number of subsidy months. We thank Markus Paasiniemi for research assistance on calculating the elasticities. 9 In addition, implicit marginal tax rates remain relatively high (>50%) even further away above the notch, as an extra month of the subsidy is reclaimed after additional 1,010 above the income limit (1,310 after 2008). Thus, the eective tax schedule for students inherently includes multiple notches. However, we only observe signicant bunching at the rst notch, which justies the analysis of the rst notch only. The analysis of the rst notch is also rationalized by the fact that students can alter the number of study subsidy months until the march of next tax year. 13

14 be highlighted that under no standard model of economic behavior would no one want to be located in the dominated region, it is clearly sub-optimal. There is 80-90% of the mass compared to the counterfactual in the region where students would save money by earning less. Thus, this is clear evidence of a very signicant optimization friction. Despite of that, it still does not tell us what is the source of the friction, whether it is that students do not know exactly how to calculate their income used to dene the income thresholds, or that they would like to locate below the threshold but something prevents them. Next, we compare the responses of students around the study subsidy notch and the MTR kink points. There is a striking dierence between bunching at notches and bunching at MTR kinks. Figure 5 shows income distributions around MTR kink points for current students (rst kink), university graduates (last kink) and students who previously bunched at the study subsidy notch (rst kink). For all of these groups we nd no signicant bunching at any MTR kink point in any year. Even though students are clearly responding to large incentives induced by the notch, they do not respond to smaller incentives created by MTR kinks. For current students this cannot be explained by the inability to respond to any local incentives, as we observe similar or even the same individuals bunching at income notches. In other words, there is no fundamental reason to assume that students are less able to aect their labor supply around the MTR kink compared to the study subsidy notch. Nevertheless, this result does not indicate that students would not respond to MTR kinks of any size. Larger changes in the MTR might induce larger observed behavioral responses, as with larger kinks it becomes more protable to adjust labor supply (see Chetty et al. 2011, and Chetty 2012). However, in addition to the size of the incentive, the underlying elasticity and the inability frictions, it might be that the MTR schedule is too obscure for many students. 5.2 Local versus global focus Above we zoomed in the notches created by study subsidies and found that they create local responses in income distribution. This type of analysis is in the very hart of the bunching method, looking at local eects created by local incentives. However, the rst indication that not all the results are completely local is that the excess mass is fairly diuse in Figure 4. That observation raises the question that to what extent the strong incentives created by the study subsidy income thresholds aect the shape of the income distribution more globally. To have a rst look at the shape of income distributions, Figure 6 plots the income distribution for students and non-students that are young part-time workers. The idea of the latter group is to serve as a rst version of counterfactual distribution for students 14

15 First MTR kink, all students Excess mass: -.09 (.107), Elasticity: -.006(.007) Distance from the kink Observed Counterfactual Last MTR kink, university/polytechnic graduates Excess mass: (.084), Elasticity: -.001(.001) Distance from the kink Observed Counterfactual First MTR kink, students who previously bunch at the notch Excess mass: (.183), Elasticity: -.044(.012) Distance from the kink Observed Counterfactual Figure 5: Bunching at MTR kink points: Current students, graduates and students who bunched at the study subsidy notch, without any income thresholds. Since students need to spend time on studying, they empirically seem to have quite often part-time jobs (in work less than 12 months a year) and students tend to be young as well. Thus, we selected from a group of non-students a subgroup that match these characteristics: individuals who have less than 12 months in working contracts per year and who are between 19 to 30 years old. The resulting income distributions show intriguing patterns in Figure6. Both groups have declining pattern to the right and most of the mass in distribution is in roughly similar income intervals. The dierences in shapes are interesting, students have a peak at low income levels, which could be explained by students not wanting to cross the income threshold. Also, there is signicantly less mass at higher income levels, at higher income levels than most thresholds. Non-students do not feature these anomalies in the shape of distribution, which is steadily declining. To have a clearer view on the role of income thresholds we repeat the exercise for students that have 9 study subsidy months per year. Prior to the reform in 2008 their income threshold is at 9620 euros. We took a bit more focused age restriction to match this group of students; non-students that are part-time workers and between 10 and 24 years of age. Figure 7 shows the resulting distributions. The income distribution for students show that most want to stay below the income threshold and there is relatively 15

16 Non students Income distributions for students and non students Non students: part time workers, aged Students Income Students Non students Figure 6: Income distributions for students and non-student part time workers thin mass above it. The distribution for non-students continues to be smooth and steadily declining around the notch. This analysis points out that perhaps all the responses that the notches create are not just the local bunching behavior. It is conceivable that notches have more global eects especially if taxpayers do not have precise control over their income. We next turn to analyzing the eect of the reform in 2008 on the whole income distribution to have a more precise look at these global eects. 5.3 Utilizing the reform to understand the sources of optimization frictions Based on the result that there are signicant share of students in the dominated region, we established that optimization frictions signicantly attenuate optimization behavior. That result by itself does not allow us to gauge into the underlying reasons for optimization frictions. Next we look into the eects created by the reform to study subsidy rules. The details are discussed in the institutions section, but the essence of the reform is that it shifted out the income thresholds by about 30%; with the same level of subsidies a student can now earn more before hitting the notch. We rst look at the income distribution of students across the years without focusing on the surrounding of any notch or conning to specic amount of study subsidies. We group always two years together to have more observations, and look how the income distribution develops from 2004 and 2005 to 2006 and 2007 before the reform and then 16

17 Non students Income distributions for students and non students Students: 9 subsidy months Non students: part time workers, aged Income Students Students Non students Figure 7: Income distributions for students with 9 study subsidy months and non-student part time workers to 2008 and 2009 after the reform. We plot the kernel densities for dierent years in the same graph to facilitate the visual comparison of income distributions. Graph 8 presents the results. From the graph it is clear that the overall shape of the distributions are similar, especially in the higher income range. It also seems that substantial amount of income has shifted out from the bottom end of distribution after the reform in To have a more close look at the eect of study subsidy on earned income, we focus on students that have 9 months of subsidy before and after the reform. This group have the same level of subsidies before and after, and the only thing that changes is the ability to earn more income before the subsidies are withdrawn. Thus we focus on the eect of incentives on earnings behavior and hold other factors constant. Graph 9 shows the results. The distributions in the years before the reforms develop similarly to each other, at least close to the threshold. This gives an idea how the distribution would evolve without the reform. The post-reform distribution in the dotted line shows drastically dierent shape. The bunch below the previous income threshold has disappeared and a new smaller bunch has appeared below the new income threshold. More generally, income distribution has shifted everywhere to the right. This is a remarkable result and highlights that the income threshold had larger eect on incomes than just the local bunching eect, otherwise the mass in the income distribution had not shifted up from such a wide range. Another interesting point about the eect of the reform on the shape of the income distribution is that mass has shifted up also beyond the income threshold into the new 17

18 Income distribution in different years All students Income Figure 8: Income distribution for all students before and after the reform dominated region. This tells us something interesting about the optimization frictions; individuals aim to be located in the range below the new threshold, but something pushes them above it. This together with the fact that the bunch disappeared from the old threshold is a strong indicator that individuals are in general aware if the system, but they either cannot calculate correct income to stay below threshold accurately, or they face unpredictable shock pushing them over the threshold, potentially coming from the labor markets. Overall the fact that the shifting out of the income threshold in the reform had an eect in such a wide range of incomes indicates that taxpayers have diculty to control their income precisely. The result suggests that some stay below quite far below the threshold for the fear that if they try to increase their income to the next possible level, they would go over the threshold. We next utilize the reform in a dierent way to try to understand whether students sometimes fail to optimize on their own accord despite of being generally aware of the system and thresholds. We do this by dividing students into new students and students who have already spent some time in the system and also by dividing rules to old rules, which have been in eect for a number of years, and new rules, which have been in eect only for a year or two. This distinction is meaningful, since for new students understanding how to optimize perfectly the fact whether rules are new or old should not matter, they are new to the student regardless. On the other hand, old students should already have had more time to learn how to optimize, but they may have frictions coming from the labor market preventing them to adjust their income level immediately. For example, they would need to switch jobs in order to adjust income, and nding a 18

19 Income distribution in different years Students with 9 subsidy months and 9 subsidy months in base year Income Figure 9: Bunching at the study subsidy notch for those having 9 subsidy months before and after the reform new job requires overcoming search costs. Graph 10 presents the bunching and dominated regions for new and old students and rules. The result is that both frictions nd support, inability to adjust income and unawareness of how to optimize exactly. The most remarkable result is found by comparing new students under the old and new rules. New students feature quite signicantly less bunching under the new rules. This is intriguing, since new students close to the threshold should want to optimize and stay below the threshold, and act according to rules they get from Social administration. Since they don not do this, it seems they had been getting instructions on how to optimize from the network of peers and more senior students. With the new rules this information is not accurate anymore, since it applies to the old rules, like what the more senior students or siblings did last year. The graph also shows that older students feature less bunching under the new rules. Given that they managed to optimize before, they should know how to optimize. The fact that they optimize by bunching close and below the threshold less often points to the direction that some of them had dicult time adjusting their income upwards with the threshold. Finally, there is no signicant dierence in the share of taxpayers in the dominated region. This is somewhat puzzling, but could be explained by precisely the inability to control income exactly, which results for many taxpayers to being located in the dominated region. If the only optimization friction would be about failure to optimize, this would be visible in the old and new students graphs as dierent shares in the dominated region. 19

20 Study subsidy notch, new students before the reform Study subsidy notch, new students after the reform Distance from the notch Distance from the notch Study subsidy notch, old students before the reform Distance from the notch Study subsidy notch, old students after the reform Distance from the notch Figure 10: Bunching at the study subsidy notch: results divided into old and new students and rules To characterize the eect of the change in the income limit due to the reform even more closely, we take students with any number of subsidy months and who were located in the bunching region in the pre-reform period and look at their behavior after the reform. Figure 11 shows that these students also bunch actively after the reform. The observed earnings elasticity at the notch for this group is (0.027). Since those having optimized before are more like to do so under the new rules indicates that there is something individual specic about the ability to optimize. However, since a large number of students are located in the dominated region above the notch, it seems that inability to adjust real labor supply causes optimization to be imperfect even for students who have demonstrated earlier that they are active optimizers. 5.4 Utilizing divided sample results We have established that inability to control labor income perfectly as well as failure to optimize seem both to explain average attenuation bias of optimization behavior. Since it may be important to know which one is more prominent, we provide some divided sample results to gain more insight into this. We divide the sample of universe of students in 20