^{1}

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This paper analyzes the effects of tax-based saving incentives on contribution behavior in Germany (Riester Pension). Using tax reform and inflation, the effect of the tax price on the decision of whether or not to contribute is analyzed. Our central estimate implies a local average elasticity of the contribution decision of -2.36. In addition, using shifts in price kinks over time, we show graphical evidence of the decision on how much to contribute. Our results show that taxpayers adjust their savings immediately if the subsidized amount increases. Consequently, the government has control over the contribution behavior on both margins by setting tax-based saving incentives.

Old age provisions can be financed as a pay-as-you-go or fully funded system. European countries usually have pay-as-you-go systems where current contributions are used to finance current provisions. Rising life spans and declining birth rates of the last decades have been generating a funding gap. Generally, this could be addressed by reforming the pay-as-you-go system itself (e.g., increasing contributions, decreasing provisions, or through governmental grants) or by reforming the whole old age provision system.

In the last decades, several European governments have reformed their retirement systems. From a governmental perspective, there are three pillars of old age provisions. Pillar 1, the traditional pay-as-you-go system, has been extended by Pillar 2, occupational pension schemes, and Pillar 3, private pension schemes. Private pension schemes are voluntary and generally subsidized [

Germany introduced the Riester Scheme in 2002. The main issue has been the financing gap of the pay-as-you-go system. Although the contribution rate of Pillar 1 is expected to increase from 19.9% in 2008 to 21.4% in 2028, the replacement rate of the German statutory pension insurance is expected to decline from 50.5% in 2008 to 44.4% in 2028 [

Due to the subsidy, the Riester Pension is superior to non-funded saving accounts, especially for families with children and low income [

This paper adds two points to the literature. We focus on parameters that the government has under its control and address these parameters to the contribution decision itself. Corresponding to governmental goals, we check the effects of the subsidy both on the decision to contribute or not (extensive margin) and on the decision of how much to contribute (intensive margin).

First, we think that, from a governmental perspective, shifts of savings toward the Riester Scheme matter. Contributed money is fixed within the Riester contract up to the age of 62 and has to be paid out on a monthly basis until the end of life. Moreover, the pension cannot be transferred from one generation to another or lent by one individual to another. As a result, we think that the substitution rate shows how expensive it is for the government to shift “free” private savings to savings where the rules are controlled by the government. The elasticity of the decision on the extensive margin with respect to the price after taxes shows how effective the governmental action is.

Therefore, we focus on the effective size of the subsidy on the saving decision. That is why we have to separate effects from social characteristics such as the number of children or income and the impact of the subsidy itself. With our tax data, we can investigate the full range of the subsidy covering the more favorable tax option. Using a comprehensive tax calculator [

Second, we investigate to what extent the government meets its goal of implementing Riester savings of a legislatively predefined amount of the gross wage. To our knowledge, we are the first who analyze the contributed amount with respect to the price after taxes of the last euro contributed. We use the evolution of the maximum subsidized amount over time to show the impact of the subsidy on the decision regarding how much to contribute (intensive margin). Therefore, we show graphical evidence of contribution behavior on the price kink around the maximum subsidized amount.

The paper is structured mainly in two parts. The first part offers a brief description of the evolution of the Riester Scheme and the tax environment, followed by our analysis of the decision on the extensive margin. We show the marginal tax price of a Riester contribution, illustrate with descriptive statistics, discuss the identification, and show our main results followed by some robustness checks. The second part shows our analysis of the decision on the intensive margin. Based on a short description of the last euro tax price and its price kink, the corresponding data are described and graphical evidence on the contribution behavior with respect to the price kink is shown.

Here we give just a brief description of the legislated Riester Scheme; for a detailed overview see Börsch-Supan and Wilke [

The tax-free subsidy is granted if an eligible person contributes to a Riester Pension (basic subsidy). Parents receive an additional subsidy for each child (child subsidy). An individual receives the full amount of subsidy if the savings are at least equal to a fixed percentage of the gross wage in the previous year (savings rate). Savings in this context mean the total saved amount, which is calculated based on the individual’s own contributions plus the subsidy. The maximum eligible amount is fixed. If the person contributes more than that amount, there is no additional subsidy. To receive the full subsidy, the own contributions have to be at least equal to a legislated fixed amount (minimum savings).

From 2002 to 2008, there was an implementation phase. The evolution of the Riester components over time is displayed in

Tax deductions are alternatively granted if they are advantageous. Tax authorities check whether the deduction of the savings from the tax base (and the subsequent tax savings) or the tax-free subsidy is more favorable and, in every year, the more favorable approach is used. As a result, the applied tax scale of the subsequent year plays a crucial role here. That is why we take a closer look at the evolution of the tax scale from 2002 to 2008.

Year | 2002/2003 | 2004 | 2005 | 2006/2007 | from 2008 |
---|---|---|---|---|---|

Basic subsidy | 38?o:p> | 76?o:p> | 76?o:p> | 114?o:p> | 154?o:p> |

Child subsidy (born after 31.12.2007) | 46?o:p> | 92?o:p> | 92?o:p> | 138?o:p> | 185?/span> (300? |

Savings rate | 1% | 2% | 2% | 3% | 4% |

Maximum eligible amount | 525?o:p> | 1,050?o:p> | 1,050?o:p> | 1,575?o:p> | 2,100?o:p> |

Minimum savings | 45?o:p> | 60?o:p> | |||

38?(1 child) | |||||

30?(>2 children) |

In Germany, taxable income is taxed by a direct progressive tax scale. Following a basic tax-free amount, the marginal tax rate is increasing linearly to the top tax rate. In contrast to other countries, the tax law is not indexed, resulting in “cold progression” every year. From 2002 to 2008 there have been major changes in the tax scale resulting from tax reform. We use a slight modification of the tax rate here: net-of-tax rate (ntr), which is calculated as one minus the marginal tax rate (ntr = 1 − mtr). The ntr can be interpreted as the price after taxes for tax-preferred goods. In

In the analysis of the incentives, we need a relative measure of the subsidy. At a glance, it seems to be obvious to use the subsidy quota (SQ) established by the German Statistical Office [

However, what we need for a meaningful interpretation with respect to individual preferences is the governmentally induced change in prices. That is why we transform the widely used SQ to an after-tax price (TP):

Corresponding to the subsidy components of the Riester Scheme, the tax price is affected mainly by taxable income and the number of children. The tax price in 2002 for different income levels for a taxpayer with up to three children is illustrated in

On the left tail, are a flat part and a growing part. In the first part, the tax price is on a constant level, because the taxpayers’ own contributions are constant.^{1} In the second part, the tax price is increasing. Although the subsidy remains constant, the taxpayers’ own contributions are increasing as their income increases. Consequently, increasing income leads to a higher tax price. However, increasing income also results in higher tax rates. Thus, tax deductions become more favorable. On the right tail, the tax deduction is more favorable than the subsidy. Following the progressive tax scale, the tax price is decreasing as taxable income is growing, resulting in a flat zone. Although this basic structure remains the same, an increase in the number of children leads to higher subsidies and therefore shifts the left tail to the bottom right.

Most important for us is the change in the tax environment over time. The Riester components vary over 2-year intervals (“Riester Stairs”) in the implementation phase, resulting in a decrease in tax price for low incomes. While for middle incomes the tax price remains constant, it is increasing for higher incomes due to tax cuts.

Because the tax scale and tax base are not indexed, middle-income taxpayers face an increase in tax price over time. Moreover, for the same income, taxpayers with different numbers of children face different changes in the tax price (

For this study, we use data from the German Taxpayer-Panel [

In our dataset, we followed 80,394 taxpayers over eight years, resulting in 643,152 observations. Because the Riester Scheme was introduced in 2002, we dropped the 2001 wave, which left 562,758 observations. To ensure that only taxpayers eligible to contribute were in our dataset, we kept only wage earners (wage > 0), which dropped 150,892 observations. As a result, our dataset consisted of seven years with 58,838 taxpayers eligible to contribute, resulting in 411,866 observations.

After these initial cuts, we dropped three groups of taxpayers as we are not sure if they constituted a plausible comparison group for the identification of the tax price effect.^{2} First, we considered that the taxpayers in our dataset with low incomes were not a plausible comparison group in particular because of the balanced structure of our tax

data.^{3} Consequently we dropped 2023 taxpayers (14,161 observations) with a sum of income less than 10,000? Second, we implemented a drop based on age. While taxpayers younger than 25 often are beginning their working life, those older than 55 often are close to their retirement. To keep only taxpayers in their main work phase, we kept only taxpayers between 25 and 55, thereby dropping an additional 10,738 taxpayers (75,166 observations). Third, we dropped an additional 4,756 taxpayers (33,292 observations) with a change in filing status (single or joint assessment) to be sure to compare the identical number of persons counted as one taxpayer over time.^{4} This led to our final dataset of 41,321 taxpayers over seven years (289,247 observations) (

In ^{5}, the subsidy and the saved amount were calculated. Afterwards, the tax calculator checked whether the tax deduction of the saved amount or the subsidy was more favorable. Last, the more favorable amount was divided by the saved amount, resulting in the subsidy quota. One minus the subsidy quota is the tax price for this taxpayer. Income after taxes was calculated as ordinary taxable income without child allowance and Riester deduction less taxes.

Label | Observations | Taxpayers |
---|---|---|

Taxpayer-panel 2001-2008 | 643,152 | 80,394 |

Wave 2001 | 80,394 | 0 |

Non-eligible taxpayer | 150,892 | 21,556 |

Resulting dataset | 411,866 | 58,838 |

Income in 2002 < 10,000?o:p> | 14,161 | 2,023 |

Age < 25 or age > 55 | 75,166 | 10,738 |

Change in filing status | 33,292 | 4,756 |

Final dataset | 289,247 | 41,321 |

Source: Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder, German Taxpayer-Panel, 2001-2008, authors’ calculations.

Label | Mean | s.d. | p5 | p25 | p50 | p75 | p95 |
---|---|---|---|---|---|---|---|

Riester-dummy (C) | 0.1546 | 0.3615 | 0 | 0 | 0 | 0 | 1 |

Tax price (TP) | 0.5144 | 0.1882 | 0.1333 | 0.4461 | 0.5647 | 0.6516 | 0.7306 |

ln(TP) | −0.7722 | 0.5426 | −2.0149 | −0.8048 | −0.5715 | −0.4279 | −0.3133 |

TP-instrument | 0.5134 | 0.1872 | 0.1333 | 0.4461 | 0.5654 | 0.6503 | 0.7251 |

ln(TP-instrument) | −0.7758 | 0.5460 | −2.0149 | −0.8071 | −0.5703 | −0.4299 | −0.3209 |

Income | 72,372 | 272,938 | 14,380 | 30,400 | 47,879 | 88,431 | 185,548 |

ln(income) | 10.7828 | 1.1419 | 9.5736 | 10.3222 | 10.7764 | 11.3900 | 12.1311 |

Income-instrument | 67,102 | 101,221 | 15,158 | 30,733 | 47,978 | 82,663 | 160,939 |

ln(income-instrument) | 10.7680 | 1.3015 | 9.6263 | 10.3331 | 10.7785 | 11.3225 | 11.9888 |

Dummy: children = 1 | 0.2385 | 0.4262 | 0 | 0 | 0 | 0 | 1 |

Dummy: children = 2 | 0.2987 | 0.4577 | 0 | 0 | 0 | 1 | 1 |

Dummy: children > 2 | 0.1047 | 0.3061 | 0 | 0 | 0 | 0 | 1 |

Age^{2} | 2,165 | 677 | 1,089 | 1,600 | 2,116 | 2,704 | 3,249 |

ln(renting and leasing) | 3.0640 | 4.1479 | 0 | 0 | 0 | 8 | 10 |

ln(dividends and interests) | 1.8569 | 3.5271 | 0 | 0 | 0 | 0 | 12,293 |

Observations | 289,247 |

Source: Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder, German Taxpayer-Panel, 2001-2008, authors’ calculations.

Many of the other variables used in regression can be taken immediately from our tax data. The dummy for the decision to contribute to a Riester Pension is C = 1 if the taxpayer contributed to a Riester Pension and C = 0 otherwise. The number of children was equal to the number of dependent children who were covered on the tax return of their parents. This variable was used to generate dummy variables for having one child, two children, or more than two children. Age and Age^{2} were generated using the date of birth of the taxpayer and the subsequent year. If the taxpayer was jointly assessed, the age of Person A (typically the person who declares more money) was used. Finally, income from renting and leasing and income from dividends and interest entered the regression in logged form.

In

In the bottom part, the evolution of the price for different numbers of children is displayed. Following our calculations above, a greater number of dependent children yielded a lower tax price. Again, over time we show different evolutions before 2004 and mainly the same shape from 2005 on with one exception: from 2004 to 2005, the price increased more sharply for taxpayers with more dependent children.

We followed Heim and Lurie [_{it} (where C_{it} = 1 if the taxpayeri contributed to a Riester Pension in yeart and C_{it} = 0 otherwise) in a parsimonious model as a function of the first euro price of the contribution TP_{it}, the income after taxes Income_{it}, and some control variables X_{it}. Included in X_{it} are other factors that were assumed to be associated with the individual contribution decision and that varied over time. We controlled for the number of children, age, and income from renting and leasing and income from dividends and interests.

The tax price effect was our main parameter of interest. The marginal tax price was calculated as described above. Because we assumed the Riester Pension to be a normal good, we expected that rising prices resulted in a lower propensity to contribute and therefore they were considered a negative sign. So, the effective size of the tax price shows how much control the government has regarding the individual retirement decision by setting the tax price via subsidizing.

The effect of income was covered because standard microeconomic theory predicts not only substitution effects but also income effects of tax changes. The after-tax income was calculated as described above. Conventional wisdom about the effect of taxes on normal goods let us assume that―ignoring substitution effects―increasing income shifted the budget constraint in a way that more goods could be consumed than before. So, a higher income should result in a higher probability to contribute to a Riester Pension. Therefore, we expected this to be a positive sign [

Because of the generous child subsidy, taxpayers with (more) children received a larger overall subsidy under the Riester contract. The number of children was found to play a dominating role in the Riester decision process. A higher number of children were found to be associated with a higher Riester propensity [

We covered age as a proxy for the time between contribution and payout of the pension. Because of the long-term character of the Riester Scheme, we expected older taxpayers to have a lower propensity and therefore to be a negative sign.

We also controlled for other old age provision channels. However, in our tax data, we did not have broad information about this. So we solely included income from dividends and interest (which was in fact poorly covered) and income from renting and leasing (which was well covered but poorly measured). There were at least two economic effects covered by these variables. On the one hand, these income sources were substitutes to Riester, so we expected them to be a negative sign. On the other hand, financial knowledge also was found to be an important factor in the Riester puzzle [

But there were other factors that could have affected contribution decisions, but were omitted in our dataset. Several individual effects were correlated both with contribution propensity and with our tax price variable. We could not control for these variables as they were not included in our dataset. This would have resulted in biased estimates. For example, suppose that taxpayers with a higher saving propensity were likely to have a higher contribution propensity and have higher income and therefore a higher tax rate resulting in lower tax prices. An estimation without covering these individual effects would have led to a biased estimate of the tax price. Because several individual saving-related characteristics were not included in our dataset, between-variation characteristics were clearly ruled out for identification issues. Consequently, we exclusively used within-variation by controlling for individual fixed effects v_{i}.

Moreover, we included time-fixed effects to cover effects that were correlated with the subsequent year and that had an impact on the contribution decision. The subprime crisis started in 2007. This could have decreased the overall saving propensity and, therefore, have affected the Riester contribution decision. If the tax price decreased in these years, the effect of the tax price would be underestimated. To deal with such issues, we included a dummy for each year after 2002, covering time-fixed effects y_{t}.

Using variations of the tax price to identify price effects revealed another issue. The tax price of the Riester Scheme is a non-linear function of actual income (see ^{6}

For our income effects, we also used only law-induced changes. This is important in the event that non-law-induced changes in income (e.g., job effects) had another impact on contribution behaviors than did law-induced income changes. We concentrated on law-induced changes because we were interested mainly in the effect of governmental action on contribution behaviors. So, for after-tax income, we applied the same instrument strategy [

Because of the limited dependent variable, the model prediction of the OLS model is flawed. The standard textbook approach is to use non-linear models such as probit or logit transformation [

In

In columns (I) and (II), we regressed our tax-related variables exclusively on the contribution decision. In specification (I), both the tax price and income after taxes were not instrumented. This results in statistically significant estimates but economically

(I) | (II) | (III) | (IV) | (V) | ||
---|---|---|---|---|---|---|

Main variables | ||||||

ln(tax price) | −0.0257*** | −0.1538*** | −0.1548*** | −0.1382*** | −0.1413*** | |

(0.0015) | (0.0143) | (0.0145) | (0.0144) | (0.0145) | ||

ln(income) | 0.0064*** | −0.0080 | −0.0083 | −0.0067 | −0.0058 | |

(0.0007) | (0.0191) | (0.0192) | (0.0190) | (0.0189) | ||

Other variables | ||||||

Number of children = 1 | 0.0106*** (0.0038) | −0.0032 (0.0039) | −0.0042 (0.0039) | |||

Number of children = 2 | 0.0031 (0.0079) | −0.0195** (0.0079) | −0.0216*** (0.0080) | |||

Number of children > 2 | −0.0069 (0.0119) | −0.0372*** (0.0119) | −0.0404*** (0.0120) | |||

Age² | −0.0005*** (0.0000) | −0.0005*** (0.0000) | ||||

ln(renting and leasing) | 0.0009** (0.0004) | |||||

ln(dividends and interests) | 0.0028*** (0.0005) | |||||

Instrumenting | No | Yes | Yes | Yes | Yes | |

Individual fixed effects | Yes | Yes | Yes | Yes | Yes | |

Year fixed effects | Yes | Yes | Yes | Yes | Yes | |

Observations | 289,247 | 289,247 | 289,247 | 289,247 | 289,247 | |

R^{2} | 0.1098 | 0.0823 | 0.0819 | 0.0931 | 0.0926 | |

First stage results | ||||||

Tax price | ||||||

R^{2} | (−) | 0.0235 | 0.0933 | 0.0936 | 0.0936 | |

F-statistic | (−) | 746.84 | 2,319.19 | 2,132.65 | 1,828.32 | |

Income | ||||||

R^{2} | (−) | 0.0164 | 0.0165 | 0.0179 | 0.0217 | |

F-statistic | (−) | 516.81 | 377.64 | 376.71 | 393.08 |

Notes: Dependent variable is the contribution decision, which is 1 if the taxpayer contributes to a Riester Pension and 0 otherwise. Specification (I) was estimated using OLS. Specifications (II) to (V) were estimated using TSLS with instrumented tax price and income after taxes. Instruments were calculated as described in the main text. In the bottom part of this table, two goodness-of-fit measures of the corresponding first stage regression are shown. Asterisks denote significance at the 10 % (*), 5 % (**), and 1 % (***) level. Source: Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder, German Taxpayer-Panel, 2001-2008, authors’ calculations.

irrelevant parameters, which maybe biased because of the potential endogeneity of the tax price. In specification (II), we addressed the potential endogeneity of the tax price by instrumenting both the tax price and the income after taxes using the synthetic tax price and synthetic income after taxes as described above. Goodness-of-fit statistics of the corresponding first stage regressions are shown in the bottom part of the table. As we show, both R² and the F-statistic are large and therefore we do not think that the instrument suffered from the weak instrument issue.^{7} This approach yields to both a statistically significant and economically relevant parameter estimate of the tax price of −0.15, while the income effect was small and insignificant.

In columns (III) to (V), several additional variables were added to serve as a proxy for other time-invariant effects that could possibly have affected the propensity to contribute. Prior findings about the Riester Scheme [

In columns (IV) and (V), we additionally added other control variables. In column (IV), age was added as a proxy for different contribution probabilities at different ages. Consistent with life cycle theory, older taxpayers had a lower propensity to contribute. In column (V), we also added retirement control variables to check if other potential saving decisions had an impact on the Riester decision. Controlling also for income from dividends and interests and real estate investments yielded only small positive effects of these other old age saving options. It seemed that the effect of financial knowledge was stronger than the substitution effect. However, the overall effect on the contribution decision was negligible.

Because the most comprehensive controls were applied in column (V), this specification acted as our central specification. There we got a statistically significant estimate of the tax price of -0.14 on the decision to contribute to a Riester Pension. The results do not show an income effect. As in the other specifications, the number of children and age yielded very small negative effects. Consistent with Angrist and Pischke [^{8} In the context of the baseline contribution rate, we would suggest a 13.5% decrease in contribution rate (from 5.93% by −0.8% to 5.13%). So, the overall increase in tax price of 5.72% would lead to a decrease in contribution rate of 13.5%, and thus let us calculate an implied elasticity of −2.36 (-13.5%/5.72%).

However, these average effects mask the heterogeneity of the evolution of the tax price in the sample. For example, taxpayers getting their first child in our sample yielded an average decrease in tax price of 14.23% ([0.5025/0.5859] − 1). Again, with our coefficient of −0.14, this would lead to an increase in propensity of 1.99% points (−0.14 × −14.23%). In the context of the baseline contribution rate, we suggest a 43.36% increase in contribution rate (from 4.59% by 1.99% to 6.58%). As a result, the overall decrease in tax price of 14.23% would lead to an increase in the contribution rate of 43.36%.^{9} The implied elasticity is −3.05 (43.36%/−14.23%).

Overall, it can be stated that the government has control over the average Riester contribution rate by setting the tax price. Moreover, the special subsidizing of parents via child subsidies led to a comprehensive shift in tax price for taxpayers getting children and consequently to a higher tax price induced contribution rate.

In

Main variables | LPM (I) | LPM (II) | Logit (III) | Probit (IV) | Probit (V) |
---|---|---|---|---|---|

ln(tax price) | −0.1413*** | −0.0155*** | −0.0932*** | −0.2254*** | −0.1418*** |

(0.0145) | (0.0015) | (0.0353) | (0.0095) | (0.0057) | |

ln(income) | −0.0058 | 0.0050*** | 0.1344*** | 0.0127** | 0.0141*** |

(0.0189) | (0.0007) | (0.0233) | (0.0060) | (0.0030) | |

Other variables | |||||

Number of children = 1 | −0.0042 (0.0039) | 0.0190*** (0.0026) | 0.4396*** (0.0808) | 0.1757*** (0.0085) | 0.1909*** (0.0083) |

Number of children = 2 | −0.0216*** (0.0080) | 0.0396*** (0.0034) | 0.7564*** (0.1029) | 0.3018*** (0.0092) | 0.3421*** (0.0082) |

Number of children > 2 | −0.0404*** (0.0120) | 0.0528*** (0.0051) | 1.0319*** (0.1459) | 0.3902*** (0.0126) | 0.4508*** (0.0110) |

Age² | −0.0005*** (0.0000) | −0.0006*** (0.0000) | 0.0004 (0.0006) | −0.0002*** (0.0000) | −0.0002*** (0.0000) |

ln(renting and leasing) | 0.0009** (0.0004) | 0.0008** (0.0004) | 0.0232** (0.0107) | −0.0116*** (0.0008) | −0.0110*** (0.0008) |

ln(dividends and interests) | 0.0028*** (0.0005) | 0.0025*** (0.0002) | 0.0536*** (0.0071) | −0.0058*** (0.0010) | −0.0056*** (0.0009) |

Instrumenting | Yes | No | No | Yes | No |

Individual fixed effects | Yes | Yes | Yes | No | No |

Year fixed effects | Yes | Yes | Yes | Yes | Yes |

Observations | 289,247 | 289,247 | 75,586 | 289,247 | 289,247 |

Notes: Dependent variable is the contribution decision, which is 1 if the taxpayer contributed to a Riester Pension and 0 otherwise. Specification (I) was estimated using TSLS with instrumented tax price and income after taxes. Instruments were calculated as described in the main text. Specification (II) was estimated using OLS. Specifications (III) to (V) were estimated using binary response models. Asterisks denote significance at the 10% (*), 5% (**), and 1% (***) level. Source: Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder, German Taxpayer-Panel, 2001-2008, authors’ calculations.

specification in column (I). If we had not instrumented for tax price and income after taxes and consequently had run a simple OLS, we would have estimated effects of our tax variable that were not economically relevant. On the other hand, children had a significant positive influence on the contribution decision. As we argued, in this specification, we could not be sure to capture tax effects correctly because of the possible endogeneity of the tax price. So, we think that the positive child effects were not causal marginal child effects economically but instead were not precisely estimated tax price effects.

In specifications (III) to (V), we used classical binary response models. As we have argued, we could not employ a solution for all issues of our identification problem (both instrumenting for tax price and fixed effects estimation). Moreover, we could not interpret the coefficients in a simple manner [^{10} Nonetheless, the corresponding tax price coefficients had the same sign and were not extremely large or small.

In

As we have seen, the government has control over the decision to contribute, at least to some extent. However, the governmental goal is not only to save one euro but also to overcome the financing gap due to reduced returns of pay-as-you-go pensions. The main idea is that employees should save a legislatively predefined amount. This amount has increased stepwise from 2002 to 2008. In this Chapter, we used the stepwise increase in the maximum eligible amount in the implementation phase to analyze the relationship between the contributed amount and the tax price of the last euro contributed.

To analyze behavior on an intensive margin, we needed a variation of the tax price with respect to the contributed amount. However, for taxpayers who received the subsidy (tax deduction), there was no tax price variation for subsidized contributions (only

(I) | (II) | (III) | (IV) | (V) | (VI) | (VII) | (VIII) | |
---|---|---|---|---|---|---|---|---|

Data cuts | ||||||||

Income < 10,000?o:p> | X | X | X | X | ||||

25 < age < 55 | X | X | X | X | ||||

No change in martial status | X | X | X | X | ||||

Main variables | ||||||||

ln(tax price) | −0.1413*** (0.0145) | −0.1413*** (0.0149) | −0.1027*** (0.0112) | −0.1362*** (0.0181) | −0.1006*** (0.0114) | −0.1384*** (0.0185) | −0.0861*** (0.0162) | −0.0879*** (0.0164) |

ln(income) | −0.0058 (0.0189) | −0.0066 (0.0167) | −0.0044 (0.0137) | −0.0041 (0.0174) | −0.0052 (0.0125) | −0.0052 (0.0156) | −0.0036 (0.0128) | −0.0046 (0.0117) |

Other variables | ||||||||

Number of children = 1 | −0.0042 (0.0039) | 0.0070* (0.0037) | 0.0012 (0.0030) | −0.0031 (0.0047) | 0.0164*** (0.0029) | 0.0073* (0.0042) | 0.0042 (0.0038) | 0.0184*** (0.0035) |

Number of children = 2 | −0.0216*** (0.0080) | −0.0032 (0.0079) | −0.0062 (0.0061) | −0.0188* (0.0100) | 0.0182*** (0.0060) | −0.0017 (0.0096) | 0.0015 (0.0085) | 0.0237*** (0.0081) |

Number of children > 2 | −0.0404*** (0.0120) | −0.0205* (0.0123) | −0.0169* (0.0093) | −0.0368** (0.0148) | 0.0124 (0.0094) | −0.0184 (0.0147) | −0.0059 (0.0128) | 0.0208* (0.0126) |

Age^{2} | −0.0005*** (0.0000) | −0.0005*** (0.0000) | −0.0006*** (0.0000) | −0.0005*** (0.0000) | −0.0004*** (0.0000) | −0.0004*** (0.0000) | −0.0006*** (0.0000) | −0.0004*** (0.0000) |

ln(renting and leasing) | 0.0009** (0.0004) | 0.0013*** (0.0003) | 0.0012*** (0.0003) | 0.0011*** (0.0004) | 0.0018*** (0.0003) | 0.0014*** (0.0003) | 0.0014*** (0.0003) | 0.0020*** (0.0003) |

ln(dividends and interests) | 0.0028*** (0.0005) | 0.0028*** (0.0004) | 0.0021*** (0.0004) | 0.0028*** (0.0004) | 0.0020*** (0.0003) | 0.0028*** (0.0004) | 0.0022*** (0.0003) | 0.0021*** (0.0003) |

Instrumenting | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |

Individual fixed effects | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |

Year fixed effects | Yes | Yes | Yes | Yes | Yes | Yes | Yes | Yes |

Observations | 289,247 | 322,539 | 358,393 | 295,190 | 397,313 | 329,343 | 371,140 | 411,474 |

R^{2} | 0.0926 | 0.0941 | 0.0942 | 0.0936 | 0.0940 | 0.0945 | 0.0978 | 0.0970 |

First stage results | ||||||||

Tax price | ||||||||

R^{2} | 0.0936 | 0.0938 | 0.0947 | 0.0942 | 0.0942 | 0.0951 | 0.0959 | 0.0961 |

F-statistic | 1,828.32 | 2,044.48 | 2,295.62 | 1,879.48 | 2,528.48 | 2,119.24 | 2,410.61 | 2,676.91 |

Income | ||||||||

R^{2} | 0.0217 | 0.0226 | 0.0160 | 0.0241 | 0.0162 | 0.0249 | 0.0214 | 0.0215 |

F-statistic | 393.08 | 456.14 | 357.34 | 447.01 | 400.61 | 514.28 | 497.37 | 553.61 |

Notes: Dependent variable is the contribution decision, which is 1 if the taxpayer contributes to a Riester Pension and 0 otherwise. All specifications were estimated using TSLS with instrumented tax price and income after taxes. Instruments were calculated as described in the main text. Specification (I) was our main specification. Specifications (II) to (VIII) differ with respect to the data cuts used, which are displayed at the top of the table. Asterisks denote significance at the 10 % (*), 5 % (**), and 1 % (***) level. Source: Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder, German Taxpayer-Panel, 2001-2008, authors’ calculations.

a small tax progression).^{11} But for all taxpayers, the tax price for contributions exceeding the maximum eligible amount switched to 1. Therefore, we focused on the tax price kink point generated by the Riester Scheme. Ignoring tax progression, the last euro tax price TP^{last} can be expressed as a step function of the contributed amount C and switches after the maximum eligible amount X:

This kink (

The location of the tax price kink was determined by individual factors (income, number of children) and institutional factors (savings rate, minimum savings, maximum savings, tax scale; see

The Riester Scheme generated different tax price kinks within one year for different taxpayers with different incomes or different numbers of children. For example, a taxpayer in year 2002 without dependent children (continuous line in

Moreover, even for a taxpayer with identical individual factors, the location of the kink X differed over time because of changes in the Riester Scheme (see

doubled to 974?(1,050?− 76? which meant that our example taxpayer with an income of 30,000?could also contribute 487?to 974?for a tax price of TP < 1. In 2006, the subsidized contribution tripled to 1,461?(1,575?− 114? and it quadrupled to 1,946?(2,100?− 154? in 2008.

In the following chapter, we take a close look at the contribution decision in our sample around the tax price kink X both between different taxpayers within one year and over time.

With the data of the Taxpayer-Panel, we could follow taxpayers over time. Starting with the dataset used in Chapter 3, our subsample used here consisted only of taxpayers contributing to a Riester contract.^{12} This led to a subsample ranging from 2,429 contributors in 2002 to 11,046 contributors in 2008. In our tax data, we had information about the contributed amount of both taxpayers receiving a tax deduction and those receiving a tax-free subsidy.

From 2002 to 2008, the subsidized amount increased stepwise every two years. Consequently, the subsidized amount has been quadrupled in three steps (see

Let us have a first look at the data. In

As we have shown, we could not interpret the contributed amount of a cross-section related to the tax price because there were different locations of the tax price kink for different taxpayers. However, we can show some graphical evidence by relating the contribution decision to the tax price kink. Similar to the subsidy quota, we normalized contributions by calculating a contribution quota CQ as follows:

Year | obs. | Mean | s.d. | p5 | p25 | p50 | p75 | p95 |
---|---|---|---|---|---|---|---|---|

2002 | 2,429 | 346 | 950 | 30 | 112 | 260 | 480 | 958 |

2003 | 3,321 | 369 | 438 | 30 | 120 | 276 | 487 | 1,184 |

2004 | 4,274 | 539 | 486 | 58 | 180 | 411 | 854 | 1,215 |

2005 | 5,693 | 566 | 530 | 60 | 180 | 466 | 920 | 1,200 |

2006 | 7,861 | 780 | 645 | 60 | 227 | 672 | 1,260 | 1,575 |

2007 | 10,005 | 804 | 750 | 60 | 250 | 720 | 1,284 | 1,575 |

2008 | 11,046 | 1,041 | 768 | 70 | 360 | 958 | 1,620 | 2,100 |

Source: Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder, German Taxpayer-Panel, 2001-2008, authors’ calculations.

A CQ < 1 meant that all contributions were subsidized and consequently the corresponding last euro tax price was before the kink. A CQ > 1 showed that the last euro tax price was equal to one. Most importantly, if a taxpayer calibrated her contribution exactly with respect to the tax price kink, the resulting CQ = 1. As we have argued, the maximum subsidized amount was different both for different socioeconomic factors and for different years. Consequently, a CQ of around 1 seemed to result from tax planning with respect to the tax price kink.

In

To uncover individual behavior, we tried to separate technical effects resulting from changes in tax law and behavior effects. Therefore, a synthetic contribution quota was

calculated by applying tax law from t to contribution decision from t − 1. This synthetic quota shows the change in contribution quota solely resulting from changes in tax law without any change in individual behavior.

In our example, the distribution of the contribution quota 2004 is displayed as the dashed line in

In

As we have seen, there was a change in behavior only in years with a governmental increase in the subsidized amount. The increase in contribution just fit the size of the governmental increase. So, the contribution adjustment resulted after every step in a similar distribution around a contribution quota of 1. This let us conclude that there is a strong relation between the tax price and the contributed amount. If the tax price kink shifts, taxpayers calibrate their contribution.

Overall, it can be stated that the government has control over the contributed amount. A shift in the maximum subsidized amount resulted in an immediate shift in individual savings. This can be interpreted as a successful rule to reach the governmental goal. On the other hand, the observed immediate reaction was a result of the very high subsidy generating tax price kinks where the tax price switched in mean from 0.51 to 1. Assuming future consumption to be a normal good, the kink structure of the tax price would lead to huge welfare losses. In other words: if the after-tax price were designed as a decreasing function of savings, we would assume welfare gains. So, the government has control over the contributed amount using an effective but expensive scheme.

Increasing life spans and declining birth rates of the last decades have been generating a funding gap of the traditional pay-as-you-go system. To close this gap, Germany introduced the Riester Scheme in 2002. For this voluntary private pension, the government grants one of the most generous tax subsidies. Consequently, the success of the retirement reform depends on the acceptance of private pensions and therefore on the effects of tax-based saving incentives on contribution behavior. In this paper, the effects of the subsidy on two different decisions were analyzed.

First, we regressed the tax price of the first euro contributed and the income after taxes against the decision of whether or not to contribute. There we got at least three results: First, our central estimate of −0.14 implied a local average marginal elasticity of the contribution decision with respect to tax price of −2.36. Second, with our identification strategy, the decision was driven mainly by price effects and not by other socioeconomic characteristics such as the number of children. Third, the income effect seemed not to have an influence on the decision.

Second, we showed graphical evidence for the decision on how much to contribute using price kinks. The location of the price kink was different both for different taxpayers and for different years. Therefore, we analyzed the distribution of contributions normalized to the price kink (contribution quota) using variations of the Riester Scheme over time. This showed us two things: First, we saw that most of our contributors (about 20%) contributed exactly on the price kink and therefore contributed exactly the subsidized amount. Second, the shifts in the location of the price kink resulted in the same (normalized to the kink) distribution. This led us to conclude that the decision on the intensive margin is very tax sensitive.

Overall, it can be stated that government has control over contribution behavior. Taxpayers showed strong responses on both margins. However, the question of whether this led to an increase in the overall savings of the household cannot be answered with our tax data. If we assume no effect on the saving rate, the results can be interpreted as a substitution effect between savings where the taxpayer is free to dispose and a contract where the rules are controlled by government.

The authors gratefully acknowledge the Research Data Centers of the Federal Statistical Office and the Statistical Offices of the Länder for providing the dataset and great support.

Kuper, S. and Schmidt, T.-P. (2016) Effects of Tax-Based Saving Incentives on Contribution Behavior: Lessons from the Introduction of the Riester Scheme in Germany. Modern Eco- nomy, 7, 1198-1222. http://dx.doi.org/10.4236/me.2016.711117