---
title: "Do savers respond to tax incentives? The case of retirement savings"
authors:
  - name: "Clément Carbonnier"
    affiliation: "Université de Cergy-Pontoise, THEMA and Sciences-Po, LIEPP"
  - name: "Alexis Direr"
    affiliation: "Université d'Orléans, CNRS, LEO, UMR 7322, and Paris School of Economics"
  - name: "Ihssane Slimani Houti"
    affiliation: "INSEE (work conducted at DG Trésor)"
date: "2014-01-14"
doi: "10.15609/annaeconstat2009.113-114.225"
keywords: [retirement savings, tax incentives, annuity, bunching, optimization frictions, marginal tax rate, regression kink, PERP, EET scheme]
language: en
type: research-article
journal: "Annales d'Économie et de Statistique"
---

# Do savers respond to tax incentives? The case of retirement savings

**Authors**
- Clément Carbonnier — Université de Cergy-Pontoise, THEMA and Sciences-Po, LIEPP
- Alexis Direr — Université d'Orléans, CNRS, LEO (UMR 7322) and Paris School of Economics — *direr@ens.fr*
- Ihssane Slimani Houti — INSEE (work conducted while at DG Trésor)

**DOI**: [10.15609/annaeconstat2009.113-114.225](https://doi.org/10.15609/annaeconstat2009.113-114.225)

**Keywords**: retirement savings, tax incentives, annuity demand, bunching, optimization frictions, marginal tax rate, EET scheme, PERP.

---

## Abstract

This article exploits a large micro-file tax return data to test whether savers respond to the presence of tax incentives by contributing more in saving accounts that mandate annuitization at retirement. A frictionless model of demand for annuity is first set, which highlights the phenomenon of bunching of savers around tax thresholds when consumers' budget set is kinked. Using French households income tax data, we do not find any bunching, which is consistent either with the absence of behavioral responsiveness to tax incentives or optimization frictions. We investigate the implications of the second hypothesis and propose an alternative test in which discontinuity in marginal rate of return on the two sides of tax thresholds is exploited. We find that the deduction scheme is effective in boosting the demand for annuity of the richest savers whose marginal tax rate is the highest, especially for the oldest savers (aged 45 and above). In most cases, it fails to raise contributions of younger and less wealthy savers.

---

## 1. Motivation and contributions

In the transition from pay-as-you-go to partly funded pension systems, OECD countries have widely adopted *exempt-exempt-taxed* (EET) tax treatment of retirement savings: contributions deducted from taxable income, accrual return tax-free, annuities taxable at withdrawal (Yoo and de Serres 2004). The policy rationale rests on a behavioural assumption — that savers respond to the implied subsidy by saving more in tax-favoured accounts. If they do not, the scheme merely redistributes wealth toward those already saving in qualified products, with possibly anti-redistributive consequences.

The paper makes the following contributions.

1. **Frictionless model of annuity demand under a piecewise-linear budget set.** A two-period life-cycle model with an EET-taxed annuity contract and two marginal tax rates yields a budget set with up to two kinks. The model produces the standard testable prediction that savers bunch where the marginal tax rate (MTR) jumps. The model also clarifies that tax deferral *per se* offers no benefit when working-life and retirement MTRs coincide: the larger taxable base at retirement (annuities exceed contributions due to compounding) exactly cancels the present-value gain from postponement. The relevant subsidy operates through the conversion rate of the annuity contract.

2. **Empirical test for bunching at French tax thresholds.** Using the *Échantillon Lourd* of French income-tax returns (≈500,000 tax units/year, 2006–2009), the paper plots taxable-income densities around the three relevant kink points $S_2, S_3, S_4$ of the 2008 schedule. No bunching is detected at any of the three thresholds. Following Chetty (2012), this is consistent either with no behavioural responsiveness or with optimization frictions (adjustment costs, inertia, imperfect knowledge of taxable income).

3. **A simulation calibration showing optimization frictions can mask bunching.** A simple Pareto-income simulation with a uniform error on contributions shows that a noise of standard deviation 2.5% of the threshold or more is sufficient to wipe out visible bunching, while preserving a positive contribution differential between the two sides.

4. **Alternative test using rate-of-return discontinuity at tax thresholds.** Even without bunching, the location of taxable income relative to a threshold causes the after-tax marginal rate of return to jump. The paper compares contributions of "right-hand" savers (just above $S_i$, who keep a chance to drop into a lower bracket at retirement and pocket the EET subsidy) and "left-hand" savers (just below $S_i$, who would need an unrealistically large income drop to lower their MTR at retirement). The location is treated as an instrument for the simulated tax premium.

5. **Heterogeneous response by income and age.** The deduction scheme effectively raises annuity contributions of the richest savers (around $S_4$) and especially the oldest, with little or counter-productive effect for younger or lower-income savers. Existing US, UK and Danish evidence (Engen, Gale and Scholz 1994; Chernozhukov and Hansen 2004; Attanasio, Banks and Wakefield 2004; Chetty et al. 2012) finds, by contrast, mostly reallocation across vehicles rather than new saving; this paper differs by focusing on mandatorily annuitised products and by exploiting threshold-based identification.

The paper notes it cannot speak to the extensive margin (the decision to open a tax-qualified account) or to the impact on total saving (only on contributions to annuity products), which are left for future work.

---

## 2. Model

### 2.1 Setup

A consumer works at age $s\in\{1,\dots,L\}$, earning $y_W$, consuming $c_s$ and contributing $x_s$ to a tax-deductible retirement plan. Capital accumulates at gross rate $R=1+r$ until age $L$ and is converted at retirement into a lifetime annuity $a$. Survival from $L+1$ to $t$ has probability $q_t$. Lifetime utility is
$$u(c_s) + \sum_{t=L+1}^{L+T} q_t \beta^{t-s} u(c_t).$$

The tax schedule has two MTRs: $\eta_1 < \eta_2$, with kink at threshold $S$. EET treatment means: $x_s$ deductible, accrual untaxed, annuities taxable. The conversion rate $k = 1/\sum_{t=L+1}^{L+T} q_t/R^{t-L}$ is set so insurers break even.

### 2.2 Euler equation and subsidy rate

Letting $\eta_W,\eta_R\in\{\eta_1,\eta_2\}$ denote the working-age and retirement MTRs, the Euler condition (Appendix A) is
$$\underbrace{\frac{u'(c_s)}{\sum_t q_t \beta^{t-s} u'(d)}}_{\text{MRS}} = \underbrace{R^{L-s}}_{\text{capitalisation}} \cdot \underbrace{k}_{\text{conversion}} \cdot \underbrace{\Bigl(1+\frac{\eta_W-\eta_R}{1-\eta_W}\Bigr)}_{1+\text{subsidy rate}}.$$

The subsidy rate $(\eta_W-\eta_R)/(1-\eta_W)$ is positive iff the MTR falls at retirement, zero if MTRs coincide, negative otherwise. It is independent of distance to retirement — the EET scheme distorts the conversion rate, not a time-discounting margin.

### 2.3 Bunching prediction

The piecewise-linear budget set has up to two kinks at $c_s=(1-\eta_1)S$ and $d=(1-\eta_1)S$. Convex preferences over a kinked set imply that present consumption (and hence taxable income net of contribution) is invariant for a non-empty interval of intertemporal wealth — bunching at the threshold. Both *workers' bunching* (taxable income $y_W-x_s$ stuck at $S$) and *retirees' bunching* (retirement income $y_R+a$ stuck at $S$) can occur. The paper focuses on the first because the second requires an implausible degree of forward-looking precision.

---

## 3. Institutional context and quantitative impact of subsidies

### 3.1 The French tax schedule (2008)

| Bracket | Upper threshold | MTR |
|---|---:|---:|
| $\le S_1$ | $S_1 = 5{,}853$ € | $\eta_0 = 0\%$ |
| $(S_1, S_2]$ | $S_2 = 11{,}673$ € | $\eta_1 = 5.5\%$ |
| $(S_2, S_3]$ | $S_3 = 25{,}926$ € | $\eta_2 = 14\%$ |
| $(S_3, S_4]$ | $S_4 = 69{,}505$ € | $\eta_3 = 30\%$ |
| $> S_4$ | $\infty$ | $\eta_4 = 40\%$ |

Income is taxed on a family-unit basis using the *quotient familial*. Households may deduct retirement contributions up to 10% of total earnings, with an absolute ceiling (€28,280 in 2012). Eligible products with mandatory annuitisation at retirement: PERP, optional part of PERE, PREFON (civil servants), COREM, C.G.O.S. *Madelin* contracts (self-employed) and PERCO are excluded.

### 3.2 Magnitude of tax incentives

Subsidy rates implied by Eq. (5) for various MTR transitions (Table 2):

| $\eta_W$ → $\eta_R$ | Subsidy/tax rate |
|---|---:|
| same → same | 0% |
| 5% → 14% | −9.5% |
| 14% → 5% | +10.5% |
| 14% → 30% | −18.6% |
| 30% → 14% | +22.9% |
| 30% → 40% | −14.3% |
| 40% → 30% | +16.7% |

Translated into a return-rate premium (Table 3), a transition from 40% to 30% MTR corresponds to roughly **+1.14 percentage points** of annual return at a one-year horizon, falling to **+0.48 pp** at a 20-year horizon (longer horizons dilute a fixed end-of-life subsidy). The French scheme thus produces material rate-of-return variation, with subsidies of comparable magnitude as reverse incentives.

### 3.3 Data

**Source.** *Échantillon Lourd*, DG Trésor / DGFiP — large stratified sample of French income-tax returns.
**Period.** 2006–2009 (incomes earned).
**Volumes.**
- ≈17 million taxpayers per year (aged 30–70).
- 879,861 to 972,878 savers per year contributing in qualifying accounts.
- 5.10–5.71% subscription rate (30–70); 6.51–7.23% (45–65).
- Mean annual contribution €1,532–€1,706 (30–70); €1,873–€2,043 (45–65).
- Median contribution €720–€790, P75 €1,405–€1,603 — distribution highly right-skewed.

The empirical analysis is restricted to households **without dependent children** to neutralise variation in the *quotient familial* between working life and retirement.

---

## 4. Empirical strategy

### 4.1 Test 1 — Bunching at thresholds (Section 4 of the paper)

Densities of taxable income (net of contributions) divided by the *quotient familial* are plotted by 1% bins of relative distance to each threshold, separately for the three age groups 30–44, 45–54, 55–70. No visible mass appears at $S_2, S_3, S_4$ for any age group. By contrast, a sharp peak is found at the **deduction-limit** threshold (contributions = 10% of earnings), confirming that savers *can* respond to a salient kink when they have direct control over the relevant variable. The asymmetry is interpreted as evidence of optimization frictions over taxable income, not over contributions per se.

A simulation exercise (Pareto income distribution + uniform contribution-noise) shows that an error standard deviation of **2.5%** of the threshold or more is enough to mask visible bunching in the data, while preserving a positive contribution differential across the threshold.

### 4.2 Test 2 — 2SLS with threshold-crossing as instrument (Section 5 of the paper)

The empirical model is
$$\begin{cases} y_j = \alpha_i + \gamma_i p_j + X_j \beta_i + \varepsilon_j & i=2,3,4 \\ p_j = a_i + c_i T_{ij} + X_j b_i + u_j & i=2,3,4 \end{cases}$$

with:
- $y_j$ = log annual contribution by saver $j$;
- $p_j = (\eta_W - \eta_R)/(1-\eta_W)$ = simulated tax premium (using forecasts of post-retirement MTR based on assumed earnings growth, replacement rate of 70%, and conversion via legal mortality tables);
- $T_{ij} = \mathbf{1}\{(y_w-x_s)/Q_w \in [S_i,(1+\delta)S_i]\}$ = right-of-threshold indicator (instrument);
- $X_j$ = age, sex, marital status, household income, individual earnings, share of household earnings in household income;
- Sample band: taxable income within $[(1-\delta)S_i,(1+\delta)S_i]$, baseline $\delta=10\%$.

**Mapping of regressions to the paper's tables.**

| Table | Specification | Sample / variant |
|---|---|---|
| 6 | 2SLS, three controls variants × three age groups × three thresholds | Baseline, $\delta=10\%$ |
| 7 | OLS of each covariate on $T_i$ | Exogeneity check on right-vs-left composition |
| 8 | 2SLS with placebo thresholds shifted ±10% | Validity / falsification |
| 9 | 2SLS at $\delta = 1\%, 5\%, 15\%$ | Window robustness |

**Identification.** Threshold crossing is treated as exogenous within the narrow band: locally random income shocks (overtime, year-end bonuses, capital-income realisations) place comparable households on either side of $S_i$. The exclusion restriction is that $T_{ij}$ affects contributions only via the rate-of-return differential, not via unobservable correlates of saving.

A regression discontinuity design is *not* used because no contribution discontinuity is expected at the threshold (Fig. 9): in a frictions environment, contributions transit smoothly across $S_i$ even though their average level differs.

---

## 5. Results

### 5.1 Main 2SLS estimates (Table 6)

Semi-elasticity $\gamma_i$ of contributions to the tax premium, baseline $\delta=10\%$, full controls in both stages:

| Threshold | Age 30–44 | Age 45–54 | Age 55–70 |
|:---:|:---:|:---:|:---:|
| $S_2$ (5.5% → 14%) | 0.141 (n.s., n=319) | **−6.051\*\*\*** (n=264) | −2.635 (n.s., n=226) |
| $S_3$ (14% → 30%) | 0.499 (n.s., n=382) | **1.282\*\*** (n=538) | 0.962 (n.s., n=547) |
| $S_4$ (30% → 40%) | **9.430\*** (n=90) | **4.581\*\*** (n=138) | **4.078\*\*** (n=200) |

Significance: \* 10%, \*\* 5%, \*\*\* 1%. Heteroscedasticity-robust standard errors.

**Headline finding.** Around the highest threshold $S_4$, a one-percentage-point increase in the simulated tax premium raises contributions by approximately **4 percent** for the 45–54 and 55+ groups (significant at 5%), and by **9 percent** for the 30–44 group (significant only at 10%). Concretely: a tax-premium increase of 10 percentage points — realistic given the values in Table 2 — translates into a roughly **40% rise in annual contribution** for older savers around $S_4$.

In raw terms (Section 5.3, Fig. 11):
- 45–54 around $S_4$: mean contribution €6,028 (right) vs €3,595 (left).
- 55+ around $S_4$: mean contribution €5,823 (right) vs €3,238 (left).

Around $S_3$, only the 45–54 elasticity (≈1.3) is statistically significant. Around $S_2$, the 45–54 elasticity is **negative** (−6.05) and significant: this is interpreted as contamination by the nearby lower threshold $S_1$, which creates conflicting incentives over the same band.

> **Authors' critical reading.** The negative coefficient at $S_2$ is read not as evidence against the model but as a structural artifact of the proximity of $S_1$. Savers just below $S_2$ may simultaneously be just above $S_1$, mixing incentives. The paper does not "fix" this econometrically; it flags it and emphasises that the cleanest signal sits at $S_4$, where the surrounding tax topology is least cluttered.

### 5.2 Exogeneity of threshold location (Table 7)

For each covariate, an OLS of $X^\ell_j$ on $T_{ij}$ controlling for the other covariates checks whether right-vs-left groups differ on observables. **Around $S_4$**, no significant difference appears — strong support for the instrument's validity at the threshold where the main effect is found. A few significant differences appear around $S_2$ and $S_3$ (e.g. household income and married-women share at $S_2$ for the 45–54 group), so identification at lower thresholds is treated more cautiously.

### 5.3 Placebo with shifted thresholds (Table 8)

When the threshold and its band are artificially shifted by ±10%, the positive elasticity at $S_4$ disappears and there is no significant positive coefficient for any shifted-right $S_4$ specification. Around shifted $S_4$, coefficients turn negative for older savers — consistent with the genuine threshold effect: savers just below the *true* $S_4$ contribute less, so they look like negative outliers when compared to the artificial group above the shifted-left threshold. The placebo confirms the real $S_4$ effect is driven by the actual tax kink, not by general income gradients.

### 5.4 Window robustness (Table 9)

Estimates at $\delta=15\%$ shrink (more heterogeneous comparison group) but the 55+ elasticity at $S_4$ remains significant at **2.96 (5% level)**. At $\delta=1\%$ and $\delta=5\%$, sample sizes collapse and standard errors blow up, but point estimates around $S_4$ for older savers remain in the 2–5 range when computable. The qualitative story — large response among older, high-income savers; weak or perverse response elsewhere — is robust.

---

## 6. Conclusion

The paper applies two complementary tests of saving sensitivity to French EET-style tax incentives. The bunching test fails to detect mass at any tax kink, which a frictionless model rejects but a Chetty (2012)-style model with optimisation frictions accommodates. The threshold-crossing 2SLS test identifies a strong response among savers around the top kink $S_4$, especially the oldest, with a semi-elasticity around 4. Younger and lower-income savers show no positive response — and at $S_2$ even a negative one, attributed to the neighbouring threshold $S_1$.

The economic interpretation is that EET subsidies most effectively reach savers who (i) face large MTR drops at retirement, (ii) are close enough to retirement to forecast their post-retirement MTR with confidence, and (iii) earn enough that capital and earned income place them well above lower thresholds.

### Limitations and research extensions

The authors flag several limitations. First, the analysis covers only the **intensive margin**: contributions conditional on contributing. The decision to open a tax-qualified account (extensive margin) requires a different theoretical and econometric framework. Second, the dataset cannot disentangle whether boosted annuity contributions among rich savers represent **new saving** or simply **reallocation** from other vehicles — the paper notes that the policy may still be socially beneficial in the reallocation case to the extent that longevity insurance is undersupplied (Davidoff, Brown and Diamond 2005; Brown 2007). Third, the simulated post-retirement MTR depends on assumptions about earnings growth, replacement rates and tax-schedule constancy, all of which are illustrative rather than estimated. Fourth, the data exclude *Madelin* and PERCO contracts and households with dependent children, limiting generality.

---

## Acknowledgments

The authors thank DG Trésor and especially the office of tax policy for database access, and Jonathan Duval for help in exploiting the dataset. Useful comments were received from Thomas Piketty, James Poterba, Antoine Bommier, Edmund Cannon, and participants at the ETH Zurich conference, the Public Economic Theory international meeting, the LAGV conference, the Netspar International Pension workshop, the AFSE conference, and seminars at the Paris School of Economics, University of Orléans, University of Cergy-Pontoise, and Sciences Po Paris. Opinions are those of the authors and do not necessarily reflect the views of DG Trésor.

---

## Main references

Attanasio, O., Banks, J., Wakefield, M. (2004). Effectiveness of tax incentives to boost (retirement) saving: theoretical motivation and empirical evidence. *IFS Working Paper* W04/33.

Bernheim, B. D. (2002). Taxation and Saving. In Auerbach & Feldstein (eds), *Handbook of Public Economics*, vol. 3, ch. 18, 1173–1249. Elsevier.

Brown, J. (2007). Rational and behavioural perspectives on the role of annuities in retirement planning. *NBER Working Paper* 13537.

Card, D., Lee, D. S., Pei, Z., Weber, A. (2012). Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in A Generalized Regression Kink Design. *NBER Working Paper* 18564.

Chernozhukov, V., Hansen, P. (2004). The effect of 401k participation on the wealth distribution: An Instrumental Quantile Regression Analysis. *Review of Economics and Statistics* 86, 735–751.

Chetty, R. (2012). Bounds on Elasticities with Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply. *Econometrica* 80(3), 969–1018.

Chetty, R., Friedman, J. N., Leth-Petersen, S., Nielsen, T. H., Olsen, T. (2012). Active vs Passive Decisions and Crowd-out in Retirement Savings Accounts: Evidence from Denmark. Mimeo.

Davidoff, T., Brown, J. R., Diamond, P. (2005). Annuities and Individual Welfare. *American Economic Review* 95(5), 1573–1590.

Direr, A. (2010). The Taxation of Life Annuities Under Adverse Selection. *Journal of Public Economics* 94(1–2), 50–58.

Engelhardt, G. V. (1996). Tax Subsidies and Household Saving: Evidence from Canada. *Quarterly Journal of Economics* 111, 1237–1268.

Engen, E. M., Gale, W. G., Scholz, J. K. (1994). Do Saving Incentives Work? *Brookings Papers on Economic Activity* 1994(1), 85–180.

Poterba, J., Rauh, J., Venti, S., Wise, D. (2003). Utility Evaluation of Risk in Retirement Saving Accounts. *NBER Working Paper* 9892.

Saez, E. (2010). Do Taxpayers Bunch at Kink Points? *American Economic Journal: Economic Policy* 2, 180–212.

Yoo, K., de Serres, A. (2004). Tax Treatment of Private Pension Savings in OECD Countries. *OECD Economic Studies* 39.

*The full reference list appears in the PDF.*