Incidence and Behavioural Response to Social Security Contributions: An Analysis of Kink Points in France

Abstract

We study the incidence of social security contributions (SSCs) in France relying on the strategy developed by Alvaredo et al. (De Econ, 2017. doi:10.1007/s10645-017-9294-7). This strategy infers the incidence of SSCSs from the discontinuities in earnings distributions created by kink points in the SSC schedule. Using administrative data on earnings for the period 1976–2010, we study approximately 200 such kink points and do not find that they systematically induce a discontinuity in the distribution of gross earnings. This allows us to reject the hypothesis that SSCs are incident on workers, at least locally around kinks. Additionally, we exploit the large variations in SSC rates across kinks and years to estimate the local incidence of both employer and employee SSCs around these thresholds. We find that employer SSCs are shifted to employers while employee SSCs are shifted to employees. These findings are consistent with the economic incidence of SSCs being aligned with their statutory incidence, locally around kink points.

Appendix: Estimation of Discontinuities in the Distribution of Earnings at Kink Points

To estimate discontinuities in the distribution of earnings at a kink point k, we set two parameters:

• (i) the window w is the total range of earnings that are considered on each side of the kink point k (we only consider symmetric windows around the kink);

• (ii) the number of bins $n_b$ is the number of sub-intervals into which the window will be divided before performing the analysis.

The bin size b is given by $b=w/n_b$.

1.1 Implementation A

Both the McCrary (2008) density test (Method 1) and the polynomial approach (Method 2) can be implemented after setting the values of the three parameters w, $n_b$ and b. Our first empirical implementation relies on fixing the window $w_1$ first, and then use the formula proposed by McCrary (2008) to determine an optimal bin size and the number of bins given the window. We use $b_1= 2*\sigma _{N}* N^{-1/2}$, where N is the number of observations in the earnings interval $[k-w_1,k+w_1]$ and $\sigma _{N}$ is the standard deviation of wage observations in this earnings interval.

We set $w_1=\min (0.4*SST, 0.9*(\text {SST}-\text {MINWAGE}))$ for the kink at $\text {SST}$, where $\text {MINWAGE}$ is the French minimum wage; $w_1=0.9*\text {SST}$ for the kinks at $2*\text {SST}$ (placebo), $3*\text {SST}$ and $4*\text {SST}$; and $w_1=3.9*\text {SST}$ for the kink at $8*\text {SST}$. These choices apply to both executives and non-executives (when relevant to them). They are aimed at including as many observations as possible, while keeping other kinks and the minimum wage outside of the considered windows.

1.2 Implementation B

In contrast to implementation A, the second implementation of Methods 1 (McCrary) and 2 (polynomial fit) relies on setting the number of observations n in the first bin to the left of the kink point. We set $n=200$ for the kink at $\text {SST}$, $n=80$ for the placebo kink at $2*\text {SST}$, $n=40$ for the kinks at $3*\text {SST}$ and $4*\text {SST}$, and $n=15$ for the kink at $8*\text {SST}$. These choices reflect a trade-off between the number of observations per bin and the number of possible bins. This is why the number of observations per bin need to be much smaller for kinks in regions of the earnings distribution with few observation. Otherwise, the bins would be too wide and there would be too few bins in a window that excludes other kinks.

The parameter $b_2$ (bin size) is then determined based on the value of n. The window is subsequently set to include a maximum of 200 bins, while still excluding other kinks and the French minimum wage: $w_2=\min (200*b_2, 0.9*(\text {SST}-\text {MINWAGE}))$ for the kink at $\text {SST}$; $w_2=\min (200*b_2, 0.9*\text {SST})$ for kinks at $2*\text {SST}$, $3*\text {SST}$ and $4*\text {SST}$; and $w_2=\min (200*b_2, 3.9*\text {SST})$ for the kink at $8*\text {SST}$. This second approach has the advantage of not arbitrarily imposing a given window.

1.3 Polynomial Degree in the Polynomial Approach (Method 2)

For both implementations of the polynomial approach (estimates 2.A and 2.B), we set the polynomial degree d as follows: $d=10$ for the kink at $\text {SST}$; $d=5$ for the kink at $2*SST$; $d=4$ for the kinks at $3*\text {SST}$ and $4*\text {SST}$; and $d=3$ for the kink at $8*\text {SST}$. The polynomial degree is lower for kinks strictly above the SST because the number of observations around those thresholds is comparatively small.