Fewer courts, less justice? Evidence from the 2008 French reform of labor courts

Abstract

The need to provide justice at reasonable cost represents a current challenge for many public authorities. Many reform projects propose to remove some courts in order to rationalize the judiciary. This paper explores the 2008 French reform of labor courts (removing 20 % of the courts) to empirically investigate the determinants of the removal decision, and its consequences on demand for litigation and case duration in the remaining courts. This represents—to our knowledge—the first attempt to evaluate the impacts of courts’ removal. Using panel data, our empirical strategy is based on probit estimations, counterfactuals, as well as 3SLS estimations. Our results show that the reform removed small and concentrated courts. It decreased demand for litigation in the targeted areas. Results also suggest that case duration might have increased in some specific courts since 2011.

Appendices

Appendix 1: Maps of judicial system

See Figs. 3 and 4.

Fig. 3

French courts before the reform and removals during the reform

Fig. 4

French courts after the reform

Appendix 2: Tables and figures

See Tables 8, 9, 10, 11 and 12.

Table 8 Correlation matrix of the independent variables of the probit specification

Table 9 Results of the OLS estimation (Robust clustered standard errors)

Table 10 Results of the 3SLS estimation

Table 11 Results of the 3SLS estimation—time subspecification

Table 12 Results of the 3SLS estimation—spatial subspecification

Appendix 3: Marginal effects

General specification The general specification is given by the following equation system:

$$\begin{aligned} duration_{it}=\,&\gamma _0+ \gamma _1 ln(newCases_{it})+ \gamma _2 r_{it} + \gamma _3 r_{it} \times relativeBurden_{i} +\gamma _4 departage_{it}\\ \nonumber&+ \gamma _5 ln(gdp)_{it} + \gamma _6 unemployment_{it} + \gamma _7 ln(pop)_{it} +\mu _i + \alpha _t+ u_{it} \end{aligned}$$

(9)

$$\begin{aligned} ln(newCases_{it})=\, &\beta _0+\beta _1 duration_{it} + \beta _2 r_{it} + \beta _3 r_{it} \times relativeBurden_{i} + \beta _4 winRate_{it} \\ \nonumber&+ \beta _5 ln(gdp)_{it} + \beta _6 unemployment_{it} + \beta _7 ln(pop)_{it} +\mu _i' + \alpha _t'+ v_{it} \end{aligned}$$

(10)

Note that these two equations do not include a control for relativeBurden only, because this would be collinear with the court fixed effects.

The marginal effects of the reform are:

$$\begin{aligned} \frac{\partial duration_{it}}{\partial r_{it}}&=\underbrace{\gamma _1 \frac{\partial ln(newCases_{it})}{\partial r_{it}}}_{\text {Indirect Effect}} + \underbrace{\gamma _2 + \gamma _3 relativeBurden_{i}}_{\text {Direct Effect}}\end{aligned}$$

(11)

$$\begin{aligned} \frac{\partial ln(newCases_{it})}{\partial r_{it}}&=\underbrace{\beta _1 \frac{\partial duration_{it}}{\partial r_{it}}}_{\text {Indirect Effect}} +\underbrace{\beta _2 + \beta _3 relativeBurden_{i}}_{\text {Direct Effect}} \end{aligned}$$

(12)

Substituting each left-hand side in the right-hand side of the other equation:

$$\begin{aligned} (1-\gamma _1 \beta _1) \frac{\partial duration_{it}}{\partial r_{it}}&=\gamma _1 \beta _2 + \gamma _1 \beta _3 relativeBurden_i +\gamma _2 + \gamma _3 relativeBurden_{i}\end{aligned}$$

(13)

$$\begin{aligned} (1-\beta _1 \gamma _1) \frac{\partial ln(newCases_{it})}{\partial r_{it}}&=\beta _1 \gamma _2 + \beta _1 \gamma _3 relativeBurden_i+\beta _2 + \beta _3 relativeBurden_{i} \end{aligned}$$

(14)

which yields:

$$\begin{aligned} \frac{\partial duration_{it}}{\partial r_{it}}&=\frac{\gamma _2 + \gamma _1 \beta _2 + (\gamma _3+\gamma _1 \beta _3) relativeBurden_{i}}{1-\gamma _1 \beta _1}\end{aligned}$$

(15)

$$\begin{aligned} \frac{\partial ln(newCases_{it})}{\partial r_{it}}&=\frac{\beta _2+\beta _1 \gamma _2 + (\beta _3+\beta _1 \gamma _3) relativeBurden_{i}}{1-\beta _1 \gamma _1} \end{aligned}$$

(16)

Time Specification The time specification include more interaction variables with the reform dummy. The time specification is defined by:

$$\begin{aligned} duration_{it}=\,&\gamma _0+ \gamma _1 ln(newCases_{it})+ \gamma _2 r_{it} + \gamma _3 r_{it} \times relativeBurden_{i} +\gamma _4 departage_{it}\nonumber \\&+ \gamma _5 ln(gdp)_{it} + \gamma _6 unemployment_{it} + \gamma _7 ln(pop)_{it} + \gamma _8 r_{it} \times numYears_{t}\nonumber \\&+ \gamma _{9} r_{it} \times numYears_{t} \times relativeBurden_{i} + \mu _i + \alpha _t+ u_{it} \end{aligned}$$

(17)

$$\begin{aligned} ln(newCases_{it})=\,&\beta _0+\beta _1 duration_{it} + \beta _2 r_{it} + \beta _3 r_{it} \times relativeBurden_{i} + \beta _4 winRate_{it} \nonumber \\&+ \beta _5 ln(gdp)_{it} + \beta _6 unemployment_{it} + \beta _7 ln(pop)_{it} + \beta _8 r_{it} \times numYears_{t}\nonumber \\&+ \beta _{9} r_{it} \times numYears_{t} \times relativeBurden_{i} +\mu _i' + \alpha _t'+ v_{it} \end{aligned}$$

(18)

Note that these two equations do not include a control for numYears only because this would be collinear with the year fixed effects. Moreover, it does not include the term $numYears_{t} \times relativeBurden_{i}$ because this would be collinear with $r_{it} \times numYears_{t} \times relativeBurden_{i}$. Indeed, the number of years is equal to zero for all courts before 2009 (numYears). Moreover, the relative burden courts receive is equal to zero for all non-receiving courts (relativeBurden). Multiplying the interaction term by $r_{it}$ would not affect the values of the new variable, which would create perfect collinearity.

The marginal effects of the reform are given by:

$$\begin{aligned} \frac{\partial duration_{it}}{\partial r_{it}}=&\underbrace{\gamma _1 \frac{\partial ln(newCases_{it})}{\partial r_{it}}}_{\text {Indirect Effect}} \nonumber \\&+\underbrace{\gamma _2+\gamma _3 relativeBurden_i + \gamma _8 numYears_{t} + \gamma _{9} numYears_{t} \times relativeBurden_i}_{\text {Direct Effect}} \end{aligned}$$

(19)

$$\begin{aligned} \frac{\partial ln(newCases_{it})}{\partial r_{it}}=\,&\underbrace{\beta _1 \frac{\partial duration_{it}}{\partial r_{it}}}_{\text {Indirect Effect}}\nonumber \\&+\underbrace{\beta _2+\beta _3 relativeBurden_i + \beta _8 numYears_{t} + \beta _{9} numYears_{t} \times relativeBurden_i}_{\text {Direct Effect}} \end{aligned}$$

(20)

which yields:

$$\begin{aligned} \frac{\partial duration_{it}}{\partial r_{it}}=\,&\frac{\gamma _2+\gamma _1 \beta _2 + (\gamma _3+\gamma _1 \beta _3) relativeBurden_{i}+(\gamma _8 + \gamma _1 \beta _8) numYears_t}{1-\gamma _1 \beta _1} \nonumber \\&+\frac{(\gamma _{9}+\gamma _1 \beta _{9}) numYears_t \times relativeBurden_i}{1-\gamma _1 \beta _1}\end{aligned}$$

(21)

$$\begin{aligned} \frac{\partial ln(newCases_{it})}{\partial r_{it}}=\,&\frac{\beta _2+\beta _1 \gamma _2 + (\beta _3+\beta _1 \gamma _3) relativeBurden_{i}+(\beta _8 + \beta _1 \gamma _8) numYears_t}{1-\beta _1 \gamma _1} \nonumber \\&+\frac{(\beta _{9}+\beta _1 \gamma _{9}) numYears_t \times relativeBurden_i}{1-\beta _1 \gamma _1} \end{aligned}$$

(22)

Spatial Specification The spatial specification is defined by the following system of equations:

$$\begin{aligned} duration_{it}=\,&\gamma _0+ \gamma _1 ln(newCases_{it})+ \gamma _2 r_{it} + \gamma _3 r_{it} \times relativeBurden_{i} +\gamma _4 departage_{it}\nonumber \\&+ \gamma _5 ln(gdp)_{it} + \gamma _6 unemployment_{it} + \gamma _7 ln(pop)_{it} + \gamma _8 r_{it} \times distance_{i}\nonumber \\&+ \gamma _{9} r_{it} \times distance_{i} \times relativeBurden_{i} + \mu _i + \alpha _t+ u_{it} \end{aligned}$$

(23)

$$\begin{aligned} ln(newCases_{it})=&\beta _0+\beta _1 duration_{it} + \beta _2 r_{it} + \beta _3 r_{it} \times relativeBurden_{i} + \beta _4 winRate_{it} \nonumber \\&+ \beta _5 ln(gdp)_{it} + \beta _6 unemployment_{it} + \beta _7 ln(pop)_{it} + \beta _8 r_{it} \times distance_{i}\nonumber \\&+ \beta _{9} r_{it} \times distance_{i} \times relativeBurden_{i} +\mu _i' + \alpha _t'+ v_{it} \end{aligned}$$

(24)

Note that these two equations do not include controls for distance nor $relativeBurden \times distance$ because they would be collinear with the court fixed effects.

The marginal effects of the reform are given by:

$$\begin{aligned} \frac{\partial duration_{it}}{\partial r_{it}}=&\underbrace{\gamma _1 \frac{\partial ln(newCases_{it})}{\partial r_{it}}}_{\text {Indirect Effect}} \nonumber \\&+\underbrace{\gamma _2+\gamma _3 relativeBurden_i + \gamma _8 distance_{i} + \gamma _{9} distance_{i} \times relativeBurden_i}_{\text {Direct Effect}} \end{aligned}$$

(25)

$$\begin{aligned} \frac{\partial ln(newCases_{it})}{\partial r_{it}}=&\underbrace{\beta _1 \frac{\partial duration_{it}}{\partial r_{it}}}_{\text {Indirect Effect}}\nonumber \\&+\underbrace{\beta _2+\beta _3 relativeBurden_i + \beta _8 distance_{i} + \beta _{9} distance_{i} \times relativeBurden_i}_{\text {Direct Effect}} \end{aligned}$$

(26)

which yields:

$$\begin{aligned} \frac{\partial duration_{it}}{\partial r_{it}}=&\frac{\gamma _2+\gamma _1 \beta _2 + (\gamma _3+\gamma _1 \beta _3) relativeBurden_{i}+(\gamma _8 + \gamma _1 \beta _8) distance_i}{1-\gamma _1 \beta _1} \nonumber \\&+\frac{(\gamma _{10}+\gamma _1 \beta _{9}) distance_i \times relativeBurden_i}{1-\gamma _1 \beta _1}\end{aligned}$$

(27)

$$\begin{aligned} \frac{\partial ln(newCases_{it})}{\partial r_{it}}=&\frac{\beta _2+\beta _1 \gamma _2 + (\beta _3+\beta _1 \gamma _3) relativeBurden_{i}+(\beta _8 + \beta _1 \gamma _8) distance_i}{1-\beta _1 \gamma _1} \nonumber \\&+\frac{(\beta _{10}+\beta _1 \gamma _{9}) distance_i \times relativeBurden_i}{1-\beta _1 \gamma _1} \end{aligned}$$

(28)

Appendix 4: Marginal effects at the national level

In order to compute the national average effect of the reform, we attribute a weight $w_i$ to each court. Let us denote $z_j$ the average number of claims between 2004 and 2007 the removed court j was dealing with. For each receiving court i, we denote J(i) the set of removed courts the receiving court i is taking on. Each weight is defined as:

$$\begin{aligned} w_i = \frac{\sum _{ j \in J(i) } z_j }{\sum _k z_k} \end{aligned}$$

(29)

It follows that $\sum _i w_i = 1$.

General Specification Let us denote f(relativeBurden) the marginal impact of the reform conditionally on relativeBurden. In the general 3SLS specification, the average national effect of the reform on the dependent variable is linear in relativeBurden (see previous section in the appendix). The national average marginal impact corresponds to $\sum _i w_i f(relativeBurden_i)$.

Moreover, because of the linearity of f(.), we have:

$$\begin{aligned} \sum _i w_i f(relativeBurden_i)&= \sum _i w_i (a \times relativeBurden_i+b) \nonumber \\&= a \times (\sum _i w_i \times relativeBurden_i)+ \sum _i w_i b \nonumber \\&= a \times (\sum _i w_i \times relativeBurden_i)+ b \nonumber \\&= f(\sum _i w_i \times relativeBurden_i) \end{aligned}$$

(30)

It follows that, because of the linearity of the marginal effect, the average marginal effect is equal to the marginal effect at the average. We can therefore compute the national average effect by considering the marginal effect at the national average.

Spatial Specification Let us denote g(relativeBurden, distance) the marginal impact of the reform conditionally on both the relativeBurden and the distance of a court. The previous section has shown that the marginal effect is a function of the form: $g(x,y)=ax+by+cxy+d$. The national average marginal impact is defined by $\sum _i w_i g(relativeBurden_i, distance_i)=\sum _i g_i$. Unlike in the general setting, the marginal impact is not linear anymore. The national marginal impact is given by:

$$\begin{aligned} \sum _i w_i g_i =&\sum _i w_i [ a \times relativeBurden_i + b \times distance_i + c \times relativeBurden_i \times distance_i + c] \nonumber \\ =\,&a ( \sum _i w_i \times relativeBurden_i ) + b (\sum _i w_i \times distance_i) \nonumber \\&\text { }+ c (\sum _i w_i \times relativeBurden_i \times distance_i) + c \end{aligned}$$

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The data yield the following results:

$$\begin{aligned} \sum _i w_i \times relativeBurden_i = 22.33678 \nonumber \\ \sum _i w_i \times distance_i = 38.71412 \nonumber \\ \sum _i w_i \times relativeBurden_i \times distance_i = 857.2087 \end{aligned}$$

(32)

Time Specification The time specification conditions the impact of the reform on both the relative burden of the receiving courts and the number of years the reform has been enforced. Since each graph of Figs. 6 and 7 is already conditioned on the year, the marginal effect is linear, and results are similar to the general specification. We can take the marginal effect at the national average to estimate the national average marginal effect.

Appendix 5: Graphs of marginal effects

See Figs. 5, 6 and 7.

Fig. 5

Marginal effect of the reform with OLS estimations

Fig. 6

Marginal effect of the reform on the duration of terminated cases

Fig. 7

Marginal effect of the reform on the (log) number of new cases