Marginal Cost of Public Funds: From the Theory to the Empirical Application for the Evaluation of the Efficiency of the Tax-Benefit Systems

Francesco Figari; Luca Gandullia; Emanuela Lezzi

doi:10.1515/bejeap-2018-0132

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Marginal Cost of Public Funds: From the Theory to the Empirical Application for the Evaluation of the Efficiency of the Tax-Benefit Systems

Francesco Figari , Luca Gandullia und Emanuela Lezzi

Veröffentlicht/Copyright: 18. September 2018

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Aus der Zeitschrift The B.E. Journal of Economic Analysis & Policy Band 18 Heft 4

Abstract

We estimate the marginal cost of public funds (MCF) as an overall indicator of the efficiency of tax-benefit systems and their reforms. The novelty of our work is the calculation of a MCF indicator fully based on empirical micro-data representative of the Italian population. This indicator combines the incentives embodied in the tax-benefit system at the intensive and extensive margins with the respective elasticities of labour supply at both margins. Our results first show the importance of taking into account the heterogeneity of the population with women (both single and in couples) facing a more inefficient system than men. Second, our micro-data based indicator shows the potential bias of MCF indicators based on stylized and hypothetical measures of work incentives.

Keywords: labour supply; marginal welfare cost; microsimulation; tax-benefit system

JEL Classification: H21; H41; H20

Appendix: Labour supply model

Static structural discrete choice models of labour supply (e. g. Van Soest 1995; Blundell et al. 2000. For a review see Aaberge and Colombino 2014) provide direct estimations of preferences through the specification of the functional form of the utility function. The assumption behind the discrete choice models is that utility-maximizing individuals choose from a discrete set of alternatives in terms of working hours to maximize the utility of the household on the basis of “preferences” over hours H and net income Y. At each point in the choice set corresponds a given budget on the basis of the earnings of each individual and the tax-benefit system rules simulated by EUROMOD (Sutherland and Figari 2013).

Suppose the utility function for a household is given by:

(5)U (Y, Hf,Hm)

subject to household income:

Y= Efwf, Hf+ Emwm, Hm+N+B (Ef, Em, N|X)−t (Ef, Em, N | X)

where the utility depends on the female Hf and male Hm hours of work and the household disposable income Y, given earnings of both partners (Ef, Em), other income (N), and benefits (B), and taxes t according to individual and household characteristics X. Other individuals living in the household and their behaviour are taken as exogenous as well. Female and male wage rate, wf and wm, are estimated for all the observations of our sample (workers and non-workers) through a Heckman wage equation to take into account the selection bias in the observed working conditions (see Table 4 and Table 5 in the Appendix).

Table 4:

Wage estimation: women

	Coefficient	Robust standard error	p-Value
Log wage
Age	0.800	0.4331	0.065
Age square	−0.143	0.1107	0.195
Age cubic	0.010	0.0092	0.282
Education middle	0.304	0.0349	0.000
Education high	0.546	0.0387	0.000
In couple	0.041	0.0250	0.102
Region^a	−0.010	0.0031	0.002
Number of children	0.016	0.0148	0.259
Number of children 0–2	0.016	0.0368	0.652
Constant	2.938	0.5659	0.000
Participation
Age	2.399	0.7928	0.002
Age square	−0.386	0.2053	0.060
Age cubic	0.015	0.0170	0.392
Education middle	0.660	0.0408	0.000
Education high	1.030	0.0614	0.000
In couple	−0.407	0.0484	0.000
Region	−0.095	0.0047	0.000
Children 0–2	−0.268	0.0727	0.000
Children 3–6	−0.289	0.0607	0.000
Children 7–12	−0.245	0.0508	0.000
Children 13–17	−0.123	0.0527	0.019
Children 18+	0.072	0.0592	0.225
Other income	−0.024	0.0086	0.006
Constant	−3.132	0.9772	0.001

Rho	0.019	0.0343	0.573
Sigma	−0.605	0.0543	0.000
Observations	8449

Note: ^aRegion = Regional Unemployment Rate
Source: own simulations with EUROMOD.

Table 5:

Wage estimation: men

	Coefficient	Robust standard error	p-Value
Log wage
Age	1.094	0.3259	0.001
Age square	−0.199	0.0868	0.022
Age cubic	0.013	0.0074	0.071
Education middle	0.226	0.0194	0.000
Education high	0.527	0.0294	0.000
In couple	0.025	0.0221	0.259
Region	−0.027	0.0030	0.000
Number of children	0.022	0.0115	0.058
Number of children 0–2	−0.031	0.0315	0.330
Constant	2.722	0.3906	0.000
Participation
Age	3.734	0.8368	0.000
Age square	−0.823	0.2275	0.000
Age cubic	0.059	0.0197	0.003
Education middle	0.336	0.0490	0.000
Education high	0.380	0.0821	0.000
In couple	0.396	0.0679	0.000
Region	−0.103	0.0073	0.000
Children 0–2	0.005	0.1018	0.958
Children 3–6	0.085	0.0879	0.336
Children 7–12	0.147	0.0755	0.052
Children 13–17	−0.045	0.0798	0.570
Children 18+	0.102	0.1009	0.312
Other income	−0.015	0.0120	0.221
Constant	−4.095	0.9740	0.000

Rho	0.019	0.0143	0.180
Sigma	−0.628	0.0458	0.000
Observations	7480

Source: own simulations with EUROMOD.

The two-stage procedure – namely first estimating wage rates and then using them in the labour supply estimations – is common practice (e. g. Creedy and Kalb 2005; Bargain, Orsini, and Peichl 2014).

The choice set of each individual is made up of five j = 1, … ., J alternatives, which means J = 5 for singles and J = 5 × 5 for couples, with choices characterized by 0–60 hours per week (specifically we have the following five hours range brackets: 1. (0–9), 2. (10–24), 3. (25–34), 4. (35–44), 5. (45–60)).^[8]

The utility function can be decomposed into a deterministic and a stochastic component:

(6)Uj=Vj+ ∈j

for each choice j = 1, …, J, where V is the portion of utility given by the observable characteristics while the error term ∈j captures the portion from unobservable characteristics. Error terms are also assumed to represent possible observational errors, optimization errors, or transitory errors.

At each alternative j, the realization of the deterministic part of the utility function (i. e. V_j) is given by the following quadratic functional form with fixed costs linear in the parameters:

(7)Vj=αYj+βYj2+γHjf+δHjm+ε(Hjf)2+ζ(Hjm)2+ηYjHjf+θYjHjm+ιHjfHjm−κfHjf>0−κmHjm>0

where income (Y) and hours of work (Hf and Hm) enter in both level and square.

Fixed costs improve the fit of the estimated model as in Callan, Van Soest, and Walsh (2009) or Blundell et al. 2000. These costs, denoted κf and κm, are nonzero for positive hour choices and depend on observed characteristics (for example, the presence of young children).

Observed heterogeneity, captured by observable characteristics, cannot be identified directly because these characteristics do not vary across alternatives and would be ruled out in the estimation. It enters through the linear utility parameters:

(8)α= α0+ α1 ′X

(9)γ= γ0+ γ1′X

(10)δ= δ0+ δ1′X

allowing marginal utilities of income (Y) and hours of work (Hf and Hm) to depend on a vector of family characteristics (X) including polynomial form of age, education level, region, and presence of children.

Assuming that the error terms is independently and identically distributed across alternatives and households according to the Extreme Value Type I distribution, the (conditional) probability of choosing the alternative k is given by the following logit expression (McFadden 1974):

(11)Prk= expUk∑jexpUk k∈J

The choice an individual faces follows in fact the probability rule

Prchoice = k = PrUHj> UHj∀k≠j, j=1,…, J

according to which the probability that an individual chooses the alternative k is equal to the probability that the utility associated with the choice k is larger than the utility associated with any other choice j.

The parameters, estimated using Maximum simulated Likelihood, are shown in Table 6, 7, and 8, respectively for couples, single women, and single men.

Table 6:

Labour supply estimation: couples

	Coefficient	Robust standard error	p-Value
Income square	−0.0002	0.0000	0.009
Income	0.001	0.0007	0.048
H^m	1.032	0.0470	0.000
H^f	0.259	0.0335	0.000
H^m × H^f	0.353	0.1051	0.001
H^m Square	−14.127	0.3560	0.000
H^f Square	−5.667	0.2432	0.000
H^m × Income	−0.001	0.0015	0.554
H^f × Income	0.001	0.0010	0.226
Spouses’ mean age × Income	−0.000	0.0003	0.125
Spouses’ mean age square × Income	0.000	0.0000	0.108
Number of children × Income	0.000	0.0000	0.638
H^m × male age	0.063	0.0178	0.000
H^m × male age square	−0.007	0.0020	0.000
H^f × female age	0.065	0.0146	0.000
H^f × female age square	−0.008	0.0018	0.000
H^m × number of children	0.003	0.0034	0.342
H^f × 1(children 0–2)	0.008	0.0073	0.249
H^f × 1(children 3–6)	−0.012	0.0028	0.000
H^f × 1(children 7–12)	−0.015	0.0027	0.000
H^f × 1(children 13–17)	−0.009	0.0027	0.001
H^m × 1(region)	−0.023	0.0026	0.000
H^f × 1(region)	−0.035	0.0020	0.000
Fixed cost (FC) for male labour	22.477	0.6189	0.000
FC for male labour × n. of children	0.077	0.1394	0.579
FC for male labour × 1(children 0–2)	0.117	0.1738	0.501
Fixed cost (FC) for female labour	7.294	0.3017	0.000
FC for female labour × n. of children	−0.086	0.0696	0.215
FC for female labour × 1(children 0–2)	0.513	0.2731	0.060

Log-likelihood	−9862.8699
Pseudo R²	0.2505
Observations	4088

Source: own simulations with EUROMOD.

Table 7:

Labour supply estimation: single women

	Coefficient	Robust standard error	p-Value
Income square	0.0005	0.0003	0.154
Income	0.0006	0.0017	0.720
Hours	0.399	0.0752	0.000
Hours square	−6.176	0.4675	0.000
Hours × Income	−0.021	0.0053	0.000
Age × Income	0.000	0.0008	0.904
Age square × Income	0.000	0.0001	0.994
Number of children × Income	−0.000	0.0001	0.000
Hours × age	0.057	0.0346	0.096
Hours × age square	−0.007	0.0043	0.089
Hours × 1(children 0–2)	−0.067	0.0239	0.005
Hours × 1(children 3–6)	−0.016	0.0077	0.041
Hours × 1(region)	−0.033	0.0045	0.000
Fixed cost (FC)	9.590	0.6394	0.000
FC × n. of children	−0.436	0.1999	0.029
FC × 1(children 0–2)	−1.684	0.8574	0.049
Log-likelihood	−1433.9093
Pseudo R²	0.1359
Observations	1031

Source: own simulations with EUROMOD.

Table 8:

Labour supply estimation: single men

	Coefficient	Robust standard error	p-Value
Income square	−0.0000	0.0006	0.923
Income	−0.0010	0.0018	0.576
Hours	0.9949	0.0964	0.000
Hours square	−13.0887	0.7986	0.000
Hours × Income	−0.0062	0.0096	0.518
Age × Income	0.0007	0.0009	0.420
Age square × Income	−0.0001	0.0001	0.431
Number of children × Income	0.0000	0.0003	0.939
Hours × age	0.0483	0.0403	0.231
Hours × age square	−0.0066	0.0050	0.188
Hours × 1(children 0–2)	−0.0183	0.1197	0.878
Hours × 1(children 3–6)	0.0749	0.0982	0.445
Hours × 1(region)	−0.0295	0.0050	0.000
Fixed cost (FC)	20.772	1.2162	0.000
FC × n. of children	−0.8203	0.8613	0.341
FC × 1(children 0–2)	−11.6082	616.374	0.985

Log-likelihood	−963.23904
Pseudo R²	0.2909
Observations	844

Source: own simulations with EUROMOD.

Table 9:

Kleven and Kreiner’s (2006) elasticity scenarios.

Income decile groups	1	2	3	4	5	6	7	8	9	10
Scenario 1
ηi	0.4	0.4	0.3	0.3	0.2	0.2	0.1	0.1	0.0	0.0
εi	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Scenario 2
ηi	0.4	0.4	0.3	0.3	0.2	0.2	0.1	0.1	0.0	0.0
εi	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
Scenario 3
ηi	0.8	0.6	0.4	0.2	0.0	0.0	0.0	0.0	0.0	0.0
εi	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
Scenario 4
ηi	0.4	0.3	0.2	0.1	0.0	0.0	0.0	0.0	0.0	0.0
εi	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
Scenario 5
ηi	0.6	0.6	0.4	0.4	0.3	0.3	0.2	0.2	0.0	0.0
εi	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1

Source: own simulations with EUROMOD.

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Published Online: 2018-09-18

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labour supply; marginal welfare cost; microsimulation; tax-benefit system