Designing Optimal Taxes with a Microeconometric Model of Labour

SupplyEvidence from Norway

Rolf Aaberge, Statistics Norway and CHILDUgo Colombino, Univ. of Torino, Statistics Norway and

CHILD

IMA2007, 20-22 August, Vienna

Purpose

Identify optimal (personal income) tax rules in Norway, using a structural microeconometric model

Traditional approach to empirical optimal taxation

The typical exercise (e.g as surveyed by Tuomala):

•Take some optimal tax formula derived from theory

•Calibrate the parameters (preferences, distribution of characteristics, elasticities etc.) using previous empirical results

•Compute optimal taxes

Traditional approach in empirical optimal taxation

Problem with this approach:

•theoretical results typically rely on some special assumptions;

•possible inconsistency between the assumptions of the theoretical model and the assumptions of the empirical analysis used to calibrate the parameters;

•difficult to include household decisions, participation decisions, quantity constraints.

A microeconometric - computational approach

• The approach adopted in this paper is different:

• we do not start from a priori theoretical results;

• we directly identify the optimal tax rule by running a microeconometric model of household labour

supply that simulates household choices and utility for any tax rule;

• the simulation searches for the tax rule that maximizes a social welfare function subject to the constraint of a constant total tax revenue.

The microeconometric model

• It is (basically) a MNL model.

• Each individual (or household) is assumed to choose within an opportunity set containing jobs.

• Each job is a bundle of hours of work, net income (given a tax rule t) and unobserved characteristics e(j).

• The tax rule is a function t: Gross Net.

• u(j;t) = V(j;t)e(j) = utility attained at job j, given tax rule t

The microeconometric model

Under suitable assumptions upon the distribution (extreme value) of the unbserved characteristics, one gets:

Prob(j is chosen) = V(j;t)/∑iBV(i;t)

The microeconometric model

Main distinctive feature of the model with respect to other MNL models used in the labour supply literature:

The job opportunity sets are different among individuals (we account for differing opportunities, differing quantity constraints etc.).

An example of the opportunity set in the (income, hours, e) space

hours

income

0

e Job J

Job K

Estimation

• V(j;t) – function of income, leisure and demographic characteristics - is given a flexible parametric specification

• The 78 parameters are estimated by ML

• The dataset is based on the 1995 Norwegian Survey of Level of Living

• It contains 1842 couples, 309 single females and 312 single males

• Only individuals with age between 20 and 62 are included

Labour supply elasticities implied by the modelMarried couples

Household income decile

Female Male

Own Cross Own Cross

I 2.54 -0.29 1.77 -0.12

II 0.97 -0.67 1.17 -0.08

III-VIII 0.41 -0.47 0.31 -0.24

IX 0.20 -0.34 0.08 -0.14

X 0.26 -0.10 0.05 -0.42

All 0.52 -0.42 0.39 -0.23

Simulating optimal tax rules

STEP 1:Given a tax rule f, compute for each individual 1,…,N

u = maxj V(j;f)e(j)

STEP 2:Compute the Social Welfare Function W(u1,…,uN). The arguments u of the Social Welfare function are made interpersonally comparable by using a common utility function

STEP 3:Iterate (on the set of tax rules) STEPS 1-2 so as to maximize W keeping constant the total net tax revenue

Social Welfare FunctionIn general we can write the SWF as:

W = (∑iui/N)(1-I) = “Efficiency” “Equality”.

∑iui/N = average utility (efficiency).

I = index of inequality of the distribution of utility.

In this exercise I is a rank-based index. It depends on the value of an inequality-aversion parameter.

For different values of this parameter, one gets different special cases (Utilitarian, Gini, Bonferroni etc.).

We also extend the above SWF to include a criterion of Equality of Opportunities (due to J. Roemer).

6-parameter piecewise linear tax rulesThe optimal tax rule is defined by 6 parameters:

E = exemption level

Z1 = upper limit of first tax bracket

Z2 = upper limit of the second tax bracket

t1 = marginal rate of the first tax bracket

t2 = marginal rate of the second tax bracket

t3 = marginal rate of the third tax bracket

It replaces the current 1994 rule, which is also piecewise linear, with seven income brackets and a smooth sequence of marginal rates (starting with .25 and ending up with .495)

In this exercise, all transfers (social assistance, benefits etc.) are left unchanged.

The top marginal tax rate is constrained to be less than or equal to .6

Net

GrossZ1 Z2E

t1

t2

t3

Net

GrossZ1 Z2E

t1

t2

t3

Net

GrossZ1 Z2

t1

t2

Actual (1994) vs Optimal tax rules according to alternative social welfare

criteria Actual

(approx.)Bonferron

iGini Utilitarian

E 17 0 6 8

t1 0.25-0.35 0.17 0.20 0.22

Z1 140 172 211 264

t2 0.35-0.45 0.38 0.37 0.33

Z2 235 700 690 720

t3 0.50 0.60 0.60 0.60

Average tax rates

Gross income (NOK) Actual (1994) rule BONFERRONI-optimal rule

50000 17.5 17.0

100000 23.9 17.0

150000 26.3 17.0

200000 28.7 19.9

400000 38.5 29.0

700000 43.2 32.8

1000000 45.1 41.0

Percentage change in labour supply when the BONFERRONI-optimal tax rule is applied

Household Income Decile

Single male

Single female

Married male

Married female

I 89.5 65.9 36.3 47.8

II 17.9 25.2 22.9 13.4

III - VIII 2.8 3.0 4.2 4.6

IX 0.0 0.0 1.5 -0.2

X 1.2 0.0 -0.7 -1.5

All 7.0 6.1 6.4 7.8

Percentage of winners when the BONFERRONI-optimal tax rule is applied

Household Income Decile

Single male

Single female

Married male

Married female

I 74 74 62 63

II 68 55 70 70

III - VIII 83 69 79 82

IX 77 42 80 83

X 77 39 74 74

All 79 62 76 78

Comments

• Similar to the current rule, optimal tax rules imply

a sequence of increasing marginal tax rates

• However, optimal rules are more progressive on high income levels and less progressive on low and average income levels (somehow consistent with the pattern of labour supply elasticities)

• Optimal rules imply a higher net income for almost any level of gross income lower average tax rate: thanks to a sufficiently large labour supply response

Comments

• Our results are partially at odds with the tax reforms that took place in many countries during the last decades.

• Those reforms, with the aim of improving efficiency and incentives, embodied the idea of lowering average tax rates by lowering the top marginal rates (OECD countries: from 67% to 47% in the period 1980-2000).

• Our results suggest instead to lower average tax rates by lowering marginal rates on average incomes and increasing marginal rates on very high incomes: this improves both efficiency and equality.

Work-in-progress

• Simulating tax rules with more parameters

• Including transfers (social policies, lump-sum benefits or taxes etc.) – Preliminary results suggest that the current level of transfers in Norway might be close to optimal

•tax reforms implemented in many developed countries during the last decades. In most cases those reforms embodied the idea of improving efficiency and labour supply incentives through a lower average tax rate and lower marginal tax rates on higher incomes. [1] Our optimal tax computations give support to the first part (lowering the average tax rate), much less to the second; on the contrary our results suggest that a lower average tax rate should be obtained by lowering the marginal tax rates particularly on low and average income brackets[2]. The optimal tax rules efficiently exploit the pattern of heterogeneous responses from different households.

References

• Aaberge, R.., J.K. Dagsvik and S. Strøm (1995): "Labor Supply Responses and Welfare Effects of Tax Reforms", Scandinavian Journal of Economics, 97, 4, 635-659.

• Aaberge, R., U. Colombino and S. Strøm (1999): “Labor Supply in Italy: An Empirical Analysis of Joint Household Decisions, with Taxes and Quantity Constraints”, Journal of Applied Econometrics, 14, 403-422.

• Aaberge, R., U. Colombino and S. Strøm (2000): “Labour supply responses and welfare effects from replacing current tax rules by a flat tax: empirical evidence from Italy, Norway and Sweden”, Journal of Population Economics, 13, 595-621.

• Aaberge, R., U. Colombino and S. Strøm (2004): "Do More Equal Slices Shrink the Cake? An Empirical Investigation of Tax-Transfer Reform Proposals in Italy“, Journal of Population Economics, 17

• Aaberge, R. and U. Colombino (2006): “Designing Optimal Taxes with a Microeconometric Model of Household Labour Supply“, IZA DP 2468.