Identifying Laffer Bounds: A Sufficient‐Statistics Approach with an Application to Germany

• DOI: http://doi.org/10.1111/sjoe.12170
• Published date: 01 October 2016
• Date: 01 October 2016

Scand. J. of Economics 118(4), 646–665, 2016

DOI: 10.1111/sjoe.12170

Identifying Laffer Bounds:

A Sufficient-Statistics Approach

with an Application to Germany∗

Normann Lorenz

University of Trier, DE-54286 Trier, Germany

lorenzn@uni-trier.de

Dominik Sachs

European University Institute, 50133 Firenze, Italy

dominik.sachs@eui.eu

Abstract

We derive a simple sufficient-statistics test for whether a nonlinear tax-transfer system is

second-best Pareto efficient. If it is not, then it is beyond the top of the Laffer curve and

there exists a tax cut that is self-financing. The test depends on the income distribution,

extensive and intensive labor supply elasticities, and income effect parameters. A tax-transfer

system is likely to be inefficient if marginal tax rates are quickly falling in income. We

apply this test to the German tax-transfer system, and we find that the structure of effective

marginal tax rates is likely to be inefficient in the region where transfers are phased out.

Keywords: Extensive margin; income taxation; Laffer curve; Pareto efficiency

JEL classification:H21; H23

I. Introduction

Although there is considerable disagreement on whether a more equitable

tax system requires higher tax rates, there seems to be a consensus among

economists that lowering income taxes from current levels does not lead

to higher tax revenue but rather to lower tax revenue.1This consensus re-

gards the effect of lowering marginal tax rates for all income levels. How-

ever, what about different reforms of the tax system? Because real-world

∗We thank Friedrich Breyer, Sarah Brockhoff, Sebastian Findeisen, Laurence Jacquet, Mathias

Kifmann, Fabian Kr¨

uger, Etienne Lehmann, Nick Netzer, Florian Scheuer, Dirk Schindler,

Esther Schuch, Jean-Franc¸ois Tremblay, Iv`

an Werning, numerous seminar participants, and

two anonymous referees. D. Sachs’ research was partly funded by a post-doc fellowship of

the Fritz-Thyssen Foundation and the Cologne Graduate School in Management, Economics

and Social Sciences.

1In the Initiative on Global Markets (IGM) economics experts panel, none of the respondents

was in favor of this idea for the US (see IGM, 2012). Trabandt and Uhlig (2011) also revisit

the Laffer curve argument for most European countries, and they conclude that decreasing

taxes is not self-financing.

CThe editors of The Scandinavian Journal of Economics 2016.

N. Lorenz and D. Sachs 647

tax-transfer systems (TTSs) are nonlinear in most countries, there is no

reason for economists to focus their analysis on linear tax reforms.

In this paper, we provide a simple sufficient-statistics test that can

uncover whether a nonlinear TTS is beyond the Laffer bound and therefore

inefficient. We consider not only the case when marginal tax rates are

too high, but also the case when they might have an inefficient structure.

The test also provides guidance on how to reform the TTS in a Pareto

improving manner.

The theoretical foundation of our work is the optimal nonlinear income

tax literature following Mirrlees (1971). This body of literature provides the

methods to address the question of whether a TTS is designed efficiently.

However, most of this literature has focused on characterizing properties of

an optimal TTS for a given social welfare function and some given eco-

nomic primitives (preferences, skill distributions). Recently, this approach

has been inverted to determine for which social welfare function a given

TTS is optimal (given the primitives). If the resulting welfare function im-

plies social marginal welfare weights that are negative, then the TTS is not

second-best Pareto efficient.2

Werning (2007) elaborates this idea and provides conditions on the skill

distribution and preferences under which a TTS is inefficient. His main

conclusion is that from a theoretical point of view “anything goes”; thus,

any kind of TTS can be justified as Pareto optimal for some skill dis-

tribution and preferences. Given knowledge about the primitives, he then

proposes a theoretical test on whether a given TTS is Pareto efficient.

This paper builds on the work of Werning (2007) and provides a

sufficient-statistics test for the efficiency of a TTS. The innovation is that

our analysis takes into account extensive labor supply responses and, more

importantly, that our test function only depends on measurable statistics.3

Information about the income distribution, extensive and intensive labor

supply elasticities, as well as income effect parameters is sufficient to de-

tect an inefficiency of the TTS. Consequently, our empirical test can easily

be conducted if information on these sufficient statistics is available.

In addition to the classical Laffer-argument – which states that marginal

tax rates are inefficiently high when they are above the revenue-maximizing

level – we argue that the structure of marginal tax rates can be a source

of inefficiency. We show that a TTS is particularly likely to be inefficient

if effective marginal tax rates are quickly falling in income.

Motivated by this theoretical observation, we apply our test to the Ger-

man TTS because it is characterized by rapidly falling effective marginal

2It was Saez (2001, p. 221) who first suggested this approach.

3In this paper, we use the two terms “extensive labor supply responses” and “participation

responses” interchangeably.

CThe editors of The Scandinavian Journal of Economics 2016.