The Timing of Income Tax Changes in the Face of Projected Debt Increases

• Author: John Creedy,Grant Scobie,Christopher Ball
• DOI: http://doi.org/10.1111/1467-8462.12261
• Published date: 01 June 2018
• Date: 01 June 2018

The Timing of Income Tax Changes in the Face of Projected

Debt Increases

Christopher Ball, John Creedy and Grant Scobie*

Abstract

This article examines the time path of the

income tax rate chosen by a hypothetical

policy-maker, in a model where an increasing

ratio of government debt to GDP is projected

in the absence of policy changes. The policy-

maker is assumed to maximise an objective

function expressed in terms of a number of

aggregate variables, including the excess

burden of taxation and a desired debt ratio.

Tax policy changes have feedback effects, as

a result of incentives and other endogenous

inf‌luences that impose constraints on the

eff‌icacy of those policies. Emphasis is given

to the importance of uncertainty in devising an

optimal policy and the consequent value of

waiting instead of imposing a sharp initial

increase in anticipation of otherwise higher

future debt.

1. Introduction

This article examines the time path of the

income taxrate chosen by a hypothetical policy-

maker in a simple proportional tax structure,

where an increasingratio of government debt to

GDP is projected in the absence of any policy

changes. In the face of demographic change,

current f‌iscal policy settings in many countries

could leadto unsustainable levels of public debt.

One approach to prevent this arising is

immediately to raise taxation rates before debt

exceeds manageablelevels. However, given the

uncertainty that inevitably surrounds long-run

f‌iscal projections, the policy-maker is faced

with the diff‌icultchallenge of selecting the most

appropriatetime path for the tax rate. The aim is

to consider, forexample, what form of objective

function is consistent with tax smoothing and

what time path is produced by a broader

objective. The purpose is not to explain past

tax policy but to clarify the conditions under

which, say, an instant response or a more

gradual rise in tax rates is warranted.

An important motivation for the present

analysis is that in New Zealand the Public

Finance Act 1989 requires the Treasury to

produce, at least every four years, a statement

on the Crown’s long-term f‌iscal position.

These statements are required to provide

40-year projections of the f‌iscal position and

identify challenges that are likely to face future

governments.

Several modelling approaches exist for the

analysis of f‌iscal sustainability. One method

involves using detailed population and labour

force projections, along with information about

a wide range of government expenditures and

taxes. An extensive database is then used,

along with assumptions about the growth rates

* Ball: New Zealand Treasury, Wellington, New Zealand.;

Creedy: Victoria Business School, Victoria University

of Wellington, Wellington, New Zealand; Scobie: New

Zealand Productivity Commission, Wellington 6143,

New Zealand. Corresponding author: Creedy, email

<john.creedy@vuw.ac.nz>. The authors are grateful to Bob

Buckle, Andrew Coleman, Arthur Grimes, Michael Johnston,

Ian McDonald, Suzy Morrissey, TugrulVehbi and a referee of

this journal for their helpful commen ts on an earlier draft

of this article.

The Australian Economic Review, vol. 51, no. 2, pp. 191–210

°

C2018 The University of Melbourne, Melbourne Institute of Applied Economic and Social Research

Published by John Wiley & Sons Australia, Ltd

of each component—which are assumed to

remain exogenous—to build what might be

called ‘bottom-up’projections. This describes,

in broad terms, the strategy adopted in the New

Zealand Treasury’sLong Term Fiscal Model

(LTFM).

1

At the other extreme is an aggrega-

tive approach using an aggregate production

function and a representative household.

2

Each

model has its own advantages, being designed

to examine specif‌ic and somewhat different

questions, and each therefore necessarily has

its own limitations.

The present article adopts a different

approach—one lying between the two

extremes. Rather than attempting to capture

all the details involved in the many types of

expenditure and tax, the present article uses a

model with four types of expenditure in

addition to debt servicing costs, and simple

income and consumption tax systems. Various

feedback effects are modelled using reduced-

form specif‌ications rather than explicit opti-

mising behaviour. The model nevertheless

contains a suff‌icient amount of detail to enable

a range of policy responses to be examined.

Furthermore, the model produces benchmark

projections of the government debt ratio

that closely approximate the more detailed

Treasury model.

A large number of policy responses to

projected debt increases is possible. These

include annual adjustments to various catego-

ries of social and otherexpenditure and changes

in a number of tax rates.Such policies are likely

to have feedback effectsthat impose constraints

on the eff‌icacy of those policies. An important

constraint on policy choices is imposed by the

need to ensure f‌iscal sustainability over the

longer term, since high and increasing debt

ratios can impose large debt servicingcosts as a

result of a rising risk premium. Similarly, the

disincentive effectsof higher tax rates constrain

the government’s ability to raise revenue. The

present article analyses the chosen time path

of the proportional income tax rate. Focus on

the income tax rate is warranted in view of

the debate concerningthe timing of tax changes

and whether some form of tax smoothing is

desired. Emphasis is given to the importanceof

uncertainty in devising an optimal policy.

3

The question of whether tax smoothing is

desirable is complex.

4

Given the nonlinear

(approximately quadratic) nature of the excess

burden of taxation, it is sometimes assumed

without further question that smoothing is

always the optimal response. However, such a

policy is likely to involve a period of budget

surplus and, putting aside the concern that

politicians may ‘raid’such surpluses, the

disincentive effects of initial high rates can

affect income growth and therefore future tax

bases.

5

In addition, large surpluses may imply

missed opportunities for public investments

that can yield productivity gains, reductions

in tax rates or other desirable tax-f‌inanced

expenditure. Even if the future is assumed to be

known with certainty, the optimal time path of

adjustment depends not only on the starting

position in relation to some desired debt ratio

target, but also on the nature of the various

feedback effects and trade-offs involved in

policy decisions.

Decision making is further complicated by

the existence of uncertainty, which is consider-

able when dealing with projections over a

mediumto long-term horizon. The problemmay

be compared with that of investment in a multi-

period project where the future returns are not

known with certainty,there is a non-recoverable

sunk cost of investing in the f‌irst period and

there is an option of waiting until later periods

before makingthe investment: see, for example,

Dixit and Pindyck (1994)and Pindyck (2008).

6

The present context does not require an initial

investment, although current actions have effects

that may be non-reversible.

7

In this article, several central variables are

subject to uncertainty, which (as explained in

Section 5) is specif‌ied in a non-parametric

manner. Although the probability distributions

of the debt ratio and other endogenous

variables in each year of the planning period

can be obtained using Monte Carlo methods,

these cannot be used in the standard approach

used to obtain option values, which assumes

that probabilitiesare known ex ante.

8

Neverthe-

less a decisionstrategy, in which expectations of

future outcomes are revised as the uncertainty

becomes resolved over time, is devised and its

properties examined.

192 The Australian Economic Review June 2018

°

C2018 The University of Melbourne, Melbourne Institute of Applied Economic and Social Research