Inflation in South Africa: An Assessment of Alternative Inflation Models

• DOI: http://doi.org/10.1111/saje.12192
• Author: Yang Liu,Johannes Fedderke
• Date: 01 June 2018
• Published date: 01 June 2018

INFLATION IN SOUTH AFRICA: AN ASSESSMENT OF

ALTERNATIVE INFLATION MODELS

JOHANNES FEDDERKE*AND YANG LIU

†

Abstract

We consider the relative empirical performance of a range of inflation models for South Africa.

Model coverage is of Phillips curve, New Keynesian Phillips curve, monetarist and structural

models of inflation. Our core findings are that the single most robust covariate of inflation is

unit labour cost. We further decompose unit labour cost into changes in the nominal wage and

real labour productivity. The principal association is a strong positive relationship between infla-

tion and nominal wages, while improvements in real labour productivity report only a relatively

weak negative association with inflation. Supply-side shocks also consistently report an association

with inflation. As to demand-side shocks, the output gap does not return a robust statistical asso-

ciation with inflation. Instead, it is growth in the money supply and government expenditure

which return robust and theoretically consistent associations with inflationary pressure.

JEL Classification: E31

Keywords: Inflation, South Africa

1 INTRODUCTION

What accounts for inflationary pressures in the South African economy?

Inflation has received a disproportionate amount of attention in the South African macro-

economic literature. Unusually for South African debates, empirically motivated papers on

inflation have shown a close adherence to theoretical priors. A core feature of the South Afri-

can empirical studies has been a resolute search for a Phillips curve type of trade-off between

prices and demand-side inflationary pressure and real economic activity. A second constant

that emerges from the empirical literature is the consistent failure to successfully support the

Phillips curve trade-off.

1

Instead, a far more pervasive finding in the South African empirical

literature has been a strong association between inflation and wage costs.

Given the extensive struggle surrounding confirmatory evidence in support of the

Phillips curve, a further surprise in the South African empirical inflation literature is the

very limited search over alternative theoretical accounts of inflation. Thus very few stud-

ies even consider monetary accounts of inflation. Nor is there much evidence of an

exploitation of the well-established link between the first and second moments of the

* Corresponding author: Professor, Pennsylvania State University, 237 Katz, State College, PA

16802, USA. E-mail: jwf15@psu.edu

†

Center of New Structural Economics, Peking University

1

The principal exception we have found in the South African literature is associated with a New

Keynesian Phillips Curve (NKPC) estimation, but which has to abandon adherence to the rational

expectations foundations of the NKPC by allowing for habit persistence, and which has to esti-

mate under the assumption of perfectly clearing and flexible markets – something of a reach in the

South African context (see Burger and Du Plessis, 2013).

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C2018 Economic Society of South Africa. doi: 10.1111/saje.12192

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South African Journal of Economics Vol. 86:2 June 2018

South African Journal

of Economics

inflation time series.

2

This is all the more surprising since a cursory consideration of

South African inflation suggests that Autoregressive Conditional Heteroscedasticity

(ARCH) structure is plausible both for the Consumer Price Index (CPI) and Gross

Domestic Product (GDP) deflator time series (see Fig. 1).

The current paper innovates in three distinct senses in relation to the South African

debate.

First, we consider the relative performance of a range of alternative inflation models.

This includes, but is not restricted to Phillips curve type models of inflation. We extend

consideration to long-run structural models of price determination, a New Keynesian

Phillips curve (NKPC) model and monetary models of inflation.

Second, we consider the utility of incorporating ARCH structure into the modelling

in improving the performance of inflation models. We do so across the full range of the-

oretical alternatives, with the exception of the structural model where econometric con-

siderations preclude this possibility. A crucial means of considering the relative

performance of the inflation models is not only goodness of fit of the models, but also

their forecast performance over a 12-quarter window at the end of the sample period

under consideration in this study.

Third, unlike previous studies we abandon theoretical purity. Instead, we allow for all

the potential covariates of inflation identified under the alternative theoretical models to

compete empirically, in order to establish their relative robustness in modelling inflation.

In summary, our core findings are that the single most robust covariate of inflation is

unit labour cost. We further decompose unit labour cost into changes in the nominal

wage and real labour productivity. The principal association is a strong positive relation-

ship between inflation and nominal wages, while improvements in real labour productiv-

ity report only a relatively weak negative association with inflation. Supply-side shocks

also consistently report an association with inflation. As to demand-side shocks, the out-

put gap does not return a robust statistical association with inflation. Instead, growth in

Figure 1. Inflation under CPI and GDP deflator [Colour figure can be viewed at

wileyonlinelibrary.com]

2

After all, the seminal Engle (1982) introduction of ARCH estimation focussed precisely on

inflation.

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C2018 Economic Society of South Africa.

the money supply and government expenditure return more persistent and theoretically

consistent associations with inflationary pressure.

The difficulty in finding a reliable impact of the output gap on inflation may well be

due to the difficulties in developing reliable output gap measures (see Fedderke and Men-

gisteab, 2017). But precisely given this limitation, it may be desirable to use alternative

measures of demand-side pressure instead, such as money supply growth and government

expenditure stances.

The paper is structured as follows. In Section 2 we describe the alternative approaches

to modelling inflation that have been used in South Africa. Section 3 adds important

observations on the modelling of costs of production for inflation models in South

Africa. Section 4 outlines the modelling approach of the current paper and Section 5 the

data we employ. Section 6 presents our results, while Section 7 concludes and evaluates.

2 APPROACHES TO MODELLING SOUTH AFRICAN INFLATION

The simplest possible model of inflation is that agents formulate expectations adaptively.

This approach is devoid of theoretical justification, and issues in the time series model

given by:

Ept

ðÞ5b01X

k

i51

bipt2i1et(1)

where Edenotes the mathematical expectations operator, p

t

is the inflation rate in period

t,andetdenotes the error term. Despite the lack of theoretical foundations of this

model, in this study we employ it as a benchmark against which alternatives are judged,

given the surprising empirical resilience of the approach noted by many studies.

A second class of models is based on a structural theoretical framework given by a version

of the Phillips curve. Thus for instance Gordon (1997) (see also Gordon, 1989) proposes:

pt5X

k

i51

aipt2i1X

m

j51

bjDt2j1cct1dzt1et(2)

where D

t

denotes excess demand, c

t

the change in unit labour cost and z

t

supply shocks.

Measures of D

t

are provided by the unemployment gap U2

UðÞwhere Uand 

Uare

the actual unemployment rate and the Non-Accelerating Inflation Rate of Unemploy-

ment (NAIRU), respectively, or the output gap y2yðÞwhere yand yare the log of actual

output and long-run trend or potential output, respectively. Supply shocks are captured

by for instance changes in relative food prices (see Pretorious and Janse van Rensburg,

1996) or real exchange rate shocks. Burger and Marinkov (2006) further extend the Gor-

don model by classifying the excess demand variable D

t

in terms of the extent of infla-

tionary pressure being generated. They do so by including variables for excess demand,

one for excess demand deemed to “overheat” the economy, Doverh

t, another for weak

excess demand Dweak

t.

3

This represents an attempt to capture the possibility of a non-

3

Doverh

tduring the weak-economy years is set to be zero, and symmetrically Dweak

tduring over-

heating periods.

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C2018 Economic Society of South Africa.