On Determinacy and Learnability in a New Keynesian Model with Unemployment

• Author: Mewael F. Tesfaselassie,Eric Schaling
• Date: 01 December 2016
• Published date: 01 December 2016
• DOI: http://doi.org/10.1111/saje.12107

ON DETERMINACY AND LEARNABILITY IN A NEW

KEYNESIAN MODEL WITH UNEMPLOYMENT

MEWAEL F. TESFASELASSIE

*

AND ERIC SCHALING

†

Abstract

We analyse determinacy and stability under learning (E-stability) of rational expectations

equilibria in a new Keynesian model of inflation and unemployment, where labour market

frictions due to costs of hiring workers play an important role. We derive results for alternative

specifications of monetary policy rules and alternative values of hiring costs as a percentage of gross

domestic product. We find that in general the region of indeterminacy and E-instability in the

policy space increases with hiring costs. Thus, higher hiring costs – consistent with European and

South African “sclerotic” labour market institutions – seem to play an important part in explaining

inflation and unemployment instability. Moreover, under lagged data-based rules, the area where

monetary policy delivers both determinacy and E-stability shrinks. These rules also perform worse

according to these two dimensions when hiring costs go up. Finally, under expectations-based rules

an additional explosive region is introduced. For South Africa, a rule based on current data – not

unlike the original Taylor rule – works better than a forward-looking rule.

JEL Classification: E5, E3, D8

Keywords: Monetary policy rules, determinacy, learning, E-stability

1. INTRODUCTION

Business cycle models with forward-looking expectations may be prone to two types of

problems. The first is real indeterminacy – the possibility that a unique, stationary

rational expectations equilibrium does not exist. The second problem – which has

received more attention recently – is expectational instability (in short E-instability àla

Evans and Honkapohja, 2001) under private sector learning. In models where monetary

policy plays a role in determining inflation and output, such as the new Keynesian model,

one may wonder what sorts of policy rules may lead the economy into indeterminacy

and/or expectational instability, so that policymakers can avoid using such undesirable

policy rules. Bullard and Mitra (2002) analyse the determinacy and learnability of

rational expectations equilibria in a purely forward-looking new Keynesian model of

inflation and the output gap. They evaluated different forms of Taylor-type rules for

setting the nominal interest rate. While Bullard and Mitra (2002) make an important

contribution, their analysis also reveals that the conditions for determinacy and

learnability of rational expectations equilibria are affected not only by the form of the

monetary policy rule but also by the structure of the economy. The version of the new

Keynesian model that they analyse is simple, in the sense that it does not feature

* Corresponding author: Senior Researcher, Kiel Institute for the World Economy, Kiellinie 66,

24105 Kiel, Germany. Tel: +49 431 8814 273.

E-mail: mewael.tesfaselassie@ifw-kiel.de

†Wits Business School, University of the Witwatersrand.

South African Journal of Economics Vol. ••:•• •• 2015

© 2015 Economic Society of South Africa. doi: 10.1111/saje.12107

1

V

C2015 Economic Society of South Africa. doi: 10.1111/saje.12107

607

South African Journal of Economics Vol. 84:4 December 2016

South African Journal

of Economics

endogenous persistence in inflation and the output gap, and is thus at odds with empirical

evidence. Moreover, as argued by, among others, Blanchard and Gali (2010), the standard

new Keynesian model does not generate movements in unemployment, as it assumes

variations in hours worked only. In order to account for unemployment dynamics, the

authors extend the standard rational expectations new Keynesian model by incorporating

search and matching in labour markets.1The resulting model of inflation and unemploy-

ment has richer dynamics, owing to the presence of lags and leads of unemployment in

the Phillips curve and of lags of unemployment in the so-called IS curve.

We analyse the determinacy and learnability of rational expectations equilibria under

alternative forms of monetary policy rules in the Blanchard and Gali (2010) model.2Our

paper’s set-up is similar to Bullard and Mitra (2002) in terms of the specification of policy

rules. However, we distinguish between a general form (analysed in Bullard and Mitra,

2002) and a special form of model specification under private sector learning. The general

form assumes that even if the structural model does not include a constant term (as in our

case), private agents include a constant term in their econometric model used for

forecasting. Thus, bounded rationality is more severe when learning is based on the

general form. In this case, indeterminate equilibria that do not fulfil the Taylor principle

(where the nominal interest rate moves more than one to one to a permanent change in

inflation) are also E-unstable. By contrast, when bounded rationality is not severe, some

indeterminate equilibria are E-stable.

Section 2 sets out the linear model of inflation and unemployment. Then, section 3

incorporates three policy rules, in each case reporting results on the determinacy and

learnability of rational expectations equilibria. In section 4, we report additional results,

including those of a calibration using data for South Africa. Section 5 concludes.

2. A MODEL OF INFLATION AND UNEMPLOYMENT

We work with three key log-linearised equations related to the Phillipscur ve, the IS curve

and a monetary policy rule (see in particular Blanchard and Gali, 2010). The Phillips

curve is given by3:

πβπ ππ π π

tt

e

tft

e

lt at

ku ku ku ka=++ + +

++−10 1 1 (1)

1See also Ravenna and Walsh (2008).

2Lubik and Krause (2004) analyse the issue of determinacy in a search and matching model of the

labour market. Kurozumi and Van Zandweghe (2008) study the determinacy and E-stability for

search and matching models along the lines of Krause and Lubik (2007) and Christoffel and

Kuester (2008).

3As shown in Blanchard and Gali (2010), inflation is positively related to real marginal cost,

which in turn is equal to the relative price of the intermediate good. From the optimal hiring

condition, the relative price of the intermediate good depends positively on current labour market

tightness (as it raises current cost per hire) and negatively on expected discounted future labour

market tightness (as more current hiring implies cost savings when the future labour market is

tighter and the associated cost per hire is higher). Current labour market tightness depends

negatively on current unemployment but positively on lagged unemployment. Similarly, future

labour market tightness depends negatively on future unemployment but positively on current

unemployment. Together these effect imply that kπ0<1, kπl>1 and kπf>1.

South African Journal of Economics Vol. ••:•• •• 20152

© 2015 Economic Society of South Africa.

608 South African Journal of Economics Vol. 84:4 December 2016

V

C2015 Economic Society of South Africa.