Regional Beveridge Curves: A Latent Variable Approach

Abstract

Dixon R., Lim G. C. and Freebairn J. Regional Beveridge curves: a latent variable approach, Regional Studies. This paper applies an unobserved components model to a panel of Australian data to identify the direction and timing of the shifts in regional Beveridge curves. The approach identifies a common factor while allowing for region-specific effects. The common factor that drives the relationship between regional unemployment and vacancy rates is extracted and it is then related to various explanatory variables. The contribution of common shocks to fluctuations in regional unemployment ranges from 18% to 68%. The paper demonstrates the usefulness of a latent variable approach and, in relation to policy, the findings suggest the need for an explicit regional policy to tackle unemployment in Australia.

Dixon R., Lim G. C. and Freebairn J. 区域贝弗里奇曲线：隐性变量研究方法，区域研究。本文将不可观测成分模型应用于一组澳大利亚数据以明确区域贝弗里奇曲线转变的方向与时机。方法在允许特定区域影响的同时确定了一个共同的因子。研究明确了这一推动地区失业和闲置率之间相互关系的共同因子，并将其与各种解释变量相关联。共同冲击影响了区域失业在18％至68％区间的波动。本文展示了隐性变量研究方法的有用性，研究结果在关联相关政策的基础上表明，解决澳大利亚的失业问题需要一个明确的区域政策。

Dixon R., Lim G. C. et Freebairn J. Des courbes de Beveridge régionales: un modèle à variables latentes, Regional Studies. Cet article cherche à appliquer un modèle à composantes non observées à un panel de données australiennes pour identifier l'orientation et le timing des déplacements des courbes de Beveridge. Ce modèle identifie un facteur commun tout en tenant compte des effets spécifiques à la région. On supprime le facteur commun qui conduit le rapport entre le chômage régional et les offres d'emploi et on le rapporte à diverses variables explicatives. La contribution des chocs communs des fluctuations du chômage régional va de 18% à 68%. L'article démontre l'utilité d'un modèle à variables latentes et, par rapport à la politique, les résultats laissent supposer qu'il faut une politique régionale explicite qui essaye de maîtriser le chômage en Australie.

Dixon R., Lim G. C. und Freebairn J. Regionale Beveridge-Kurven: ein Ansatz mit latenten Variablen, Regional Studies. In diesem Beitrag wird ein Unbeobachtete-Komponenten-Modell auf ein Panel australischer Daten angewandt, um die Richtung und den Zeitpunkt von Veränderungen in regionalen Beveridge-Kurven zu identifizieren. Durch diesen Ansatz wird unter Berücksichtigung regionsspezifischer Effekte ein gemeinsamer Faktor identifiziert. Der gemeinsame Faktor, der für die Beziehung zwischen regionaler Arbeitslosigkeit und dem Anteil der unbesetzten Arbeitsplätze ausschlaggebend ist, wird extrahiert und anschließend in Bezug zu verschiedenen erklärenden Variablen gesetzt. Der Beitrag von gemeinsamen Schocks zu den Fluktuationen bei der regionalen Arbeitslosigkeit beläuft sich auf 18% bis 68%. In diesem Artikel wird die Nützlichkeit eines Ansatzes mit latenten Variablen nachgewiesen; in politischer Hinsicht lassen die Ergebnisse auf die Notwendigkeit einer expliziten Regionalpolitik zur Bekämpfung der Arbeitslosigkeit in Australien schließen.

Dixon R., Lim G. C. y Freebairn J. Curvas regionales de Beveridge: un enfoque con variables latentes, Regional Studies. En este artículo empleamos un modelo de componentes no observados en un panel de datos de Australia para identificar la dirección y los momentos de los cambios en las curvas regionales de Beveridge. Con este enfoque identificamos un factor común teniendo en cuenta los efectos específicos para las regiones. Obtenemos el factor común que impulsa la relación entre el desempleo regional y los índices de vacantes y lo relacionamos con varias variables explicativas. La contribución de las perturbaciones comunes a las fluctuaciones en el desempleo regional varía de un 18% a un 68%. En este artículo demostramos la utilidad de un enfoque de variables latentes; y con respecto a la política, los resultados indican que es necesaria una política regional explícita que reduzca el desempleo en Australia.

Keywords:

• Beveridge curve
• Regional unemployment
• Unobserved components model

• 贝弗里奇曲线
• 区域失业
• 不可观测成分模型

• Courbe de Beveridge
• Chômage régional
• Modèle à composantes non observées

• Beveridge-Kurve
• Regionale Arbeitslosigkeit
• Unbeobachtete-Komponenten-Modell

• Curva de Beveridge
• Desempleo regional
• Modelo de componentes no observados

JEL classifications:

• E32
• R11
• R12

Acknowledgements

The authors are grateful to the Editors and the two anonymous referees for very helpful comments on an earlier version of the paper.

Notes

For examples, see Jones and Manning (1992) and Wall and Zoega (2002) for the UK; Borsch-Supan (1991) for Germany; and Samson (1994) for Canada.

For a concise introduction to the Beveridge curve and related theoretical constructs, see Cahuc and Zylberberg (2004, ch. 9).

For an exposition of the Hansen model of the Beveridge curve, see Dixon et al. (2010).

Readers are no doubt aware that in 2010 The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded jointly to Peter Diamond, Dale Mortensen and Christopher Pissarides ‘for their analysis of markets with search frictions’, a topic intimately connected with the Matching Model and the relationship between unemployment and vacancies.

It is assumed that the Matching Function is strictly increasing in each of its arguments and that .

For this reason it is not wise to think of the business cycle as only resulting in movements along a given Beveridge curve. Holt (1996) also makes this (important) point.

It is also common in the literature to use the lagged vacancy rate as the instrument to avoid simultaneity bias. This practice is followed herein. Essentially the same results are obtained if the current vacancy rate is used instead of the lagged vacancy rate.

Unfortunately these ‘explanatory variables’ cannot figure explicitly in equation (7) as they are available only at a national and not at a regional basis.

Harvey (1990) provides an excellent exposition. The software used in the paper are GAUSS and EViews.

For the regional elasticities of unemployment with respect to vacancies (the ), only five distinct significant coefficients were found. It appears to be the case that contiguous (smaller) regions experience similar labour market conditions as their bigger neighbours and hence these smaller regions (economically speaking) have been grouped with the economic regions. The grouped regions are: VIC plus SA plus TAS, the regions in the south-east of Australia; and WA plus NT, the two mineral resource-rich states in the west and north.

For a discussion of this, see Pissarides (2000), Petrongolo and Pissarides (2001), Shimer and Smith (2001), and Cahuc and Zylberberg (2004).

Measures of the degree of regional specialization invariably show the ACT as the most specialized of all the regions.

Another way to put this is to say that it is not wise to assume γ = 0.5, which many modellers do (if the Beveridge curve is a rectangular hyperbola, then γ = 0.5 and β = –1).

These groupings likely correlate with regional industry structure. Measures of similarity of industry structure for Australian states and territories invariably show WA and QLD as having very similar structures and that they are more alike in this respect than they are with any of the other states and territories. For comparisons of industrial structures across the states and territories of Australia using Krugman's measure of similarity (or dis-similarity) amongst other measures (Krugman, 1991, pp. 75f.; Krugman, 1993, pp. 250f.), see Dixon and Shepherd (2000) and Dixon and Freebairn (2009).

The Lilien index is a time-series of the weighted standard deviation of industry growth rates (Lilien, 1982, p. 787).

All of the variables in the equation are I(0).

The rate of growth in non-farm GDP at constant prices is used.

Long-term unemployment is defined as persons who have not held a job for fifty-two weeks or more. The ‘long-term unemployment rate’ is the ratio of the number of long-term unemployed to the labour force.

The labour market programme measure is public expenditure on active LMPs per unemployed person expressed as a proportion of GDP. This is available on an annual basis back to 1986 from various years of the OECD Employment Outlook. This series has been interpolated to yield quarterly estimates.

The equation is estimated using quarterly data over the period 1984Q1–2008Q2, giving ninety-eight observations. R² = 0.318. Estimated coefficients on the Lilien index and the replacement ratio were not significantly different from zero at the 10% level and were omitted from the final equation (the significance and sign of the other variables were unaffected).

Obviously, with α (and β) constant across time, the value of will be constant over time for any region, hence the use of the word ‘static’ to describe it.

This demonstrates the gains from using an approach that does not assume that the effect of common shocks across the regions are identical.

These findings for Australia – (1) that there are persistent differences in unemployment rates between the states and (2) that common or national shocks are not always the main source of variations over time in any one state's unemployment rate – have been noticed by other authors (using different methods to that deployed here). For a survey of the literature on these topics, see Dixon and Shepherd (2011).

The series for the equilibrium rate of unemployment for the nation closely resembles that recently reported by Kennedy et al. (2008) whose estimates are based on aggregate unemployment and vacancy data.

Where is calculated using equation (8); and is calculated using equation (9).

The Krugman measure is related to a measure with a long history in regional studies called the ‘Coefficient of Regional Specialisation’ (Isard, 1960, pp. 270ff.; Dixon and Thirlwall, 1975, pp 16f.). For examples of the use of this variable in the context of studying regional co-movements, see Clark and van Wincoop (2001), Barrios et al. (2003), Barrios and de Lucio (2003), Imbs (2004), Belke and Heine (2004), and Poncet and Barthelemy (2008).

Data for employment by industry are available for fifty-three industries covering all sectors in the economy. The average value of KI for each pair of regions over the sample period was used. This gave essentially the same results as those obtained if the values of the KI for the middle year of the sample period (1993) were used.

TAS (a large island to the south of VIC) is separated from VIC by the Bass Strait, which is around 250 kilometres wide. Since there is considerable sea and air traffic between TAS and VIC (and much less direct sea or air traffic between TAS and other states), TAS has been recorded as being adjacent to (having a border) with VIC, but not being adjacent to any other state. In terms of climate, etc. TAS is more like VIC than any other state.

For examples of the use of this variable in the context of studying regional co-movements, see Clark and van Wincoop (2001), Barrios and de Lucio (2003), and Imbs (2004). It clearly has its origin in the gravity model of trade and other regional interactions.

The equation is estimated for the twenty-eight off-diagonal observations given in Table 6. R² = 0.480. A regression with KI and (the logarithms of) size and distance separately yielded essentially the same result for KI and a positive coefficient on Size and a negative coefficient on Distance. However, the coefficients on Size and Distance were not significantly different from zero at the 10% level. Since the two variables were highly correlated, it was decided to combine them (as explained in the text) into a single Gravity variable.

Dixon and Shepherd (2000) found that Australian states and territories with similar industrial structures also have similar unemployment rates.

Interestingly, no role for adjacency (in other words, no evidence of an internal border effect) is found; this is not uncommon in the literature on this topic.

Of course, policy, and especially labour market policy, which is targeted towards particular groups of people, can affect different regions differently, even if the policy is uniform across Australia, depending upon the region's share of the target group (policies aimed at the long-term unemployed and which apply regardless of their place of residence, may nonetheless affect TAS (say) more than other states if the proportion of all long-term unemployed who are in TAS is higher than TAS's share of the total population – to take just one example).

A small number of observations for WA in early 1984 were missing in the file downloaded from DX. These were interpolated using data from the Australian Bureau of Statistics (ABS) (n.d.) publication Job Vacancies: Australia (Catalogue Number 6231) for 1984. Also, from 17 March 1998, changes in public service regulations have meant that most Australian Public Service vacancies, previously only available to current public service employees, are open to all Australian citizens. Commencing in May 1998 these vacancies fell within the scope of the Job Vacancies and Overtime survey. This change produced an increase in the number of Australian Public Service vacancies being reported. However, leaving aside the ACT, the effect on the time-series for total (public plus private) vacancies seems to have been quite small.