Shifting the Beveridge Curve: What Affects Labor Market Matching?

Elva Bova; João Tovar Jalles; Christina Kolerus

doi:10.5089/9781484326466.001.A001

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Shifting the Beveridge Curve

What Affects Labor Market Matching?

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Ms. Elva Bova

Ms. Elva Bova
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João Tovar Jalles

João Tovar Jalles
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Ms. Christina Kolerus

Ms. Christina Kolerus
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Contributor Notes

Authors’ E-Mail Addresses: elvabova@gmail.com, JJalles@imf.org, CKolerus@imf.org

Publication Date:: 12 Apr 2016

eISBN:: 9781484326466

Language:: English

Keywords:: WP; output gap; financial crisis; job sharing; labor force growth; outward shift; labor turnover; labor market dynamics; unemployment growth

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This paper explores conditions and policies that could affect the matching between labor demand and supply. We identify shifts in the Beveridge curves for 12 OECD countries between 2000Q1 and 2013Q4 using three complementary methodologies and analyze the short-run determinants of these shifts by means of limited-dependent variable models. We find that labor force growth as well as employment protection legislation reduce the likelihood of an outward shift in the Beveridge curve,. Our findings also show that the matching process is more difficult the higher the share of employees with intermediate levels of education in the labor force and when long-term unemployment is more pronounced. Policies which could facilitate labor market matching include active labor market policies, such as incentives for start-up and job sharing programs. Passive labor market policies, such as unemployment benefits, as well as labor taxation render matching signficantly more difficult.

Abstract

To understand the effects of policy on unemployment in Britain we would have to explain first, how policy has affected the willingness of firms to hire new workers and how it has affected the willingness of the unemployed to look for and accept new jobs.

Pissarides 1986

I. Introduction

Although much of the increase in unemployment since the global financial crisis has been attributed to cyclical factors (Kugler, 2014), mismatches between labor demand and labor supply have become more relevant in comparison with pre-crisis years. Evidence illustrates that positive signs of recovery, such as an increase in the advertised number of vacancies starting in the last quarter of 2009, coexist with stubbornly high levels of unemployment suggesting significant labor demand and labor supply mismatches (Figure 1). More importantly, long-term unemployment has increased markedly in the aftermath of the global financial crisis. As OECD data show, the number of unemployed increased by almost 50 percent between 2007 and 2013. The number of long-term unemployed increased by more than 80 percent. Given the path dependency associated with long-term unemployment, addressing labor mismatches becomes an even more urgent task.

Figure 1.

OECD Average Unemployment and Vacancies in the Great Recession

(Percent of labor force)

Citation: IMF Working Papers 2016, 093; 10.5089/9781484326466.001.A001

Source: OECD.

Improving the efficiency of labor market matching requires policies beyond those aimed at stimulating aggregate demand, since frictional unemployment originates from institutional inefficiencies, skill gaps between demand and supply market forces, and from any factor that dissuades job seekers to accept a job or makes employers choosier in their job selection process.

Frictions and mismatches in the labor market can be captured by the so-called Beveridge curve, which relates vacancies to the number of unemployed. An economic slowdown, during which the job destruction process is more volatile than the job creation process (Mortensen and Pissarides, 1994), would lead to a downward movement along the curve corresponding to lower vacancies and higher unemployment. A recovery, in turn, would trigger an upward ride. Some policies, such as the short-time working scheme applied by several countries during the global financial crisis, might prevent or attenuate an increase in unemployment. Such policy could even lead to an inward shift of the curve if the number of vacancies is decreasing—due to a slowdown in economic activity—at a given unemployment level. On the contrary, during periods of jobless recoveries, for instance, the Beveridge curve would feature an outward shift as vacancies are constant and unemployment is increasing.

This paper assesses the role of policies and institutions in shifting the Beveridge curve for a sample of 12 OECD countries over the 2000Q1-2013Q4 period. First, we detect shifts in each country’s Beveridge curve and determine their magnitude and direction by means of three methodologies: visual examination, cointegration techniques and non-linear estimation. In a second step, with a panel probit model, we assess several factors that could influence the probability of these shifts, to better understand which policies and institutions can affect the efficiency of labor market matching. Our main findings can be summarized as follows:

Shifts. Out of the 12 OECD countries examined, 10 exhibit a shift of their respective Beveridge curve. We identify seven countries with outward shifts, i.e., deteriorations of labor market matching, which in many cases took place at the onset of the global financial crisis, and two countries with inward shifts. One country features both, an outward and inward shift.
Labor market structure. We find strong and robust evidence that labor force growth reduces the likelihood of an outward shift of the Beveridge curve throughout our specifications. Also, higher labor market protection makes outward shifts less likely and is thus is negatively associated with frictional unemployment. Further, we find that outward shifts are more likely the higher the share of employees with intermediate education in the labor force.
Categories of unemployment. We find robust evidence that frictions increase the larger the share of long-term unemployed to the total number of unemployed, possibly due to outdated skill sets or employers’ bias against this group. Our preferred specification of the model also provides evidence that matching is more difficult the larger the share of female job seekers and young job seekers, while it is easier the larger the share of elderly workers, possibly due to more experience.
Policies. Tax and expenditure policies can play a role in reducing frictional unemployment. We find that higher social security contributions and more generally the tax wedge are more likely to shift the Beveridge curve outward and have a detrimental impact on matching, especially at higher levels of income. As expected, a similar effect is found for higher unemployment benefits, as those lower the urgency to find a job. On the other hand, spending on active labor market programs has a positive impact on reducing frictions in particular when these are aimed at providing incentives for start-up and promoting job sharing programs.
Interactions. Our results show that during the 2008 global shock the negative impact of unemployment benefits on frictional unemployment was stronger, while the role of long-term unemployment was smaller as was the impact of low and intermediate levels of education. There was no significant change in the impact of the determinants identified above, including testing for complementarities across labor market institutions, confirming the finding by Bassanini and Duval (2009).

Our study builds on the existing literature on the Beveridge curve and provides several contributions. First, this is the first cross-country study on Beveridge curves and their dynamics based on a broad sample of OECD countries (with the exception of Euro Area countries examined in Bonthuis and others, 2013; and Arpaia and Turrini, 2014); second, we provide a set of complementary methodologies for detecting shifts in the curves; third, our study introduces a fiscal policy angle to the analysis of the underlying conditions that could exacerbate the matching process; and, fourth, we test the implications of the 2008-09 shock on some of the factors that affect frictional unemployment in normal times.

The remainder of the paper is organized as follows. Section 2 presents the theoretical framework underlying the Beveridge Curve and reviews the literature. Section 3 presents the econometric methodology employed. Section 4 discusses our main findings; and the last section concludes.

II. Literature Review

A. Theoretical Framework

The Beveridge curve is an empirical regularity which relates vacancies to the number of unemployed. The underlying intuition behind the curve is that as vacancies increase the number of unemployed declines, entailing a negative slope for the Beveridge curve. First described by William Beveridge in 1958, the curve has been widely examined in the economic literature and found its most famous application in the search and matching model by Diamond and others (1994).

Beveridge curves differ markedly between countries and also change over time. Albeit downward sloping in theory, some Beveridge curves assume all different kinds of shapes, implying that economies feature very heterogeneous levels of mismatches. For instance, some countries manage to quickly reduce mismatches after economic downturns while others do not.

Beveridge curve dynamics can be distinguished between movements on the curve and movements of the curve. Assuming a stable relationship, movements along the curve occur over the business cycle as vacancies open/close, and workers exit/enter into unemployment. At times of recessions, for instance, unemployment is high and job vacancies are limited, a state which corresponds to points on the upper left branch of the curve when unemployment is set to be on the vertical axis and vacancies on the horizontal axis (Bleakley and Fuhrer, 1997). Hence, the Beveridge curve – precisely the position on the curve – can work as a tool to detect the state of the labor market, for instance whether the market is tight or not.

Movements of the curve or shifts are, instead, associated with changes in frictional unemployment, namely improvements or deteriorations in the efficiency of searching for jobs and/or applicants, i.e. in labor market matching, or simply structural changes in searching activity. Several factors can affect shifts in the Beveridge curve. The position of the curve vis-à-vis the origin can, indeed, depend on labor force characteristics, the institutional setting, and various types of mismatches. Amongst labor force characteristics, many authors have focused on the shares of young and old workers in the total labor force; female labor force participation; and the share of high-skilled to low-skilled workers. Long-term unemployment, often taken as measure of hysteresis, can shift the curve outward as it can discourage workers and render their search less effective. Also, long-term unemployment may lead to a deterioration of human capital or an ‘out-dated’ skill set and may stigmatize the unemployed, giving a negative signal to potential employers (Johansen, 2004). Institutional factors include employment protection legislation, active labor market policies, the generosity and duration of the unemployment benefits, and the level of real wages. As for mismatches, most papers study mismatches across skills, geographical regions and sectors.

In general, movements on the curve reflect cyclical changes while movements of the curve reflect structural changes affecting frictions in the labor market. However, some authors contest the distinction between movements of the curve and movements along the curve, and find that business cycle conditions can also affect movements of the curve (Blanchard and Diamond, 1989; Börsch-Supan, 1991; Wall and Zoega, 2002). Evidence related to the recent financial crisis has indeed reopened the issue as the weakening of aggregate demand seems to have induced a deterioration in matching efficiency. Long-term data analysis of the U.S. labor market for the period 1951–2000 illustrates that episodes of deterioration in matching coincided with economic recessions (Diamond and Sahin 2014). This finding invalidates the long assumed orthogonality between labor market matching and aggregate demand and suggests that in bad times vacancies are not filled up as quickly as in good times in a systematic way. A major link between negative aggregate demand shocks and deterioration in the matching is the occurrence of long-term unemployment. This phenomenon typically starts during a recession and continues into the recovery period, and which is found to be an important factor behind frictional unemployment. Closely related are skill-mismatches which emerge in a process of accelerated creative destruction. Also, economic recessions and demand slowdowns are characterized by high uncertainty, which may lead to a more cautious hiring process.

B. Empirical Studies

The literature on labor market matching is vast. Many studies aim at identifying the Beveridge curve in a specific country, and then try to capture moments of shift in the curve and, finally, investigate the reasons that caused these shifts. In some cases, Beveridge curves are specified embedded in a Cobb Douglas production function with constant returns to scale on the input factors unemployment and vacancies (Blanchard and Diamond, 1989). Most studies, however, specify the curve as a negative relationship between the unemployment rate and the vacancy rate, holding the hiring rate constant (see, e.g., Börsch–Supan, 1991; Johansen, 2004; Bonthuis and others, 2013). In some instances, the vacancy rate is expanded to include a quadratic term (Wall and Zoega, 2002; Valletta, 2005), which more accurately captures the non-linear - convex shape - of the curve. In their analysis of OECD countries, Hobijn and Sahin (2012) construct fitted Beveridge curves by considering the vacancy rate at which the unemployment rate equals its turnover-steady-state value, i.e. when new hires as a fraction of employment equal the growth rate of the labor force. Groenewold (2003) uses cointegration techniques to model the relationship between vacancies and unemployment (and, in some specifications, wages). Overall, most studies seem to find a negative and statistically significant relationship between unemployment and vacancies, hence corroborating Beveridge’s theoretical hypothesis. The coefficient of the relationship between unemployment and the vacancy rate usually ranges between -5 and -1.

In order to identify shifts, most authors rely on visual inspection, which they subsequently subject to statistical tests (Börsch–Supan, 1991; Wall and Zoega, 2002). Bonthuis and others (2013) identify shifts through an interaction term between the labor shortage variable (proxy for vacancy rate) and the crisis which they assume to be the turning point of the relationship between unemployment and vacancy rate. Wall and Zoega (2002) and Valletta (2005) identify shifts from the estimated coefficient of the year time dummies. To assess whether changes in the Australian Beveridge curve consist of movements on the curve or of the curve, Groenewold (2003) decomposes the variance of unemployment growth. He finds that the vacancy rate has little impact on the variance and concludes that most of the dynamics are shifts and not movements of the curve. To the best of our knowledge, this paper is the first to identify shifts, their directions and magnitudes through the interplay of three techniques: visual examination, cointegration and non-linear testing, as described below.

In terms of methodologies used to assess factors underlying the shifts, panel analysis is the most widely applied technique (Börsch-Supan, 1991; Johansen, 2004). Wall and Zoega (2002) use the estimated intercepts of the Beveridge curves as the dependent variable of a panel for the U.K. counties. Bonthuis and others (2013) use the shifts as dependent variables in a pooled probit model to examine the role of structural and institutional variables and Bonthuis and others (2015) apply the Jordà (2005) local projections method to predict determinants of shifts.

Finally, the main determinants of shifts in the Beveridge curve are documented to be:²

1) Type of unemployment and labor force: Long-term unemployment is seen as a crucial determinant of shifts (Jackman and others, 1990; Franz, 1987; Börsch-Supan, 1991; Johansen, 2004; and more recently Arpaia and Turrini, 2014). Börsch-Supan (1991) also finds that outward shifts are more common when a higher proportion of women are unemployed, and Bonthuis and others (2015) find that a higher female participation rate reduces the probability of outward shifts. Futher, Bonthuis and others (2013) show that old-age workers perform worse in terms of matching than young workers.
2) Institutions and policies: Johansen (2004) on Norway and Jackman and others (1990) on the United Kingdom find that active labor market policies have a very sizeable impact on reducing frictional unemployment, especially if targeted to the long-term unemployed. Similarly, Arpaia and Turrini (2014) find that active labor market policies do enhance matching efficiency, but their impact is not significant when restricting the sample to post-crisis years. The extension of unemployment benefits is found to drive outward shifts in the United States and Sweden during the Great Recession (Hobijn and Sahin, 2012). Not much evidence has been found on the role played by labor market institutions (employment protection legislation, unions, and temporary contracts) and the study by Bonthuis and others (2013) presents inconclusive results.
3) Geography and skills: For the United States, geographical mismatches in employment growth are found to play a role (Valletta, 2005; Abraham, 1987), while they are not found significant in driving matching efficiency in the Eurozone (Arpaia and Turrini, 2014). Educational or skill mismatches caused shifts in the Euro area, the United States and Germany (European Central Bank, 2002; Börsch-Supan, 1991; Hobijn and Sahin, 2012; Bonthuis and others, 2013; Arpaia and Turrini, 2014). In particular in Portugal, Spain and the U.K., skill mismatches were largely associated with the decline in construction employment following the housing bust (Hobijn and Sahin, 2012), a finding consistent with Bonthuis and others (2013, 2015).

III. Methodology and Data

To assess the role of policies and institutions in the matching process we begin by identifying dates and direction of such shifts for a subset of 12 OECD countries, for which sufficient quarterly data on vacancies were available for the period 2000Q1–2013Q4. We then use this information to regress the shift variables on a set of institutional, structural and policy variables of relevance.³

A. Identification of Shifts

To evaluate the extent to which policies and institutions affect labor market matching we first identify shifts in the Beveridge curve for each individual country. An outward shift coincides with a worsening in the matching (increasing unemployment for a given number of vacancies), while an inward shift coincides with an improvement in the matching (decreasing unemployment for a given number of vacancies).

Following most empirical studies, we begin by visually examining Beveridge curves of all countries in our sample so as to detect the presence of breaks and their direction. We plot Beveridge curves with the level of vacancies on the horizontal axis and the level of unemployment on the vertical axis over the sample period. Although telling, graphical evidence may not fully reveal the existence of a shift, especially when data points are overlapping. Hence, we complement the visual examination with two forms of econometric estimation of the Beveridge curve and its dynamics. First, following Groenewold (2003), we perform a cointegration analysis (also allowing for endogenously determined breaks in the potential long-run relationship) by country, which assumes a linear relationship between unemployment and vacancies, and test for the existence and timing of shifts of this relationship. Second, using the dates identified visually and through cointegration analysis, we test the significance and the direction of the shift non-linearly by means of the use of a hyperbolical functional form similar to Börsch-Supan (1991), which aims to reproduce a Beveridge curve convex to the origin.

Cointegration

With respect to the cointegration analysis, we follow the standard procedure and begin with a stationarity inspection by testing for the presence of unit roots for each country’s series of unemployment and vacancies. In addition to standard Augmented Dickey Fuller (ADF) and Phillips-Perron (PP) unit root tests, we employ the four tests (M-tests) proposed by Ng and Perron (2001) (NP) based on modified information criteria (MIC): the modified Phillips-Perron test MZ_α, the modified Sargan-Bhargava test (MSB), the modified point optimal test MP_T, and the modified Phillips-Perron MZ_T. These procedures improve the PP-tests both with regard to size distortions and power.⁴ Furthermore, we identify the optimal lag structure in the cointegrating relationship using several information criteria (favoring the AIC as common practice in the literature).⁵ Finally, the presence of cointegration is tested using the Johansen’s trace test (Johansen and Juselius, 1990) and the long term coefficients are obtained through the Stock-Watson-Shin’s Dynamic OLS estimation.

As emphasized by Bruggemann and others (2003), it is important to formally investigate the stability of the cointegrating vectors further, once a long-run relationship has been identified.⁶ To detect the presence of shifts in the Beveridge curve, we test for breaks in the cointegrating relationship following Gregory and Hansen’s (1996) approach. We apply their ADF and PP tests allowing for a break in the level or regime, to check whether the cointegrating relationship between vacancies and unemployment has been affected by a break; if the answer is positive we then indicate the timing of the break.

Non-linear estimation

The previous set of tests is complemented by estimating the Beveridge curve in its convex representation with the following hyperbolic functional form:

\begin{matrix} u_{t} = a_{0} + b_{0} . S H I F T + \frac{1}{v_{t}} & (1) \end{matrix}

Using equation (1), we test for the validity of the breaks identified through visual specification or through the ADF and PP tests by including the breaks in the regression and examining their statistical significance. The sign of the coefficient obtained for the break allows us to distinguish between outward (positive) or inward (negative) shifts of the Beveridge and assess the magnitude of the shift. Specification (1) basically tests for an upward shift of the curve, assuming no change in the slope. Alternatively, we also test for a rightward shift and a combination of shift and change in convexity. We obtain similar results for the alternative specifications. Overall, equation (1) was found to be the most stable, and the one best reflecting the visual representation of each country’s Beveridge curve.

Shift variables

Based on the three methodologies described above, we determine the final break date and direction of the shift by country to create a shift variable for our subsequent analysis. The variable is defined binary and captures two states, a state equal to one that corresponds to those quarters after outward shifts (or before inward shifts); and a state equal to zero corresponding to those quarters before an outward shift (or after an inward shift). With this specification, a change from zero to one of the dummy would coincide with a deterioration of the matching, while a change from one to zero would translate into an improvement.

For robustness, we also provide two alternative specifications for the shift variable. Based on the non-linear estimation results of equation (1), we replace the ones in the above described dummy with the estimated coefficients b0 to get a sense of the magnitude of the shift across countries (“Shift size”). Finally, we create an additional variable to take into account the cross-country differences in matching efficiency before and after the shift. The variable “Mismatch” assumes the value a0 before the shift and a0 + b0 after the shift.

B. Factors Underlying the Shifts

To assess how labor market characteristics and policy variables can influence the matching of labor demand and supply, we estimate limited dependent variable models, namely panel probit and logit models, using the previously identified shift dummy as dependent variable. Drawing from the empirical literature we distinguish two main factors affecting matching: labor market characteristics (labmark) and fiscal policy-related factors (fiscal). In each specification, we include the contemporaneous and lagged output gap to control for the cyclical position of the economy as well as the growth in the labor force. In the fiscal or policy-related analysis we also include the overall balance. We conduct estimations using a panel probit, and for robustness a logit with random as well as fixed effects. Time fixed effects are included and estimated in all model specifications. The unbalanced panel probit (logit) uses the following specification: ⁷

\begin{matrix} Prob(Shift=1|fiscal,labmark)= Φ (δ g a p + fiscal' α + labmark' β & (2) \end{matrix}

The structural model can be written as:

\begin{matrix} \begin{matrix} {Shift}_{it}^{*} = δ g a p + {fiscal}_{i t}' α + {labmark}_{it}' β + ɛ_{i t}, \\ {\begin{matrix} Shift \end{matrix}}_{it} = 1 if {Shift}_{it}^{*} > 0, and 0 otherwise. \end{matrix} & (3) \end{matrix}

with i = 1 …, 12; t = 2000:1 …, 2013:4; ε_it is the error term; and α,β and ϕ are the vectors of the parameters to be estimated.

Labor market characteristics

Concerning labor market characteristics, we consider real wages, the number of temporary contracts over the labor force and the index of strictness of employment protection legislation reflecting the ease of individual and collective dismissals. To avoid endogeneity problems, real wages are included with a lag, and to avoid capturing trend behavior, we express them in growth rates. We then add variables on the composition of the unemployed population: age, gender and the share of long-term unemployed to the total number of unemployed. We also account for differences in the level of education of the labor force, distinguishing between advanced, intermediate, and basic education.

The impact of real wages on matching might be conceptually ambiguous depending on the elasticity of labor demand and labor supply. If the labor supply channel prevails, at a given reservation wage, higher real wages would, in fact, induce the unemployed to accept more jobs, possibly also outside their particular sphere of competence, which would lower both unemployment and vacancies, and therefore causing an inward shift of the curve. On the demand side, however, higher wages would make the employer ‘choosier’ and less reluctant to accept workers not fully matching the advertised vacancy profile thereby prolonging the hiring process. An alternative explanation for an outward shift due to wage increases has been put forward by Mehrotra and Sergeyev (2012). The authors show that productivity shocks followed by wage increases in some sectors can trigger a reallocation of labor across sectors which could lead to a—temporary—outward shift in the Beveridge curve.⁸

A large number of temporary contracts might make the advertised vacancies less desirable from a supply-side perspective; on the other hand, the existence of temporary contracts may speed up hiring procedures notably in times of great uncertainty. By increasing hiring and firing costs, stricter employment protection legislation (EPL) reduces job destruction and job creation and thus flows into and out of unemployment (Pissarides 2010). While the net impact on overall unemployment depends on which flow falls more, a lower labor turnover would reduce overall searching activity and thus affect frictional unemployment positively Also, if job seekers confer importance to secured positions, matching would be faster in more protected labor markets.

Finally, the composition of the unemployed population can also play a role in case the employer has a stigma or bias towards young or old unemployed, long-term unemployed or female unemployed; or in case these groups feature out-dated and/or lower skills. Looking at the educational level of the labor force in more detail, we explore the existence of skill mismatches between labor demand and labor supply, which could arise in the context of technological changes and/or creative destruction possibly accompanying economic crises.

Fiscal and labor market policies

Concerning labor market policies, we examine the role played by the tax wedge and its components (employer and employee social security contributions) considered by different types of earners.⁹ We then look at active labor market policies and unemployment benefits, all expressed as government spending as a share of GDP. Components of active labor market policies include incentives for startups, job creation, job rehabilitation, general employment, job rotation and training.

Any policy that pushes up the take home pay is expected to have the same effect for the supply side as an increase in nominal wages, such as decreases in the tax wedge due to lower employee social security contributions. Reductions in employer social security contributions could lead to more hiring, or, if passed on to the employee, increase the take home pay but without increasing the employers’ wage costs. Spending on active labor market policies would improve matching as it is intended to address skill-gaps or other labor supply deficiencies. On the contrary, large unemployment benefits may constitute a limitation for matching as they increase the reservation wage and reduce incentives for active job seeking of the unemployed.

Interaction analysis between some of these factors could provide relevant insights regarding the role of institutions under shocks or under certain policies. This hypothesis is explored in an interaction analysis where we found no significant complementaries among policies and institutions but found significant effects of the 2008 shocks on unemployment benefits and education.

C. Data

Our sample covers 12 OECD countries between 2000Q1 and 2013Q4, chosen on the basis of data availability for the vacancy series.¹⁰ We use several sources of data.

IMF data from the WEO and IFS databases are used for the quarterly series of GDP, the output gap and the fiscal balance. The output gap is obtained as the ratio of the difference between nominal and potential output to potential output, where potential output is calculated through HP-filtering.
OECD quarterly data are used for wages (proxied by wages in manufacturing and expressed as an index with base 2010) and for unemployment groups (female, long-term, youth and elderly unemployment). OECD annual data are used for (i) employer and employee social security contributions and the tax wedge per household of a single person with no children at 100, 67 and 167 percent of average earnings; (ii) for spending (as percent of GDP) on components of passive and active labor market policies; (iii) for employment protection legislation and temporary contracts.
ILO provides annual data on the labor force and its education structure.

As quarterly movements matter, we convert data which are only available on an annual basis to a quarterly series, using the Denton procedure. As indicated by Di Fonzo and Marini (2012), the procedure entails shaping the quarterly distribution of an annual variable using the distribution of a benchmark quarterly variable. For all labor-related variables and unemployment benefits we use the quarterly series of unemployment as benchmark. For active labor market policies we use quarterly spending as a share of GDP.

IV. Empirical Analysis

A. Timing and Direction of Shifts

Visual examination

Figure 2 displays the Beveridge curves for all 12 countries in our sample based on the number of job vacancies and unemployed.¹¹ For most countries, surprisingly, there is a clear pattern of shifts and two parallel or displaced curves. This is very nicely illustrated for Australia or Hungary, for instance. In some countries, however, such as Finland and Norway, there seems to be only one curve—irrespective of the use of seasonally adjusted or non-seasonally adjusted data.

Cointegration analysis

At a one percent significance level the unemployment series have a unit root for all countries. For vacancies, the hypothesis of a unit root is rejected for the United States in both the ADF and PP tests and for Finland and Sweden in the PP test, while the ADF test statistics is very close to the critical value (Table 1). Overall, these results provide a basis for testing the existence of an underlying cointegration relationship.¹² The underlying specification—including a constant and/or trend—was chosen based on graphical inspection.

Figure 2.

Beveridge Curves (I)

Citation: IMF Working Papers 2016, 093; 10.5089/9781484326466.001.A001

Source: OECD data.

Figure 2.

Beveridge Curves (II)

Citation: IMF Working Papers 2016, 093; 10.5089/9781484326466.001.A001

Source: OECD data.

Table 1.

Unit Root Tests

Note: critical values for 1% confidence for constant and no trend: ADF -3.55; PP -3.55; for constant and trend ADF - 4.137; PP -4.133;

Table 1.

Unit Root Tests

	Unemployment			Vacancies
	Specification	ADF	PP	Specification	ADF	PP
	Constant or Trend	ADF	PP	Constant or Trend	ADF	PP
Australia	C	−1.45*	−1.32*	C & T	−0.61*	−1.27*
Austria	C&T	−2.10*	−2.29*	C	−2.81*	−2.54*
Czech Republic	C	−2.73*	−2.16*	C	−2.05*	−1.78*
Finland	C&T	−1.44*	−1.92*	C&T	−3.44*	−6.72
Germany	C&T	−1.74*	−1.33*	C	−1.22*	−1.38*
Hungary	C&T	−2.42*	−2.20*	C&T	1.12*	−0.46*
Norway	C	−2.37*	−1.87*	C&T	−2.35*	−2.87*
Poland	C&T	−2.12*	−1.57*	C&T	−1.94*	−2.62*
Portugal	C&T	−2.03*	−2.28*	C	−3.11*	−1.96*
Sweden	C&T	−1.65*	−2.12*	C&T	−3.52*	−5.35
United Kingdom	C&T	−2.33*	−2.37*	C	−1.19*	−2.55*
United States	C&T	−2.15*	−1.64*	C&T	−3.64	−3.67

Note: critical values for 1% confidence for constant and no trend: ADF -3.55; PP -3.55; for constant and trend ADF - 4.137; PP -4.133;

Table 1.

Unit Root Tests

	Unemployment			Vacancies
	Specification	ADF	PP	Specification	ADF	PP
	Constant or Trend	ADF	PP	Constant or Trend	ADF	PP
Australia	C	−1.45*	−1.32*	C & T	−0.61*	−1.27*
Austria	C&T	−2.10*	−2.29*	C	−2.81*	−2.54*
Czech Republic	C	−2.73*	−2.16*	C	−2.05*	−1.78*
Finland	C&T	−1.44*	−1.92*	C&T	−3.44*	−6.72
Germany	C&T	−1.74*	−1.33*	C	−1.22*	−1.38*
Hungary	C&T	−2.42*	−2.20*	C&T	1.12*	−0.46*
Norway	C	−2.37*	−1.87*	C&T	−2.35*	−2.87*
Poland	C&T	−2.12*	−1.57*	C&T	−1.94*	−2.62*
Portugal	C&T	−2.03*	−2.28*	C	−3.11*	−1.96*
Sweden	C&T	−1.65*	−2.12*	C&T	−3.52*	−5.35
United Kingdom	C&T	−2.33*	−2.37*	C	−1.19*	−2.55*
United States	C&T	−2.15*	−1.64*	C&T	−3.64	−3.67

Note: critical values for 1% confidence for constant and no trend: ADF -3.55; PP -3.55; for constant and trend ADF - 4.137; PP -4.133;

Cointegration analysis à la Johansen-Juselius indicates that unemployment and vacancies display a long run relationship for most countries, except Australia, Finland, Germany, Hungary, and the United States. For the Czech Republic, cointegration exists only under a quadratic trend (Table 2). The optimal lag structure was determined by applying a range of tests and selection criteria.¹³ Estimates of the cointegrated coefficients obtained through the Stock-Watson-Shin are reported in table A2 in Appendix A.

Table 2.

Johansen-Juselius Cointegration Tests

Johansen Trace Test

Table 2.

Johansen-Juselius Cointegration Tests

Johansen Trace Test

	Lag	Data Trend	None	None	Linear	Linear	Quadratic
	Lag	Test type	No intercept No trend	Intercept No trend	Intercept No trend	Intercept trend	Intercept trend
Australia	2		0	0	0	0	0
Austria	5		1	1	1	1	2
Czech Republic	2		0	0	0	0	1
Finland	5		0	0	0	0	0
Germany	5		0	0	0	0	0
Hungary	3		0	0	0	0	0
Norway	5		0	1	2	0	2
Poland	6		1	1	2	0	0
Portugal	5		2	1	0	1	2
Sweden	5		2	2	1	1	2
United Kingdom	3		0	1	1	1	2
United States	2		0	0	0	0	0

Table 2.

Johansen-Juselius Cointegration Tests

Johansen Trace Test

	Lag	Data Trend	None	None	Linear	Linear	Quadratic
	Lag	Test type	No intercept No trend	Intercept No trend	Intercept No trend	Intercept trend	Intercept trend
Australia	2		0	0	0	0	0
Austria	5		1	1	1	1	2
Czech Republic	2		0	0	0	0	1
Finland	5		0	0	0	0	0
Germany	5		0	0	0	0	0
Hungary	3		0	0	0	0	0
Norway	5		0	1	2	0	2
Poland	6		1	1	2	0	0
Portugal	5		2	1	0	1	2
Sweden	5		2	2	1	1	2
United Kingdom	3		0	1	1	1	2
United States	2		0	0	0	0	0

Cointegration results are very sensitive to the presence of a break in the cointegrating relationship, hence a cointegration test would generally fail to capture a long run relationship if the series feature a structural shift. To test for a break in the cointegration, we follow Gregory and Hansen’s procedure (1996) which detects the presence of cointegration under breaks and provides information about the time of the break (Table 3).¹⁴ We find that when accounting for a break, either in the intercept (level shift) or in the intercept and slope (regime shift) breaks, the series for unemployment and vacancies are cointegrated for Australia, Finland, Germany, Hungary, Norway, Portugal, Sweden, the United Kingdom, and the United States; and Austria, Finland, and Poland when considering the Z statistic. The only countries for which no cointegration was found is the Czech Republic and Norway. Interestingly, breaks tend to cluster around the global financial crisis.

Table 3.

Testing for Regime Shifts in Cointegration: Gregory-Hansen

Note: ADF * and Z_α‘refer to the Augmented Dickey-Fuller (ADF) and to the Phillips Z_α * tests statistics; null of no cointegration. * denote significance at the 10% level or lower, using the critical values from Gregory and Hansen (1996), Table 1.

Table 3.

Testing for Regime Shifts in Cointegration: Gregory-Hansen

	Unemployment and Vacancies
	Level shift				Regime shift
Country	ADF test		Phillips Test		ADF test		Phillips Test
	ADF * stat	Estimated break date	Zα * stat	Estimated break date	ADF* stat	Estimated break date	Zα * stat	Estimated break date
Australia	−6.97*	2008Q3	−55.906*	2008Q4	−6.75*	2008Q3	−55.613*	2008Q4
Austria	−3.80	2004Q4	−38.54*	2004Q3	−3.88	2006Q4	−38.45	2004Q2
Czech Republic	−3.73	2010Q3	−17.89	2007Q3	−3.59	2010Q1	−15.56	2009Q1
Finland	−3.93	2010Q2	−92.57*	2004Q3	−4.05	2010Q4	−94.20*	2004Q3
Germany	−4.86*	2009Q1	−11.06	2008Q1	−5.36*	2001Q4	−18.27	2005Q2
Hungary	−4.13	2011A1	−35.43	2010Q3	−3.47	2011Q1	−42.34*	2011Q1
Norway	−4.17	2007Q3	−32.14	2008Q2	−3.57	2007Q4	−36.95	2005Q2
Poland	−3.68	2004Q1	−37.65*	2003Q3	−3.75	2004Q1	−37.29	2003Q3
Portugal	−5.59*	2007Q3	−22.41	2006Q3	−5.32*	2007Q3	−23.84	2010Q4
Sweden	−4.92*	2008Q1	−39.93*	2006Q1	−4.66	2008Q1	−39.78	2005Q3
United Kingdom	−5.98*	2005Q3	−26.77	2001Q3	−5.85*	2002Q3	−31.43	2001Q3
United States	−5.04*	2008Q3	−36.46*	2008Q3	−5.18*	2008Q3	−39.21	2006Q3

Table 3.

Testing for Regime Shifts in Cointegration: Gregory-Hansen

	Unemployment and Vacancies
	Level shift				Regime shift
Country	ADF test		Phillips Test		ADF test		Phillips Test
	ADF * stat	Estimated break date	Zα * stat	Estimated break date	ADF* stat	Estimated break date	Zα * stat	Estimated break date
Australia	−6.97*	2008Q3	−55.906*	2008Q4	−6.75*	2008Q3	−55.613*	2008Q4
Austria	−3.80	2004Q4	−38.54*	2004Q3	−3.88	2006Q4	−38.45	2004Q2
Czech Republic	−3.73	2010Q3	−17.89	2007Q3	−3.59	2010Q1	−15.56	2009Q1
Finland	−3.93	2010Q2	−92.57*	2004Q3	−4.05	2010Q4	−94.20*	2004Q3
Germany	−4.86*	2009Q1	−11.06	2008Q1	−5.36*	2001Q4	−18.27	2005Q2
Hungary	−4.13	2011A1	−35.43	2010Q3	−3.47	2011Q1	−42.34*	2011Q1
Norway	−4.17	2007Q3	−32.14	2008Q2	−3.57	2007Q4	−36.95	2005Q2
Poland	−3.68	2004Q1	−37.65*	2003Q3	−3.75	2004Q1	−37.29	2003Q3
Portugal	−5.59*	2007Q3	−22.41	2006Q3	−5.32*	2007Q3	−23.84	2010Q4
Sweden	−4.92*	2008Q1	−39.93*	2006Q1	−4.66	2008Q1	−39.78	2005Q3
United Kingdom	−5.98*	2005Q3	−26.77	2001Q3	−5.85*	2002Q3	−31.43	2001Q3
United States	−5.04*	2008Q3	−36.46*	2008Q3	−5.18*	2008Q3	−39.21	2006Q3

While informative, the results of the cointegration analysis show in some instances the limitations associated with a linear representation of the Beveridge curve. The following section therefore examines non-linear specifications in more detail.

Non-linear estimation

To identify timing and direction of shifts in the Beveridge curve, we complement graphical analysis and estimation of the break tests with the non-linear estimation of the curve. As explained in Section 3, the non-linear estimation is run on a Beveridge curve, which includes the shift dummy based on the break dates identified by visual examination and cointegration analysis.¹⁵ The regression outcome in Table 4a provides an indication of the distance of the curve from the horizontal axes, more precisely, the level of unemployment in place when vacancies are infinite. This distance corresponds to the constant before the shift, and the constant plus the shift interaction after the shift. The coefficient associated with the shift is significant for all countries examined. Positive shifts (deterioration in the matching) are found in Australia, Austria, Hungary, Portugal, Sweden, the United Kingdom, and the United States and negative shifts (improvement in the matching) are found in the Czech Republic, Finland, and Germany. Poland’s dummy—coded as first outward shift and then inward shift—is also significant confirming the double shift in the Beveridge curve. The results are robust against the inclusion of a slope parameter (Table 4b).

Table 4a.

Nonlinear Estimation: Vertical Shift