The Beveridge curve Magister thesis in Economics

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The Beveridge curve

- A comparison between the three largest

labour market regions in Sweden; Stockholm-, Västra Götaland- and Skåne county and the effect of the building of the Öresund Bridge on the labour market matching efficiency of

Skåne county.

Magister thesis in Economics

Author: Nelly Sand Supervisor: Lars Behrenz Examiner: Tobias König

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Abstract

This paper investigates the relationship between vacant job positions and unemployed workers, illustrated by the Beveridge curve, a tool for observing the matching process and the condition of a labour market. The Swedish case is studied together with its three largest labour market regions, i.e., Stockholm-, Västra Götaland- and Skåne county. A comparison opens up a discussion of whether local labour markets with similar characteristics located in different parts of the country behave similarly or in what way they distinguish. Furthermore, these three regions are expected to influence the Swedish Beveridge curve to a larger extent, which is also examined in the paper.

In addition, the effect of an exogenous shock, such as the building of the Öresund Bridge, expanding the labour market of Skåne county by connection to another metropolitan area, Copenhagen, is studied. This is done by comparing the matching efficiency before and after the bridge is opened. Moreover, the effect in Skåne is then analysed in accordance with the same period for the other regions included, to get an indication of whether the bridge alone provides a change in matching efficiency or if changes are connected to national events that influence all regions similarly.

The analysis is based on monthly data from year 1996-2020, collected from the Swedish Public Employment service and Statistics Sweden, primarily. Graphical illustrations of the Beveridge curve in combination with OLS regressions provide concluding results that the Beveridge curves for the three regional labour markets observed are shaped rather similarly and experience shifts and movements during the same time points, generally. Skåne county is the exception and experience more horizontal and vertical movements compared to Stockholm- and Västra Götaland county and the Swedish average. Furthermore, there are statistically significant estimates ensuring the negative relationship between unemployment- and vacancy rate, i.e., a downward sloping Beveridge curve for all regions. Not enough evidence on the effect of the Öresund Bridge on the matching efficiency of Skåne county is provided to present a valid conclusion regarding this topic.

Keywords

Beveridge curve, matching function, unemployment, vacancy, exogenous shock, Sweden, Stockholm, Västra Götaland, Skåne, county.

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Acknowledgements

First, I would like to address my gratitude to my supervisor, Lars Behrenz, and examiner, Tobias König, for guidance and support throughout the research and writing process. Further, I send a special thanks to Joakim Jansson, who has been very helpful regarding the statistical work and whose knowledge has been of much importance for the outcome of the thesis. Finally, I express my gratefulness to students and teachers participating at seminars in the courses 4NA06E and 5NA01E at Linnaeus University in the spring term of year 2021, for giving their wise comments and advice that have contributed to the improvement of my work.

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1 Introduction

In the field of labour economics, research on unemployment rate and its fluctuations is always a relevant topic. Policy makers pursue a lower unemployment rate, which is why it is important to study the efficiency of the matching process of jobseekers and employers and the underlying sources for existing inefficiency. The Beveridge curve shows the negative relationship between unemployment and unfilled job vacancies and can summarize the state of the labour market in a simple graphical illustration. Movements along the curve can give a hint of where the economy is located in the business cycle, while the positioning of the curve in relation to the origin indicates the general labour market activity. This is sometimes referred to as the intensity of reallocation, i.e., the movement of workers between jobs and sectors.

However, the shape and location of the Beveridge curve is a result of all decisions made by workers and firms regarding skills, hires, separations, wage settings, etc., which are underlying factors explaining a certain level of unemployment and vacancies. Hence, the Beveridge curve is not a structural economic relationship.

Changes in exogenous components will influence the combination of unemployment and vacancies for a fixed locus and its position (Bleakley & Fuhrer, 1997). It is, however, important to remember that the state of an economy is ever changing, and a lot of things happen at the same time. This can make it difficult to distinguish the effects of different factors on the position of the Beveridge curve, in terms of a macroeconomic analysis.

A key factor to the unemployment duration is the effectiveness at which available workers are matched to vacant jobs. Due to an imperfect labour market with frictions, mismatches arise since the skills supplied by the workers do not perfectly match the skills demanded by the firms. When frictions are smaller, the matching technology is better, in general, indicated by a Beveridge curve positioned closer to the origin in the unemployment-vacancy- (UV-) space. Furthermore, the Beveridge curve is often studied on a national aggregated level, but regional labour markets can experience different patterns in the Beveridge curve. Changes in the composition of the labour force is also a factor that contributes to the behaviour of the Beveridge curve, such as a higher/lower labour force participation rate of women and immigrants (Kosfeld et.

al., 2008).

In previous literature the Beveridge curve is most commonly studied on a national level. This is interesting when the aim is to get an overview of the labour market conditions of a country, or for comparisons between countries. However, the national Beveridge curve can behave differently compared to a regional study, which is why it is interesting to further develop such an analysis. Research on the Beveridge curve have, for instance, been presented regarding regional data by Wall & Zoega (2002), Valletta (2005), Lincaru (2010), Eklund et. al. (2015), Kolsrud (2018) and Holmes

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and Otero (2020). Differences nationally and regionally can be due to an aggregation bias, implying that high matching efficiency in one region can be counteracted by low efficiency in another region, and when they are added they provide an average national estimate. Regional Beveridge curves might therefore look different compared to the national case. Hence, a regional analysis can give new dimensions to the explanation of why a certain regional labour market behave in a way that differs from other regions or the national example. Furthermore, exogenous shocks that influence the economic conditions of a country are often analysed nationally, while it influences the local labour markets differently.

The aim of this paper is to investigate how the three major labour market regions in Sweden, Stockholm county on the east coast, Västra Götaland county (including Gothenburg) on the west coast and Skåne county (including Malmö) in the south, perform in the matching process of unfilled job vacancies and unemployed workers, compared to each other and the national example, behaving as a benchmark for the analysis. Is the matching efficiency higher in the biggest metropolitan areas of the country due to higher availability and versatility in the job opportunities and characteristics of the unemployed workers? Or do we see an opposite trend due to a larger population and a slower hiring process, where the job creation in expanding areas does not correspond to the characteristics of the labour supplied in the region, as found by Aranki and Löf (2008)? Perhaps the national Beveridge curve is reflected in these three regional estimations since they are the biggest markets of the country and therefore influence the national curve notably. This will be discussed in accordance with empirical estimations and graphical illustrations.

The study consists of 300 observations for each region with monthly data on unemployment- and vacancy rate from January 1996 to December 2020. As far as my knowledge goes, a similar comparison between mentioned regions has not been conducted, which is why it is interesting to investigate to what extent these three labour market regions affect the national aggregated Beveridge curve. Will they behave equally having similar features or what differences will cause different- looking Beveridge curves? The Beveridge relationship is a very simple tool to express the state of the labour market economy, which makes it favourable to use to inform a public audience. Moreover, an economy that experience problems in the matching process and not effectively finds a balance between labour demand and supply, will potentially have a lower economic growth in the long-run, compared to what it could have been with a well-functioning labour market. This provides incentives for policy makers and economists to study the matching process of the labour market. In case of an unemployment rate higher than necessary, the existing resource of production is not fully used, which causes a welfare loss that could be reduced with better labour market matching. This brings attention to the importance of treating problems in the recruiting process (Eklund et.al., 2015).

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Using the Beveridge curve as a tool for an overview of the labour market conditions of a country or smaller region can possibly work as a useful indicator pointing in which direction the labour market policy should lay its focus. The common goal is to have a low vacancy rate in combination with a low unemployment rate, i.e., a Beveridge curve positioned close to the origin. This implies that there are few frictions in the matching process, e.g., the unemployed worker is reached and informed about the vacant position, applies and get hired in a quick-acting process.

The unemployed workers actively search for jobs and the firms provide an effective hiring process. This scenario is cost-effective for both parties and the utility-, production-, and welfare losses are diminished. To reach high matching efficiency, it is required that the unemployed workers are prepared and possess the qualities demanded by the firms. In this context, the Beveridge curve is a measure of the outcome of the labour market development.

Furthermore, the paper studies if an exogenous shock, such as the building of the Öresund Bridge between Sweden and Denmark, affects the matching efficiency by expanding the labour market region of Skåne county and Malmö by direct connection to another metropolitan area, Copenhagen. Will this increase the matching efficiency of Skåne county compared to before the building of the bridge, also in comparison to the other two regions, or will it be unaffected? Both scenarios are possible since only one side of the bridge is part of this analysis, the Swedish side.

The main results of the paper are that there exists a negative relationship between unemployment- and vacancy rate in all regions observed. There seem to be most efficient labour market matching in Stockholm county, and worse in Skåne county.

Västra Götaland is very similar to the Swedish case. No evidence is found for the Öresund Bridge alone increasing the matching efficiency of Skåne county.

The remainder of the paper is organized in the following way. Section 2 presents a historical overview of the three regions in focus. Section 3 provides a literature review, mainly consisting of studies on the Beveridge curve and the matching function in theory and applications to empirical data. Subsequently, section 4 presents the theoretical framework of the Beveridge curve, the matching function and the state of equilibrium, followed by section 5 which describes the data and definitions of measures used in the regressions and graphical illustrations. Section 6 gives an overview of the methodological framework and section 7 presents the results. Section 8 provides a discussion and analysis of the results. Finally, section 9 summarizes and concludes.

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2 Historical overview

2.1 The Beveridge curve

The inverse relationship between unemployment and vacancies, illustrated by the UV- curve, was originally created as a measurement device for policy makers. This would give an overview of the state of the labour market in the economy and play as a decision basis. In the post-World War II period, the Keynesianism had drawn most attention in economic analyses. The UK faced low levels of unemployment in the 1950´s and feared how fluctuations in aggregate demand would affect the inflation rate. This made the British economists Dow and Dicks-Mireaux search for an indicator that would make it possible to reduce unemployment without providing inflation, through guidance of Keynesian fiscal policy. The model showed that vacancies and unemployment coexist simultaneously, independent of whether there is excess demand or excess supply of labour (Rodenburg, 2011).

The unemployment-vacancy- (UV-) relation influenced the economic theory in four distinguished ways. Firstly, the concept of unemployment could be decomposed in different categories, simplifying the direction and implication of economic policies.

Secondly, the UV-curve, together with the Phillips curve¹, was a further developed method to analyse and clarify the early work of Keynes and Beveridge on the subject of full employment. Thirdly, the coexistence of unemployment and vacancies in equilibrium had, up until then, not been explained, since most markets could be analysed in a simple neoclassical way of market clearing. This raised the awareness of the fact that the labour market may not clear as easily as other markets. Finally, in the 1980´s, focus was given to equilibrium theories such as the search- and matching models of unemployed workers and job openings. Empirical evidence was provided, and the graphical UV-relation was named the Beveridge curve. A paradigmatic change from the Keynesian aggregate demand management, including the concepts of excess demand and cyclical unemployment, to a neoclassical search theory, occurred due to the UV-relation being able to measure and explain these parts and behaviour of the labour market (Rodenburg, 2011).

2.2 Region specific overview

In this paper the three largest labour market regions in Sweden are considered.

Stockholm county includes 26 municipalities over an area of 6,519 km². The major cities, in population and area, are the capital of Sweden, Stockholm, Sollentuna/Upplands Väsby and Södertälje. Västra Götaland county consists of 49 municipalities and a total land area of 23,942 km². The county´s major cities are Gothenburg, Borås and Trollhättan. Skåne county includes 33 municipalities over an area of 11,303 km² and the major cities are Malmö, Helsingborg and Lund. In terms

1 The graphical relation between unemployment rate and inflation.

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of population, the municipalities of Stockholm, Gothenburg and Malmö are the three biggest cities in Sweden, with a population of 975,551 people, 583,056 people and 347,949 people, respectively (SCB, 2020). Approximately 20% of the total Swedish population have residence in Stockholm county, 16,7% in Västra Götaland county and 13% in Skåne county, adding up to almost half of the Swedish population.

All three regions provide many opportunities to gain a degree of higher education from a university. Stockholm county has 14 universities, including Stockholm University, which is the biggest in Sweden, counted by number of registered students, 39,154 students in the spring of 2020. Västra Götaland county have five larger universities, where the University of Gothenburg is the biggest with 34,770 students registered. Lund University is the largest with 30,374 students, among the five existing universities in the region of Skåne county (Uka, 2020). Malmö has a relatively new university, established in 1998 and licenced as a university in 2018 (Mau, 2021).

2.3 The Öresund Bridge

In March 1991, the Swedish and Danish authorities made an agreement of building a bridge connecting Malmö and Själland. On the 1st of July 2000, the 15.9 km Öresund Bridge was inaugurated by Queen Margrethe of Denmark and King Carl XVI Gustaf of Sweden and the first passengers of cars and train could make the international trip (Oresundsbron, 2020). This expanded the labour market region of Malmö, by providing the possibility for unemployed workers to search for jobs in an even larger metropolitan area of Copenhagen. The bridge has been said to work as an “extended public employment service” (Motion 2014/15:195). The region of Öresund includes Skåne county on the Swedish side and Själland, Mön, Falster, Lolland and Bornholm on the Danish side. This geographical area counts as the biggest labour market of the Nordic countries (Malmöläget, 2010). Therefore, the building of the bridge can be considered a positive shock to the labour market with the potential to increase the matching efficiency. The fact that the bridge was built due to a political decision issued by authorities, it can be considered an exogenous event that transforms the labour market region. The establishment becomes a natural experiment providing an opportunity to investigate its effect on the matching efficiency. It is exogenous since the bridge itself does not affect the behaviour of individuals, referring to job search intensity and working preferences, for instance.

2.4 Country specific overview

In the beginning of the 21^st century, the difference between working and being unemployed in Sweden was small, due to high taxes and high unemployment benefits.

This combination makes the unemployed less likely to search for jobs. In 2007 a reduction in the income tax was imposed, followed by an increased labour force participation rate, and Sweden experienced among the highest employment rates in Europe, for all age groups. In addition, the long-term unemployment was among the

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lowest in Europe. On the contrary, different kinds of economic crises are historically positively correlated with unemployment. For example, in 2006-07 there was high business activity in Sweden, accompanied by a low unemployment level due to high labour demand. In the autumn of 2008, the global financial crisis negatively affected the Swedish labour market. During the 2010´s, Sweden faced high levels of unemployment. Furthermore, in the aftermath of the financial crisis in 2008-09 there was a “shift” in the employment pool, where the workers with higher education became employed to a wider extent than people with lower education. This implies that there was a high share of highly educated people employed in the labour market, since the financial crisis hit the jobs requiring lower qualification the hardest. Hence, there are relatively few jobs in the Swedish labour market that do not require special knowledge and in 2014, the share of low qualification jobs was the lowest in the European union. This implies that the existing potential is not fully used, which can be identified by a low matching efficiency and a lack of low qualification jobs in the market (Spector, 2015).

In the recent years, it seems like the unemployment pool is overrepresented by young people, people with lower education and immigrants. There is evidence for an outward shift of the Beveridge curve as recruiters tend to have a hard time finding the proper candidates for the vacant positions, which is time consuming. The Swedish unemployment rate was stabilized around 8% between 2011-2014 and then it decreased. Another kind of crisis then hit the world economy, the covid-19 pandemic, which made the Swedish unemployment rate in 2020 again rise above 8%. This shows how different occurrences, socially and economically, globally and locally, can affect the labour market of a country and smaller regions, positively or negatively (Spector, 2015; SCB, 2021).

3 Literature review

3.1 American and British literature

The early studies and theoretical framework on the Beveridge curve primarily consist of research regarding the UK and the US, making these countries well represented in the literature. Different scenarios affect the relationship between unemployment and vacancies differently, gathering many dimensions to the analysis of the Beveridge curve.

In 1958, Dow and Dicks-Mireaux made a study on the reliability of the existing empirical investigations on unemployment and vacancies and how they perform as indicators of the labour demand in the economy. This raise awareness to the unemployment-vacancy relationship and its usefulness when studying trends in the labour market. The authors rank the difference between labour demand and labour supply for Great Britain and seven separate industry sectors over the post-war decade

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of 1946-1956, by creating an index for excess labour demand. It lowers when there is a match with labour from the pool of excess supply, making the index a measure of net excess demand. A 45°-line from the origin in the UV-space will represent a zero net excess demand of labour. With unemployment rate on the vertical axis and vacancy rate on the horizontal axis, a point on the Beveridge curve above the 45°-line indicates a low labour demand and a point below indicates a high labour demand. In addition, to measure unemployment and vacancies, working hours and rate of labour turn over, are also considered when investigating the excess demand. The authors argue that an upward pressure on labour demand will be associated with an increased number of unfilled vacancies and reduced unemployment rate. The main findings of the study are that there are large differences between the different industry sectors included, also compared to the national level analysis. Overall, there exists excess demand during the first years after World War II, but it lowers with the economic recession of 1952 (Dow and Dicks-Mireaux, 1958; Rodenburg, 2011).

A lot of literature on the Beveridge curve and the matching function relates to the early work of Pissarides in 1985 and 1986. He studies the behaviour of unemployment and real wages in equilibrium and most importantly, the adjustment process between equilibriums by modelling job vacancies explicitly. He argues that researchers previously had focused primarily on the development in equilibrium, due to shocks, and not the path in-between. He makes use of the findings that vacancies affect unemployment and react faster to shocks than do unemployment (Pissarides, 1985).

Furthermore, Pissarides made one of the first studies on the simultaneous determination of vacancies and unemployment by the usage of data on in- and outflows to/from unemployment. He argues that the flow analysis is more informative than studies based on the unemployment stock and captures both differences in the flows as well as levels. The paper from 1986 is based on data from the UK, where the unemployment rate of male workers increases from around 3% to 15% during the period from the late 1960´s to the mid 1980´s. The downward-sloping Beveridge curve is constructed in theory and the author claims that a rise in inflow rate to unemployment will shift the curve to the right and a reduction in inflow rate will correspond to an inward shift to the left. The findings of the study implies that the fall in labour demand after year 1974 was the main reason for the large increase in unemployment (Pissarides, 1986).

Pissarides presents theoretical framework that underpins some of the research done in the field of labour economics. In a paper from 1992, Pissarides investigates the duration dependence of matching, due to lower employment probabilities if long-term unemployed workers are discriminated against in the hiring process in case of homogenous applicants. The argument for this situation is that long-term unemployed workers lose their skills and search intensity to a wider extent than short-term unemployed workers. These factors reduce the probability of employment. However, it is not always the case that both short-term- and long-term unemployed workers are

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available for the firms to choose between. Then there is a decision to make, whether to hire the long-term unemployed instantly or wait for a short-term unemployed worker to make an application. Then the firms choose between an initial profit loss if the long-term unemployed is less productive than required or the waiting cost of not filling the vacant job position. Longer unemployment durations will also imply decreased quality of the unemployment pool which will discourage job openings.

When there are less available jobs, there will be fewer successful matches and the duration of unemployment tend to increase even more. However, it is not realistic that the unemployed workers are homogenous and there are other factors affecting the search intensity, such as unemployment insurance and the demographic composition of job seekers (Pissarides, 1992).

Another theoretical topic is job creation and job destruction. In a paper from 1994, Mortensen and Pissarides argue that higher a vacancy rate induces more job matches and thereby lower unemployment. On the contrary, higher vacancy rates also imply more separations and thereby higher a unemployment rate (Mortensen & Pissarides, 1994). In 1998 the authors ad another dimension to the analysis, by examining the effect of technological progress on job creation and job destruction. When investment is irreversible and the new technology comes with updated capital, it most often results in increased productivity, causing job destruction. However, if the new technology is adapted at a low enough cost, existing capital will be renovated, and job destruction avoided. Furthermore, higher implementation costs will cause a rapid drop in job creation, and a faster technological progress induce a lower number of jobs in equilibrium. The reverse happens in case of low renovation costs, since a faster productivity growth will generate a rise in job creation (Mortensen & Pissarides, 1998).

Turning to the early work on the unemployment-vacancy relationship, Blanchard and Diamond (1989) argue that this is essential for the understanding of the labour market and its functioning, as well as the effect of shocks, and study the matching process and sources of shocks. They plot a Beveridge curve for the US from monthly data between 1952-1988 and find counterclockwise loops around a downward sloping locus. In addition, they document clear outward shifts to the right during the post- World War II years, but between 1984-1988 the reverse happens, and the curve shifts to the left. This implies a roughly constant vacancy rate in combination with a 2%

decrease in unemployment rate. The loops are interpreted as aggregate activity shocks affecting the unemployment rate mainly in the short- and medium-run, while the shifts represent long-run changes in reallocation intensity or effectiveness (Blanchard &

Diamond, 1989).

In a corresponding working paper, the authors´ view and construction of the aggregate matching function is presented. They focus on the flows and stocks of jobs and workers to formulate a picture of the labour market. The matching function, h=α m

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(U, V), explains how new hires² (h) depend on the match (m) of the number of unemployed workers (U) and unfilled job vacancies (V). α is a scale parameter that can capture changes in skill distribution and geographically, sometimes referred to as mismatching, adding a deterministic trend parameter to the model. Moreover, they assume homogenous workers, Nash bargaining³ and that a match is independent of wages, for simplicity (Blanchard & Diamond, 1989).

The theories of the matching function and process are further included in research in combination with the Beveridge curve. National and regional analyses separately and together show different results across and within countries and there are many underlying explanations and theories for the reasons behind the shape and positioning of the Beveridge curve in the UV-space.

Wall and Zoega (2002) try to identify explanations for the observed shifts in the aggregate and ten regional British Beveridge curves for 1986-1995, and sort out how much is due to structural changes in the matching process or changes in the business cycle. This regional approach allows for discussions of regional mismatches contributing to the analysis on the aggregate level. The regression model that is estimated for each region in this study is a log-linear specification: ln(uit) = αi + τtD + βln(vit) + εit, where u is the unemployment rate⁴, αis a regional fixed effect, D is a vector of dummies for the year variable, v is the vacancy rate⁵, ε is the error term and the subscripts i and t denotes specific counties and years, respectively. The authors observe both outward and inward shifts during the period, and the regional estimates seem to follow the national results. Further, they conclude that the high persistent unemployment rate in Great Britain, at the time of the study, cannot be fully explained by the Beveridge curve. It may partly be due to a hysteresis effect⁶ and structural changes, but the results show evidence that the position of the Beveridge curve also depend on the business cycle (Wall & Zoega, 2002).

Bleakley and Fuhrer (1997) provide graphical illustrations of the US Beveridge curve on monthly data from 1960 to 1996, showing mainly a negative relationship between unemployment and vacancies. Moreover, they try to identify to what extent changes in the Beveridge curve depends on changes in the job matching process, having the goal of the Federal Reserve Bank in mind, i.e., remaining as close as possible to full employment, given the inflation goals. The authors present evidence of a distinct outward shift of the curve and flatter slope in the 1970´s and the beginning of the 1980´s, i.e., higher levels of unemployment for given vacancy levels. During the

2 Flow into employment.

3 The surplus from matching a worker and a firm is profitably distributed between the two parties.

4 Unemployment rate = Number of unemployed workers (U) / Labour force (L).

5 Vacancy rate = Number of unfilled job vacancies (V) / Labour force (L).

6 The hysteresis effect explains how movements along a Beveridge curve can induce a next period outward shift due to long unemployment spells and deterioration of human capital.

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1990´s the Beveridge curve shifts back (inwards) to approximately the same position as the locus for 1960, which was the starting point in the analysis. The authors consider three different explanations for the shifts, i.e., decreased labour force growth rate⁷ (upper right outward shift), lower degree of reallocation⁸ in the labour market (outward shift) and increasing matching efficiency (inward shift). The matching function used is theoretically corresponding to Blanchard and Diamond (1989), only with different notations; Ht = A f (Ut, Vt), where A is the factor of productivity. For simplicity, a Cobb-Douglas function with constant returns to scale⁹ is used, Ht = AtUtαVtβ. The authors conclude that the observed outward shift could be explained by increases in unemployment and vacancies due to the entrance of the baby boom generation into the labour force, while a higher matching efficiency in combination with the baby bust¹⁰ generation entering the labour force, account for the inward shift of the Beveridge curve (Bleakley & Fuhrer, 1997).

In a paper from 2005, Valletta examines the aggregate and regional Beveridge curves for the US between 1976 to 2005. The equation used for OLS estimations on the national level and for the nine regions included in the study is: ut = α + β1vt2

+ τY + εt. Y denotes the year dummies for the time effect. The inclusion of a quadratic vacancy rate term corresponds to convexity of the Beveridge curve. There are statistically significant results ensuring the negative relationship between vacancy- and unemployment rate for all nine regions as well as the aggregate level. The findings are in line with conclusions drawn by Blanchard and Diamond (1989), that an increased effectiveness in the job matching process is evident, causing the Beveridge curve to shift inwards during the late 1970´s and the early 1980´s.

Furthermore, the regional dispersion clearly contributes to the position of the national Beveridge curve and predictions made in other studies (see Abraham, 1987; Katz &

Krueger, 1999). The common finding is that the declining trend in dispersion of the labour force across states and improved labour market performance in the 1990s, consist with the actual outcome. This gives credibility to the theoretical idea of regional mismatching, implying that in case of an increasing labour demand in one region and decreasing in another, unemployed workers are forced to move across geographical regions to find available jobs. Such a reallocation is costly as well as time-consuming, increasing the likelihood of both high unemployment- and vacancy rates. This may cause an outward shift of the Beveridge curve and as discovered by

7 Larger groups that enter the labour market could be graduating students (correspond to a baby boom about 20 years earlier) or a higher rate of female and immigrant labour market participation. Hence, the demographic composition of the working-age population experience shifts.

8 General level of job creation, job destruction and separations.

9 α + β = 1. If U and V are doubled, the number of new hires will be doubled. Furthermore, if A is doubled, the number of new hires is doubled, given the number of U and V.

10 The aftermath of the baby boom.

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Valletta and others, an inward shift occurs when the regional mismatches are few (Valletta, 2005; Valletta & Hodges, 2006; Abraham, 1987).

In a more recent paper by Holmes and Otero (2020), panel data on unemployment and vacancies for 48 US states between 2005m5¹¹ and 2018m7 is used to illustrate an inverse relationship between unemployment rate in one state and vacancy rate in another. The main findings are that shifts in the Beveridge curve and changes in the matching efficiency depend on a combination of distance between states, homeownership (including differences in affordability between states) and labour force participation. In the aftermath of the global financial crisis in 2008-09 the Beveridge curve shifts outwards, implying a decreased matching efficiency. The inclusion of homeownership aims to catch the effect that homeowners tend to be less mobile across states than renters, showing a positive relationship between the regional factors, homeownership and level of unemployment. The Oswald hypothesis¹² can be considered to explain the negative effect of homeownership on the matching efficiency across states, given the relative affordability (Holmes & Otero, 2020).

3.2 European literature

European countries have been studied in this area of research as well, separately and also commonly in comparison to each other. This is mostly due to the international relationships and across border collaborations provided by, for example, the European Union which makes it interesting to investigate how the included countries behave when they are subject to similar economic situations. Of course, the Swedish national and regional case is of most interest for this paper, but also Scandinavian cases in general, since these countries historically have similar country specific characteristics.

A study was made on regional and aggregated data by Kosfeld et. al. (2008) to investigate the job-matching efficiency in the German labour market. The authors use panel data on unemployment and vacancies during the period 1992-2004, finding an outward shifting Beveridge curve. They connect the shift to an increasing rate of long- term unemployment and an increased degree of job-mismatch along with business cycle fluctuations. Regional mismatches are rejected as an explanation for the shift (Kosfeld et. al., 2008).

Another study on regional data is provided by Lincaru (2010), who examines the short-run relationship between vacancies and unemployment in the Romanian labour market. Estimated Beveridge curves are provided for 16 occupational groups within eight regions between the first quarter of 2005 to the third quarter in 2009. The main results presented implies that the eight regional Beveridge curves included tend to

11 2005m5 means the 5^th month (May) of year 2005.

12 The Oswald hypothesis suggests that a high level of homeownership is associated with a high unemployment rate, due to homeowners being less mobile compared to renters.

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follow the overall national curve rather well, and in the Romanian case the vacancies seem to create matches in the labour market to a larger extent than new unemployment affects hiring (Lincaru, 2010).

Bouvet (2012) presents a study on regional and national data for five European countries for the period 1975-2004. 60 regions are included, and Beveridge curves are estimated for Belgium, Germany, the Netherlands, Spain and the UK. Movements along a stable Beveridge curve is spotted for all countries in the late 1970´s to the mid-80´s, with a vertical pattern for the Belgian and Spanish cases. In the second half of the 1980´s, all five nations experience an outward shift of the Beveridge curve. For all countries except Germany, there is a similar adjustment pattern of rising unemployment rate and falling vacancy rate between 1984 to the beginning of the 1990´s during recession. This is followed by inward shifts and a better matching efficiency, again for four countries, Germany excluded. Similar results are found by Börsch-Supan (1991), where the data set consists of yearly observations from 1963 to 1988. He studies monthly data from January 1985 to December 1986, and counterclockwise loops are observed, which are not visible in the yearly data analysis.

This suggests that the unemployment rate is less flexible than the vacancy rate.

Further, when analysing the regional effect on the aggregate level, there seem to be evidence for an aggregation bias. Hence, there are significant outward shifts in each of the nine regions studied (at time of the outward shifts on the national level Beveridge curve), but a weighted average for the different states (weighted against each state´s labour force), suggests that these shifts are of smaller magnitude than shown on the aggregate level. This gives reasons to suspect an aggregation bias as an explanation for part of the outward shift for the whole country (Börsch-Supan, 1991).

The specification used by Bouvet (2012) on both regional and national data is the following: uit=αi+β1+β2vit+β3v²it+β4Xit+β5Zi,t+β6outputgapit+β7Wit+ηit. In this model unemployment (u) is the dependent variable estimated on a regional/country fixed effect (α), vacancies (v), a vector of variables controlling for the demographic composition of the labour force and unemployment pool (X), a vector of labour institution variables (Z), business cycle (outputgap), and a vector controlling for structural changes (W). The quadratic term is positive and statistically significant for all countries, both in regional and national estimations, which implies convexity to the origin of the Beveridge curve. The author suggests that there is evidence for an unemployment hysteresis, both regionally and nationally. Labour market institutions explain a lot of the positioning of the Beveridge curve and minimum wage laws and generous unemployment benefits are implications that tend to shift the curve outwards. On the contrary, a structural shock, such as productivity growth, provide inward shifts. Furthermore, the locus of the Beveridge curve is affected by changes in the business cycle on a regional level but not on a country specific level (Bouvet, 2012).

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Bjørsted et. al. (2016) examines if the labour market policies in Sweden and Denmark have improved the matching efficiency by reducing the frictional unemployment.

They make a comparison between these Nordic countries and European countries, finding that the labour market indicators recovered faster from the financial crisis in 2008-09 in the north. Active labour market policies, such as guidance concerning unemployment and education, different training programmes helping workers to search and find jobs or language study programmes for immigrants etc., seem to matter more for employment than labour market flexibility, especially hiring and firing regulations. However, evidence from the national Beveridge curves reveals that well-designed active labour market policies seem to have been the key for both nations to avoid mismatches to a wider extent (Bjørsted et. al., 2016).

As labour market training has been provided in Sweden since the 1930´s, they have managed to handle and adjust the labour market in times of economic shocks in the 1970´s and 80´s, avoiding as large increases in unemployment rate as other countries have experienced. An empirical investigation suggests that changes in the labour supply made the rising unemployment rate persist on a high level. However, labour market policies seem positively correlated with the matching efficiency, flattening the Beveridge curve and shifting it inward, closer to the origin, while unemployment benefits and its duration cause outward shifts (Jackman et. al., 1990).

Kolsrud (2018) studies the Norwegian economy between 2003-2013 for 19 counties, 14 occupations and on an aggregated level. A separate analysis between natives and immigrants is also provided. Evidence from the Beveridge curve show an increased matching efficiency over the period. However, the indicators unemployment variability and unemployment-vacancy mismatch increase rather than decrease on a regional level, suggesting that the inward shift of the Beveridge curve towards lower levels of both vacancy- and unemployment rates, might not be due to an improved balance between demand and supply of workers in the labour market. When looking at immigrants and natives separately, immigrants tend to be more mobile and settle in regions where labour is demanded, equating the balance of demand and supply more effectively than natives. The author comment on the limitations of the data, that vacancies and unemployed workers are not fully registered, but concludes that the findings seem reasonable (Kolsrud, 2018).

Focusing on the Swedish case, Eklund et.al. (2015) presents a circumstantial report on the matching efficiency in the Swedish labour market and how it has developed over time between the first quarter of 1981 and the second quarter of 2014. They aim to analyse to what extent structural factors, such as higher education, the housing market and the regional labour market size affect the matching efficiency. Studying the housing market together with the labour market is argued to be relevant due to its effect on the geographical mobility of workers Furthermore, the rental regulations are also of importance in this argument. The authors find evidence of a successively worse matching in the Swedish labour market, due to a Beveridge curve moving to

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the right, away from the origin, during the period of measure. One possible explanation for the outcome is that the educational system is not adapted to the development in the labour market, resulting in a mismatch between the qualities of the unemployed workers and the skill-level demanded by firms. Furthermore, the analysis of the labour market regions is primarily based on quarterly panel data between 1993-2012. Other than the Swedish Beveridge curve, estimations are provided for Stockholm, Gothenburg, Malmö, Örebro and Jönköping. There is a common pattern that workers with low education experience a higher unemployment rate compared to highly educated people, on average. This is graphically explained by Beveridge curves positioned further to the right in the UV-space. The lower educated group also seem to be more sensitive to changes in the business cycle (Eklund et. al., 2015).

The behaviour of the Swedish Beveridge curve follows the trend of many European countries and the US, i.e., outward shifts in times of recessions and after the crisis in 2008-09, there are signs of recovering but the unemployment rate stabilizes at a higher unemployment rate compared to before the crisis. The regression results show evidence of smaller regions experiencing a higher deterioration of the matching efficiency, compared to larger regions. This is simply explained by larger regions having a larger pool of vacancies and unemployed workers to be matched. Regarding the effect of the share of highly educated people in a region on the matching, there is a positive coefficient when all education levels are included. This implies that highly educated workers have an easier time getting employed in a region where the overall share of highly educated people is high. Furthermore, homeownership tend to be positively correlated with unemployment rate, which is also found by Holmes and Otero (2020) (Eklund et. al., 2015).

There have been many studies done on the behaviour of the labour market, regionally and nationally, when exogenous shocks hit the economy. The post-World War II period and various financial crises in modern time have been of interest for many researchers, concluding that the Beveridge curve generally make an outward shift in case of such negative economic shocks. The unemployment rate increases for a given level of vacancies as the demand for labour goes down. Furthermore, as the economy recovers, the Beveridge curve tend to shift inwards, which is in line with the theoretical implications of the model (see; Hobijn & Sahin, 2013; Bonthuis et. al., 2016; Bonthuis et. al., 2015; Blanchard & Diamond, 1989). Such patterns have been observed in Sweden after the financial crises in 1990-94 and 2008-09 (see; SCB, 2013; Håkanson, 2014; Jonsson & Theobald, 2019; Eklund et. al., 2015). Håkanson (2014) argues that after the crisis in 2008-09, the matching efficiency in the Swedish labour market declined and the economy remained longer than usually in a recession.

One possible explanation could be the composition of the unemployment pool, where people less attached to the labour market, such as individuals with presecondary education as highest completed education level, born outside of Europe, in ages 55-

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64 years old or people having a functional limitation reducing the working capacity, are overrepresented in the unemployment pool. In addition, during this period, the long-term unemployment and the average unemployment duration increased. These events together make the unemployment rate persist on a high level, even if the economy have recovered from a recession. Hence, the labour supply is high and poorly matched to the demand, and while there are many vacancies, the unemployed people have irrelevant qualifications (Håkanson, 2014).

Aranki and Löf (2008) argue that the matching efficiency varies between regions in Sweden. Regions with higher population density, such as Stockholm, Västra Götaland and Skåne, tend to show a lower efficiency in comparison to regions with lower population density. This is not in line with the theoretical framework implying the opposite scenario, i.e., that regions with high population density should experience a high labour market matching efficiency. The Swedish results could be due to the job creation in expanding areas not corresponding to the characteristics of the labour supplied in the regions, which results in bottle necks in terms of mismatches. This further affects the wage formation and the national employment growth negatively (Aranki & Löf, 2008).

To summarize, countries behave differently in times of economic events, mostly due to cyclical factors and structural differences (see; Sala et.al., 2012). In the aftermath of the financial crisis in 2008-09, many European countries experienced outward shifts of the Beveridge curve, and in the recovering process while the vacancy rate increased notably, the unemployment rate reacted slowly and stabilized at a higher level compared to before the crisis. However, not all countries behaved similarly.

There was evidence of counterclockwise loops in adjustment to the labour demand shock and in Germany, an inward shift of the Beveridge curve was observed during the financial crisis. Since the adjustment process of the unemployment rate can be relatively slow, an outward shift is not a definite sign of a decline in the labour market matching efficiency. Hence, a shift can be temporary when the economy adjust unemployment to the labour market changes (Arpaia & Turrini, 2014).

Elsby et. al. (2015) make a developing survey on the Beveridge curve, arguing that many factors and approach angles are omitted in the historical baseline model. Wage determination, vacancy creation, volatility of vacancy dynamics, unemployment duration dependence, labour market lows in participation and off- and on-the-job search effort are channels that seem to affect the Beveridge curve. The authors argue that this should be considered in a wider extent in future research (Elsby et. al., 2015).

These are, however, variables that are hard to observe in a way to correctly make credible conclusions and will not be considered in this paper.

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4 Theoretical framework

4.1 The Beveridge curve

The Beveridge curve is named after the British economist and baron William Henry Beveridge (1879-1963), whose main field of research was in social security, and he contributed to the building of the welfare state in Great Britain in post-World War II (Britannica, 2021). He had an interest in the causes of unemployment and identified the negative relationship between job vacancies and unemployment in the 1940´s.

The aim was to investigate how far the British economy was from full employment (Bleakley & Fuhrer, 1997). His work in this area was further developed by the British economists J.C.R Dow and L.A. Dicks-Mireaux in 1958.

The Beveridge curve is a graphical illustration showing the relationship between unemployment rate (on the horizontal axis) and the job vacancy rate (on the vertical axis) expressed as proportion of the labour force. The fact that unfilled vacancies coexist with unemployment implies that there is a labour demand which differ from the offered labour supply (Dow and Dicks-Mireaux, 1958; Rodenburg, 2011). The variables are typically negatively related, implying that a higher vacancy rate is associated with a lower unemployment rate, resulting in a Beveridge curve with a negative slope coefficient. Movements along the curve reflect the business cycle, where there is job creation and destruction, and people move in and out of unemployment. At a point where there is a high level of vacancies and a low unemployment level, the economy tends to experience a high business activity. On the contrary, in a recession, the theory predicts a limited level of vacancies together with a high unemployment level. These movements on the Beveridge curve are connected to structural unemployment, referring to unemployed people not being demanded in the labour market, e.g., if there is no production or no firms searching for the skill composition that the unemployed possess (Bova, Jalles & Kolerus, 2018;

Spector, 2015; Rodenburg, 2011; Eklund et.al., 2015).

The position of the curve in the UV-space can be caused by several different factors.

Characteristics of the labour force, such as the distribution between young and old workers, share of female labour force participants and high- versus low-skilled proportions have been studied in previous literature. Furthermore, institutional settings¹³ and mismatches between the unemployed workers and the hiring firms could be reasons for shifts of the Beveridge curve. These shifts are connected to frictional unemployment, i.e., deteriorations and improvements in the effectiveness in the search for jobs and applicants (labour market matching). The frictional unemployment occurs due to employers and jobseekers having a difficult time finding each other. One explanation for this could be that the two parties are located in distant

13 E.g., employment protection legislation, unemployment benefits, real wage levels and active labour market policies.

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geographical areas. Both the structural and frictional unemployment are part of the total unemployment.¹⁴ The duration of unemployment plays an important role in this setting as well. Long-term unemployed (who have been out of the labour market for more than one year) tend to experience difficulties in the matching process. This is explained in the literature by the possibility of getting an outdated skill composition and thereby being less attractive in the hiring process, compared to short-term unemployed (Bova, Jalles & Kolerus, 2018; Spector, 2015; Rodenburg, 2011; Eklund et.al., 2015).

However, there is empirical research in terms of a Swedish field experiment, suggesting that there is no causal relationship between long-term unemployment spells in the past and the hiring decision of firms. Nor is there any difference in treatment between long- and short-term unemployed, implying that there is an understanding that the matching process takes time. This result, however, is slightly different depending on the skill level of the worker and working experience.

Moreover, in the case when recruiters choose between two equally qualified workers, one with a longer ongoing unemployment and one with an employment, the latter tends to be offered the vacant spot. Some of these findings are not in line with previous research, which is argued to be due to unobserved heterogeneity, and no such evidence has been found in the US, but shows that there are occasions when reality and theory behave in opposite directions (Eriksson & Rooth, 2014).

When estimating the Beveridge curve on empirical data, relying on constant returns to scale will provide a Beveridge curve that is convex to the origin, which is in line with the theoretical hypothesis (Valletta, 2005; Börsch-Supan, 1991; Bova, Jalles &

Kolerus, 2018).

Figure 1. The shape of the Beveridge curve according to theory.

14 Definition of structural and frictional unemployment from Ekonomifakta.se.

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Figure 1 summarizes the theory as a graphical illustration of the negative relationship between unemployment and vacancies as shares of the labour force, giving the Beveridge curve. Movements along the original black curve reflects fluctuations in the aggregate demand in the economy. An expanding economy moves to the upper left corner of the curve, while contractions move the economy towards the lower right corner. When staying on the same curve, the matching efficiency is constant.

The red curves illustrate shifts of the original Beveridge curve. A shift to the upper right corner of the UV-space (away from the origin) implies a lower matching efficiency in the labour market and a shift to the lower left corner (towards the origin) shows evidence of an improved matching efficiency (Eurostat, 2020). Shifts are associated with exogenous changes in the economy. If the search intensity of firms and workers is reduced (or the choosiness increased), the outflow from unemployment will be lower and the curve shifts to the right. Such factors could be increased unemployment benefits through social security coverage, unionization and employment protection legislation. Similarly, in case of a rise in occupational or geographical mismatch the curve will also shift to the right, hence for any given vacancy rate, there would be less outflow from the unemployment pool. Of course, these events can happen in the reverse direction, resulting in inward shifts of the Beveridge curve (Pissarides, 1986; Wall & Zoega, 2002).

To summarize, changes in search effort, individual characteristics of the unemployed workers, search effectiveness or hysteresis effects can all cause the Beveridge curve to shift, and these factors are further caused by policy implications, and other exogenous events in the labour market. The Beveridge curve illustrates a complex cluster of events in a simplified model that enables interpretations of the labour market conditions (Pissarides, 1986; Wall & Zoega, 2002).

Jackman et. al. (1990) argue that labour market policies are tools for reducing unemployment, where employment services and training programmes increase the job finding rate at a given number of vacancies and employment subsidies increase the labour supply at a given wage level. The authors present an overview of the theoretical effects of policy implications on the Beveridge curve:

• Shifts in the Beveridge curve. Labour market policies are often focusing on the long-term unemployed workers and groups of workers who face greater obstacles in the searching process than others. This could for example include people with no, low or unfinished education or immigrants with linguistic difficulties. The aim is then to increase the matching rate for a given number of unemployment- and vacancy stocks. Both variables will be reduced in case of successful implementations.

• A flatter Beveridge curve. Policies aiming to construct a flatter curve will improve the marginal rate of job matching. Thus, an increased vacancy stock, decrease the unemployment level more than proportionally.

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• Higher speed of adjustment. The economy can recover faster from an employment shock when policies are implemented. The counterclockwise loops found in the Beveridge curve during an adjustment process will indicate the problem and policies help displaced workers to find jobs faster.

• Unemployment insurance. The higher the unemployment insurance and unemployment benefits, the greater the choosiness of active participation in the job searching process. Hence, unemployment benefits will increase the reservation wage and the duration of the benefits will influence the search intensity. This generates an outward shift of the Beveridge curve.

Furthermore, high unemployment benefits give the unemployed workers improved wage bargaining strength. This increases the wage level, and indirectly shifts the vacancy supply outwards, resulting in an increased equilibrium unemployment level (Jackman et. al., 1990).

4.2 The matching function

The Beveridge curve is determined by the stock and flow of unemployed workers and job vacancies. The net flow of workers into and out of unemployment is an ongoing process where unemployed workers search for jobs and find a match to a firm which is hiring.¹⁵With a more efficient job-matching process, the outflow from unemployment increase, which will correspond to an inward shift of the Beveridge curve (Bleakley & Fuhrer, 1997). The number of vacancies explain the distance between the intersection of the upward sloping supply- and downward sloping demand curves, below the equilibrium wage (w<w*), in a regular labour market illustration with wages and employment on the vertical and horizontal axis, respectively. Similarly, the distance between the two curves, at a point above the equilibrium (w>w*), accounts for the number of unemployed workers in the economy (Börsch-Supan, 1991).

The matching function needs to be specified to derive the Beveridge curve. A similar function is used in most literature, presented as equation (1):

𝑀 = 𝑀(𝑈, 𝑉) 𝑀_𝑈 > 0, 𝑀_𝑣> 0; (1) where M denotes the number of new hires in the labour market, i.e., a match. M is a function of the number of unemployed workers, U, and unfilled job vacancies, V.

Thus, the simple interpretation follows the logic that a higher level of unemployed workers searching for jobs, in combination with an increase in number of vacancies, will result in more matches. For the matching function to be expressed in rates it needs to satisfy constant returns to scale and it can be written as a Cobb-Douglas function:

15 In the simplest version of the matching process, the supply and demand side find each other randomly (Håkanson, 2014).

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𝑀 = 𝐴𝑈^𝛼𝑉^1−𝛼 (2) where A corresponds to a matching technology parameter which measure the ability for unemployed workers to match vacancies. Furthermore, dividing equation (2) by the labour force, L, and setting number of matches equal to number of separations (true for a state of equilibrium), equation (2) can be rewritten in the following way:

𝑀⁄ = 𝑆 𝐿𝐿 ⁄ = 𝐴(𝑈 𝐿⁄ )^𝛼(𝑉 𝐿⁄ )^1−𝛼 (3)

Finally, equation (3) can be written in the logarithmic functional form:

ln(𝑠) = 𝐴 + 𝛼 ln (𝑢) + (1 − 𝛼) ln (𝑣) (4) where lower case s denotes the separation rate (S/L), u is the unemployment rate (U/L), v is the vacancy rate (V/L), and A is the intercept expressed as the matching technology parameter. Equation (4) gives the implicit Beveridge curve as a negative relationship between unemployment rate and vacancy rate, given a fixed intercept and separation rate. Since the matching function is convex to the origin, mismatches appearing in submarkets, e.g., regions, can possibly cause shifts of the aggregate Beveridge curve (Wall & Zoega, 2002; Holmes & Otero, 2020; Petrongolo &

Pissarides, 2001).

It takes time for the unemployed workers and the hiring firms to find each other, and the average duration of such a process could, for example, depend on whether the firms use advertisement of job openings and how available it is to the searching workers. Shifts in the matching function that are not associated with decision making, depend on technological progress, which simplifies the advertisement and search process (Petrongolo & Pissarides, 2001). The number of vacancies and successful matches will also depend on the costs that the two parties face. It is costly for the firm to end an employment and search for a new employee, and it is costly for the worker to participate in the job searching process. The possible gain from a successful match must exceed the costs for the firm and the worker to participate (Spector, 2015).

4.3 State of equilibrium

The state of equilibrium behind the Beveridge curve is characterized by an equal inflow and outflow to/from unemployment and do not depend on the stocks of unemployment and vacancies (Holmes & Otero, 2020). If the size of the labour force, denoted by L, equals the number of employed and unemployed workers, denoted by N and U respectively, the relation L = N+U holds. Further, if s is the separation rate and f is the job finding rate, the inflow to unemployment is calculated as sN while the outflow is given by fU. In a state of equilibrium, the condition sN = fU will hold, and

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can be rewritten for the steady state unemployment rate u*=U/L=s/(s+f). The Beveridge curve will then illustrate this equilibrium (Rodenburg, 2011).

The matching function in equilibrium as the share of hires (h) can be given by dividing equation (2) by unemployment stock (U):

ℎ = 𝐻 𝑈⁄ =𝐴[𝑈^𝛼𝑉^1−𝛼]

⁄ 0 < 𝛼 < 1 𝑈 (5) Using the specification for unemployment and vacancy as shares of the labour force (u = U/L and v = V/L) and applying it on equation (5) will give equation (6):

ℎ = 𝐴 (𝑈

𝐿)

⁄ ∗ [𝑈 𝐿⁄ ]^𝛼∗ [𝑉 𝐿⁄ ]^1−𝛼

ℎ = 𝐴 𝑢⁄ ∗ 1^𝛼∗ 𝑣^1−𝛼

ℎ = 𝐴[𝑣 𝑢⁄ ]^1−𝛼 (6)

Equation (6) illustrates how the vacancies and unemployed workers as shares of the labour force together give an expression for the share of new hires. The labour demand will decide the value of h, i.e., a higher labour demand will increase (v/u), resulting in an increase in h as more hires will be done, and vice versa. As before, A corresponds to matching technology or matching efficiency and 1-α implies that h is increasing with decreasing speed in terms of (v/u).

Recalling the definition of the equilibrium, that the inflow equals the outflow to/from unemployment and using s as the separation rate and L denotes the labour force, gives the following expression:

𝐴𝑈^𝛼𝑉^1−𝛼= 𝑠𝐿 (7)

Further, dividing equation (7) by the labour force gives equation (8) as a relationship between unemployment rate and vacancy rate.

𝐴𝑢^𝛼𝑣^1−𝛼= 𝑠(1 − 𝑢) (8) Using equation (8) and solving for the vacancy rate gives expression (9).

𝑣 = (𝑠 𝐴⁄ )¹^⁄^(1−𝛼)∗ 𝑢^−𝛼^⁄^(1−𝛼)∗ (1 − 𝑢)¹^⁄^(1−𝛼) (9) Equation (9) directly corresponds to the Beveridge curve in the state of equilibrium, implying that if v increase, the second and third terms will decrease simultaneously as the parameter A increase. Hence, in that case, the matching efficiency improves, shifting the Beveridge curve closer to the origin. This could be due to technological improvements, making the availability and information about job vacancies better and more widely spread and thereby, avoiding mismatches since the most appropriate worker is reached and able to apply for the job (Romer, 2018; Wall and Zoega, 2002).

The Beveridge curve Magister thesis in Economics