Is there a labour market mismatch in Estonia? Measuring regional, occupational and industrial labour market mismatch

ABSTRACT Despite the fast growth in the Estonian economy, unemployment has remained high for extended periods of time. This paper analyses and quantifies the mismatch between registered unemployment and vacancies and how it has contributed to unemployment in the Estonian labour market at the (county) regional, occupational, and industrial levels for the time span 2011-2021. We apply the search and matching theory and the mismatch index framework, and our findings show that around 4–5 per cent of potential hires have been lost in the Estonian labour market because of mismatch. The contribution of mismatch to the level of unemployment is roughly 5–8 per cent, meaning that if the match between unemployed individuals and vacancies was efficient, unemployment would have been 5–8 per cent lower. Mismatch has the smallest impact at the regional level and the largest at the industrial level.


Introduction
Unemployment has been at a persistently high level in Europe and the United States since 2008, which makes it important to understand its roots.The International Monetary Fund (IMF) has shown that labour markets have been tighter in the European Union (EU) and non-EU economies since the Covid-19 pandemic and vacancies have increased across sectors (Duval et al., 2022;Forsythe et al., 2022).There has been intense debate in the United States about how labour mismatch is estimated (Daly et al., 2012;Hobijn & Şahin, 2013;Kugler, 2014;Şahin et al., 2014), but there is scarce evidence about the part that mismatch plays in unemployment in Europe (Arpaia et al., 2014), even though understanding this is crucial for designing better policy.
The cornerstone of any analysis of labour market mismatch is the search and matching theory of Pissarides (2011;2000), which has its roots in the research promoted by Diamond (1982), Mortensen and Pissarides (1994), and Mortensen (1982).The matching function developed by Pissarides (2000) models the process of job creation in a tractable way.The theory posits that flows into and out of unemployment, meaning the formation and destruction of job matches between unemployed people and vacancies, occur constantly.This process is affected by various frictions in the labour market that hinder the creation of new matches, such as the mismatch between the people who are unemployed and the vacancies that are available (Pissarides, 2000).
Such mismatch can be one driver of unemployment and indicate there are inefficiencies in how unemployed individuals are matched with job vacancies (Pissarides, 1985).The Beveridge curve has been used to analyse the efficiency of matching, as it illustrates the negative relationship between unemployment and job vacancies (Abraham & Katz, 1986;Blanchard et al., 1989;Elsby et al., 2015).Movements along the curve are usually driven by cyclical factors, while shifts in the Beveridge curve are associated with structural changes in the labour market.When the economy is expanding and the labour market is tight, the unemployment rate is low, and so firms post vacancies to attract the small pool of unemployed jobseekers.
An increase in mismatch would shift the Beveridge curve outwards as the unemployment rate increases, which happens during a recession (Hobijn & Şahin, 2013;Pissarides, 2011).Firms stop hiring and people lose their jobs, making the labour market less efficient.There are now more unemployed individuals than before for a given number of vacancies, implying that the labour market is no longer effective at matching vacant positions with unemployed job seekers.The Beveridge curve is estimated and its dynamics analysed to study changes in mismatch empirically.It is not clear from the theoretical point of view though whether the shift is necessarily caused by efficiency problems, as the curve might also shift outwards because of supply shocks (Diamond & Şahin, 2015).
Mismatch might persist over a longer time because of an erosion of human capital (Ball, 2009), long spells of unemployment, or extended periods of jobless recovery (Bonthuis et al., 2013;Groshen & Potter, 2003;Mortensen & Pissarides, 1999).Labour market rigidity might come from levels of geographic and skills mobility being low, or from workers being unwilling or unable to retrain (Rogut & Tokarski, 2002, p. 63).
This article focuses on the case of Estonia, quantifying the extent of the labour market mismatch and its contribution to unemployment.Estonia is a country that has structural employment challenges because it has an ageing population, and wider skill mismatches than in other OECD countries among employees who are underqualified or have studied unwanted subjects, while around 40% of the registered unemployed have only general education and have not completed higher or vocational education (OECD, 2021).On the labour supply side, there are labour shortages resulting from the ageing of the population and skill mismatches, a low level of labour productivity, and low levels of value added because of skill shortages.These factors together mean that studying and improving the matches between workers and jobs is important if the economic capacity of the Estonian labour market is to be increased.
Our study provides further insights into the topic and analyses the dynamics of unemployment within the country.It makes a twofold contribution to the literature.First, it uses only administrative data on registered unemployment and vacancies for the first time to estimate the labour market mismatch index at the regional, occupational and industrial levels for an Eastern European country.Second, its analysis of mismatch and how it contributes to unemployment offers new information about labour market efficiency within a country.
To the best of the knowledge of the authors, this is the first study to quantify the mismatch at different levels and how they contribute to unemployment in an Eastern European country.The empirical analysis covers the time span January 2011 to January 2021 and uses registry data from the Estonian Unemployment Insurance Fund (EUIF), which collects monthly information on unemployment and vacancies in Estonia.The paper follows the work of Şahin et al. (2014) and Patterson et al. (2016) for the empirical analysis, which follows from the search and matching theory of Pissarides (2000).We adopt the matching function to summarize how effective the labour market is at creating jobs, and at combining vacancies and job seekers.
Our findings show that the Estonian labour market exhibits labour market mismatch at all three of the levels considered, the regional or county, occupational, and industrial levels.The labour market mismatch average around 4-5 per cent across all the levels and they contribute around 5-8 per cent to the overall level of unemployment.The contribution is largest at the industrial level and smallest at the regional level.
The paper proceeds as follows.Section 2 provides a short literature overview while Section 3 introduces the data used in the analysis.Section 4 presents the Estonian labour market and Section 5 describes the methodology applied.The baseline results and robustness analyses are presented in Section 6.Finally, Section 7 contains a discussion and Section 8 concludes.

Literature
A lot of previous studies on labour market mismatch have looked at the US labour market, and they have yielded mixed results.Barlevy (2011) observes a decrease in matching efficiency in 2008-2010, using this as a proxy for mismatch in the labour market.Daly et al. (2012) study the dynamics of the natural rate of unemployment and the effect of mismatch, and do not conclude that there is any rise in mismatch or unemployment.Furthermore, their analysis of the dynamics of the Beveridge curve does not provide any insight into the different types of mismatch that exist in the labour market and how they contribute to changes in the unemployment rate.
The methodology of the mismatch index, which is based on the search and matching theory framework of Şahin et al. (2014), is used to estimate mismatch at different levels.Şahin et al. (2014) estimate the extent of mismatch at various levels and how they contribute to the unemployment rate in the US labour market.Their conclusion is that mismatch increased at both the industry and occupation levels during the global recession but have declined in recent years, while regional mismatch have remained quite stable and low.The framework was applied on German data, but the results of Bauer (2013) do not show any significant increase in industrial, occupational, or regional mismatch over the time span 2000-2010.
Writing slightly later, Hutter and Weber (2017) are able to include the years after the global recession in their analysis, and they find that mismatch increased at the qualification and occupation levels after the recession, while mismatch at the regional level decreased.Erken et al. (2015) study the trend for the level of unemployment in the Netherlands and show that 18% of the unemployment rate stems from sectoral mismatch.Similarly, Marthin (2012) finds for Sweden that geographical mismatch increased unemployment by around 0.3 percentage point during the period considered.
The mismatch index has proven useful for analysing labour market dynamics.Patterson et al. (2016) conclude that sectoral mismatch explains up to two-thirds of the deviation of labour productivity from its growth trend in the United Kingdom (UK) after the global recession.Hutter and Weber (2017) find that forecast models for job matching that include indicators for mismatch outperform base models that do not have a measure for mismatch.
The analysis by Pizzinelli and Shibata (2023) using data for the US and the UK additionally shows that there is mismatch in both labour markets, while there was a sharp but only temporary rise in mismatch during the Covid-19 pandemic.More recently, Herz and van Rens (2020) develop a framework for the US labour market to analyse how much issues around worker mobility, job mobility, and wage determination contribute to mismatch.Their findings suggest that the most significant underlying reason for mismatch is barriers to job mobility (Herz & van Rens, 2020).
The mismatch index methodology and the analytical framework of Herz and van Rens (2020) have not been used for studying labour mismatch in the Estonian labour market.More aggregated variables such as educational mismatches as a proxy for skills mismatches (Lamo & Messina, 2010) have generally been used instead.A recent work (EC, 2019) has also shown that sectoral mismatch increased sharply in Estonia during the global recession but declined back to their previous level after the crisis, while the Beveridge curve showed an increase in mismatch during the recession and a decrease after it.This study tries to apply the mismatch index framework to study mismatch in the Estonian labour market.

Data
The data used for the empirical analysis in this paper are monthly data taken from the Estonian Unemployment Insurance Fund (EUIF) for the time span January 2011 to January 2021. 1 The data are from an administrative dataset containing information about unemployed people and vacancies, and they have the advantage of being representative of the population of Estonia.Monthly data on vacancies at the ISCO 2 and NACE 3 1-digit levels 4 are used, with the ISCO data used to estimate occupational mismatch, and the NACE data used for industrial mismatch.The NACE 1-digit level is used because there are not enough observations at a higher level.When the previous occupation of the unemployed person or the area of activity of their previous employer is unknown, the individual is left out of the empirical analysis.To estimate mismatch at the regional level, time series on unemployment and vacancies across Estonian counties are used.
If the county where the unemployed person or the vacancy is located is not known or if it is registered abroad, the data are dropped from the empirical analysis.The time series for unemployment and vacancies at aggregated levels are illustrated in Figures A1 and A2 in Appendix A. Data on hiring are needed at the regional, occupational and industrial levels for the different labour market aggregate matching functions and mismatch to be estimated.The time series for hiring is illustrated in Figure A3 in Appendix A. The data on hiring at the regional level depict the transitions out of unemployment into employment across counties.
To calculate how mismatch contributes to unemployment, monthly data on separations are taken from the dataset of the EUIF as transitions from employment to unemployment.The number of people employed is taken from the database of Statistics Estonia, but as those data are only available on a quarterly basis, the monthly number is approximated by setting the number of people employed to be equal to the corresponding quarterly number.The number of people hired and the number unemployed are taken from the EUIF.
Data on hiring are not collected at the ISCO or NACE levels though, and to overcome this limitation, we estimate hiring at the occupation and industry levels by using the vacancy outflow method, which takes the difference between vacancies available during a month and those available at the end of a month for each ISCO and NACE level, as in Patterson et al. (2016).There are still a few limitations with these data, as they take information from individuals who have registered as unemployed with the EUIF.This means that the information most probably reflects a lower number for people unemployed than the actual number of unemployed individuals in the labour market.Given that it is not mandatory to register vacancies at the EUIF, vacancies might additionally be slightly underreported.
The tendency for people to register as unemployed has not remained constant over time, and this could affect the level of mismatch in earlier years.An additional data source for Estonia that reports unemployment and vacancies is Statistics Estonia, but their data do not contain the deep level of disaggregation that is needed for this analysis.For this reason, we estimate the models using only the dataset from the EUIF.In the empirical model, mismatch at the occupational and industrial levels are found from monthly data on people unemployed that give the unemployed person's previous occupation and their previous employer's area of activity.

The Estonian labour market
After the global economic crisis, the Estonian labour market had high and persistent unemployment, which then fell to its lowest level of 4.5 per cent in 2019 (see Figure A4 in Appendix A).The unemployment rate then rose to 6.8 per cent in the first half of 2020 during the Covid-19 pandemic, mainly because hiring for jobs dropped sharply as a consequence of the restrictions imposed by the government to tackle the pandemic (Statistics Estonia 2021, Table TT330).The country, however, has an ageing population and a shrinking labour force (OECD, 2021), which highlights the importance of understanding frictions and making the labour market work more efficiently.The process of matching the labour supply with demand, and the trends in this process, are illustrated by the Beveridge curve (Figure 1).Movement along the Beveridge curve represents changes in the cyclical component of unemployment.A shift in the Beveridge curve reflects a change in the natural rate of unemployment.An upward shift in the Beveridge curve, indicating that there are more vacancies available for a given level of unemployment, represents a decrease in the efficiency of matching between the number of people unemployed and vacancies.
In 2011 the number of vacancies was low and the unemployment rate was high, with unemployment at around 15% in the first quarter of 2011.The curve shifted inward from 2012 to 2014 as unemployment decreased while demand for labour and job vacancies increased significantly.This reflected a tightening in the labour market as efficiency in matching unemployed job-seekers with vacant positions improved.From 2015 to 2017, employers posted more and more job openings that were not filled.This was reflected in a rise in the job vacancy rate while the level of unemployment remained relatively stable and low.
This suggests that a larger number of vacancies were needed to move unemployment down only a small way.This may indicate that there were some efficiency issues within the labour market in the country.In contrast, the recent data from the pandemic show a slight outward shift in the Beveridge curve.Both the job vacancy rate and the unemployment rate increased, suggesting there was a deterioration in labour market matching.The Beveridge curve for Estonia follows a different path to those seen in the other two Baltic countries (Figure A5 in Appendix A), as it exhibits an anticlockwise looping movement over the business cycle (Eesti Pank 2022).
Although Estonia recovered relatively quickly from the global economic crisis, the job vacancy rate remained stable until 2016.That rate then rose in 2016-2019, but it did not reach such high levels as it did in Latvia.The unemployment rate remained lower in Estonia than it did in Latvia and Lithuania, suggesting the labour market may have been more efficient, especially when low unemployment was accompanied by a lower job vacancy rate.Following the outbreak of the Covid-19 pandemic in 2020, the outward shift in the Beveridge curve was not as significant in Estonia as it was in Latvia and Lithuania.
Figures 2-4 look at the individual labour markets at the three levels of regional, occupational and industrial, and they show the labour market tightness u, which is the ratio of vacancies to unemployment (Pissarides, 2000).At the regional level shown in Figure 2, the labour market becomes tighter in Harju County in North Estonia, which is the region that has a larger share of economic activities than other counties in Estonia and where the capital Tallinn is, after the global economic crisis, meaning that there is more demand for labour.There is a notable decrease in the ratio of vacancies to unemployment u during the Covid-19 pandemic, particularly in the first half of 2020, which indicates that people who were unemployed faced difficulties in finding suitable job matches.The level of labour market tightness u is lower in South Estonia and Central Estonia, which indicates that it is more difficult for the unemployed to find a suitable vacancy in those regions than it is in North Estonia.This might be because South Estonia is more rural and is geographically distant from the capital Tallinn in North Estonia.These factors make it more challenging to find suitable jobs that match the skills and qualifications of the workforce.The labour market tightness u in West Estonia by contrast suggests a high degree of seasonality, as it is more volatile than in other regions.
North-East Estonia, which is Ida-Viru County, has a different level of u and its dynamics are different to those in other regions, and it generally seems to be lower than in other regions.As Figure A6 in Appendix A shows, the region has a high number of unemployed individuals, with an unemployment rate that is some 6.8 percentage points higher than the rate in the rest of the country.These dynamics suggest there may be mismatch in the labour market.The economic structure of North-East Estonia has been primarily based on the mining industry and oil shale production.These industries have, however, experienced a decline because of efforts to meet the climate goals set by the Estonian government and the European Union (EC, 2019).This policy shift towards reconversion may explain why the unemployment rate is higher and labour force participation rates are lower in that county.
By occupational level, the occupation categories of 'service and sale workers' (ISCO 5), 'craft and related trades workers' (ISCO 7), 'plant and machine operators and assemblers' (ISCO 8) and 'elementary occupations' (ISCO 9) consistently have more labour market tightness u across the entire time series (Figure 3). 5 This suggests that it is more difficult for employers to fill vacancies in these ISCO categories.However, labour market tightness u decreased in the first half of 2020 for 'services and sales workers' (ISCO 5), most probably because of the restrictions imposed during the Covid-19 pandemic, when there were fewer vacancies in this area.
Reduced labour market tightness u is generally apparent for industrial-level categories like 'information andcommunication' (NACE J), 'financial and insurance activities' (NACE K), and 'real estate activities' (NACE L) (Figure 4).This should indicate that the labour market is less tight in those industries, meaning there are fewer vacancies and more people unemployed, but it is more likely that this arises because of data quality issues, as it is probably less common for vacancies in those industries to be posted with the EUIF.
Equally, the ratio is generally higher for the categories 'agriculture, forestry and fishing' (NACE A), 'accommodation and food service activities' (NACE I) and 'administrative and support service activities' (NACE N), where it is more common for vacancies to be posted with the EUIF, and where it is difficult to find people for jobs that demand lower skills and so offer lower salaries.
At the beginning of 2020, when the Covid-19 pandemic erupted, the sectors 'accommodation and food service activities' (NACE I), 'transporting and storage' (NACE H) and 'construction' (NACE F) saw labour market tightness u decline, meaning that there were fewer vacancies and more people unemployed in those sectors, which might be because of the travel restrictions that were imposed.However, the category 'agriculture, forestry and fishing' (NACE A) saw a sharp increase in the number of vacancies, again because of the travel restrictions since the agricultural sector employs seasonal migrant workers.
The descriptive analysis for the data on unemployment and vacancies shows there are different dynamics in the labour market tightness u across the regional, occupational and industrial levels.Some segments have a higher ratio of vacancies to unemployment, indicating that it is difficult for employers to fill vacancies, while some categories have a much lower ratio that indicates it is difficult for the unemployed to find a suitable job match from the available vacancies.This might indicate a possible mismatch in the Estonian labour market, which is studied in the following parts of the paper.

The empirical model
The empirical analysis follows the methodology in Şahin et al. (2014), who provide an empirical tool in the form of the mismatch index.The mismatch index uses the matching function, which predicts the number of hires, or new job matches created each quarter, by using the number of unemployed job-seekers and the number of vacancies posted by firms.Any variation in hiring that cannot be explained by these two variables is attributed to matching efficiency (Sedláček, 2016).
The matching function can be written as where M t is the number of job matches, U t the number of people unemployed, V t the number of vacancies at time t, and F the matching efficiency, where 0 , a, b , 1.The assumption of constant returns to scale (CRS), or a + b = 1, follows the work by Petrongolo and Pissarides (2001), in which a matching function in the form of a Cobb-Douglas function with CRS fits the empirical analysis.The mismatch index is depicted in Equation 2 and is derived from the aggregate matching function shown in Equation 1 by assuming a Cobb-Douglas function and requiring the matching elasticity to be constant over the entire time series (Blanchard & Diamond, 1990;Pissarides, 2000).We estimate the mismatch between people unemployed and vacancies for the time span 2011-2021 on monthly data at the regional, occupational and industry levels using the following mismatch index: where MM t indicates the mismatch for regions, occupations and industries depending on which level the mismatch is estimated at, f i are the time-invariant market-specific matching efficiencies, a is a time-variant aggregator of the market-specific efficiency weighted by the vacancy share a, and V it and U it correspond to marketspecific vacancies and unemployment.The subscript t indicates the time period, and subscript i indicates the disaggregated labour market by county, industry or occupation.The definition of the mismatch index MM t is derived from the article by Şahin et al. (2014), while the modified estimation for f t is taken from Bauer (2013) and Erken et al. (2015).
The parameters a and b show the sensitivity or share of job matches to changes in the numbers of people unemployed and vacancies, and determine what kind of impact unemployment and vacancies have in forming job matches.To estimate the marketspecific matching efficiencies f i , the matching functions at different levels were estimated by extracting the numbers of vacancies V it and people unemployed U it from a more disaggregated labour market.The time series model follows the aggregate matching function in Equation 1 (Bauer, 2013;Erken et al., 2015;Patterson et al., 2016;Şahin et al., 2014) to estimate the vacancy share a (Equation 3): where M t is the number of hires in period t, D Q2 t , D Q3 t and D Q4 t are the seasonal quarterly dummies 6 , and 1 t is the error term.All other notations and variables are the same as in the previous equations.Quarterly dummies are included in the model to account for seasonality.
To estimate mismatch indexes at different levels using Equation 2, Equation 3 is modified to estimate market-specific matching efficiencies f i using panel regression methods.The model for estimating mismatch at all of the occupational, industrial and regional levels is given in Equation 4: where the subscript i denotes a specific market as a county, an occupation at the ISCO 1-digit level, or an industry at the NACE 1-digit level, and 1 it is the error term.All other notations and variables are the same as in the previous equations.To calculate the mismatch at all levels and to estimate the matching efficiencies f i , the model in Equation 4is used.
The Augmented Dickey-Fuller test was performed for all the models in Equation 3 and Equation 4, and it showed stationary time series.A Hausman test was additionally performed, and it suggested that the random effects model should be preferred over the fixed effects model.This aligns with the search and matching theory, as changes in matching efficiencies f i are assumed to be uncorrelated with the independent variable V it U it in the random effects models.These changes result in shifts of the Beveridge curve rather than movements along the curve (Bauer, 2013).The model in Equation 4 is consequently estimated using random effects and incorporating county, occupation, and industry-specific effects to capture the market-specific matching efficiencies f i .These matching efficiencies are then used to compute mismatch indexes at different levels following Equation 2. Additionally, we estimate how mismatch at the regional, occupational, and industrial levels contribute to unemployment, using a method based on counterfactual unemployment.Mismatch in unemployment, which represents the contribution of mismatch to unemployment, is determined as the difference between actual unemployment and counterfactual unemployment.
Counterfactual unemployment reflects the number of individuals unemployed in the absence of any mismatch.The calculation of counterfactual unemployment follows the framework developed by Şahin et al. (2014), with adjustments inspired by Erken et al. (2015) to use the number of individuals unemployed instead of rates, as in Şahin et al. (2014).The counterfactual number of people unemployed was calculated as in Equation 5: where , where S t are separations, E t is the number of people employed, MM t is the mismatch index as estimated by Equation 2, a is the vacancy share as estimated by Equation 3, H t are the hires, U t is the number of people unemployed, and U * t is the counterfactual number of people unemployed, where U * 1 = U 1 .

Results
This section presents the main results of the matching function estimations, the mismatch indexes, and mismatch in unemployment.The important results of the matching function estimations are the vacancy share, or elasticity, which is identified by the coefficient a and used to compute further the mismatch indexes using Equation 2. The estimations for the aggregate matching function model in Equation 3 are presented in Table 1 assuming CRS: The matching efficiency has a value of 0.291 if computed as the exponential of the intercept.We interpret this to mean that if the numbers of people unemployed and vacancies are equal and the time dummies are set to zero, then there will be one efficient match for every four unemployed individuals in the labour market at time t.Bauer (2013), however, underlines that the interpretation depends on the model specification.When the model shown in Equation 3 is estimated but with the one-periodlagged variable V t−1 U t−1 included, the intercept remains the same.
The coefficient a for the vacancy share V t U t found from Equation 3 and referred to as matching elasticity is estimated to be 0.478.This value aligns with the previous empirical findings of Patterson et al. (2016) and Şahin et al. (2014), who estimated it to be around 0.5.The small difference between our results for a and those of previous empirical studies might suggest that changes in the number of vacancies do not lead to substantial variation in hiring.However, it is important to note that this outcome may also be affected by the choice of which specific data and model are used in the analysis.
To validate these results and ensure that the mismatch estimations are reliable, we present the trend of the mismatch index from January 2011 to January 2021 using a vacancy share or elasticity of a = 0.478, and also a = 0.345.The figure a = 0.345 is obtained by estimating the model in Equation 3 without assuming CRS.This lets us see whether the CRS condition that we applied in Table 1 affects the results for the mismatch indexes.The estimates for the vacancy and unemployment shares, which are a and b in Equation 1, are estimated separately and presented in Table 2.
Using the aggregate matching function shown above does not give a different trend to that in the results in Table 1.This suggests that the Cobb-Douglas function from Equation 1fits the data well.The sum of the coefficients for people unemployed (U = 0.411) and vacancies (V = 0.345) is approximately 1, showing that the assumption of CRS holds in the Estonian labour market during the period considered in this study.This is also supported by direct testing of whether a + b = 1.The vacancy share is 0.345, which is only 0.1 lower than the main results.Matching efficiency, which is the exponential of the intercept, has a value that is slightly higher at 2.841 but statistically insignificant, making it difficult to interpret accurately.
In conclusion, the CRS assumption holds, and the results are robust.The main results from when the model in Equation 4is estimated with random effects are outlined as follows.The mismatch indexes were estimated using the two vacancy shares or elasticities of a = 0.48 and a = 0.35. Figure 5 displays the main results, showing the trend of the mismatch index for the timespan January 2011-January 2021 at the three levels of regional, occupational, and industrial, with vacancy shares of both a = 0.48 and a = 0.35.
The mismatch index at the regional level maps specifically onto the counties in Estonia, and it exhibits a stable trend.There is a slight downward trend in 2016-2020, followed by a  sharp increase in the mismatch index in April 2020 to its maximum value of 0.062 (Table 3 in Appendix B).This increase can be attributed to the rise in unemployment, particularly in sectors such as tourism and services like restaurants, as a consequence of the Covid-19 pandemic restrictions that were applied in the country.
The trend line for occupations has a spike with the highest value for the mismatch index occurring in October 2011 7 and the lowest in February 2012.This time series exhibits some volatility, which is probably due to the seasonality of unemployment, vacancies, and hiring.There are several other spikes, particularly one in the early months of 2020 that reflects the surge in unemployment across most categories except 'skilled agricultural, forestry, and fishery workers' (ISCO 6), as shown in Figure 3.There was also a decline in vacancies for the 'services and sales workers' category (ISCO 5) during that period.
The time series for the mismatch index at the industrial level exhibits a more volatile trend than those at the previous levels, particularly before the second half of 2014. 8It peaks in October 2011 at 0.16, then hits its minimum value of 0.03 in July 2015.The sharp spike in October 2011 can be attributed to the exceptionally high number of vacancies in the 'Public administration and defence; compulsory social security' category (NACE O), that were an outcome of the population census survey conducted in 2011.
There are similarities across all levels in the results for the mismatch with the two different vacancy shares.The average mismatch at the regional level is 0.046 for α = 0.35 and 0.037 for α = 0.48.At the occupational level, the average mismatch index is 0.043 for α = 0.35 and 0.046 for α = 0.48, while at the industrial level, it is 0.052 for α = 0.35 and 0.052 for α = 0.48.These values hover around 4-5 percent, indicating that the labour market is not allocating labour resources optimally, resulting in a reduction in hiring because of regional mismatch at the county level, occupational mismatch at the ISCO 1-digit level, or industrial mismatch at the NACE 1-digit level.Table 3 in Appendix B presents the detailed results.
Since mismatch occurs when unemployed individuals and vacancies in the labour market are not aligned because of differences in skills, location, or other characteristics, a lower degree of matching efficiency could be considered an indicator of possible mismatch in the labour market.The matching efficiencies at the county level range from 0.822-1.171,with Viljandi County having the highest efficiency at 1.171, followed by Lääne County at 1.089.Valga County at 0.856 and Ida-Viru County at 0.822 exhibit the lowest matching efficiencies (Appendix B, Table 4).
The matching efficiencies for occupations range from 0.845 for ISCO 7 'craft and related trades workers' to 1.433 for ISCO 0 'armed forces occupations'.Those across industries vary between 0.816 for NACE F 'construction' and 1.301 for NACE O 'public administration and defence; compulsory social security' (Tables 5-6 in Appendix B).The results estimated using fixed effects are shown in Appendix C for comparison.However, the mismatch indexes and the matching efficiencies are close to those from the estimations using random effects.
As there are some spikes in our estimations, we additionally provide robustness analyses by excluding the time series from after 2019.We conduct a robustness analysis for the mismatch indexes for both vacancy shares a using Equation 4 for the period January 2011 -December 2019 to compute the mismatch indexes from Equation 2(Figure B1 in Appendix B), but there are no substantial differences between those mismatch indexes and the ones in Figure 5.At the regional and industrial levels, the main results and the robust mismatch indexes differ on average by −0.010 to −0.004 with both α = 0.35 and α = 0.48.This indicates that the main results have mismatch indexes that are on average 0.010 or 0.004 smaller.
The mismatch indexes do not differ significantly from the those of main results at the occupational level either.In this case, the differences between the mismatch indexes in the main results and those from the robustness analysis are positive at 0.009 for α = 0.35 and 0.005 for α = 0.48.In conclusion, comparing the main results with the results of the robustness analysis shows that the estimations do not exhibit significant differences in magnitude or dynamics across any of the regional, occupational or industrial levels analysed.
We also estimated mismatch in unemployment from Equation 5, which quantifies the contribution of mismatch to the overall level of unemployment at the regional, occupational and industrial levels.Figure 6 illustrates the results for both the actual number of people unemployed and the counterfactual unemployment of the number of people unemployed in a scenario where there is no mismatch in the labour market.The disparity between the number of individuals unemployed and the counterfactual unemployment can be interpreted as the extent of unemployment from mismatch, and indicates how much higher the number of individuals unemployed is because of mismatch.
In most periods, the counterfactual number of people unemployed remains below the actual number of people unemployed, which is to be expected since unemployment should be lower if there is no mismatch.However, the actual number of people unemployed is lower than the counterfactual number of people unemployed at the beginning of the time series, which could be a consequence of data quality issues or the selection of the starting point U * 1 for the iteration process.Towards the end of the time series, there is some overlapping of the data series, probably because of the rapid increase in the number of people unemployed at the beginning of 2020.
The actual number of people unemployed is on average higher than the counterfactual number of people unemployed at the regional, occupational and industrial levels.The effect of mismatch on unemployment averages 1559 at the regional level, 1976 at the occupational level, and 2331 at the industrial level.The contribution of mismatch in unemployment to the overall number of people unemployed is approximately 5.5% at the regional level, 6.6% at the occupational level, and 7.6% at the industrial level.

Discussion
Our results for estimating mismatch indexes building on the framework of Şahin et al. (2014) show that there is mismatch of about 4-5 per cent on average at all three of the regional or county, occupational and industrial levels observed in Estonia.The mismatch indexes at the regional level exhibit similar results to those from previous empirical studies conducted in the US (Şahin et al., 2014) and Sweden (Marthin, 2012), where the county-level mismatch index was also below 0.1.The mismatch indexes at the occupational and industrial levels, however, show lower estimates than those from previous studies (Bauer, 2013;Erken et al., 2015;Marthin, 2012;Shibata, 2013).The mismatch indexes remained overall within similar boundaries to those found for the UK in the study by Pizzinelli and Shibata (2023).Like Pizzinelli and Shibata (2023) also found for the US and the UK, mismatch increased sharply at the beginning of the Covid-19 pandemic, but only temporarily.
The results for the matching efficiencies f i indicate which labour market exhibits greater efficiency in matching and where it is lacking, in which case there is a mismatch between unemployed individuals and job vacancies.The overall range of matching efficiencies is in line with empirical studies that have investigated various labour markets (Bauer, 2013;Erken et al., 2015;Marthin, 2012;Shibata, 2013).
Our findings at the regional or county level show that Viljandi and Lääne counties in South and West Estonia had the highest levels of matching efficiency.Rapla and Pärnu counties in Central and West Estonia also had higher matching efficiencies, which is in line with the analysis presented in the review of the Estonian labour market in Section 4. Ida-Viru County in North-East Estonia had the lowest matching efficiency, probably because its unemployment rate is high and the number of vacancies is limited.This can be attributed to the economic restructuring of the region, which has seen a decline in the mining industry.
At the occupational and industrial levels, efficient allocation between vacancies and unemployed people was observed in categories that require specialized skills such as 'armed forces occupations' (ISCO 0), 'education' (NACE P), and 'human health and social work activities' (NACE Q), where both the number of individuals unemployed and the number of vacancies were relatively low.It is likely that individuals with the necessary skills can quickly find a suitable job in these sectors, as there is also a high level of demand for labour.The matching efficiency was lowest in 'construction' (NACE F) and for 'craft and related trades workers' (ISCO 7), where there was also a large number of individuals unemployed (Figures 3 and 4).Interestingly, although the level of demand for labour was high in 'information and communication' (NACE J) in Estonia, matching efficiency was not low.However, this observation may be affected by data limitations.
Our findings show that mismatch contributes on average about 5.5% to unemployment at the regional level, 6.6% at the occupational level, and 7.6% at the industrial level.That contribution seems to be in a similar range to the employment loss resulting from mismatch in the UK (Pizzinelli & Shibata, 2023).Our results indicate that the contribution of mismatch in Estonia is on average smaller than the contribution in the US (Şahin et al., 2014).It is also important to note, however, that Şahin et al. (2014) include the global economic crisis in their analysis, which we do not in ours, and that both unemployment and mismatch were higher then.
These results suggest that the mechanism for matching unemployed individuals with available vacancies in the Estonian labour market has some inefficiencies, leading to a potential loss of hiring opportunities and contributing to unemployment.However, it is important to note that just because there is a low aggregate level of mismatch, there is not necessarily a low degree of mismatch at the disaggregated level, as demonstrated in previous empirical studies (Bauer, 2013;Marthin, 2012;Şahin et al., 2014).
It should additionally be noted that there are not only transitions from unemployment to employment, but also job-to-job transitions, which Eeckhout and Lindenlaub (2019) suggest hinder the unemployed in finding a job in the recovery phase of a recession.Vacancies are not always filled by an unemployed person.Furthermore, it is important to note that the willingness of firms to list vacancies with the EUIF differs between occupations and industries, as those like construction (NACE F) or craft and related trades workers (ISCO 7) that have labour shortages probably use the option of listing vacancies more.That is why it might also be that a vacancy disappears from the market, but is not actually filled, since no suitable candidate was available at that moment.
Estonia's labour market has a low index level for employment protection legislation (EPL) and a high degree of flexibility, which may make the allocation of labour resources between unemployed individuals and job vacancies more efficient, potentially explaining the lower levels of mismatch (Flaig & Rottmann, 2013) than those found in previous studies (Bauer, 2013;Erken et al., 2015;Marthin, 2012;Shibata, 2013).However, as OECD (2021) notes, the active labour market policies (ALMPs) in Estonia could be improved to engage groups that are currently vulnerable, such as people with low skill levels and less work experience, in the labour market.Increasing the skill levels with ALMPs could be a possible way of reducing the level of mismatch.
Our study suggests there is mismatch at the regional or county level in Estonia, which is also in line with the remark by OECD (2021) about stark differences in regional labour markets.It might therefore be valuable at the regional level to consider regional policies, such as how the workforce could be differently reallocated in other regions while investment could be directed to different areas of the country and not primarily to the region where the capital Tallinn is.This would also help keep the share of the population in rural areas higher, reducing the time needed for commuting by people who work in Tallinn but do not live in that area.

Conclusions
This paper adopts the framework proposed by Şahin et al. (2014) and examines the labour market imbalances in Estonia.Our analysis of the matching process reveals that there is mismatch within the Estonian labour market across all the levels studied of regional or county, occupational, and industrial.There are similarities between the mismatches and they are relatively small in magnitude, averaging around 4-5 per cent.Furthermore, our findings indicate that mismatch contributes approximately 5-8 per cent of the overall rate of unemployment, contributing most at the industrial level and least at the regional level.
Our findings suggest that there might be efficiency gains in the Estonian labour market if a better match could be found between job-seekers and vacancies.We acknowledge that further studies are needed given that the method we apply does not answer the question of why there is mismatch in the labour market.Another dynamic to consider might be analysis of over-education or under-education and how that affects mismatch overall in the market.Research at the occupational level could study how successful the reallocation of job-seekers with lower levels of education or inexperienced jobseekers is, and how the dynamics of that change over time.Having better data in a more granular format would definitely be an important point for the next work to consider.
While a low level of matching efficiency serves as an indicator of labour market frictions, it would be beneficial to assess labour markets at a more granular level using detailed data and to conduct additional analysis to gain further insights into the dynamics of vacancies and unemployment creation.Exploring job and worker mobility, wage determination issues, and other factors would provide a clearer understanding of inefficient labour markets, allowing more effective labour market policies to be designed and formulated in future (Herz & van Rens, 2020).Our findings indicate where the inefficiencies are relevant, but this work is just a first step towards understanding the dynamics within the Estonian labour market, and explaining the mechanisms and why some frictions emerge.

Notes
1. Data on people unemployed and vacancies at the level of occupations from the ISCO classification and industries from the NACE classification were provided by EUIF upon request.Data on unemployed people and vacancies at the level of counties and data on hiring were downloaded from the website of the EUIF.2. International Standard Classification of Occupations, Table 1  ers, undifferentiated goods and services producing activities of households for own use' (NACE T) are left out from the estimation of the model and the calculation of the mismatch index at the industrial level to give more accurate results. 5.The spike in the number of vacancies in the category of clerical support workers (ISCO 4) is probably a result of the population census survey in 2011.6.The data provided by the EUIF are not seasonally adjusted, and in the empirical analysis we introduce dummy variables to remove the seasonal factor.
7. The spike in the mismatch index in October 2011 is caused by a one-off extraordinarily high number of vacancies appearing in the category of clerical support workers (ISCO 4), which is most probably an outcome of the population census survey 2011.8.The EUIF explains that the number of people unemployed whose previous employer's NACE was known increased rapidly from July 2014 because of a change in the regulations that required all employers to register their employees in the employment register (Töötamise register (TÖR)).

Figure 1 .
Figure 1.Beveridge curve for Estonia, 2011Q1-2020Q4.Notes: Time series January 2011 -December 2020, quarterly data.Unemployment rate and job vacancy rate in %, seasonally adjusted.Triangles with a year number present the data for the first quarter.Source: Eurostat (2023): Job vacancy statistics by NACE Rev. 2 activityquarterly data; OECD (2021): Short-Term Labour Market Statistics, Harmonized Unemployment Rate.Composed by authors.

Figure 3 .
Figure 3. Ratio of vacancies to unemployment in Estonia across occupational levels.Notes: Based on the ISCO classification.The different trend for the occupation 'armed forces' (ISCO 0) arises from the number of observations.Labour market tightness u, or the ratio of vacancies to unemployment.Source: EUIF, January 2011 -January 2021 composed by authors.

Figure 4 .
Figure 4. Ratio of vacancies to unemployment in Estonia across industrial levels.Notes: Based on the NACE classification.Labour market tightness θ, or the ratio of vacancies to unemployment.The EUIF explains that in the course of 2014 the number of people unemployed whose previous employer's NACE was known started to increase following a change in the regulation that meant all employers had to register their employees in the employment register (Töötamise register (TÖR)).Therefore, for time series comparison purposes, the figure excludes data from before October 2014.Source: EUIF, October 2014 -January 2021, composed by authors.

Figure A5 .
Figure A5.Beveridge curves for Latvia (left panel) and Lithuania (right panel), 2011Q1-2020Q4.Notes: Time series January 2011 -December 2020, quarterly data.Unemployment rate and job vacancy rate in %, seasonally adjusted.Triangles with years represent data for the first quarter.Source: Eurostat (2023): Job vacancy statistics by NACE Rev. 2 activityquarterly data; OECD (2021): Short-Term Labour Market Statistics, Harmonized Unemployment Rate.Composed by authors.

Figure C1 .
Figure C1.Mismatch indexes for Estonia at the regional, occupational and industrial levels, using a fixed effects model.Notes: For different vacancy share α values, period 01.2011-01.2021.Source: EUIF, authors' calculations using the fixed effects model specification.

Table 1 .
Results of the aggregate matching function estimations assuming CRS.

Table 2 .
Results of the aggregate matching function estimations without assuming CRS.

Table B5 .
Matching efficiencies across occupations in Estonia.

Table B6 .
Matching efficiencies across industries in Estonia.