A simultaneous approach for cross-sectional dependence comparing unemployment rates for men and women

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A simultaneous approach for cross-sectional dependence comparing

unemployment rates for men and women

Abstract

This study examines the effect of serial dynamics, common factors and spatial dependence. The data used is acquired from 21 European countries for the harmonized unemployment rates for men and women from the OECD (2019) and intra export data acquired from the World Bank (2019). A simultaneous approach model accounting for serial dynamics, spatial dependence and common factors is applied. Moreover, a trade-flow W-matrix is incorporated to explain the difference in unemployment rate. Cross-sectional dependence for both men and women is tested for. Empirical evidence of serial dynamics, common factors and spatial dependence is found for both men and women. Moreover, men are relatively more affected by structural shocks rather than women. Furthermore, women are more affected than men by serial dynamics effects. Negative spillover effects are found for both men and women when a country is trading. These negative effects affect women less than men.

Keywords: Common factors, spatial dependence, serial dynamics, Okun’s Law, harmonized

unemployment rate, trade-flow matrix, cross-sectional dependence, simultaneous approach

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I. Introduction

There has been a progressive rise in unemployment in the European Union (EU) since the 1970s (Martin, 1997). This rise has captivated substantial attention and initiated various debates from economists, and numerous competing explanations have been advanced. Initially, this

phenomenon was analyzed in a national and aggregate EU dimensional scope. For example, Krugman (1993, 1994), argues that Europe (compared to the United States) suffers from various economic, social and institutional rigidities which prevent its labor markets from adjusting to rapidly changing competitive and technological conditions. Others suggest that the higher unemployment in Europe is caused by increases in aggregate wage pressure that emerged after the oil shocks of the early 1970s (Jackman, 1995; Nickell and Bell, 1996; Jackman, Manacorda and Petrongolo, 1999). Another potential explanation is that Europe’s high unemployment has mainly been the result of the shift from full-employment demand management to the tight monetary and fiscal policies followed in many of the member states of the EU since the early 1980s. More recently, there has been a growing interest in the regional scope of unemployment across the EU (Martin, 1997). These studies argue that the regional disparities in EU is relatively high (compared to, for example, the United States). In addition, Bertola (2000) argues that inflexible wages and low labor mobility are the causes of the large and persistent unemployment differentials across European regions. Research shows that personally experiencing

unemployment considerably reduces life satisfaction (Pittau, Zelli and Gelman, 2010).

Furthermore, it appears that unemployment not only reduces life satisfaction of individuals being unemployed but also those who are employed. Potential explanations are the perception of an increasing risk of losing a job, of being trapped in the job one has or to aversion to social inequality.

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3 be introduced, along with some descriptive graphs and tables. Section IV includes the

econometric model itself and the methodology. Furthermore, the functional form is explained, and the assumptions will be presented. Section V consists of the results, which are obtained from the outcomes of the empirical research. Moreover, the outcomes will then be translated to

consequences for the hypotheses. Section VI refers to discussions regarding the topic and implications. Section VII concludes the research and summarizes the findings.

II. Literature review

Different attempts have been made in trying to quantify regional unemployment. Studies on regional unemployment rate on its own exists out of different scopes. The studies can be sub-divided into three topics. Firstly, studies on serial dynamic effect suggest that the regional

unemployment rates tend to be strongly correlated over time (Blanchard and Katz, 1992; Hyclak, 1996). Next, studies on cyclical sensitivity (around 1960s) have focused on common factors, which is also known in the literature as ‘strong’ cross-sectional dependence (Chudik et al., 2011). These studies propose that regional unemployment rates are parallel to the national unemployment rate (Thirlwall, 1966; Brechling, 1967; Pesaran, 2006). Lastly, spatial econometric studies focusing on spatial dependence, also known as ‘weak’ cross-sectional dependence, believe that regional unemployment rates are correlated across space due to the interconnections between regions (Burridge and Gordon, 1981; Molho, 1995; Anselin, 2001; Overman and Puga, 2002; Patacchini and Zenou, 2007; Chudik et al., 2011). The spatial econometric approach assumes that the structure of cross-sectional correlation is related to location and distance among units. This structure is defined according to a pre-specified metric given by a connection or spatial matrix that characterizes the pattern of spatial dependence according to pre-specified rules. Hence, cross-sectional correlation is represented via a spatial process, which relates each unit to its ajoints (Chudik and Pesaran, 2013). Ignoring the concept of spatial dependence when testing hypothesis based on standard panel data estimators can lead to misleading or biased inferences (Baltagi and Pirotte, 2010).

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4 condition. This condition facilitates the derivation of the asymptotic properties. This kind of transformation is advantageous for the derivation of asymptotic properties. However, it loses the cross-sectional information in its process (Basak and Das, 2018). Literature focusing on the distinction between common factors and spatial dependence highlights a challenge. Specifically, there are two potential causes for the observed spatial correlation. First, the observed correlation across space can be a result of shared factors where outcomes change as these factors change. Second, the observed correlation across space could also be the resulting spillover effects induced by local interactions between regions (Vega and Elhorst, 2016). Therefore, using a methodology accounting for both forms of cross-sectional dependence is important (Kuersteiner and Prucha, 2018; Bailey and Pesaran, 2016). The study by Vega and Elhorst (2016) that

addresses serial dynamics, spatial dependence and common factors came to a crucial conclusion. They stated that approaches that do not simultaneously account for or ignore these three

phenomena may lead to a biased inference. Therefore, it is important to include all three issues (serial dynamics, spatial dependence and common factors) and account for them simultaneously when testing for regional unemployment rates.

Vega and Elhorst (2016) were the first to apply serial dynamics, spatial dependence and common factors simultaneously in relation to the regional unemployment rates. These pioneers applied their model to the Netherlands. This study builds on and extends the study of Vega and Elhorst (2016) by expanding the sample with data on European countries. Specifically, this study uses a sample of 21 European countries based on quarterly data acquired from 2003 up until 2018. Allegedly, research on the unemployment gap in OECD countries demonstrate that

whereas in some countries the gender gap in unemployment rates is small (mainly non-European countries such as United States, Australia, Canada and New Zealand), this gap is still very large in other OECD (primarily European) countries, especially in Mediterranean countries such as Spain, Greece, Italy and France (Azmat, Güell, and Manning, 2006). In some of the

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5 dependence. Taking the equal importance into consideration, this paper will use the

terminologies common factors (strong cross-sectional dependence) and spatial dependence (weak cross-sectional dependence) throughout the paper.

To conclude, taking into account the relevance of measuring the regional unemployment rates including serial dynamics, spatial dependence and common factors simultaneously as well as the differences in gender in context of unemployment, this paper aims to create a model accounting for all these factors. Furthermore, this model will be tested on 21 European countries based on quarterly data acquired from 2003 up until 2018. Linking the stylized facts together with our macroeconomic indicator, the total unemployment rate, unemployment rate for men and for women, it is expected that the unemployment rate per country is correlated with that of Europe for men and women. Furthermore, it is expected that the unemployment rate is correlated over time. Lastly, it is suspected that the unemployment rate of both men and women is

correlated across space. Disparities between the results of men and women is suspected due to biases towards the female gender.

III. Data Description

For this research, data from OECD has been acquired. The data consists of quarterly

unemployment rates for 21 European countries over a time period of 2003 until 2018 (N = 21, T = 64). The countries that the data is acquired from of are given in Figure 1. The data has been divided into three specifications, namely total unemployment rates in the respective countries, the unemployment rate of men and the unemployment rate of women. The unemployment rates are calculated by dividing by the total, men and women labor force, respectively. Important to mention is that this paper is dealing with multiple countries, in contrast to the research of Halleck-Vega and Elhorst (2016), which focuses on unemployment rates within one country. Therefore, the data and the resulting findings of this research will not be comparable to the findings of Halleck-Vega and Elhorst (2016). Utilizing different countries as data comes with a challenge; the existence of different national definitions on how to calculate the unemployment rate. These different definitions lead to incomparable international results. This potential

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6 find work (OECD, 2019). Using this definition, the data is more accessible for international comparing. This data range covers data from both before and after the economic crisis and is hence up most intriguing in addressing whether cross-sectional dependence is valid and what effect it has on those countries.

Figure 1: Map of the 21 European countries highlighted.

Table 1 reports the correlation coefficients of the total harmonized unemployment rates for all the observations up until sixteen years apart. The correlation coefficients seem to be reasonably large and to diminish over time. These results will be further addressed in section IV,

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7 dynamics coefficient effect than that of men. These traits of high correlations have been deemed for by imposing serial dynamics effects.

Table 1: Correlation Matrix over time for total harmonized unemployment rates

2003q1 2005q1 2007q1 2008q1 2009q1 2010q1 2011q1 2013q1 2015q1 2017q1 2018q4 2003q1 1 2005q1 0.972695 1 2007q1 0.798523 0.852553 1 2008q1 0.653643 0.667434 0.899633 1 2009q1 0.439936 0.338246 0.358101 0.591199 1 2010q1 0.479043 0.374946 0.242797 0.401404 0.927822 1 2011q1 0.415031 0.310376 0.299328 0.510877 0.921996 0.912599 1 2013q1 0.301855 0.230848 0.364157 0.575059 0.664816 0.557852 0.826285 1 2015q1 0.270698 0.217126 0.366408 0.564395 0.550405 0.421124 0.702113 0.965159 1 2017q1 0.213562 0.158096 0.294231 0.48399 0.486873 0.367419 0.62401 0.897427 0.972917 1 2018q4 0.16962 0.108864 0.254321 0.453389 0.465435 0.335757 0.575813 0.848889 0.936453 0.983882 1

Figure 2 shows the total harmonized unemployment rates of the 21 European countries alongside the total European harmonized unemployment rates. It shows that most of the individual

countries’ total harmonized unemployment rates are in line with that of Europe. There are, however, a few outliers which are worth mentioning. On an important note, it is worth highlighting that the horizontal axis consists of the numbers 1 until 64; the 64 quarters from which the data was acquired. In most countries there has been a steady decline of the total harmonized unemployment rate dating from the first quarter of 2003 until the economic recession, so the second or third quarter of 2008. The exceptions are Austria, Belgium, Great Britain, Ireland, Hungary, the Netherlands, Portugal and Sweden. These countries have been rather steady from the first quarter of 2003 until the economic recession.

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8 a higher total harmonized unemployment rate and that were steady are Austria, Belgium,

Germany, the Netherlands and Poland. These countries might be interconnected as such that they would impact the unemployment rate positively (e.g. trade). This could be seen as evidence of spatial dependence. Countries that got a substantial higher increase in their total harmonized unemployment rate relative to other European countries were Estonia, Latvia, Ireland, Portugal, Spain and Greece. The rest of the countries suffered from an increase in their total harmonized unemployment rate following the economic recession, although not as much as the formerly mentioned countries.

Between the time periods 30 and 40, the second quarter of 2010 and the fourth quarter of 2012, most countries experienced a steady total harmonized unemployment rate except for the countries that experienced a proportional big increase as a result of the recession, namely Estonia, Latvia, Ireland, Spain and Greece. Surprisingly, Estonia and Latvia experienced a decrease in their total harmonized unemployment rate, whereas the latter three confronted a further increase in their total harmonized unemployment rate. This situation of Greece might possibly be explained by the Greek government debt crisis which occurred as an aftermath of the economic crisis in 2008. Greece required bailout loans in 2010, 2012 and 2015 and is the first ever developed European country not able to make an International Monetary Fund loan repayment (CTV News, 2015).

After the time period 40, the fourth quarter of 2012, most countries seem to experience a decrease in their total harmonized unemployment level. During this period, the countries that formerly experienced a substantial higher increase, now experience a substantial faster decrease relative to the others. Three countries that have adopted a rather steady total harmonized

unemployment rate throughout time are Austria, Finland and France. In general, most countries seem to be paralleling the European total harmonized unemployment rate. However, Germany has been in a steady decrease ever since the first quarter of 2003. Furthermore, the countries that experienced a substantial increase suffered more from the economic recession but also benefitted more from the restoration of the crisis. Hence, these countries could still be perceived as

following the European total harmonized unemployment rate.

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9 rate for women than for men. This is in line with the study performed by Azmat, Güell, and Manning (2006), stating that the Mediterranean countries still suffer from a gender

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11 Different tests are computed to test properly for both common factors and spatial

autocorrelation or in other words, to account for cross-sectional dependence, the cross-sectional dependence and local cross-sectional dependence (Pesaran, 2004, 2015). The former accounts for common factors whereas the latter accounts for spatial autocorrelation. However, the local CD test can only be implemented based on a pre-specified matrix 𝑊describing the spatial

composition of the 21 European countries in the data sample. The elements of this 𝑁 𝑥 𝑁 matrix are denoted by 𝑤𝑟𝑗 (𝑟 = 1, … , 𝑁; 𝑗 = 1, … , 𝑁). In this research a Trade-Flow matrix is adopted, where the latest available data concerning trade between countries are set and distributed normally.

Intra-exports data of 2015 from the World Bank is acquired, i.e. the exports from and to Germany. Intra-export data of all the 21 European countries is found. Exports are a well-known indicator of gross domestic product and thus harmonized unemployment rate (Sheehey, 1992). This study hypothesizes that the trade-flow matrix will explain the cross-sectional dependence more accurately, as it is part of explaining the gross domestic product in a country and, thus, might affect the unemployment rate (e.g Okun’s Law).

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12 in the harmonized unemployment rate of 21 European countries. To test whether the origin of these cross-sectional dependence is weak or strong, so the existence of spatial dependence and/or common factors, the α-statistic is used. The range of this value is between 0 and 1. An α-value of 0 < α <1

2 implies weak cross-sectional dependence, and thus the existence of spatial dependence. An α-value of 1

2< α < 1 means moderate to strong cross-sectional dependence and implies that more research is required. An α-value of 1 indicates strong cross-sectional dependence, and thus the existence of common factors. The α-value found in this study is close to 1 in all three specifications. These findings lead to the conclusion that there is evidence found in favor of at least moderate to strong cross-sectional dependence. Whether there is evidence of spatial dependence (and serial dynamics) will be investigated later.

IV. Methodology

An interesting question is how to make up for cross-sectional dependence if a likely origin of interconnection between countries consists of spatial autocorrelation and common factors. As both concepts are potentially present in the applied settings of this study (see section III), these topics will get increasing consideration in this paper. Literature imposes different approaches to adress this problem. Accordingly, different methods will be used in this study. Starting off, the two-stage model will be displayed. Next, the unified simultaneous model will be used. This will be done to highlight the potential similarities or differences using different models.

In the two-stage approach proposed by Bailey et al. (2016), the first stage concerns de-factoring of the harmonized unemployment rates, which is seen as an origin of the common factors. These researchers came up with two approaches in modelling common factors. The first one is by using the cross-sectional averages and the second one is by using a principal

components approach. The former is applied in this paper as it is more ingrained in the literature on cyclical sensitivity. This model yields the following three functions, which is the basic form of the Brechling-Thirlwall (1966, 1967) type cyclical sensitivity models:

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13 where µ_𝑐𝑡denotes the harmonized unemployment rate of every country (𝑐 = 1, … , 𝑁 at a

particular point in time 𝑡 = 1, … , 𝑇). µ𝑁𝑡 denotes the European harmonized unemployment rate at time 𝑡. 𝑒_𝑐𝑡 denotes an independently and identically distributed error term for 𝑐 and 𝑡 with zero mean and constant variance (𝜎_𝑒2_{). Furthermore, every country 𝑐 has its own intercept and its own} coefficient. As previously mentioned, since some countries suffer differently from structural shocks than others, heterogeneity is especially to be wary of. This approach has a lot of alignment with Pesaran (2006) since they both make use of the cross-unit averages of the variables. Nonetheless, a few minor differences are worth mentioning. First, whereas Pesaran (2006) uses cross-sectional averages at each point in time, the cyclical sensitivity models suggest using the European harmonized unemployment rate at time 𝑡. Since the size of the labor force is different amongst countries, these two are close to each other but not identical. Second, Pesaran (2006) also takes all the averages of the K-explanatory variables into account. Nevertheless, following the research of Bailey et al. (2016), which does not contain any explanatory variables, neither does this study. Hence, when comparing cross-sectional averages, only the dependent variable is left. Last, when transitioning from a two-stage model to a unified simultaneous model, the cross-sectional averages at time 𝑡 but also at 𝑡 − 1 are incorporated. The residuals of Equation (1) result in the following:

ê_ct = µ_ct – γ̂_0c – γ̂_1cµ_Nt (2)

similarly for the specifications men and women

By taking the residuals, the common European effects result, in which the dependent variable emerges and can be adopted in the second stage as a net accumulation of fluctuations. As a matter of fact, Brechling (1967) explained the residuals as the regional cyclical segment. Though, similar to Bailey et al. (2016), in the second stage, not only common factors have to be accounted for, but spatial dependence as well. That is why the de-factored equation will be continued to be modelled. The dynamic spatial panel model will be adopted to incorporate the harmonized unemployment rate all together, of men and women within the countries. This results in the following model for the three specifications, respectively.

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14 similarly for the specifications men and women

where 𝑒̂_𝑐𝑡 ix defined similarly as in Equation (2). 𝑤_𝑐𝑗 is the trade-flow matrix 𝑊. As countries cannot trade with themselves, the diagonal segments of this matrix are equal to zero. 𝛼_0,𝛼₁, 𝛼₂ and 𝛼3 are the parameters associated with the constant, lagged dependent variable, the lagged dependent variable in space, and the lagged dependent variable both in space and time, respectively. 𝛼₁is incorporated to address that the harmonized unemployment rates of the countries are strongly correlated over time. 𝛼₂is assigned to be the coefficient of the spatial autoregression, and 𝛼3 the lagged coefficient of the spatial autoregression. 𝜀𝑐𝑡 is denoted as the independently and identically distributed error term for 𝑐 and 𝑡 with zero mean and constant variance 𝜎_𝜀2_{. This extended model includes a fixed effect of the countries, denoted as (𝜎}

𝑐). Another addition is the fixed effect of the time period, denoted as (𝜆𝑡). The fixed effect parameters are denoted with parentheses, because they are optional. In case they are included, the constant lagged term 𝛼0 will not be incorporated to avoid a perfect multicollinearity.

There are, however, some essential differences between the model from Equation (3) and a basic dynamic spatial panel data model of harmonized unemployment rate of countries

accounting for spatial dependence. The latter can be seen to be the following:

µct = α0+ α1µct−1+ α2∑ (wcjµjt) N j=1 + α3∑ (wcjµjt−1) N j=1 + (σc) + (λt) + εct (4)

where all aspects are equivalently denoted as in Equation (3), though 𝑒̂_𝑐𝑡 is replaced by

respectively µ𝑐𝑡. Another critical issue is whether to include (𝜎𝑐) and (𝜆𝑡), so whether to include country-specific and/or time-period fixed effects. Lee and Yu (2010) argue that spatial

dependence may be overestimated if time-period fixed effects have been left out. Contradictory, both the country-specific fixed effects and time-period fixed effects may be insignificant in Equation (3). This can be explained by looking at Equation (4). The coefficients are

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15 the same outcome as (𝜎_𝑐), the country-specific fixed effects. For that reason, the country-specific fixed effects may be insignificant in Equation (3). Moving on to the explanation for why, (𝜆𝑡), the time-period fixed effects may be insignificant. As the European harmonized unemployment rate over time reflects the overall business cycle, it might be an adequate replacement for time dummies. Additionally, the two-stage model is more flexible, so adding time dummies has the effect that all variables are demeaned.

In contrary to the models mentioned, Halleck-Vega and Elhorst (2016) propose a methodology accounting simultaneously for both spatial dependence and common factors. This can be done by substituting Equation (2) into Equation (3) with 𝑒𝑐𝑡 = 𝑒̂𝑐𝑡. However, as

mentioned (𝜎_𝑐) and (𝜆_𝑡), the country specific fixed effects and the time-period fixed effects, are expected to be insignificant. Hence, these two variables are not included. The following are the results of such mutation for the three specifications:

(µct− γ0c− γ1cµNt) = α0 + α1(µct−1− γ0c− γ1cµNt−1) + α2∑ (wcj(µjt− γ0j − N j=1 γ_1rµ_Nt) + α₃∑ (w_cj(µ_jt−1− γ_0j− γ_1rµ_Nt−1) N j=1 + ε_ct (5)

After rearranging terms, the following equation results:

µct = α0+ γ0c− α1γ0r− α2∑ (wcjγ0j) N j=1 − α3∑ (wcjγ0j) N j=1 + α1µct−1+ α₂∑ (w_cjµ_jt) N j=1 + α₃∑ (w_cjµ_jt−1) N j=1 + γ_1r(1 − α2)µNt+ γ1r(−α1− α3)µNt−1+ εct (6) similarly for the specifications men and women

where the first aggregate term is a heterogeneous constant. The other terms depict the country-specific regional growth rate at time t. This growth rate relies on its serially lagged value, spatially lagged value, and its lagged value for both space and time for the three specifications. Furthermore, the second and third to last terms depict the country-specific harmonized

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16 and 𝑡 − 1 for the three specifications. The last term, 𝜀_𝑐𝑡,is denoted as the independently and identically distributed error term for 𝑐 and 𝑡 with zero mean and constant variance 𝜎_𝜀2. Simplifying Equation (6) leads to the following:

µ𝑐𝑡 = 𝛽1µ𝑐𝑡−1+ 𝛽2∑ (𝑤𝑐𝑗µ𝑗𝑡) 𝑁 𝑗=1 + 𝛽3∑ (𝑤𝑐𝑗µ𝑗𝑡−1) 𝑁 𝑗=1 + 𝛽4µ𝑁𝑡+ 𝛽5µ𝑁𝑡−1+ ή𝑐+ 𝜀𝑐𝑡 (7)

where 𝛽1 = 𝛼1, 𝛽2 = 𝛼2, 𝛽3 = 𝛼3, 𝛽4 = 𝛾1𝑟(1 − 𝛼2), 𝛽5 = 𝛾1𝑟(−𝛼1− 𝛼3), 𝑎𝑛𝑑 ή𝑐 = 𝛼0+ 𝛾_0𝑐− 𝛼₁𝛾_0𝑟− 𝛼₂∑ (𝑤_𝑐𝑗𝛾_0𝑗) 𝑁 𝑗=1 −𝛼₃∑ (𝑤_𝑐𝑗𝛾_0𝑗) 𝑁 𝑗=1

. In Equation (7) the first three composite

terms are the same for all countries. However, the subsequent two terms are different for various countries. By not indulging the constraint 𝛽_4𝑐/(1 − 𝛼₂) = 𝛽_5𝑐/(−𝛼₁− 𝛼₃) for 𝑟 = 1, … , 𝑁 and related to the fact that µ_𝑐𝑡 and µ_𝑐𝑡−1 share the same coefficients, the simultaneous model

develops into a more persuasive model than the two-stage model presented earlier. The fourth and fifth composite term accounts for country-specific fixed effects. Therefore, the intercepts are different per country. As mentioned earlier, time-period fixed effects are insignificant as perfect multicollinearity results otherwise.

To conclude, it must be brought to attention that the mentioned models are special cases. Equation (4), representing the spatial panel data model without common factors can be obtained by incorporating the constraints 𝛾_1𝑐= 0 for 𝑟 = 1, … , 𝑁 in Equation (6), which is identical to 𝛽4𝑐 = 𝛽5𝑐 in Equation (7). However, the latter is only true if Equation (4) does not include any time-period fixed effects. The reason for this has been stressed earlier in this section. Next, Equation (1), representing the cyclical sensitivity model (or the common factors model) without spatial dependence, can be achieved by incorporating the constraints 𝛼₁ = 𝛼₂ = 𝛼₃ = 0 in Equation (6) or 𝛽₁ = 𝛽₂ = 𝛽₃ = 0 in Equation (7). Lastly, the two stage models suggested by Bailey et al. (2016) can be arrived at by enforcing the constraint 𝛽4𝑐/(1 − 𝛼2) = 𝛽5𝑐/(−𝛼1− 𝛼₃) for 𝑟 = 1, … , 𝑁 in Equation (7).

However, Halleck-Vega and Elhorst (2016) heretofore researched whether to use the two-stage model or the simultaneous approach when dealing with serial dynamics, spatial

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17 interdependent and could give biased results. Consequently, this study will use the simultaneous approach model and accordingly, Equation (7) for the estimations moving forward.

V. Results

As mentioned in section IV, the simultaneous approach proposed by Halleck-Vega and Elhorst (2016) is used in this paper. Halleck-Vega and Elhorst (2016) state that the two-staged model should be avoided for as there might be interdependency between spatial dependence, serial dynamics and common factors, which will result in biased outcomes. Thus, the simultaneous approach will be implemented in this research. Table 2, C1 and C2 show the estimation of Equation (7) for the three specifications, total, men and women, respectively. Furthermore, it must be highlighted that the country-specific fixed effects are included to let the intercept to be different for different regions. However, the time-period fixed effects are not included as they are already accounted for when looking at common factors and would otherwise result in perfect multicollinearity with the European harmonized unemployment rates.

First, Table 2, the table for the first specification, which represents the total harmonized unemployment rates is presented. The serial dynamics coefficient, 𝛼1, is 0.9665 and is highly statistically significant. This means that evidence is found for serial dynamics while comparing the total European harmonized unemployment rates with the trade-flow matrix. In short, the total harmonized unemployment rates of individual countries at 𝑡 point in time are affected by the total harmonized unemployment rates at 𝑡 − 1 point in time.

Continuing with the coefficients of α2, the spatial dependence based on ∑ (𝑤_𝑐𝑗µ_𝑗𝑡) 𝑁

𝑗=1

.

There is evidence of a highly significant spatial dependence based on ∑ (𝑤𝑐𝑗µ𝑗𝑡) 𝑁

𝑗=1

with a

coefficient of 0.2433. Another spatial dependence coefficient, 𝛼3, is based on the assumption

∑ (𝑤_𝑐𝑗µ_𝑗𝑡−1) 𝑁

𝑗=1

. The corresponding coefficient is -0.1055, and there is evidence of highly

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18 and vice versa. Hence, trading with another country will influence the trading country’s

unemployment rate positively.

Moving forward with the common factor coefficient 𝛽₄based on µ_𝑁𝑡.It can be shown that all countries, except for Germany, are statistically significant on a 5% level. The higher the common factor coefficient, the more cyclically sensitive a country is. In other words, the higher the common factor coefficient, the larger the impact is on a specific country when the total European harmonized unemployment rate changes. In Table 2, it is observed that Estonia, followed by Latvia, has, by far, the largest coefficient and is, thus, more cyclically sensitive than any other country. Furthermore, it can be shown that Austria, the Netherlands, France, Finland and Italy have relatively low coefficients and, thus, are the least cyclically sensitive European countries.

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Table 2: Simultaneous approach to serial dynamics, spatial dependence and common factors including a pre specified Trade-Flow W-matrix, specification one (total)

Common factors 𝜷𝟒𝒄 Error term 𝜷𝟒𝒄 𝜷𝟓𝒄 Error term 𝜷𝟓𝒄

Austria 0.2085 (0.1016) -0.2173 (0.1172) Belgium 0.3993 (0.1524) -0.4211 (0.1847) Czech Republic 0.7017 (0.1349) -0.7217 (0.1455) Germany 0.1797 (0.1634) -0.2858 (0.2735) Denmark 0.5977 (0.1356) -0.6409 (0.1507) Spain 1.8307 (0.1602) -1.8605 (0.1722) Estonia 2.3612 (0.1536) -2.5765 (0.1630) Finland 0.3055 (0.1123) -0.3173 (0.1376) France 0.2951 (0.1291) -0.3494 (0.1804) Great Britain 0.3604 (0.1332) -0.4995 (0.1763) Greece 0.9102 (0.1677) -0.6911 (0.2053) Hungary 0.6595 (0.1415) -0.759 (0.1551) Ireland 1.3729 (0.1520) -1.5303 (0.1645) Italy 0.3067 (0.1334) -0.3091 (0.1801) Latvia 2.3117 (0.1523) -2.5557 (0.1618) The Netherlands 0.2384 (0.1130) -0.2022 (0.1320) Poland 0.8041 (0.1380) -0.7393 (0.1487) Portugal 0.7175 (0.1512) -0.8134 (0.2051) Slovakia 1.0794 (0.1433) -1.0356 (0.1528) Slovenia 0.5957 (0.1500) -0.5343 (0.1665) Sweden 0.4795 (0.1428) -0.5563 (0.1686)

Serial dynamics Error term

𝛼1 0.9665 (0.0049)

Spatial Dependence Error term

𝛼2 0.2433 (0.0774)

𝛼3 -0.1055 (0.0308)

R-squared 0.9983

Log-likelihood -549.218

Next, the results for men and women is evaluated in the same fashion as the total harmonized unemployment rates. Following the further research with a comparison of the evaluated results of the harmonized unemployment rates for men and women.

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20 including serial dynamics, spatial autocorrelation and common factors with a pre-specified trade flow w-matrix for both men and women, respectively. Table C1, the table for the second

specification, rep the harmonized unemployment rates for men. The serial dynamics coefficient, 𝛼₁, is 0.9737 and is statistically highly significant. This means that evidence is found for serial dynamics while comparing the total European harmonized unemployment rates with the trade-flow matrix. In short, the harmonized unemployment rates of individual countries at 𝑡 point in time are affected by the total harmonized unemployment rates at 𝑡 − 1 point in time.

Continuing with the coefficients of 𝛼₂, the spatial dependence based on

∑ (𝑤𝑐𝑗µ𝑚𝑒𝑛𝑗𝑡) 𝑁

𝑗=1

. There is evidence of highly significant spatial dependence based on

∑ (𝑤𝑐𝑗µ𝑚𝑒𝑛𝑗𝑡) 𝑁

𝑗=1

with a coefficient of -0.2188. Another spatial dependence coefficient, 𝛼3, is

based on the assumption ∑ (𝑤𝑐𝑗µ𝑚𝑒𝑛𝑗𝑡−1) 𝑁

𝑗=1

. The corresponding coefficient is 0.349 and is

statistically highly significant. Combining the spatial dependence coefficients 𝛼2 and 𝛼3 results in a coefficient of 0.1222. This coefficient is lower than that of the total harmonized

unemployment rate. A higher coefficient for the specification for women is expected. Moving forward with the common factor coefficient 𝛽₄,based on µ_{𝑚𝑒𝑛𝑁𝑡}.It can be shown that all countries are statistically significant on a 1% level. In Table C1, it is observed that Sweden and Slovakia have by far the largest coefficient and is, thus, more cyclically sensitive than any other country. Furthermore, it can be shown that Greece, Hungary, Spain and Austria have relatively low coefficients and, thus, are the least cyclically sensitive European countries for the second specification.

However, all the common factor coefficients 𝛽₅ based on µ_{𝑚𝑒𝑛𝑁𝑡−1} are statistically highly significant. Reiteratively, due to the coefficients having higher error terms, the 𝛽₄ coefficients are validated and the coefficients of 𝛽5 are invalidated.

Lastly, the results for the third specification in Table C2, the harmonized unemployment rates for women, are examined. The serial dynamics coefficient, 𝛼₁, is 0.994 and is, in

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21 Proceeding with the coefficients of 𝛼₂, the spatial dependence based on

∑ (𝑤𝑐𝑗µ𝑤𝑜𝑚𝑒𝑛𝑗𝑡) 𝑁

𝑗=1

. There is evidence of highly significant spatial dependence based on

∑ (𝑤𝑐𝑗µ𝑤𝑜𝑚𝑒𝑛𝑗𝑡) 𝑁

𝑗=1

with a coefficient of -0.2134. Another spatial dependence coefficient, 𝛼3,

is based on the assumption ∑ (𝑤_𝑐𝑗µ_{𝑤𝑜𝑚𝑒𝑛𝑗𝑡−1}) 𝑁

𝑗=1

. The corresponding coefficient is 0.4351 and

is statistically highly significance. Combining the spatial dependence coefficients α2 and α3 results in a coefficient of 0.2217. This coefficient is larger than that of the second specification.

Similar to the second specification, the common factor coefficient 𝛽4 based on µ𝑤𝑜𝑚𝑒𝑛𝑁𝑡, is statistically highly significant in all countries. In Table C2, it is shown that Sweden, followed by Slovakia, has by far the largest coefficient and, hence, more cyclically sensitive than any other country for the third specification. Also, it can be seen that Denmark, Spain and Portugal have relatively low coefficients and, thus, are the least cyclically sensitive European countries for the third specification. Following the same reasoning as in the first and second specification, the coefficients based on 𝛽₅ are disregarded.

VI. Discussion

This study made a first attempt in trying to create a model to quantify the regional

unemployment rate that is applicable to different countries and has tested this on a sample of 21 European countries. When comparing the second and third specification with each other, a serial dynamics effect of 0.9737 for men and 0.994 for women are found. It can be said with

confidence that evidence of the harmonized unemployment rates of individual countries at 𝑡 point in time are affected by the harmonized unemployment rates at 𝑡 − 1 point in time is found. Although, the third specification seem to be slightly more affected by that statement. It is

expected that this is due to the fact that generally people tend to favor hiring males over females (Ridgeway, 2001). As a result, the unemployment rate for men decreases relatively more

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22 of men.

The spatial autocorrelation coefficient is 0.1222 in the second specification and 0.2217 in the third specification. In words, when country A trades with country B, women are affected more negatively with respect to unemployment rates. This is odd, as you might expect a decrease in unemployment following a trade flow towards another country. However, one might argue that trading with a country increase efficiency on firm productivity level. This, in change, leads to reshuffling of resources from less to more efficient producers (Pavcnik, 2002). Furthermore, employment was reallocated towards more technological advanced sectors, and less

technological sectors got taken over by i.e. machines (Bloom, Draca and Van Reenen, 2016). The difference, however, in negative spillover effects between women and men can be assigned to the fact that men over women tend to be hired, especially in more technological advanced sectors (Ridgeway, 2001). Hence, the unemployment drops more rapidly in the third

specification over the second as a result of the negative spillover effects concerning trade. Lastly, when estimating common factors for both specifications, only the coefficients of 𝛽₄are included, as these are more accurate and relevant when comparing the error terms of 𝛽₄ and 𝛽5. It is apparent that the values for the second specification, men, are substantially larger than those of the third specification, women. To give the aforementioned examples: the two countries with the largest coefficients of the second specification, Sweden and Slovakia, estimate common factor coefficients of 3.4858 and 3.3653, respectively. The two countries with the largest coefficients of the third specification, Sweden and Slovakia as well, estimate coefficients of 2.6293 and 2.1244. Furthermore, the two smallest coefficients are 0.5314 and 0.5717 for men and 0.4292 and 0.4835 for women. This affirms that men in European countries are more cyclically sensitive than women when looking at harmonized unemployment rates. This means that in time of prosperity or economic expansion, the unemployment rate of men is relatively lower than that of women. However, in times of economic recession or economic downturns, the unemployment rate of men is affected more and, hence, are relatively higher than women. Sahin, Song and Hobijn (2010) state that this is due to a higher gender inflow rate of unemployment. This higher rate, in turn, reflects the deterioration of male-dominant industries. Furthermore, it was more difficult to enter or reenter the labor force in those industries.

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23 relationship between the regional unemployment rate and GDP growth. This negative

relationship is known in the literature as Okun’s Law. Okun’s Law (Okun, 1962) is one of the most well-known and widely used concept of measuring unemployment relationship and is used in policy making. Hitherto, much research has been conducted on this concept. Despite the much focus and research on Okun’s Law, there still seems to be unclarity and inconsistency within the findings. For example, whereas older studies assumed the Okun’s Law to be a linear relationship, more recent empirical studies found proof for this relationship to be non-linear. A non-linear relationship means that other determinants will have an impact on the future employment rate and will consequently influence the policy making as well (Moosa, 1997; Freeman, 2001). This makes it very interesting and relevant to conduct further research on Okun’s Law using the model created in this research.

If the study was concerning about the change in unemployment rate, the simultaneous approach for cross-sectional dependence might be useful in understanding Okun’s Law. A simple version of Okun’s Law is the following formula:

100 ∗ (𝛥𝑌) 𝑌) = 𝑎 − 𝑏𝛥µ⁄ (8)

where Y is the GDP, ΔY is the GDP change from one period in time to the next, 𝑎 is the average annual growth rate, 𝑏 is the factor relating to unemployment changes and 𝛥µ is defined as the change in unemployment from one time period to the next. One would need to, as mentioned previously, add an explanatory variable as in Pesaran’s model (2014) to try and understand Okun’s Law in such a cross-sectional dependence model better. A potential explanatory variable would be the GDP growth rate.

Furthermore, Lso Niebuhr (2003) states that findings concerning spatial effects among European labor markets have implications for regional policy. The existence of unemployment clusters, i.e. similar labor market conditions in neighboring regions, suggests that policies that promote labor mobility across longer distances and national borders might be appropriate to reducing differences in regional unemployment. Moreover, as Burgess and Profit (2001) note, significant spillover effects between neighboring regions imply the existence of wider

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24 local unemployment will also have positive effects in neighboring labor markets. This calls for close cooperation and common measures between regions in order to diminish severe labor market problems. Thus, when looking at unemployment or incorporating Okun’s Law, a more appropriate pre specified W-matrix would be a contiguity based spatial weight matrix.

Allegedly, this research suffers from two shortcomings. The first one, and most prominent one being the endogeneity problem. This research does not include explanatory variables meaning the variables explaining the parameters are basically the dependent variable itself. For future research, could include explanatory variables such as GDP growth to explain the unemployment rate. However, this gives rise to another endogeneity problem, namely reversed causality. Unemployment could be explained by the GDP growth rate, but this could also hold vice versa.

The second limitation concerns the heterogeneity problem. Since not every European country absorbs an economic shock and thus structural shock the same way, one could expect heterogeneity problems as the cyclical sensitivity coefficients might be skewed. One could add weighted averages per country as a result of a structural shock. This is, nonetheless, almost impossible to account for as there is a lot of volatility involved. The same skewness holds for the difference of anticipation per shock on women and men in those respective European countries (Sahin, Song and Hobijn, 2010). The shock has a far more substantial adverse effect on men than women.

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VII. Conclusion

This paper has presented several literatures identifying serial dynamics, spatial autocorrelation and common factors. This paper makes use of a simultaneous approach proposed by Halleck Vega and Elhorst (2016) by utilizing the trade-flow 𝑊-matrix trying to explain the difference in harmonized unemployment rates for three specifications, namely total, men and women. The data is divided in the previously mentioned subcategories to conduct research on the

aforementioned phenomena. The data consists out of 21 European countries for 64 quarters ranging from 2003 until 2018. It is explained why the two-stage model, also highlighted in Section 4, is not the model used to explain these phenomena as serial dynamics, spatial dependence and common factors all together are most likely interdependent and, hence, may result in biases. Furthermore, all three of the stylized facts are discussed in Section 3. Using a correlation matrix, given in Table 1, A1 and A2, it is highlighted that there might be serial dynamics involved. Furthermore, the trend of the real growth rate of 21 European countries has been established. This trend is compared to the European real growth rate, given in Figure 2, B1 and B2. It is apparent that most European countries, with the exemption of a few follow the European trend and, hence, are cyclically sensitive.

Equation (7) is estimated with the help of a pre-specified trade-flow 𝑊-matrix for all three specifications, given in Table 2, C1 and C2. All three specifications find evidence in favor of serial dynamics, spatial dependence and common factors. Next, specification two is compared with three. It is found that women are more affected by serial dynamic effects than men as men tend to get offered jobs more often and women stay home relatively more for household

purposes. Furthermore, women’ spatial autocorrelation coefficient is higher than that of the men’ specification. This means that when countries trade with each other, the unemployment rate of women increases relatively more than men. Lastly, it is confirmed that men in European

countries are more cyclically sensitive than women when looking at harmonized unemployment rates. This means that in time of prosperity or economic expansion, the unemployment rate of men is relatively lower than that of women. However, in times of economic recession or economic downturns, the unemployment rate of men is affected more and, hence, are relatively higher than women. This is in line with the findings of Sahin, Song and Hobijn (2010).

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26

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29 PHENOMENON 1. Scottish Journal of Political Economy, 13(2), 205-219.

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IX. Appendix

Appendix A

Table A1: Correlation Matrix over time for harmonized unemployment rates for men

2003q1 2005q1 2007q1 2008q1 2009q1 2010q1 2011q1 2013q1 2015q1 2017q1 2018q4 2003q1 1 2005q1 0.97867 1 2007q1 0.84024 0.8699 1 2008q1 0.57494 0.56441 0.82954 1 2009q1 0.33055 0.25043 0.33494 0.52184 1 2010q1 0.41222 0.33608 0.2929 0.32394 0.9332 1 2011q1 0.31867 0.21997 0.24713 0.45603 0.92286 0.89009 1 2013q1 0.10263 0.01186 0.08585 0.38974 0.56363 0.45292 0.77462 1 2015q1 0.0596 -0.0179 0.0463 0.34174 0.40814 0.28452 0.60924 0.94856 1 2017q1 0.02324 -0.0532 0.01405 0.28323 0.36769 0.26301 0.53946 0.86422 0.96302 1 2018q4 -0.0387 -0.1088 -0.0118 0.26428 0.32772 0.20269 0.45003 0.78316 0.9147 0.97339 1

Table A2: Correlation Matrix over for total harmonized unemployment rates for women

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31

Appendix B

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32

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33

Appendix C

Table C1: Simultaneous approach to serial dynamics, spatial dependence and common factors including a pre specified Trade-Flow W-matrix, specification two (men)

𝛼1 0.9737 (0.0056)

𝛼2 -0.219 (0.5710)

𝛼3 0.3491 (0.0837)

R-squared 0.9894

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34

Table C2: Simultaneous approach to serial dynamics, spatial dependence and common factors including a pre specified Trade-Flow W-matrix, specification three (women)

𝛼1 0.994 (0.0056)

𝛼2 -0.2134 (0.5610)

𝛼3 0.4351 (0.1085)

R-squared 0.9924