Considering the drawbacks of simple OLS regression, experts suggest using probit regression model. This is the most appropriate tool to analyze the probability of one's being self-employed and mismatched at the same time. Probit regression model takes only binary or dichotomous response variable, as it was discussed above and besides, it has a normal distribution of the error term which allows the model to solve the problems of OLS regression by fitting a non-linear function to the data being analyzed. Probit regression model highly values the restrictions of the response variable which is between 0 and 1 (Gujarati, 2011, p. 247) and uses maximum likelihood estimation and giving the coefficients which range from 0 to 1, however, it can be incorrect to interpret the exact coefficient of change or to discuss the exact probabilities for the response variable. In order to test the hypothesis, the data for response variable, explanatory variables are put into the probit regression model which has a following form where x represents the mismatch categories and other control variables, which help to stabilize the relationship and to come up with a correct result of the regression and y observes the probability of one's being self-employed (Kucel & Vilalta-Bufн, 2019).

Probit regression results would come up with some indicator of b coefficients which are within 0-1 interval. This would potentially show the extent of response variable change when covariate changes by 1 unit. Still, this b coefficient would be insufficient to correctly interpret the results of the function, where the goal is to derive the effect of relationship between self-employment and overqualification. The only thing which can be discussed is the direction of the relationship, for example whether the probability of experiencing overqualification is higher among self-employed without mentioning the exact numbers of probability. In order to derive the certain degree of the probability, marginal effects of the probability should be calculated. This would assist to predict the certain probability of being self-employed and overqualified in comparison of being matched in their positions, holding all other variables constant. There are several ways of calculating marginal effects.

The first method of calculating marginal effects is known as average marginal effects estimation, where the first step includes calculating the marginal effects of each observations of the model and then estimate the average of all obtained values. The other method, marginal effects at the mean, considers estimating the mean for the specific covariate and then count the marginal effect for this specific value (Gujarati & Porter, 2006, p. 567). However, it is believed that there is no significant difference between these two methods of calculations, this study is intended to use average marginal effects estimation.

This way, the further part of the paper presents the results obtained by running the probit regression analysis on 6 models in total. First three models estimate the regression for three different age categories - 20-29, 20-30 and 24-34 respectively. The remaining 3 models calculate the regression for the same age categories but with exclusion of Moscow, Moscow oblast and Saint-Petersburg, as it is known that those large regions are very disparate from other regions of Russia in terms of economic and social development and overall labour conditions and opportunities (Shevchuk et al., 2015). Overall, the methods which are being applied in this paper are consistent with the suchlike papers (Bender & Heywood, 2011; Congregado et al., 2016; Kucel & Vilalta-Bufн, 2019; Shevchuk et al., 2015).

4. Description of the results

As the next step before calculating regression, it is important to look at detailed descriptive statistics and understand the way variables are presented and used in regression models. Table 3 shows the mean comparison test for all the variables used in the study. The final sample accumulates 16 233 individuals aged 20-34. As a robustness check, age interval is changed in several models, hence the number of observations in regression can be different from the number of observations in descriptive statistics. The first two columns show the mean values of all variables separated by employment status - wage employee and self-employed. As it is evident from the table, number of wage employees is much higher than of self-employed, 15 321 over 912, respectively. Remaining two columns show the standard error of difference and the significance for those errors. Rows, in turn, represent the variable of interest and control variables used in the regression within their categories.

Table 3 Descriptive statistics (means, percentages, std. deviations) for variable of interest and control variables

The most interesting figure to consider in descriptive statistics table is a variable indicating mismatch among individuals. Hereby, results showed by the mean statistics are quite consistent with the hypothesis of this study. Self-employed tend to experience all types of mismatch more than wage employees. Looking at the statistics, 81.2% of wage and salary workers are matched in their jobs, while only 71.3% of self-employed are known to be matched. This is approximately 10% less than wage employees. The rate of being overqualified is higher for self-employed (18.8%) which is 4,2% more than overqualification rates among paid employees. The least rate of mismatch in both of the employment groups is presented by underqualification with 7.3% among self-employed and only 4.2% among wage and salary employees. The mean differences are highly significant in all categories of mismatch variable. Differences between sex of individuals are quite high and statistically significant. This way, 63.4% of men are self-employed against 36.6% of women, it gives a result that self-employment among women is 26,8% less than men. Overall, men are more likely to be self-employed compared to women. Age of self-employed is likely to be a bit higher than the age of salary workers: on average 29.3 for self-employed and 28.8 on average for wage employees. Married or cohabiting respondents are more self-employed (63.3% against 60.2%) than employed in jobs with salaries but the difference of mean is not significant. Settlement is another interesting variable to look at. Mean test shows that rural population is more likely to be self-employed than urban population, however the difference of means are not significant. Presence of children under the age of 9 seems to promote self-employment with a significant value of the mean because results show that 51% of self-employed have children under 9 years old compared to 49% among self-employed those who does not have children. Another continuous variable indicating the cumulative years of schooling shows almost similar mean values both for wage and salary employees and self-employed: the mean length of schooling for self-employed is 13.5 years, while wage employees tend to have 13.6 years of schooling in general. Difference between two groups is not so large and also the significance level of the difference is quite low.

Additionally, models include dummy variables controlling for the regions of Russian Federation because, as previously mentioned, some regions may be more favorable for self-employment than others and the income may be distributed differently.

Generalizing the results of descriptive statistics, it can be preliminary said that the rate of mismatch is higher among self-employed, men are more often self-employed compared to women, married people are more likely self-employed with insignificant mean difference, presence of children positively correlates with status of being self-employed, self-employed tend to have shorten length of education compared to wage and salary employees with a low level of mean significance. The remainder part of this paper includes results of probit regression on different models within results of marginal effects.

Table 4 presents the results of probit regression models within different age groups and regional characteristics. As it was mentioned earlier, various studies define young people in different age groups. However, for this study purposes, the main age interval was chosen 20-29 depending on the simple logic that in Russia, post-secondary education ends starting from 20 and there is a high probability that youth aged 20 can already be self-employed or employed in salary jobs. And the highest level of this interval was chosen because there may be many youths studying bachelor's, master's and postgraduate levels which normally last up to 29 years of youth. Other (20-30, 24-34) age intervals were also included in the regression table in order to check the robustness of the effect, meaning that whether slight replacement of start and end values of age can significantly affect the results of the regression. Hence, if answer is yes, then the model would be unstable. The first 3 columns include observations from previously mentioned centralized regions and cities of Russia such as Moscow, Moscow Oblast and Saint-Petersburg. The remaining 3 columns do not include observations from those regions. The main idea behind excluding those regions was relying on the possibility of robustness check and exclusion would allow to see whether the sample and results of regression are sensible for those regions.

Hence, looking at the result of the main age category (20-29) with 7 990 observations, it is clear that mismatch, in general, positively correlates with being self-employed. If a person is overqualified, he is more probably self-employed if compared to matched individuals. Underqualification, in turn, also stimulates the probability of being self-employed. Moreover, the results are all statistically significant and consistent with Bender & Roche, (2013), who argues that there are more people in state of mismatch among self-employed than among wage and salary employees. Although most of the results for control variables were expected, it is vital to look at some of them. Variable indicating sex of the person states that women are less likely to be self-employed compared to men and the indicators are statistically significant. This phenomenon has been justified by many scholars for a long time (see, for instance, Blanchflower & Oswald, 1998; Williams, 2004; Lazear, 2005). Age and age squared shows more interesting results. Among youth aged 20-29, the older they get the more the probability of being self-employed, however in the beginning, age lessens this probability. Among young people being single positively influences the fact of being self-employed, meaning that married people are more probably wage and salary employees. But the probability of being single has a weak statistical significance. With regard to years of schooling, regression shows that more length of obtained education reduces the probability of being self-employed. That is, if one has more education, he/she is more prone to work as a wage and salary employee. The results are statistically insignificant for the variable of settlement. Accordingly, living in rural areas of Russia decreases the probability of being self-employed. Finally, people with children under the age of 9 are more probably entrepreneurs.

Moving on to the next models which also include centralized regions but with different age groups (20-23, 24-34), results are quite similar to the main model (20-29), even so there are some interesting distinctiveness. So, consistent with the hypothesis, both of the models show that probability of being self-employed is higher among overqualified and underqualified. The direction of all other control variables is also quite similar to the first model except for age and age squared, marriage and settlement which will be discussed further.

Table 4 Probit regression models with different age intervals (20-29, 20-30, 24-34) and including/excluding centralized regions of Russia (Moscow, Moscow Oblast and Saint-Petersburg)

So, age group 20-30 with total 9 756 observations show that being single promotes the fact of being self-employed however, there is no statistical significance indicated in this model unlike in 20-29 age group. Other variables are quite similar to the results obtained in the first model. The more interesting results are observed when the age group was moved to 24 from 20 and 34 from 29, which then resulted with total 14 418 observations. As it is evident, the number of observations in the third model is way more than in first two models. At a glance, it can be concluded that the rate of self-employment is higher among this group age, meaning that the number of self-employed and, probably, the wage employees rises after on, between 20-34 years old. Ceteris paribus, the variable of age in the third model shows the opposite direction of first two models. It states that, as people get older (the age increases) the effect of age on being self-employed lessens, meaning that the older one gets, the less the probability of being self-employed. This is a quite interesting phenomenon because as the results show, age is important somewhat until one gets 30-31 and after this moment, age shows inverted U-shape and it gives the opposite effect. Also, the fact of living in rural areas reduces the probability of one's being self-employed and, what is more important, this indicator has a statistically significant result unlike the previous two models, even if the level of significance is relatively low.

As stated earlier, the latter three models are calculated in the same way but without including centralized regions as Moscow, Moscow Oblast and Saint-Petersburg. Here, the exclusion should have made the model more reliable compared to those with inclusion. So, in the fourth model, excluding centralized regions the final number of observations is 7 785 against 7 790 in the first model, meaning that only 5 observations were from central regions. Overall, it is evident that results have not changed in any matter, however the variable for marriage has lost its significance compared to the first model. The fifth model accounts for 9 523 (233 excluded) observations, and the sixth model includes 14 053 (365 excluded) models after the exclusion of central regions. Results obtained in the last two models are almost the same with only minor significance differences. Now, it is rational to conclude that different samples are not affected by the presence of centralized regions.

Having run a regression analysis on several models, it would be rational to look at some estimates, assessing the regressions goodness of fit. Firstly, looking at the bottom of Table 4, estimates of Pseudo R2 report approximately the same results in each model: 8%, 7%, 6%, 7%, 7% and 6% respectively. The predicted probability of obtaining 1 in dependent variable (self-employment) is relatively low, however this estimate cannot be considered enough to fully assess the regression. Hence, the more reliable measure can be AUC or the area under the ROC curve, which is presented at the bottom of Table 4. So, overall, all regression models are able to predict up to roughly 70% of positive outcome in the dependent variable. In particular, the level of this estimate can be argued as good enough following the fact that the degree of estimation is certain in all models.

After taking a quick look over results of probit regression, it is vital to see the exact magnitudes of change by calculating average marginal effects of all variables. That is to say, having a full table with marginal effects would potentially allow to see how each regressor influences the probability of getting 1 in the dependent variable. In case of this study - it is important to see how being self-employed is affected by different factors. Hence, Table 5 presents calculated marginal effects for all variables and for all models. Overall, there are 6 models each corresponding to 3 age intervals and whether centralized regions are included in the analysis.

Starting from the first column which includes the main model of this study with young people aged 20-29 and including centralized regions, one can observe that results are consistent with the hypothesis of this study. Experiencing an overqualification increases the probability of being self-employed by 2.8%, meaning that if a person is overqualified, he is 2.8% more probably self-employed compared to those individuals who are matched. However, the results for underqualification show that being underqualified increases the probability of being self-employed by 3.4% which is larger compared to the overqualified individuals. The probability, here, is assumed comparing the reference category of mismatch which is the state of being matched in the job. Following the results, it is possible to report that mismatch (underqualification/overqualification) is also persistent among self-employed and what is more interesting, overqualification is higher than matched workers. These outcomes are considered statistically significant and consistent with results obtained by Bender & Roche, (2013) and Shevchuk et al., (2015).

Moving on, results show that being a female decreases the probability of being self-employed by 1.6% compared to men. For several decades, many scholars have been concluding that males are more prone to become self-employed compared to men. Moreover, the intentions of being self-employed is higher among men. Results are consistent with several scholar (see, for example, Lazear, 2005; Minola et al., 2016; Sanchez et al., 2015; Simoes et al., 2016; Williams, 2004).

Age appears to have significantly negative effect in the beginning of careers among those aged 20-29. In particular, if a person is in the beginning of his/her 20th, then they are less likely to be self-employed, however an increase of age up until 29 in this model shows positive likelihood of being self-employed. This model shows inverted U-shaped relationship between age and self-employment, which is consistent with results presented by Simoes et al., (2016).

Table 5 Marginal effects for all variables within different age groups (20-29, 20-30, 24-34) and including/excluding centralized regions of Russia (Moscow, Moscow oblast and Saint-Petersburg)

The fact of being married seems to have a negative effect on self-employment reducing the probability of self-employment by 1%, but results are not statistically significant and they are not consistent with the same study conducted on Russian self-employed (Djankov et al., 2005) or other self-employment studies (Williams, 2004). They indicate that self-employed are often happened to be married. Continuous variable showing years of schooling shows negative and significant effect on self-employment, meaning that with 1-year increase in education, the probability of being self-employed decreases by 0.5%. Discussing the effects of different living areas on likelihood of being self-employed, the results of regression show that people living in rural areas 0.7% less likely to be self-employed compared to individuals living in urban areas. But this result is statistically insignificant. Interestingly, existence of children under the age of 9 positively effects the likelihood of self-employment. It assumes that if a person has a child under 9, he is 1.6% more likely to be self-employed than wage employee. Results are statistically significant and consistent with the assumptions of Dawson et al., (2014). And finally, the marginal effects includes dummies for regions in order to stabilize the model as it was described previously.

Moving to the next models with different age intervals, it is easy to observe that magnitude of overqualification is stable in the second model with 20-30 year old interval, however the third model with interval of aged 24-34 shows a slight decrease to 2.5%, meaning that among young people aged 24-34 overqualification increases the probability of self-employment for 0.3% less than in the first two age groups. However, underqualification seems to increase together with age in all presented models. This way, underqualification increases the probability of self-employment to 4.1% and 4.7% among youth aged 20-30 and 24-34 respectively. Being a female makes self-employment less probable in the second and third models with 0.3% increase in each age group until 24-34. Interestingly, the same results are obtained for age coefficients in the third model. In particular, among youth aged 24-34 the variable age increases the probability of self-employment in the beginning of the career, but then it turns out to decrease the probability with a result of the same inverted U-shape graph - first rise then fall. Those results were also described as possible when applied to different age groups by several scholars (see for, example. Simoes et al., 2016). Other control variables in the second and third models are resulted with the same magnitudes compared to the main model.

Finally, when marginal effects for each age category are tested excluding Moscow, Moscow oblast and Saint-Petersburg from the models, regression shows almost the same results with first three models meaning that including those central regions would not harm the results of the model. Even if general results are similar, one noteworthy fact is that probabilities for underqualification in the last model (24-34, central regions excluded) account the highest results among all models, meaning that underqualified youth in between 24-34 are 5% more probable to be self-employed with highly significant indicators compared to their matched colleagues.

Conclusion

This paper provides a unique contribution to the literature on overqualification issues in Russia. Through analysis of relationship between mismatch and self-employment among youth, this study investigates whether self-employed youth in Russia are more prone to be mismatched in their positions. Using CMLC data from the Russian Federal State Statistics Services, the probit regression model proves the hypothesis proposed in this study. Regression models, which include robustness check between different age groups and with inclusion/exclusion of central regions, show stable results of mismatch meaning that there is a strong relationship between overqualification and self-employed youth. The following part will stress on the detailed description and explanation of results obtained during the analysis.

Looking at the main variable of interest, self-employed youth are proved to experience more mismatch (under/over-qualification) compared to wage and salary employees. All 6 models show statistically significant and positive effect of qualification mismatch on the outcome of self-employment. Mismatch, in turn, is divided into overqualification and underqualification. Interpreting the results, the fact of being overqualified increases the likelihood of getting 1 in dependent variable or, in other words, the outcome of being self-employed by 2.8% in age groups of 20-29 and 20-30, however among youth aged 24-34, overqualification shows 2.5% of likelihood, which is 0.3% less than in previous groups. In particular, underqualification shows interesting results, namely - the fact of being underqualified increases the probability of being self-employed by 3.4%, 4.1% and 4.7% respectively for the first 3 models. In other words, confirming the H1, Russian young people who are involved in self-employment are in most cases mismatched. The possible reason is that most young people face difficulties in the beginning of their careers to find a job where they are matched in terms of further job and career opportunities or financial stability. Therefore, most of them become self-employed even in those fields for which they are overqualified (e.g. scientist self-employed in wholesale sector). This is also an explanation put forward in Spatial mobility theory (Bьchel & Van Ham, 2003), when young people end up being mismatched and self-employed due to some shortcomings in life or lack of opportunities in the market. Underqualification, on the other hand seems to have a higher influence on self-employment due to other reasons. After graduation from colleges (post-secondary education) young people try to find a job with a good salary, however, most of the jobs with satisfying wages require much higher education. This makes young graduates start businesses in a more advanced fields and end up being underqualified (for instance, welder being self-employed in accounting or marketing). This explanation is consistent with Job Competition Theory (Thurow, 1975), which states that educational level and credentials become the most important indicator of knowledge for employers. Another possible explanation, or more detailed of the previous one would be referring to Lazear, (2005), according to which, self-employed are `jack off all trades', which makes them a compilation of different skills and abilities, that, in turn, allows the high rates of underqualification among self-employed. Lastly, results for mismatch are fully consistent with Bender & Roche, (2013), who also concluded that self-employed are more prone to experience mismatch compared to wage and salary employees.

The direction of control variables affecting self-employment are almost identical in all models except for the age which gives inverted U-shape and besides the first two models represent one half of inverted U-shape, meaning that in 20-29, 20-30 age groups, age negatively effects self-employment in the beginning of a career, but in the future it shows negative effect. Opposite situation is observed in the third model, where age shows the second half of inverted U-shape. In early 24-34, age shows positive effect on being self-employed compared to more future situation, when age decreases the likelihood of self-employment somewhere in the end of the 24-34 interval. Simoes et al., (2016) in their work confirm that age can have inverted U-shaped effect with a threshold until which the rise may be seen. Following the results of current study, if a person is a woman, the likelihood of being self-employed falls by 1.6%, 1.9% and 2.2% respectively for each of the three models. Another explanation might be the fact that women have less developed social capital or weaker social network which is a key to self-employment. The reasons might be various, starting from family responsibilities and lack of time or because their jobs have less status which makes work-related contacts less than among men (Koellinger et al., 2013).

Other noteworthy indicator is a marriage and presence of children. All 6 models report higher incidence of self-employment for those who are not married, however, results are statistically insignificant. Other scholars report marriage as a key indicator which promotes self-employment (Djankov et al., 2005; Williams, 2004). But Цzcan, (2011) criticizes the traditional approach of marriage measurement as done in this study which is through a dummy variable with value 1 if an individual is married and 0 otherwise. He argues that combining singlehood, being divorced or being widowed into one group of unmarried is problematic since features can alter among these groups. This is, probably, the reason why marriage gives negative effect on self-employment in this study. On the other hand, Sorgner and Fritsch (2013) and Cowling, (2000) derived opposite results for marriage. Cowling, (2000), in particular, researching 13 different countries, reported that marriage does not have a positive impact of self-employment.

The results of having children under the age of 9 years old seems to stimulate self-employment, this way if a person has children under 9 y.o., the probability of him being self-employed increases by 1.6%, 1.7% and 1.2% in three models accordingly. It is observable that when age reaches a certain threshold (the last model with 24-34 group), the impact of having children reduces by 0.4% compared to the first model. Simoes et al., (2016), argues that self-employment is often associated with independence and flexibility, which can be an advantage in having children. Moreover, the fact of having children increases the concerns with financial issues and opens up possibilities to have higher returns while being self-employed (Dawson et al., 2014). Most of the studies discuss the positive effect of having children on self-employment approximately to 3% points (see, for instance, Brown, 2011; Wellington, 2006; Zhengxi Lin & Picot, 2000).

Looking at the variable indicating the length of educational attainment, one could observe negative and significant effect on self-employment, particularly, 1 additional year of education decreases the likelihood of being self-employed by 0.5% among 20-29 and 20-30 groups and by 0.3% among 24-34. Most probably, years of schooling affect the positive outcome in self-employed until some threshold as it is described with ages because the decreasing affect is observed among the elder age groups. Negative and statistically significant results of educational attainment among self-employed youth are consistent with results obtained by Williams, (2004).

This research is argued to be one of the pilot in Russia, since there are almost no empirical studies have been conducted on the topic of mismatch unlike in Europe and the US, where mismatch topic have been popular for many decades. However, dividing different employment types while analyzing mismatch has appeared in the research since 2016, when Bender & Roche, (2013) has shed a light on the topic. The results of this paper conclude that there is a significant and positive relationship between mismatch and Russian self-employed youth. Interestingly, underqualification shows stronger effect on self-employment compared to overqualification. Hereby, the contribution of this research paper is assumed to be scientific rather than practical. Derived results of analysis would be helpful for the scholars in future research.

Although results accept H1, there are some limitations one should consider in the future. Firstly, due to dataset constraints it was impossible to differentiate between specialties of education in order to see the detailed effect between each education group. But this opportunity would allow to see which education fields are more prone to mismatch or, more interestingly, to self-employment. Similarly, there was no possibility to look at different sectors of economy, meaning that the differentiation between individuals' field of work was hidden. The availability of data on this information would help to observe grouped relationship of overqualification or self-employment between diverse work groups. The last and the most important limitation occurs from previous data constraints. Since there is a lack of data on different fields of work, the research strategy could not exclude all farmers and workers of agriculture from self-employment category. But exclusion of farmers would be quite important step in the work because considering the estimation of self-employment variable, in most of the Russian regions, in particular, rural settlements, there is a high concentration of farmers who, usually, are not employers nor fully entrepreneurs, because their work is dependent on season but they are reported as self-employed by Rosstat. Once farmers are included in the regression, the probability of mixing real self-employment in a more advanced understanding is very high.

Moving on to the discussion of future research directions, actually, this topic needs to be analyzed way deeper. First of all, the first option of enhancement would be to calculate mismatch using different approaches, so to say subjective methods, because sometimes `the subjective method is argued to be better than the objective method (Congregado et al., 2016). By the way, the research would highly benefit if mismatch is calculated using overskilling and underskilling methods following the evidence that qualification is not always the best measure of mismatch. Besides, as Lazear, (2005) argued, self-employed tend to have various skills, so most probably the method of overskilling and underskilling will give different results when analyzed with self-employment. Secondly, it would be also interesting to observe the outcomes of mismatch on different job-related benefits such as wage penalty, job dissatisfaction, etc. in the context of different employment types. Another possible option of enhancement is related to previously mentioned limitation of the work about obtaining certain fields of occupations and analyzing the narrow groups of employees by field.

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