The Role of Social Capital on the Searching Behaviours of a Job Seeker in the Multiple Labour Markets

Introduction

Finding a good job is a stressful but very important process for unemployed seekers, therefore many of them urge for help and support from their family, friends or other relatives when looking for a job. More than half of the workers surveyed by Pellizzari (2010) found jobs via their social networks. Many studies focused on the influence of job seekers’ social capital on job search outcomes (Manroop & Richardson, 2016). They found that the quality (Wanberg, 2012), the scale (Allen, 2000) and the diversity (Stoloff et al., 1999) of social capital had a significant and positive effect on several important aspects, that is, the information of job opportunities (Calvo-Armengol & Jackson 2007; Reis & Ferreira, 2015), likelihood of receiving job offers (Easley & Kleinberg, 2010; Van Hoye et al., 2009) and re-employment (Cingano & Rosolia, 2012; Van Hoye et al., 2009). The social capital acquired by a job seeker is also associated with the employee’s benefits, such as increasing the welfares of workers, reducing the leave rate of employees (Boyas et al., 2012), decreasing the ability of being dismissed (Zhao, 2002) and increasing the monetary and non-monetary wages of workers (Franzen & Hangartner, 2006; Liu, 2017).

However, there is a dearth in the literature about the micro-level of the influence of social capital on day-by-day searching processes and the challenges faced by the job seekers (Mowbray et al., 2018, pp. 239; Wanberg, 2012, pp. 389). Therefore, this study primarily aims to build a simple searching model to analyse the variation of social capital level on the searching behaviours of job seekers when they search for a job in two different sectors.

The Model

Our model considers an unemployed search for a job in two different markets j = {A, B} with a set of market conditions that are known (or believed) by the job seeker. Each market is defined by an offer arrival rate, α _j , lay-off rate, λ, quit rate, γ and wage-offer distribution denoted as F (w) In which, the wage offered from market j, denoted as w, is a random variable drawn independently from a constant and exogenous distribution function F (w).

The searching process is an infinite series of repeated searching behaviours until the seeker becomes an employee. We assume the market conditions are stationary and the searching process is divided into several small discrete periods, and the length of each period is δt ≥ 0.

In each period of length δt, the job seeker makes S searching behaviours per unit of time in the two markets j = A, B, and pays the search cost c per searching behaviour. Social capital will provide more job information for the seeker (Calvo-Armengol & Jackson, 2007) and support the personal recommendations about the potential employers (Reis & Ferreira, 2015), so the search cost c(θ) is a diminishing function of social capital, in which θ is the volume of social capital in market j = A, B of the job seeker.

After several searching behaviours during each period, the job seeker may/may not receive the job offers. In which, the wage offers from market j, j = A, B, are randomly drawn from the wage distribution function F (w). The offers are assumed to expire immediately if denied, thus for the seeker there is no possibility to be recalled to a previous job offer. The probability of receiving a job offer from the market j, following a Poisson process, depending on the supply–demand conditions and the searching effort of the seeker in this market, is α (θ). σ(S) with j = A,B. Where α is defined as the ability that a job offer from market j arrives across the period. The empirical evidence supported that social capital could help the seeker improve the ability to receive job offers (Easley & Kleinberg, 2010; Van Hoye et al., 2009). Therefore, the offer arrival rate α (θ) is the increasing function of social capital. The term σ(S) is the ‘searching effort’ function of the seeker which is assumed to be an increasing function of social capital. On the contrary, 1 – Σ α(θ). σ (Sj), j = A is the probability that the seeker does not receive any job offer in both A and B markets across the period, thus he or she must continuously search in the next period.

In the case of receiving a job offer, at the starting point of time of the next period, the seeker has to decide whether to accept a job or continue to search by comparing the benefits of the two options. If accepting a job, the seeker will accept the highest wage offer in each market and reject others: w j = m a x w j 1 , w j 2 , . . . w j n , j = A , B .

In the stationary of market conditions, the wage, the layoff rate and the quit rate in each market are assumed to be unchanged over time. However, the layoff rate and quit rate of each worker, also assumed following a Poisson process, are different because of the difference in the social capital of the worker (Boyas et al., 2012; Zhao, 2002). Therefore, the expected discounted value, with a discount rate per period r, of future income if the seeker accepts a job in market j at wage w is defined by:

V j w j = w j + λ j θ j . V u + γ j θ j . V u r + λ j θ j + γ j θ j , j = A , B

(1)

where V is the expected benefit of an unemployed seeker; λ(θ). is the layoff rate in the market j which is a decreasing function of social capital, ∂ λ j ∂ θ j < 0 (Van Hoye et al., 2009); γ(θ). is the quit rate in the market j which is a decreasing function of social capital, ∂ γ j ∂ θ j < 0 (Boyas et al., 2012).

Our model starts at the time t₀, an unemployed seeker initially search for a job in two different markets, the expected benefit of the unemployed seeker at t₀ is defined by:

V t 0 u = - ∑ j S j . c θ j . δ t 1 + r . δ t + b . δ t 1 + r . δ t + ∑ j α j θ j σ S j . δ t . E m a x V t 1 j w j , V t 1 u 1 + r . δ t + 1 - ∑ j α j θ j σ S j . δ t . V t 1 u 1 + r . δ t , j = A , B

(2)

where b is the income of unemployed worker per unit of time, it includes the value of leisure, home production activities and unemployment insurance.

⇔ r . V t 0 u = − ∑ j S j · c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) · E [ max ( V t 1 j ( w j ) , V t 1 u ) − V t 1 u ] + ( V t 1 u − V t 0 u ) δ t ⇔ r . V t 0 u = − ∑ j S j · c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) · E [ max ( V t 1 j ( w j ) − V t 1 u , 0 ) ] + ( V t 1 u − V t 0 u ) δ t

(3)

When the length of a period is small: δt ↓ 0, and the market conditions are constant, the capital gains from changes in evaluation, lim δt → 0 V t 1 u - V t 0 u δ t = 0 , it means V t 1 u = V t 0 u = V u . Therefore, Equation (3) can be rewritten:

⇔ r . V u = − ∑ j S j . c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) . E [ m a x ( V t 1 j ( w j ) − V u , 0 ) ] .

(4)

In which, the job seeker will accept the job if V t 1 j ( w j ) > V u , and reject if V t 1 j ( w j ) < V u . Let w j * is the reservation wage of the job seeker in market j which make the seeker indifferent in choices, means w j * is the threshold wage. Formally, the reservation wage is the minimum wage offer that is acceptable by unemployed and is determined by V t 1 j ( w j * ) = V u

⇔ w j * + λ j ( θ j ) . V u + γ j ( θ j ) . V u r + λ j ( θ j ) + γ j ( θ j ) = V u , j = A , B ⇔ w j * = r V u .

(5)

Replace Equation (5) into Equation (4):

w j * = − ∑ j S j . c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) . ∫ w j * ∞ [ w j + λ j ( θ j ) . V u + γ j ( θ j ) . V u r + λ j ( θ j ) + γ j ( θ j ) − V u ] d F j ( w ) ⇔ w j * = − ∑ j S j . c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) . ∫ w * ∞ [ w j − r . V u r + λ j ( θ j ) + γ j ( θ j ) ] d F j ( w ) ⇔ w j * = − ∑ j S j . c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) r + λ j ( θ j ) + γ j ( θ j ) . ∫ w j * ∞ [ w j − w j * ] d F j ( w ) , j = A , B .

(6)

Proposition 1: An increase in the amount of social capital in a market will help increase the reservation wages in both markets equally.

Proof: Differentiating the Equation (6) demonstrates that

∂ w j * ∂ C < 0 , ∂ w j * ∂ α j > 0 , ∂ w j * ∂ λ j < 0 and ∂ w j * ∂ γ j < 0 , j = A , B .

That is, the higher social capital in a market will create a rise in the reservation wage in that market as it help reduce the search cost, increase the offer arrival rate, decrease the lay-off rate and quit rate of the job seeker in that market.

However, in our model, this difference does not exist, the reservation wages of a job seeker are similar between the two markets even though there is a difference in the amount of social capital and other factors.

Remember Equation (5), w j * = r V u .

Because the benefit of unemployed of a seeker at a point of time is unique, in the case the discount rate is also similar, the reservation wage of a seeker in two markets are equal, although the search cost, offer arrival rates, lay-off rates, quit rates and wage distributions vary.

Therefore , we have w A * = w B * = w * = r V u

(7)

Noted that the worker is indifferent between accepting a job (at reservation wage) and rejecting that job. Therefore the interest of the seeker about the ability to be unemployed by lay-off, quitting and not receiving a job offers in the future is of no use in the stationary environment (see more in the Appendix). It is absurd that the job seeker rejects a higher-paying job in either market to accept a lower-paying job in another just out of fear of unemployment, if other things are equal.

With Equation (7), Equation (6) can be rewritten:

w * = − ∑ j S j . c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) r + λ j ( θ j ) + γ j ( θ j ) . ∫ w * ∞ [ w j − w * ] d F j ( w ) , j = A , B

(8)

Differentiating the Equation (8), we have:

∂ w * ∂ α j > 0 ; ∂ w * ∂ λ j < 0 ; ∂ w * ∂ γ j < 0 ; ∂ w * ∂ C < 0 , j = A , B

We also have

∂ α j ( θ j ) ∂ θ j > 0 , ∂ λ j ( θ j ) ∂ θ j < 0 , ∂ γ j ( θ j ) ∂ θ j < 0 , ∂ c ( θ j ) ∂ θ j < 0

It means that an increase in the amount of social capital in either market increases the possibility of receiving the job offers in that market, thus it is worth waiting for a higher-paying job in a labour shortage market by setting a higher general reservation wage. On the contrary, it is less worth waiting for a high-paying job if it is costly to find or likely to end early due to a disadvantage of social capital.

Proposition 2: Sometimes, the job seeker may accept the second-highest wage offer.

Proof: From Equation (7): w A * = w B * = w * = r V u

If there is a difference in the discount rates, the reservation rates will differ between the two markets.

Assume r A > r B → w A * > w B *

If w A * > w A > w B > w B * , the job seeker will accept the wage offer w _B even though the highest offer wage is wA.

It is advisable to accept a lower-paying job if the job seeker expects that this job will be more valuable in the future.

Proposition 3: The number of job-search behaviours is influenced by social capital. The job seekers tend to demonstrate their searching behaviours in the market, where they have a higher degree of social capital.

Proof: Form Equation (8), the first-order condition for the optimal searching behaviours in each market per period is:

∑ j α j ( θ j ) . σ ′ ( S j ) r + λ j ( θ j ) + γ j ( θ j ) . ∫ w * ∞ [ w j − w * ] d F j ( w ) = c ( θ J ) , j = A , B

(9)

The optimal number of job-searching behaviours is achieved when the marginal benefit of an additional searching behaviour equals the marginal cost of searching behaviour.

From Equation (9), it is clear that if other conditions of the two markets are identical, the job seeker would search more hardly in the market with a higher offer arrival rate, lower lay-off rate, lower quit rate and lower searching cost.

Because of ∂ α j ( θ j ) ∂ θ j > 0 , ∂ λ j ( θ j ) ∂ θ j < 0 , ∂ γ j ( θ j ) ∂ θ j < 0 and ∂ c ( θ j ) ∂ θ j < 0 , we can conclude that the job seekers tend to demonstrate their searching behaviours in the market where they have a higher degree of social capital. This trend of the job seeker may not give him a higher wage (Proposition 1) but will help shorten the expected searching time, which is defined as follows.

T = 1 ∑ j α j ( θ j ) σ ( S j ) . ∫ w * ∞ d F j ( w ) , j = A , B

Besides, another point of this conclusion is that all else constant, if there is an increase in the lay-off rate, a decrease in the job offer rate or an increase in the quit rate in either market will reduce the optimal volume of searching behaviours in that market and rise the optimal amount of searching behaviours in the other market. This implies that the seeker will adjust his/her search effort between the two markets to respond to the disparities and the changes in the lay-off rates, job offer rate and quit rate. These factors are all influenced by the amount of social capital of job seekers in each market. Thus the relative difference in the amount of social capital of job seekers between the two markets is also an important factor affecting the distribution of job search behaviours in each market.

Conclusion

Although our theoretical model is simple, it effectively explains the effect of social capital on job seeker’s behaviours. The key point of our model is that the job seeker should prioritize all of his resources towards the amount of social capital in a particular market rather than spreading across multiple markets. This effectively affects increasing the common reservation wage. In addition, this also helps the job seeker to demonstrate his/her searching behaviours in either market and thus shortening the expected searching time.

Appendix

From Equation (6)

w j * = − ∑ j S j . c ( θ j ) + b + ∑ j α j ( θ j ) σ ( S j ) r + λ j ( θ j ) + γ j ( θ j ) . ∫ w j * ∞ [ w j − w j * ] d F j ( w ) , j = A , B

(6)

Assume that, in each market, a job seeker only receives a wage offer which is equal to his reservation wage in that market:

w A = w A * and w B = w B *

(6.1)

On replacing Equation (6.1) into Equation (6), we have: w A * = w B * = − ∑ j S j . c ( θ j ) + b .

At the reservation wage, the job seeker does not care about the ability to be unemployed by lay-off, quitting and not receiving a job offer in the future.