We extend the model studied by [14] to allow for two types of employment contracts: temporary and permanent. We employ a discrete-time framework and assume that both workers and firms discount the future by a constant rate (which is a discount factor). Many workers are either employed or unemployed, and the measure of workers is normalised to one. On-the-job searches are ruled out, and thus only unemployed workers search for jobs. Firms are measured by the free entry/exit condition. All workers and firms are assumed to be risk-neutral.

This model explicitly includes labour market friction; therefore, job seeking and recruiting activities are time consuming. We assume that the meeting process is described by constant-returns-to-scale matching technology, , where u and v are measures of unemployed workers and vacancies, respectively. During each period, a firm with a vacancy encounters a job seeker with probability, and an unemployed worker encounters a vacancy with probability. Let the former probability be denoted by and the latter probability denoted by, where denotes labour market tightness. By assuming the constant-returns- to-scale matching technology, these probabilities can be represented as functions of only market tightness,. We assume that and as, and that and as.

The production technology and the learning processes regarding match quality are based on [13] and [14] . We first consider the production technology; a unit of production is a matched worker-firm pair, and the productivity of each job is match-specific.⁹ As in the above literature, match-specific productivity is observed at the end of the period; it is represented by, where is a zero-mean, independently and identically distributed, random variable and follows a uniform distribution with support. is the true quality of a match, which is either high or low; matches with high productivity are represented by, and matches with low productivity are represented by. Owing to the presence of the noise term, neither the worker nor the firm can observe the true productivity of the match.

Match quality is considered to be both an inspection and an experience good. When a job seeker and a vacant firm meet, they observe a signal, which represents the probability that the match will be good. This signal is drawn from the cumulative distribution and is independent across matches. We assume that firms make hiring decisions based only on the realisation of. After forming a match, a worker and a firm observe productivity (y) and update their information about the true match quality. If realised productivity falls in the range, the worker and firm learn that the match has high productivity. Similarly, if realised productivity falls in the range, the match is revealed to be of low quality. If realised productivity is in the range, nothing is learned (we assume that). Thus, the learning process is a form of “all-or-nothing”. Let denote the probability that the true match quality is revealed. In this setting, a match of an unknown type with prior probability will be revealed as high productivity with probability and will be revealed as low productivity with probability.

In this model, two types of contracts are considered: temporary and permanent. In addition, there are two states of permanent contracts: pre-existing and newly created. When pre-existing permanent workers are dismissed, firms must pay fixed dismissal costs (firing taxes). However, no cost is imposed when new permanent workers and temporary workers are dismissed. The transfer component of dismissal costs is not considered in this paper.¹⁰

Separations from permanent jobs occur (i) when the match quality is revealed to be bad or (ii) when each firm experiences the negative shock with constant probability. With respect to temporary jobs, however, we further assume that employees are dismissed if the true quality of the match is not revealed. In this regard, we implicitly assume that the maximum length of temporary contracts is legally limited and that a firm with a temporary job neither rehires its employee through a permanent contract in the next period. More details regarding this point are provided in the next subsection. When the use of temporary contracts is rather restrictive in this way, offering a permanent contract when opening a vacancy is a better choice for employers within certain range of a signal. We will show in a later section that there exists a unique cut-off value of that is determined by the equivalence between offering permanent versus temporary contracts. This contrasts with the situation in which firms always prefer offering temporary contracts, as assumed in [13] and other related literature that is based on a model of endogenous job destruction.

To derive the values of firms with each type of contract, some notation must be defined. Let us denote the value of a firm with a temporary job and a signal by and the value of a firm with a permanent job and a signal by, where I is an indicator function that takes zero for a new permanent match and one for a pre-existing match. The value of a vacant job is denoted by V.

The expected value of a firm that has a temporary job and a signal is represented by

where is the wage paid for a temporary job. As defined above, is the probability that a match will be good, and flow productivity is given by the expected value, using. At the end of the period, a match-specific shock is realised, with the employer learning that the true quality of a match is high with probability and low with probability. With probability, the quality of a match is not revealed. In this case, the prediction regarding the quality of a match cannot be revised, and the employment relationship is terminated because temporary contracts cannot be renewed in the next period. We note that instead of this strong assumption, the model can be extended to allow for continuing temporary contacts in the next period. Let us denote the retention probability by (s is the probability that the current employment relationship under a temporary contract terminates); Equation (1) is rewritten as follows:

Then, Equation (1) is a special case of (1’) when. For a large s, we can show the unique existence of, which makes employers indifferent towards temporary versus permanent jobs. Furthermore, the main results of this paper would not be essentially affected under this generalised situation. As mentioned in [30] , the transition rates from temporary employment to regular employment as of both one year and three years after the reference period are much lower in Japan than in many European countries. Particularly in Japan, the employment status of temporary workers is likely to be unchanged as of one year after the reference period, which means that they will be hired as temporary employment within the same firm. The term in the second line of (1’) captures this observation. Therefore, although this paper focuses on the simplest case, we substantially consider a situation in which a temporary match with unknown productivity can be retained in the next period with some probability.¹¹ For comparison, if the last term in (1) were replaced by, employers always prefer temporary employment to permanent employment.

The expected value of a firm with a permanent job and signal is represented by

where is the wage paid for a permanent job of type I. Newly created matches are not covered by employment protection, and the outside option of these matches thus does not include dismissal costs. Conversely, all matches are covered by employment protection one period later, and employers must pay dismissal costs for firing workers. The final term in (2) represents the situation in which the separation of matches of unknown quality depends on the realised value of. In the steady-state equilibrium, however, all matches of unknown quality are retained in the form of permanent contracts because, as we will show in a later section, is strictly greater than zero. We suppose that the quality of a match is unchanged when the match is retained.

The expected value of a vacant firm is represented by

where c denotes the flow recruiting costs and is the hiring threshold for contract type j (P represents “permanent”, and T represents “temporary”). We here assume that, as formally shown below. In Equation (3), the employers’ choice regarding whether an employment match is designated as permanent or temporary depends on the realisation of the signal.

Let us denote the value of being employed in a temporary job with signal as. The value of being employed in a permanent job with signal and the value of being unemployed are denoted by and U, respectively (I is the indicator function that was defined above). The expected value of being employed in a temporary job with signal is represented by

where represents the constant disutility of work.

The expected value of being employed in a permanent job with signal is represented by

and the expected value of being unemployed is represented as follows:

Let us define the joint surplus generated from forming a match as follows:

where each equation is evaluated at any. The first equation represents the surplus of a permanent job with current status I. The second equation represents the surplus of a temporary job. The type of match formed depends on the level of the observed signal. We suppose that the wage for each job is determined by a standard asymmetric Nash bargaining process, and we denote the worker’s bargaining power by. Under this wage determination mechanism, the worker and the firm that form a match divide the surplus according to the following sharing rule:

Using these sharing rules, we derive the expressions for joint surplus as follows. First, the joint surplus values for permanent jobs are given by

where we use the free-entry condition that the values of vacancies in each state are equal to zero:. Second, the surplus generated by forming a temporary match is represented by

We first consider the hiring decisions of firms with permanent jobs. Because firms can choose a form of contract with no cost, a firm decides to hire a worker on a permanent basis if offering a permanent contract is more profitable than offering a temporary contract. The corresponding condition for determining the optimal hiring standard is given by. To obtain a concrete expression for this condition, it is useful to express in a more tractable form. From (10), we obtain

Utilising (9), (10) and (12), the following two results are derived:

The first result depicts the relationship between and. The surplus generated by a pre-existing permanent job is equal to the sum of the surplus generated by a newly created permanent job and the cost of dismissal. The second result indicates that is independent of, where represents the differentiation of with respect to. After a match is revealed to be good, the surplus in this case is expressed by

This automatically holds under the assumption provided in Proposition 1.

We assume that is sufficiently high that the numerator of (15) is positive, which would indicate that (14) has a positive sign and that is increasing in.¹²

We next consider the existence of that satisfies. It follows from (9) and (11) that

and the condition is expressed as

This results in

Subsequently, (11) yields the explicit form of, which is characterised by:

Because must be greater than zero, we suppose that the realisation of is unprofitable and that the following condition is satisfied for a given:

This condition requires that be sufficiently low for any positive.¹³ Otherwise, even if the true productivity is with probability one, the expected costs of recruiting job seekers are lower than the expected net productivity, and every worker-firm pair yields non-negative profits, regardless of the realisation of. We do not consider this case.

For the value of a that is a solution to Equation (17), the following proposition is obtained.

Proposition 1. There exists a unique that satisfies (17) and is contained in the interval if (19) holds and is sufficiently high to satisfy the following condition for a given:

Furthermore, is strictly greater than.

Proof. See Appendix A.

Condition (20) is required for the presence of, which is contained in the interval. Similar to (19), condition (20) will be satisfied under a reasonable value of d. We here note that there are countries in which the hiring threshold for permanent jobs is quite high and most newly created jobs are temporary.¹⁴ This case is obtained for a sufficiently large d. In this case, becomes close to one, and it is optimal for most firms with vacancies to offer temporary contracts.

The determination of hiring thresholds is described in Figure 1. is given by an intersection of the horizontal axis and, and is given by an intersection of and. As shown in Figure 1, employers set a higher hiring threshold for permanent contracts relative to temporary contracts. The crucial difference between the two is whether dismissal costs are imposed. If takes a low value, a contract is more likely to be terminated. In a permanent contract, an employer must pay these termination costs, and a lower increases the probability of this event. Therefore, a high probability of a good match is necessary for a permanent contract to compensate for the higher expected costs. We further note that employers’ choice between permanent and temporary contracts is endogenous and that a unique value of exists. Given the assumption that temporary jobs last one period, a portion of newly created jobs take the form of permanent contracts.

We further note that for. This implies that and for any that is greater than. Therefore, employers prefer retaining a permanent worker to dismissing him (or her), even when the true quality of the match is not revealed, because the probability that the quality of a match is good remains high in permanent jobs.

The measure of vacant jobs that is posted in equilibrium is determined by the free-entry condition. Equation (4),

with, implies

where

The LHS of (21) increases in because is a decreasing function of. The impact of on the RHS of (21) is more complicated, but we are able to show that it decreases in. Differentiating the RHS of (21) with respect to yields

From (15), decreases in, and the following results hold:

Regarding the first two results, increased market tightness reduces the meeting probability of employers; therefore, employers raise their hiring thresholds to ensure profits. Taking from (16) that for any, we conclude that the RHS of (21) decreases with. The conclusion of this subsection can thus be summarised as follows:

Proposition 2. There exists a unique value of that satisfies the job creation condition (21).¹⁵

As observed by [17] , it is difficult to show analytically the unique existence of a steady-state equilibrium in a Pries-Rogerson type model in which permanent and temporary jobs are incorporated. However, our model overcomes this difficulty and enables us to investigate the impact of employment protection analytically.

Let us denote the steady-state measure of permanent workers by and the measure of temporary workers by. Similarly, the measure of matches that are known to be good is denoted by, and the measure of matches of unknown quality is denoted by. In the steady-state equilibrium, the following equivalence conditions must hold in each employment pool.

The equivalence of the inflow and outflow from the employment pool of temporary contracts yields the following condition:

The LHS of (22) reflects the assumption that every temporary contract is terminated in the next period and that each temporary worker will be either employed with a permanent contract or unemployed. Regarding the RHS of (22), only worker-firm pairs that realise a signal contained in form temporary contract matches.

In the pool of high-quality employment, the equivalence of the inflows and outflows yields

where

The LHS of (23) indicates that a negative shock, which occurs with probability, causes the separation of the employment relationship. The RHS of (23) indicates that matches for both temporary and permanent positions of unknown type are revealed to show high productivity with probability multiplied by the expected value of the signal (represents the probability that an unknown match with a signal is found to be good).

In the employment pool of permanent jobs with unknown productivity, the following equivalence condition is obtained:

In the LHS of (26), outflows from this employment pool result from negative economic shocks and the revelation of matches that are either low or high productivity. The RHS of (26) captures inflows into this pool; it is composed of newly formed matches with signals that exceed. Note that represents the measure of matches of unknown productivity in permanent contracts. Figure 2 represents the employment flows that are described in this subsection.

Together with two additional conditions,

(22), (23) and (26)-(28) determine the steady-state value of and u. Solving these equations, we obtain

where

Because the surplus sharing rules have already been derived, we are able to solve the Nash wage equations for each type of employment contract. From (4) and (8), the wage equations for temporary contracts are given by

Similarly, it follows from (5) and (7) that the wage equations for permanent contracts of type I are given by

Note that wages do not play a crucial role in the characterisation of the steady-state equilibrium because wages in both types of jobs are determined by the standard Nash bargaining problem and it is sufficient to focus on the surplus sharing rules given by (7) and (8).

The steady-state equilibrium in this model is characterised by , which are determined by (17’), (18), (21), (19)-(36). Because and are uniquely determined, other endogenous variables are also uniquely determined.

To examine the effects of dismissal costs on firms’ hiring decisions in a steady-state equilibrium, we first consider how these costs affect labour market tightness. For that purpose, the effects of d on the hiring thresholds must be identified. It follows from (15) and (18) that for a given, a response of to a change in d is given by

where stands for. Higher dismissal costs increase the hiring threshold for temporary jobs because an increase in the future expected surplus is offset by the increased dismissal cost (decreases with higher dismissal costs).

From (17’), a change in d has the following effect on for a given:

where

Although (38) is somewhat complex, we are able to identify its sign explicitly. The result is summarised in the following Lemma.

Lemma 1. An increase in dismissal costs raises for a given if (20) is satisfied.

Proof. See Appendix B.

We provide the same interpretation as in the case of. Using the results regarding the hiring thresholds described above, the effect of an increased dismissal cost on job creation is examined. The effect of an increase in d on the RHS of (21) for a given is given as follows:

From (37) and Lemma 1, we obtain the following proposition regarding the effect of dismissal costs on job creation.

Proposition 3. The sign of (39) is negative and if is sufficiently high.

Proof. See Appendix C.

For a higher, a change in d has a minimal impact on (it tends to zero as goes to one). Then, the positive impact of d on the expected profits from having a permanent job is negligible. Higher dismissal costs raise the hiring threshold for each type of employment contract for a given labour market tightness, and firms with vacancies thus take a longer time to form matches. This outcome decreases the expected profit from vacancies and job creation.

The result obtained in Proposition 3 may be standard and intuitive. However, the main focus of this paper lies in how the costs of firing employees affect employers’ hiring policies. At first glance, it appears to be difficult to obtain clear-cut results regarding the effect of dismissal costs on hiring thresholds, and. The reason for this finding is that increasing d has a negative indirect effect on and through changing the labour market tightness, whereas increasing d has a positive direct effect on and, as (37) and Lemma 1 show. However, we are able to find conditions under which signs of and are identified. Regarding, we then obtain the following proposition.

Proposition 4. Suppose that is sufficiently high to satisfy the following conditions:

Then, increasing dismissal costs for permanent jobs raises the hiring threshold if z is sufficiently high to satisfy the following conditions:

Proof. See Appendix D.

We will provide a graphical explanation of Proposition 4 based on Figure 3. The left side of Figure 3 depicts how the equilibrium value of responds to an increase in d. Recalling that is determined at the intersection of and, which are linear functions of, we focus changes in the slope and intercept of each surplus. It follows from (11) and (15) that higher dismissal costs make the slope of steeper and increase the intercept of. In contrast, the impacts of d on the slope of and the intercept of are indeterminate because it follows from (12), (13), (15) and the result that we obtain

The signs of these equations depend on the magnitude of. When z is sufficiently high and is low, however, a change in the slope of has limited impact on the determination of. Therefore, we should concentrate on the intercept of. A lower value of indicates that the true match quality is not likely to be revealed. Because permanent contracts are assumed to be retained even if the true match quality is unknown at the end of each period, employers are able to save future dismissal costs. This effect mitigates the reduction of expected profits caused by increased dismissal costs and decreases the magnitude of (a higher will have the similar effect). Then, is likely to decrease, which leads to an increase in (goes to as demonstrated in Figure 3). Therefore, when a match’s productivity is more dispersed and it is difficult to expose the true quality of the match through on-the-job screening, increased dismissal costs raise the hiring threshold for permanent jobs.

Remembering that Proposition 3 is likely to hold under a higher value of, we suppose that for simplicity in the following analysis. Regarding the effect of d on, then we obtain the following proposition.

Proposition 5. Increasing dismissal costs for permanent jobs decreases if (i) z is sufficiently high (is low) such that at least the following condition holds:

and (ii) the expected costs of a vacancy are less affected by a change in.

Proof. See Appendix E.

Although the effect of d on the slope of is ambiguous, this has a lesser impact on for a lower, and an increase in the intercept of dominantly lowers the hiring threshold for temporary jobs. Therefore, the overall effect of increasing d on is likely to be negative under the condition (44) (goes to, as demonstrated in Figure 3).

It is worth noting that changes in dismissal costs have different impacts on hiring thresholds between permanent and temporary contracts under similar conditions on z (match productivity is more dispersed). As noted in (37) and Lemma 1, a direct impact of d on each hiring threshold is positive for a given. Furthermore, because and for, the indirect impact of d on these thresholds through is negative. However, Proposition 4 states that the total impact of d on is positive for a lower value of (a higher value of z), whereas Proposition 5 states that the total impact of d on is negative under the similar condition. We will consider the reason for the difference in the reaction to a change in d between and.¹⁶

First, we focus on the hiring threshold for temporary contracts. For a given and any, it follows from (11) that an increase in d decreases through, but its impact lessens as decreases. Then, the upward pressure of d on is mitigated. We further note that a change in has a larger impact on under a lower value of. A higher decreases the probability of finding a job seeker for firms with vacancies. Because only temporary contract matches in which the true quality is revealed to be good are converted to permanent contracts, a lower, which means a decrease in the probability that the true quality is revealed, increases the separation probability of temporary jobs, and firms suffer longer recruitment durations. Then, a lower amplifies the impact of on, and the negative indirect effect of dismissal costs on exceeds its positive direct effect. Thus, the hiring threshold for temporary contracts is reduced.

Second, regarding the hiring threshold for permanent contracts, note that satisfies. As explained in the previous paragraph, the direct impact of d on is mitigated under a lower. From (12), (13) and (14), the impact of d on, which shifts downward for a given, is not affected by the value of if is close to one. The impact of a downward shift of is likely to be greater than the impact of a shift of. Regarding the impact of on, a significant point to be emphasised is that a lower decreases the separation probability of matches associated with permanent contracts because a permanent job does not separate until its true type is revealed to be bad. Although a higher decreases the success rate of recruiting, employers can avoid suffering this adverse effect when has a lower value. Then, the lower contributes to a positive sign of. In total, the difference between and in the hiring threshold reaction to a change in dismissal costs reflects the difference in how (or z) affects both the direct and the indirect effects of d on each hiring threshold.

Because this paper focuses on the screening role of temporary contracts, we have an interest in the impact of dismissal costs on the screening function of temporary contracts from the viewpoint of firms. In this regard, the average productivity of permanent jobs will be appropriate. If temporary contracts are effectively used as screening devices and potentially unproductive matches are eliminated, employers will expect an increase in the productivity of permanent jobs. Using the results regarding the effect of d on and, we examine how changing dismissal costs affects the average productivity of permanent jobs.

We first define the average productivity of permanent jobs as follows:

where is defined as

There are two types of permanent jobs: (i) the true match quality is good; (ii) the true match quality is not revealed. Note that the productivity of the latter type is expressed using. We then obtain the following proposition.

Proposition 6. Suppose that the results of Proposition 4 and Proposition 5 hold. Then, increasing firing costs for permanent jobs increases their average productivity.

Proof. See Appendix F.

This proposition shows that higher dismissal costs improve the average productivity of permanent jobs because of (i) the increased proportion of good-quality jobs among permanent jobs and (ii) a rise in the conditional expectation of inspection probability (). Regarding the fact (i), a rise in attributed to an increase in d (Proposition 4) implies a reduction of employment flows into the pool of permanent jobs with unknown match quality (unemployed workers are more likely to be hired in temporary jobs). The rise in also has the following impact on flows into permanent jobs with good match quality: a higher means a higher probability that match quality will be revealed to be good and that more workers will move from the pool of permanent jobs with unknown match quality to the pool of permanent jobs with good match quality. What is important in obtaining the result of Proposition 6 is that an increase in average productivity depends on how dismissal costs affect the hiring standard for temporary jobs. Although reducing by increasing d, which occurs in Proposition 5, reduces the number of workers who move from the pool of temporary jobs to the pool of permanent jobs with good match quality, the proportion of jobs with good quality among permanent jobs increases. This phenomenon occurs because more workers become temporary employees because of the reduction in and permanent workers tend to have experienced temporary jobs. Because only temporary jobs that are revealed to have good match quality are converted into permanent contracts, the reduction in, which reduces the ratio of permanent workers in the pool of matches with unknown productivity, increases. Regarding the fact (ii), a higher hiring threshold for permanent jobs increases the possibility that the true quality of a match is good. This contributes to the higher average productivity of permanent jobs.

We here examine how the dismissal costs for permanent jobs affect the average productivity of temporary jobs and the ratio of temporary employment. Regarding the average productivity of temporary jobs, we obtain the following proposition:

Proposition 7. An increase in dismissal costs has an ambiguous impact on the average productivity of temporary jobs.

Proof. See Appendix G.

The reason for this result is that increasing dismissal costs has two opposite effects: a decline in the hiring threshold for temporary jobs and an increase in the hiring threshold for permanent jobs. The former effect results in the decreased average productivity of temporary jobs, whereas the latter effect helps to increase average productivity. Therefore, a change in average productivity depends on which effect overcomes the other.

Furthermore, it follows from (30) and (31) that the relative ratio of temporary employment is expressed by

where is defined as

Simple calculations show that an increase in d increases this ratio. Therefore, higher firing costs for permanent jobs increase the proportion of temporary employment. This result is consistent with the finding by [33] that showed that more stringent protection of workers on open-ended contracts increases the reliance on fixed- term contracts by employers aiming to achieve their desired levels of worker turnover.

The qualitative analysis conducted in this paper suggests that reducing dismissal costs for permanent jobs increases job creation and the proportion of permanent employment when match productivity is more dispersed (z is large). Using a similar framework, [13] finds that the increased use of temporary contracts is a second-best solution relative to reducing permanent employment protection: the latter policy will have a stronger impact on unemployment and social welfare than will reducing employment protection for temporary workers.¹⁷ Although policies of easing employment protection for permanent jobs appear to be problematic because of political pressure from permanent workers (see [35] ), these policies will be the first choice if they are viable.¹⁸ However, we should emphasise that Proposition 6 suggests that the favourable effects of weakening employment protection for permanent jobs will be in exchange for reducing the average productivity of permanent jobs when match productivity is more dispersed. In other words, if temporary contracts are expected to screen workers before they are promoted to permanent employment, increasing labour market flexibility by reducing dismissal costs for permanent jobs makes this screening role less significant because employers become less selective in hiring workers as permanent employment and the proportion of matches with unknown productivity increases.

We finally note the finding of [3] that fixed-term contracts are used as devices for screening workers for permanent positions, especially in uncertain economic environments. Although we must be careful when using the word “uncertain”, statements in Proposition 4 and Proposition 5 are consistent with their finding in the sense that temporary contracts are likely to become a major route to obtaining permanent positions (increases and decreases for a sufficiently higher z). On that basis, these propositions show how the impact of changing dismissal costs on employers’ hiring decisions is affected by the uncertainty in productivity. Together with the effectiveness of the screening role of temporary contracts, policy makers should take into account the effect of employment protection legislation on employers’ hiring strategies regarding both permanent and temporary contracts in a given uncertain economic environment.