Páginas Web

Matching theory tries to explain the formation of a relationship between a complementary pair of individuals. Each relationship (hereafter called match) is attributed a certain value according to the quality of the match, for instance individual productivity in a specific job (Jovanovic, 1979b). Thus, matching theory explains why some relations are maintained and others are separated. This theory focuses on the situation when partners are already matched, which places the matching subsequently after the end of the search process.

Mortensen (1988) regarded two kinds of matching as comparable: marriage and employment. Both relationships are entered voluntarily and generate benefits for both agents since they can exploit opportunities they would not have separately. The quality of a match is determined by the degree both partners fit to each other. Each subject disposes of a bundle of “traits” – demography, biography, personality – which determines the matching quality. Since the

21 Theoretical Considerations and Related Literature

degree of fit differs for every potential pair of individuals, an assignment problem derives. Gale and Shapley (1962) were the first to present a simple matching model for the marriage market in which a number of n men and n women are paired. Individuals rank each other in accordance to their preferences. Then each individual can decide whether to enter a match or to stay single. A relationship is considered stable when both individuals do not want to split up in order to realise a better match. Hence, both members of a partnership have to be compensated for their forgone utility of remaining single or their outside options. In the notation by Mortensen (1988) the total surplus of entering a relationship is defined as:

𝑠_𝑖𝑗 = 𝑓_𝑖𝑗 + 𝑚_𝑖𝑗 − 𝑓_𝑖𝑜− 𝑚_𝑖0 (2.2)

whereas sij stands for the total utility gained by entering the match, fij respectively mij stand

for the utility of females and males, fi0 and mi0 reflect the opportunity costs. Hence, the model

implies that every match generates a surplus that would not derive if both partners were separated.

To allow for heterogeneity of both employers and employees, Crawford and Knoer (1981) set up a model for a number of m workers and n firms (indexed i = 1, …, m and j = 1, …, n). For each potential firm-worker pair there is a vector of work-related outcome variables such as

job satisfaction (aij), productivity (bij), and salary (sij). Under the assumption of

substitutionability of job satisfaction and salary, the individually rational decision of job seekers is defined as follows:

𝑎𝑖𝑗 + 𝑠𝑖𝑗 ≥ 𝑎𝑓(𝑖,𝑗)+ 𝑠𝑓(𝑖,𝑗) (𝑎𝑖𝑗 (𝑖) ≥ 0 𝑎𝑛𝑑 𝑠𝑖𝑗 (𝑖) ≥ 0) (2.3)

Job seekers accept a job offer (or are not willing to leave the firm) if the monetary and non- monetary benefits are at least as high as any other salary and satisfaction combinations in the market. The firm’s rational decision can be described by:

𝑏𝑖𝑗− 𝑠𝑖𝑗 ≥ 𝑏𝑔 (𝑗)𝑖− 𝑠𝑔 (𝑗)𝑖 (𝑏𝑔 (𝑗)𝑖 ≥ 0 𝑎𝑛𝑑 𝑠𝑔 (𝑗)𝑖 ≥ 0) (2.4)

which means that employees are employed or kept when the marginal benefit of this employee is larger than the benefit of any other employee in this position. Under the constraint of imperfect information it becomes obvious that this equilibrium cannot be found easily. In their model, Crawford and Knoer (1981) described a salary adjustment process in which the market equilibrium is found.

Although both models differ as regards to the degree of heterogeneity and the adjustment process, in both approaches a Pareto efficient allocation exists in which the generated surplus is maximised. On entering the new partnership, a bargaining problem accrues as the generated

22 Theoretical Considerations and Related Literature

surplus has to be divided between the matching parties. How this surplus is shared between the two parties is not part of the model. However, a stable equilibrium requires a division in which each party gains more or equal compared to the best alternative match (Mortensen, 1988). Whereas the division of surplus might be rather difficult in the marriage example, the surplus associated to a labour market matching can be shared more easily as employers’ (productivity) and employees’ (wage) surpluses can be valued monetarily. Assuming that wages are related to individual productivity, an increase in matching quality is likely to increase wages. Hence, being able to signalise high matching quality is likely to be beneficial

for both employers and employees.9

A growing yet already large stream of the literature analyses the relationship between P-O

fit10 and various organisational outcomes. Kristof-Brown et al. (2005) provided a meta-

analysis of 172 studies which investigate the relation between P-O fit and pre-entry (e.g. job acceptance) and post-entry (e.g. performance, satisfaction). Their results indicate a strong and meaningful correlation between P-O fit and both pre- and post-entry outcomes. These findings imply the importance of P-O fit for organisations to maintain a productive workforce and to secure their competitiveness.

Though, finding a mutually beneficial partner to match with is less trivial than described above. As both employer and employee do not dispose of complete information, ex-ante matching quality cannot be assessed. Hence, unsatisfactory matches are likely to occur which lead to turnover. Regardless of the exact distribution of matching quality it is obvious that a certain proportion of applications would not lead to the best available match. Hence, expected average matching quality is below the matching quality of the best available match. As employers adjust their wage setting strategy to this volatility in the expected matching quality, offered wages are below the highest possible wage which would be adequate the employee fitting best. As a result, procurement of further information to reduce information asymmetries could be beneficial for employees and employers in order to find the best available matching partner. This rationale connects search models and matching models as search effort is likely to increase matching quality.

9

See Pissarides (1994) for a bargaining model in which the matching surplus is shared between employer and employee.

10 _{Kristof (1996: 3) defined supplementary and complementary fit as two related aspects of P-O fit.} Supplementary fit can be understood as a congruence of individual and organizational characteristics (personality, values/norms, corporate culture). Supplementary fit occurs when, on the one hand, “an organization satisfies the individuals’ needs, desires, or preferences” and, on the other hand, the “individual has the abilities required to meet organizational demands”.

23 Theoretical Considerations and Related Literature