Eugenio Jose

Silva Bitti
email: ebitti@usp.br

Muriel Fadairo
email: muriel.fadairo@univ-st-etienne.fr

Cintya Lanchimba
email: cintya.lanchimba@epn.edu.ec

Vivian-Lara Silva
email: vivianlara@usp.br

Cristina Franco

Spatial strategies in Brazilian Franchising; Behavior categories and Performance Outcome

Keywords: Franchising, Location Strategy, Spatial Competition, Emerging Market, Panel Data M21, C23 Franchising, Location Strategy, Spatial Competition, Emerging Market, Panel Data. JEL

This empirical article deals with the location strategy and performance outcomes of franchised chains in Brazil. Brazilian franchising has experienced vertiginous process of expansion in recent years, being present in different regions of this country of continental size, including the most remote and less developed. Based on the background literature in economics and management regarding location choices and spatial competition in retailing, we use a new and unique dataset to distinguish several behavior categories in spatial strategies of franchising chains in Brazil, via a two-step cluster analysis. The performance outcomes are then studied with econometric estimations on panel data. Our results provide evidence that the choice for agglomeration, and the location in areas with a high population and a high human development index, lead to higher chain performances.

Introduction

This empirical article studies the location strategy and performance outcome of franchised chains in Brazil.

Brazilian franchising has experienced vertiginous process of expansion in recent years, being present in different regions of the country, including the most remote and less developed.

At the moment, Brazil is going through an important economic and political crisis. For 2014, the most optimistic projections attribute growth of less than one digit to the national gross domestic product. As a reflection of this low economic performance, the Brazilian retail sector showed modest growth of 2.2% in 2014. However, franchising in Brazil continues to grow. Thus, according to the Brazilian Franchising Association (ABF), the total income of Brazilian franchising in 2014 grew 7.7% compared to 2013. This growth continued in 2015. Indeed, during the first half of 2015, the income increased 11.2% compared to the same period in 2014, while only for the 2nd quarter of 2015, the income growth was estimated at 13.1% (ABF, 2015).

Despite the current economic crisis, Brazil stands as one of the main emerging economies for the 21st century, and is part of the BRICS, in addition with Russia, India, China and South Africa. One main feature regrouping these emerging countries is their continental dimension, specifically for Brazil, Russia, India and China, which raises the issue of spatial inequalities and agglomeration phenomena in the economic development [START_REF] Fally | Economic geography and wages in Brazil: Evidence from microdata[END_REF][START_REF] Lessmann | Spatial inequality and development ; Is there an inverted-U relationship?[END_REF][START_REF] Cheong | The impacts of structural transformation and industrial upgrading on regional inequality in China[END_REF]. Thus, more than elsewhere, the geographical dimension is a critical point in this context and, at the microeconomic level, location choices are key strategical elements for the economic actors.

Regarding Brazilian franchising, the Southeast accounted for 58.8% in the spatial allocation of franchised units during the first half of 2015, followed by the South (14.9%), as presented in Appendix 1. These regions are the richest of the country. However, other regions have attracted the attention for network expansion. The Northeast is a special case, accounting for 14.1% of franchised units in Brazil in 2015, while it was estimated at around 2% in 2013/2014 (ABF, 2015). Central West and North, in turn, represent respectively 8% and 4.2% in 2015. However, while franchising issues in the BRICS economies is a major field of interest at the moment (Dant & Grünhagen, 2014), and despite several interesting articles dealing more specifically with Brazilian franchising [START_REF] Azevedo | Governance inseparability in franchising: Evidences from case-studies in France and Brazil, 2nd EMNet Conference[END_REF][START_REF] Dant | A cross-cultural comparation of the plural forms in franchise networks: United States, France and Brazil[END_REF][START_REF] Falbe | Nafta and franchising: A comparison of franchisor perceptions of characteristics associated with franchisee success and failure in Canada, Mexico, and the United States[END_REF][START_REF] Lafontaine | International franchising practices in Mexico: Do franchisors customize their contracts[END_REF][START_REF] Silva | Franchising and the acceleration of the food service sector in Brazil: Opportunities for the food industry?[END_REF][START_REF] Streed | International market entry expansion of retail networks: Determinants of market entry failures[END_REF][START_REF] Vance | Internationalization of Brazilian franchisors: profiles and strategies[END_REF][START_REF] Fadairo | Signaling the quality of a business concept; Evidence from a structural equations model with Brazilian data[END_REF][START_REF] Michael | Can franchising be an economic development strategy for developing nations? An empirical investigation[END_REF][START_REF] Resende Melo | Internationalization of Brazilian franchise chains: a comparative study[END_REF], the locational aspects of franchising in Brazil remains mainly unexplored -the only exception being an article by [START_REF] Bitti | Vectors of influence on the contractual mix: geographical dispersion vs. automation in Brazilian franchised chains[END_REF] -, and represents a gap in the literature.

In the retailing literature, location is clearly, and for a long time, considered as a major determinant of firm performance [START_REF] Jones | Location, Location, Location: Analysing the retail environment[END_REF], and as one of the most critical factor of performance in the case of retail networks [START_REF] Cliquet | Integration and territory coverage of the hypermarket industry in France : a relative entropy measure[END_REF]. Thus, in their central articles in the retail location literature, [START_REF] Applebaum | Methods for determining store trade areas, market penetration, and potential sales[END_REF] and [START_REF] Cliquet | Integration and territory coverage of the hypermarket industry in France : a relative entropy measure[END_REF] define the key concepts of store trade areas, market penetration, and potential sales [START_REF] Applebaum | Methods for determining store trade areas, market penetration, and potential sales[END_REF], in addition with the important concept of entropy, measuring the territory coverage of a retail network [START_REF] Cliquet | Integration and territory coverage of the hypermarket industry in France : a relative entropy measure[END_REF][START_REF] Streed | International market entry expansion of retail networks: Determinants of market entry failures[END_REF].

However, as underlined by [START_REF] Ehrmann | Inner strength against competitive forces: successful site selection for franchise network expansion[END_REF], locational strategy for network expansion has received little attention in the franchise literature. When addressed, the geographic dimension is most often taken into account as a way to evaluate the monitoring costs between headquarters and the outlets of franchise chains [START_REF] Brickley | The choice of organizational form: the case of franchising[END_REF][START_REF] Norton | Franchising, brand name capital, and the entrepreneurial capacity problem[END_REF][START_REF] Minkler | An empirical analysis of a firm's decision to franchise[END_REF][START_REF] Maness | Incomplete contracts and the choice between vertical integration and franchising[END_REF][START_REF] Bitti | Vectors of influence on the contractual mix: geographical dispersion vs. automation in Brazilian franchised chains[END_REF][START_REF] Combs | Why do firms use franchising as an entrepreneurial strategy? A metaanalysis[END_REF][START_REF] Perryman | Who should own it? An agency-based explanation for multi-outlet ownership and co-location in plural form franchising[END_REF].

Considering these gaps in the literature, and based on previous researches in economics and strategic management, this paper addresses the following issue: in the Brazilian case of franchised networks, is it possible to highlight different profiles of location choices, and to distinguish the most efficient location strategies?

To characterize the different profiles of networks, we use the concept of behavior categories, referring to Porter (1980)'s strategic groups, defined as sets of firms in an industry that display similar competitive profiles, and to [START_REF] Meyer | Configurational approaches to organizational analysis[END_REF]'s configurations, relating to groups of firms with a common organizational profile. Behavior categories in the locational strategy of franchising networks in Brazil are distinguished by means of a two-step cluster analysis. We use a unique and recent panel dataset enclosing interesting information in terms of geographical location. The study variables for the empirical analysis are derived from the literature relating retailing and location choices. Finally, we perform econometric estimations, and relate behavior categories in location choices to network performance outcomes.

The paper is organized as follows. Section 2 presents the background literature, and identifies relevant choices determining the locational strategy of multi-outlet chains. Section 3 describes the data, providing information on the data collection and the study variables, in addition with summary statistics. The cluster analysis and the estimations are respectively presented in Section 4 and Section 5. Section 6 concludes.

Related research

In view of the objective to investigate behavior categories in Brazilian franchising, this article is related to the clustering tradition of networks in the franchise literature. Several important contributions can be mentioned, [START_REF] Carney | Vertical integration in franchise systems: agency theory and resource explanations[END_REF], [START_REF] Combs | Can capital scarcity help agency theory explain franchising? Revisiting the capital scarcity hypothesis[END_REF]), Combs et al. (2004[START_REF] Gonzalez-Diaz | Differences in contract design between successful and less successful franchises[END_REF], which relate specific strategies characterizing groups of franchise chains with performance outcomes. As mentioned by [START_REF] Combs | Can capital scarcity help agency theory explain franchising? Revisiting the capital scarcity hypothesis[END_REF], the clusters can be derived inductively or theoretically. We give priority to the second case, where the variables used for the clustering process are related to theoretical results. We present hereafter the theoretical background of our analysis.

Given the importance of location choices, previously emphasized, a vast literature dealing with consumer spatial behavior and retail location exists. The aim of this analytical section is not to review this wide research field, but to highlight the theoretical results, in economics and management, relevant to distinguish behavior categories in the location strategy of franchised chains in Brazil. This strategy relates to the choice of where to locate retail outlets. From the background literature, four main determinants of the geographical location strategy of franchised networks can be distinguished. We discuss them in the following.

The choice for agglomeration versus dispersion

Spatial competition, where customer behaviors are influenced by the cost of transportation and the relative locations of purchaser and purveyor, can give rise to a variety of retail location patterns. Agglomeration of retail outlets is one of the most relevant. Indeed, contrary to the aspatial competition of standard microeconomics models, spatial competition has monopolistic features leading to agglomeration. Space introduces monopolistic elements, as in spatial markets all firms enjoy some degree of monopoly power over their immediate market area.

In this analytical context, Hoteling (1929)'s pioneering contribution formally demonstrates the benefits of clustering. Hoteling's model shows that in a duopoly of maximizing firms selling identical products from fixed locations, in a bounded linear market, firms cluster at the center of the market area, guaranteeing themselves one-half share of the market. The modeled noncollusive duopolistic competition results in price stability, and is characterized by the principle of minimum differentiation regarding locational decisions. This demonstration can be extended to several types of locations, not only spatial, for example location in terms of product differences. Still, Hoteling's analysis stands as the main normative theory of retail location, and the principle of minimum differentiation as the most relevant explanation of the agglomeration of similar retail firms.

However, in addition to the benefits of clustering, the risk of cannibalization must be taken into account [START_REF] Pancras | Empirical investigation of retail expansion and cannibalization in a dynamic environment[END_REF]), since we focus on the location choices of retail outlets within the same chain. Cannibalization relates to spatial competition between geographically proximate retail outlets, when the presence of a new unit captures sales of other outlets. The spatial strategy of franchising chains, depending on the choice of where to locate their retail units, is affected by this cannibalization effect. This intra-chain competition effect may thus influence the spatial choices in the way of dispersion versus agglomeration. [START_REF] Pancras | Empirical investigation of retail expansion and cannibalization in a dynamic environment[END_REF] estimate this cannibalization effect and provide evidence for a significant decay in cannibalization with distance. In a context of network expansion, they measure the net impact of a new store opening on the overall chain performance. This impact results from the joint and contradictory effect of incremental sales versus cannibalization. Estimating via econometrics and panel data the parameters of a demand model that captures spatial competition, they highlight a clear empirical link between cannibalization and distance.

With the concept of entropy, [START_REF] Cliquet | Integration and territory coverage of the hypermarket industry in France : a relative entropy measure[END_REF] defines a tool to measure the territory of geographic coverage of a retail chain. If a population of stores is concentrated in one spatial area, entropy is minimum. It is maximum with dispersion.

While the choice for agglomeration versus dispersion concerns the density of retail outlets, spatial strategies also deal with site selection decision, in other words with the choice to locate stores in a specific region or city.

The choice for a specific region or city

With the nearest center hypothesis postulated by the classical central place theory [START_REF] Christaller | Die zentralen Orte in Süddeutschland[END_REF]Losch, 1954), customers necessarily shop at the closest store. Gravity models underline also the importance of geographical distance, but demonstrate that the attractiveness of a retailing location, and therefore the choice to locate in a specific place, is not exclusively related to it.

These models include thus a variety of other factors in the attraction concept.

Gravity models are derived from the laws of Newtonian physics. In this literature, [START_REF] Reilly | The Law of Retail Gravitation[END_REF], [START_REF] Huff | Defining and estimating a trading area[END_REF] and [START_REF] Huff | Delimiting the areal extent of a market area[END_REF] played a pioneering role. Reilly's law of retail gravitation states that consumers trade off the cost of travel to a retail outlet with the attractiveness of alternative shopping opportunities.

More generally, gravitational models allow to study attractiveness phenomena and spatial interactions, considering other attributes in addition to distance related to the potential of a local or regional area, as demographic weight, gross domestic product, or socioeconomic characteristics.

These models suggest thus that there are differences in location quality. As emphasized by [START_REF] Ehrmann | Inner strength against competitive forces: successful site selection for franchise network expansion[END_REF], this is the case with the whole location theory [START_REF] Ghosh | Locating stores in uncertain environments: a scenario planning approach[END_REF][START_REF] Lee | Spatial adjustment of retail activity: a spatial analysis of supermarkets in metropolitan Denver", 1960-1980[END_REF][START_REF] Craig | Models of the Retail Location Process: A Review[END_REF][START_REF] Ghosh | Location strategies for retail and service firms[END_REF][START_REF] Jones | The retail environement[END_REF][START_REF] Simons | Site attributes in retail leasing: an analysis of a fast-food restaurant market[END_REF][START_REF] Kelly | Competitive impact model for site selection: the impact of competition, sales generators, and own store cannibalization[END_REF][START_REF] Peterson | Enterprise-wide analytical solutions for distribution planning[END_REF][START_REF] Christensen | The Strategic Importance of Location: Location Decisions and the Effects of Firm Location on Innovation and Knowledge Acquisition[END_REF][START_REF] Park | An exploratory study to identify the site selection factors for U.S. franchise restaurants[END_REF][START_REF] Khan | Restaurant Franchising[END_REF][START_REF] Park | An exploratory study to identify the site selection factors for U.S. franchise restaurants[END_REF].

Recognizing that some places are more lucrative, or have a greater potential to be profitable, than others, [START_REF] Ehrmann | Inner strength against competitive forces: successful site selection for franchise network expansion[END_REF] study the location decisions in the expansion of franchising networks. These authors show that, in addition with endogenous network characteristics, exogenous location factors related to market perspective criteria, as population density or local income, affect location decisions.

Additional determinants of the location strategy

First mover advantage versus new entrant advantage

The timing is also part of spatial strategies. Indeed, the first firm to locate in a market can capture strategic sites. This first mover advantage acts thus as a barrier to entry and delays the entry of new competitors by affecting their locational choices.

Distinguishing competitive advantages at several stages of a franchise life [START_REF] Lillis | Competitive advantage variation over the life cycle of a franchise[END_REF], and studying territorial expansion of franchised chains in geographically fragmented markets [START_REF] Julian | Franchisor geographic expansion[END_REF], [START_REF] Lillis | Competitive advantage variation over the life cycle of a franchise[END_REF] and [START_REF] Julian | Franchisor geographic expansion[END_REF] develop the idea that when franchisors attempt to capitalize on the first mover advantage by preempting the most desirable locations and saturating the market, locations are dispersed.

In addition, the empirical findings of [START_REF] Carney | Vertical integration in franchise systems: agency theory and resource explanations[END_REF] highlight the heterogeneity of strategies in franchising chains. These authors argue that the need for spatial preemption, and the accompanying rapid growth, is particularly important when franchisors have innovative retail concepts.

Finally, considering the short-and long-run incentives to franchise, and monitoring problems related to geographic dispersion, [START_REF] Martin | Franchising, liquidity constraints and entry[END_REF] explain the intensive use of franchising in the early growth stages, arguing that growth and preemptive strategies are most important for young franchisors.

However, the alternative strategy can be interesting too. Later entrants may have an advantage since they are better able to react to changing conditions 2.3.2. Location choices and network ownership structure As previously mentioned, in the franchise literature, the location issue is most often taken into account within the agency theory framework and the related monitoring cost problem.

Since the pioneering contributions of Rey & Tirole (1986a, 1986b), Mathewson & Winter (1983a[START_REF] Mathewson | Vertical integration by contractual restraints in spatial markets[END_REF], 1984[START_REF] Mathewson | The Economics of Franchise Contracts[END_REF], agency theory, focusing on the delegation of tasks, is the main theoretical context to study franchising. The literature highlights free-riding behaviors in retail networks, and underlines the deriving need for the headquarters to monitor the outlets [START_REF] Brickley | The choice of organizational form: the case of franchising[END_REF][START_REF] Lafontaine | Incentive contracting and the franchise decision[END_REF][START_REF] Lal | Improving channel coordination through franchising[END_REF][START_REF] Michael | The Elasticity of Franchising[END_REF].

Network expansion and spatial dispersion increase the monitoring agency problem. In other words, with the geographical dispersion of the network, the costs of monitoring managers and enforcing quality standards increase. Monitoring outlets in geographic markets that are far from headquarters is more costly, due to the number of monitoring personnel required and to the related travel expenses [START_REF] Carney | Vertical integration in franchise systems: agency theory and resource explanations[END_REF].

Because they are independent firms, franchisees are more likely to provide efforts, requiring thus less monitoring. This situation would impact the ownership structure of retail networks, mixing strategically company-owned units and franchised units as part of their location strategy. This argument finds empirical support in the econometric work on franchise data. Indeed, as emphasized by [START_REF] Perryman | Who should own it? An agency-based explanation for multi-outlet ownership and co-location in plural form franchising[END_REF], the most common test of the monitoring cost prediction in the framework of the agency theory investigates the relationship between the geographic dispersion of a chain and its ownership composition, that is the proportion of franchised outlets or, on the reverse, the proportion of company-owned outlets. [START_REF] Brickley | The choice of organizational form: the case of franchising[END_REF], [START_REF] Norton | Franchising, brand name capital, and the entrepreneurial capacity problem[END_REF], [START_REF] Lafontaine | Agency theory and franchising some empirical results[END_REF], [START_REF] Maness | Incomplete contracts and the choice between vertical integration and franchising[END_REF], [START_REF] Combs | Why do firms use franchising as an entrepreneurial strategy? A metaanalysis[END_REF], [START_REF] Combs | Why do firms use franchising as an entrepreneurial strategy? A metaanalysis[END_REF], [START_REF] Bitti | Vectors of influence on the contractual mix: geographical dispersion vs. automation in Brazilian franchised chains[END_REF], provide evidence that outlets located close to headquarters are more likely to be company owned, while retail units in more distant locations are more likely to be franchised. Moreover, monitoring costs arising from the geographical dispersion of the chain would be sufficient to explain the franchise option. More generally, at the chain level, the higher the geographical dispersion, and thus the related monitoring cost, the lower the proportion of company-owned outlets.

Therefore, a clear link is established between spatial strategies of franchising networks and the chain ownership structure.

The Data

We use recent panel data for the period 2009-2014, regarding 335 franchise networks. The sample franchise chains occupy 1,397 Brazilian municipalities, and are present in the 26 Brazilian states.

Our unique dataset compiles information from three main distinct sources: the ABF's Official Franchise Guides, the websites of franchise chains, and the Brazilian Institute of Geography and

Statistics (IBGE).

We present hereafter the data collection process, and then the study variables derived from the analytical framework. We discuss the relevance of the sample, comparing with the full population. Finally we provide summary statistics.

Data collection

Our first source is the ABF's Official Franchise Guide. This annual publication provides valuable information on the Brazilian franchise sector. More precisely, the guide contains data concerning chain characteristics, as the franchise fee, the total number of outlets, the required investment level of the franchisees, the number of employees, and so on. We obtained data for the period 2009-2014.

In order to achieve a better understanding of how the ABF collected the information used to construct our dataset, we performed interviews with executives from this organization. Specifically, we performed interviews with the President of the ABF, his executive director, and his marketing analyst, who is responsible for both collecting and pooling information provided by the franchised networks.

The ABF has an internal information system accessible to associated franchised chains, which are free to update information regarding their network in real time. The chains have an interest in keeping up-to-date information, since the Guide is an important communication channel with potential franchisees. Divergent or even fake information could damage the reputation of the chain, or make the search for potential franchisees mode difficult. Therefore, there is a strong incentive for franchising networks to offer good quality information.

In addition, the ABF controls for the consistency of the data, analyzing systematically the annual variations before publishing official information. Any anormal variation is checked and corrected.

However, the ABF does not already have a scientific advising council. For this reason, the ABF marketing department performs both the monitoring and the validation of provided data. If necessary, specialized consultants are hired for more specific studies.

The websites of the sample franchise networks are our second main source of information.

The manual capturing of website data was used to perform control checks, and to complete the missing values from the ABF guides. In addition, we used this data source to collect spatial information regarding the Zip codes of cities were the franchised chains are established, in addition with the proportion of network outlets operated in shopping malls. When the network websites were incomplete, we used the PEGN publication, which is a SME specialized Brazilian media.

As our analysis requires localized data, we use a third source of information, the Brazilian Institute of Geography and Statistics (IBGE). We collected information about georeferencing (longitude and latitude) of the municipalities where franchising networks are established, the Gross Domestic Product (GDP), the population, and the Human Development Index (HDI).

The IBGE information comes from censuses conducted in 1991, 2000 and 2010.

Municipalities HDI data are also available in the United Nations Development Program (UNDP) website for the years 1990, 2000 and 2010.

We pooled the different sources of information, performed crosschecks, and matched the data in order to stabilize the final sample enclosing the required information for our empirical analysis.

Finally, as all the Brazilian chains are not associated to the ABF, we controlled for the bias in our sample compared to the franchise network population in Brazil. To do so, we performed an initial analysis with some Brazilian franchising consolidated information available on the ABF website. Table 1 presents the 11 segments of the franchising industry in Brazil, based on the ABF taxonomy. For each segment, we tabulated data regarding the total income of the segment, the number of chains and the number of outlets (company-owned and franchised) in 2014. It is thus possible to compare the franchising sector in Brazil as a whole, to both the whole "ABF chains" and our final sample. Table 1 presents the absolute values and the ratios for each sector in comparison to the total for each of the three variables used in the bias analysis1 .

Two segments appear over-represented in our sample (as in ABF as a whole): Food and Shoes & Accessories. This over-representation occurs for the three variables. The proportion of chains in these segments is between ABF associated chains compared to the Brazilian franchising sector as a whole; and it is greater in the sample compared to ABF. This is also the case for the total income and for the total number of outlets. Conversely, segments of House & Building and Business, Services & Other Retails appear underrepresented. The sample contains 11.3% of all chains operating in Brazil, 26.6% of the outlets. The sample networks represent 31.2% of all sector incomes. In summary, data indicate a bias in the sample relative to the population: the sample networks are typically larger, and the sector representation does not reflect exactly the population. For this reason, some dose of parsimony should be included when analyzing the results.

However, we insist on the good quality of the data, compiling three different and complementary sources of information. Our unique sample consists of a six-year panel, in a wide range of activities, and contains geographical information. The aforementioned bias regarding some specific segments calls for the use of sector dummies in the econometric estimations in order to control it.

Measurement

We present hereafter the study variables, used in the empirical estimations, and in the cluster analysis determining behavior categories in spatial strategies of franchising chains in Brazil.

The variables for the cluster analysis are based on the background literature regarding location choices in franchising or, more broadly in retailing. In line with our analytical framework, these variables are the following: the network geographic dispersion, the percentage of network outlets located in shopping malls, the weighted average human development index of the network location area, and the weighted average population of the network location area. In addition with these localized variables, we include complementary variables related to the location strategy: the network age, the percentage of company-owned units, and the chain brand value.

In the econometric estimations, the dependent variable is the average monthly income per outlet. The core explanatory variable is the network location strategy constructed via the cluster analysis. We add variables to control for the influence of the sector, of the headquarter nationality, and of the ABF certification of excellence.

More details are provided in the following.

3.2.1. Variables defining the chain location strategy (Cluster Analysis)

Location variables

Network Geographic Dispersion

The construction of this variable is based on the geographic location of the network outlets.

First, we surveyed the addresses of all the sample network outlets in 2011 and 2014. We created thus two specific data sets containing information regarding the Brazilian municipalities where the franchising chains are established. Then, we georeferenced the cities where the stores are located, getting their latitude and their longitude.

On this basis, we constructed geographic clusters for each network regrouping stores located in the same area. Each cluster is thus an area of agglomeration of network outlets. We defined the center for each cluster so that the cumulative distance between the stores and the cluster center is the smallest possible1 .

The distance criterion is the Euclidean distance based on the latitude and the longitude of the cities where each store is located. For example, assuming that a store A is located in the point (x A , y A ) and a store B is located in the point (x B , y B ), the Euclidean distance between them is defined as follows:

!(#, %) = (() * -) , ) -+ (/ * -/ , ) -)

Our variable, the network geographic dispersion, is measured as the distance between the stores in the clusters, to which we add the distance between the centers of the chain clusters.

Percentage of network outlets located in shopping malls

Jointly with the outlet addresses, we also captured whether the store is located in some kind of shopping mall. Thus, for each chain in our sample, we are able to define the proportion of outlets located in shopping centers, in a percentage base.

Weighted average HDI of the network location areas

The Human Development Index (HDI) is a socio-economic indicator developed by the Units Nations Development Program (UNDP) in the early 90's to measure both the countries socioeconomic development of countries and their constituent units (states, provinces, municipalities, etc.).

This multidimensional indicator aims at going beyond the only economic issue, and captures, in addition with economic features, some aspects related to public health and education.

Moreover, given its synthetic character, the index allows establishing a ranking and, as a result, certain comparability between countries and regions. More precisely, the HDI compiles three indexes relating to three distinct socioeconomic dimensions:

• Longevity -which measures life expectancy at birth and also reflects the health of the population;

• Education -an index operationalized by a combination of the adult literacy rate and the combined enrollment rate in primary, secondary and higher education;

• Income -a measure of population's purchasing power based on GDP per capita adjusted to the local cost of living to make it comparable across countries and regions, through the methodology known as purchasing power parity.

The IBGE provides information regarding the HDI for each Brazilian state and municipality.

Since its inception in the early 90's, the HDI has been recorded three times (1990, 2000 and 2010). In our study, we use the index calculated by the UNDP in 2010.

Our study variable is the weighted average HDI of cities where the network is established. We use as weight the number of stores per town.

Weighted average population of the network location areas

The Brazilian Institute of Geography and Statistics (IBGE), implements for the Brazilian government a population census approximately every 10 years, with the last three censuses conducted in 1991, 2000 and 2010. Out of this period, the IBGE estimates the population per municipality by linearizing the trend indicated by the last two censuses. We used the IBGE estimates for 2011 regarding the population of the cities were the sample chains were established, in 2011 to calculate the weighted average, using the same procedure as with the HDI.

Additional variables related to the location strategy

Network age

The age of the network is the difference between the year of the first franchised unit and each year in our panel.

Percentage of company owned-units

This variable represents for each franchising chain the proportion of company-owned units in the total of the chain outlets.

Brand value

The ABF yearbooks provide information about a total of thirteen types of supports that the associated franchisors offer to their franchisees. Parts of them are obligatory, as defined by the Brazilian Law of Franchising (No. 8955/94). The other supports are optional. They are: legal support, choice of plant and equipment, support for financing leverage, promotional support, financing of project, marketing project, organizational design, design/production layout of the new store, and advertising and marketing.

In our dataset, all these types of supports are represented by a dummy variable. We add these dummies to construct a proxy of the brand value, related to the franchisor's effort.

Variables used to study the performance outcome (Econometric estimations)

Dependent variable

Network average monthly income per outlet

The performance indicator is the dependent variable of our econometric models. We used the network average monthly income per outlet. This information is available in the ABF Franchising

Guide. We collected the information from 2009 to 2014.

Core explanatory variable

Location strategy

The network location strategy is the main explanatory variable of our econometric models. We constructed this variable with a two-step cluster analysis (section 4), using the variables previously presented (subsection 3.2.1.).

Control variables

Sector dummies

The ABF Guide offers a sector classification. We made the choice to use this official classification of the franchising chains in Brazil to construct sector dummies. The classification is presented in Table 1.

Foreign

We constructed an additional dummy variable to indicate whether chains operating in Brazil have a Brazilian or a foreign headquarter.

ABF label "certification of excellence"

The ABF Seal of Excellence is awarded to distinguish chains achieving a minimum level of satisfaction among its franchisees. This certification is based on a survey of the franchisees, conducted by the ABF. The results are published annually in the Franchising Guide.

Franchising chains that reached the specified satisfaction ratings are identified with the label.

It is important to mention that chains have to pay to be part of the contest. Franchisees satisfaction indexes include the overall chain performance (the franchisor quality in coordinating the whole chain), the brand performance with regard to profitability, and operating performance of the chain (class support to franchisees).

We used a dummy variable to indicate the chain situation during the period 2009-2014.

Summary statistics

Table 2 reports the means, standard deviation, and correlation matrix. Because the presence of a few missing values may bias the estimations, we completed the data with the average values.

Descriptive statistics indicate that the variables are quite homogenous in the sample, as shown by the means higher than the standard deviations. However, this is not the case with the variables dispersion and percentage of company-owned units, characterized by some degree of heterogeneity.

Behavior categories in spatial strategies

Methodology

In order to construct the variable location strategy, that will be the core explanatory variable in the estimations, we use a two-step cluster analysis. This statistical multivariate technique is indeed developed in two phases. The aim is to achieve the maximum intra-group homogeneity and the biggest inter-group heterogeneity that would otherwise not be apparent.

To carry out this analysis, in the first stage, the individuals are distributed into pre-clusters, which become single individuals in the second stage. This second stage consists in applying a hierarchical algorithm in the pre-clusters. The advantage of this method is that categorical and continuous variables can be included. In addition, the number of clusters is automatically selected and the method allows controlling for the quality of the clustering process.

As previously mentioned, our analysis is based the following variables: the network geographic dispersion, the percentage of network outlets located in shopping malls, the weighted average human development index of the network location area, and the weighted average population of the network location area. In addition with these localized variables, we include complementary variables related to the location strategy: the network age, the percentage of company-owned units, and the chain brand value.

As we use a panel dataset, we consider here each franchised network for a specific year as a different individual the other years. This methodology enables to capture changes in strategy over time.

Finally, we use the variable network geographic dispersion as criterion to order the clusters, and to construct on this basis the ordered qualitative variable location strategy.

We perform two additional cluster analyses i.e. two additional ways to construct the variable location strategy, for robustness checks in the econometric estimations. All the clustering processes present a good quality level, as shown in Appendix 2.

Data analysis and features of the three behavior categories

The first and main clustering process allows us to distinguish three groups of franchising networks in Brazil. On the basis of descriptive statistics for each group2 , the following comments can be offered to specify the three behavior categories.

The first group that we label "concentrated beginners franchisors" contains the youngest networks (15.9 years), with a low geographic dispersion. These chains are established in cities with a moderate population and HDI. The franchisors in this group have established franchised units almost immediately. These networks are also characterized by a moderate presence in shopping malls. Regarding the contract design, the royalty rate and the upfront fee of these chains are smaller in average compared to the two other groups.

We label the second group "concentrated mature franchisors". This second category consists of older networks (27.1 years), with a moderate geographic dispersion. This group is distinguished by a positive and significant relationship between the HDI and the total number of units; the units are located in cities with a high population. In addition, the networks are mainly present in shopping malls. In this group, the presence in shopping malls is positively and significantly related to the royalty rate. The reason of this correlation could be the strong brand name value, compared to the other two groups.

The third group is labeled "dispersed mature franchisors". The networks in this group have a high level of geographic dispersion, and they are the oldest (29.78 years) in average in the sample. The age is positively and significantly related to the number of cities where the network is established.

In addition, the number of cities where the network is established is significantly and negatively related to the percentage of company-owned units. This correlation is clearly higher compared to the other two groups. This seems to indicate that the expansion process experienced by these chains is strongly driven by franchising.

From this analysis, two main discriminating variables are highlighted: the network geographic dispersion and the network age. As previously mentioned, we make the choice to order the ordered qualitative variable location strategy, constructed with the two-step cluster analysis, using the network geographic dispersion. This variable is the main regressor in our econometric models, as presented hereafter.

Performance outcome of spatial strategies

Methodology

Regarding the choice of the econometric model, as we use panel data, we compare first the random effects model and the fixed effects model. Both of them address the problem of the unobserved heterogeneity by specifying an error term constant over time for each unit (fixed effects model) or randomly distributed over time for each unit (random effects model).

Estimation results

Our estimation results are reported in Table 3, and concern the influence of the location strategy on franchised chain performances (models 1 and 2).

For robustness checks, we perform estimations with alternative construct of the location strategy 3 (models 3-6). We comment first the good global significance of the models, highlighted by the Wald Chi2 tests. In addition, comparing the estimations of the models based on three, seven and nine clusters, the models including or not sector dummies, and the models including or not control variables, we conclude that the results are robust.

The main result of this set of estimations is the clear significant influence of the location strategy on the network performance. As clusters are ranked regarding the dispersion variable, the negative sign means that higher network geographic dispersion generates a lower performance. In other words, agglomeration would favor chain performance.

3 Cluster analyses with seven and nine groups, in model (3---4) and (5---6), respectively.

The two control variables have also a significant impact on the network performance.

Logically, a positive relationship is highlighted between ABF labeled chains and performance.

The headquarter nationality (Brazilian versus no-Brazilian) has also an effect on the chain performance. The negative sign indicates here that chains with Brazilian headquarters are more likely to achieve higher performances.

As the location strategy variable sums up several strategic decisions of the franchised chain, we estimate additional models including as regressors the variables initially used in the clustering.

The aim is to go further in the comments, based on complementary results. The full estimation results of these models (models 7-10) are presented in Appendix 3. We provide a summary of these results in Table 4.

Here again we obtain a good global significance of the estimated models, and the results are robust. The significant and negative sign of the variable Network geographic dispersion provides support to the preceding empirical results, indicating that agglomeration favors chain performance.

These estimation results provide additional evidence.

First, the location in shopping center impacts significantly and positively chain performance.

Multiplicative variables have no significant impact, suggesting that the interaction of dispersion with the network age or with the proportion of company-owned units does not affect the performance.

Consistent with the gravity models, location in area with a high HDI, or a high population, increases chain performance. We obtain a reverse and surprising sign with the GDP (model 7).

Concerning the control variables, the sign regarding the variable foreign is consistent with preceding results; the network age and the brand value favor the chain performance, which stands to reason.

Conclusion

The literature in economics and management underlines the role of location choice as one of the most important decision regarding retailing. Indeed, location is paramount as it defines the access and attraction of large numbers of customers, impacting thus the chain market-share and profitability.

Studying Brazilian franchising, we focus on spatial strategies of franchising chains in this continental sized emerging country.

In order to highlight the potential determinants of location choices, we first survey previous literature related to location decision and spatial competition between the franchisees of a same chain.

Our analytical framework takes into account the complexity of store location problems, and the different factors potentially relevant. Four determinants of the location strategy are distinguished: the choice for agglomeration of the chain outlets versus dispersion in the space, the choice for a specific region or city, related to the socioeconomic features of the area, the choice for a preemption strategy to get a first mover advantage, related to the network age, and the location choice related to the ownership strategy of the chain.

The empirical analysis is conducted on a new, recent, and unique panel dataset compiling information from three complementary sources, and containing geographical data, for the Brazilian case. With a two-step cluster analysis, we compile information related to location decisions to distinguish several spatial strategies of franchising chains in Brazil. These strategies are then submitted to econometric estimations in order to derive performance outcomes.

Our results show that the choice for agglomeration leads to higher chain performances, which is consistent with the Hoteling's model prediction. In addition, our estimation results provide evidence for the gravity model, as the chains located in area with high population and human development index reach higher performances.

Appendix 1. Brazilian franchising around the country

Source: Brazilian Franchising Association (2015)

Appendix 3. Additional results for the performance outcome of spatial strategies

Table 1 -Bias Analysis -Comparison between the Brazilian franchising sector, ABF associated chains, and the sample (source: ABF 2014)

 1

	Segments	Total Income (R$ million)				Total Number of Outlets					Total Number of Chains
	ABF Classification	Sector		ABF		Sample	Sector		ABF		Sample	Sector	ABF		Sample
		R$	%	R$	%	R$	%	Un.	%	Un.	%	Un.	%	Chains	%	Chains	%	Chains	%
	Shoes & Accessories	8.847	6,9	7.247	8,8	5.982 14,9	8.285	6,6	6.390	8,1	4.787	14,3	216	7,3		9,8	39	11,6
	Food	25.635	19,9 22.472 27,3 18.562 46,2	21.720	17,3 19.394 24,6 11.085 33,2	685	23,3	258	27,4	119	35,5
	House & Building	7.320	5,7	4.489	5,5	701	1,7	5.380	4,3	4.262	5,4	424	1,3	159	5,4		7,3	4	1,2
	Advertising, Informatics & Electronics	3.867	3	525	0,6	230	0,6	3.336	2,7	1.049	1,3	207	0,6	142	4,8		3,6	4	1,2
	Education	8.538	6,6	6.885	8,4	4.264 10,6	14.732	11,7 10.714 13,6 7.307	21,9	298	10,1		10,4	44	13,1
	Sports, Health, Beauty & Leisure	23.288	18,1 11.436 13,9 4.581 11,4	20.670	16,5 11.928 15,1 4.956	14,8	547	18,6	136	14,4	54	16,1
	Hoteling & Tourism	9.329	7,2	3.483	4,2	1.023	2,5	2.674	2,1	791	1	160	0,5	49	1,7		1,5	3	0,9
	Cleaning	1.159	0,9	1.403	1,7	382	0,9	3.426	2,7	2.586	3,3	800	2,4	97	3,3		3,4	5	1,5
	Business, Services & Other Retails	26.726	20,7 15.332 18,6	828	2,1	28.616	22,8 5.041	6,4	1.015	3	305	10,4		9,2	22	6,6
	Cars	4.490	3,5	3.872	4,7	1.244	3,1	8.032	6,4 12.733 16,2	648	1,9	115	3,9		3,1	4	1,2
	Clothes	9.677	7,5	5.115	6,2	2.369	5,9	8.770	7	3.939	5	1.998	6	329	11,2		10	37	11
	TOTAL	128.876		82.259		40.166		125.641		78.827		33.387		2.942		943		335

Table 1 -Summary statistics and correlations

 1

		Average	SD	1	2	3	4	5	6	7	8	9	10
	1. Location Strategy	2.43	0.62	1	,000 ** .012 ,000 **	.000 ,000 **	.033 ,000 ** .042 .025
	2. Network Dispersion	0.40	2.49	,000 **	1	-,080 ** ,000 ** -,100 ** -,083 ** -,061 ** -,096 ** -,053 * -.042
	3. % of network outlets in Shopping Malls	0.42	0.39	.012 -,080 **	1	-.039 ,089 ** -,052 * ,000 ** ,000 ** ,000 ** ,000 **
	4. Network Age	21.66	15.09	,000 ** ,000 ** -.039	1	-.016 -,046 *	.006 -,050 * -.003 ,000 **
	5. % of Company-Owned Units	0.21	0.25	.000 -,100 ** ,089 ** -.016	1	,000 ** ,000 ** ,044 * ,095 ** ,000 **
	6. Brand value	10.78	2.36	,000 ** -,083 ** -,052 * -,046 * ,000 **	1	.024 ,065 ** ,052 * .005
	7. Mean Population of the network location area	3.29	2.32	.033 -,061 ** ,000 ** .006 ,000 **	.024	1	,000 ** ,000 ** ,000 **
	8. Mean HDI of the network location area	0.78	0.01	,000 ** -,096 ** ,000 ** -,050 * ,044 * ,065 ** ,000 **	1	,000 ** ,082 **
	9. Mean GDP of the network location area	125.01	98.84	.042	,053 * ,000 ** -.003 ,095 ** ,052 * ,000 ** ,000 **	1	,100 **
	10. Performance	84.76	76.79	.025	-.042 ,000 ** ,000 ** ,000 **	.005 ,000 ** ,082 ** ,100 **	1
	* Three variables have a higher scale than the others, and are thus divided by 1000 000: Network Dispersion, Mean GDP of the
	network location area, Mean Population of the network location area.

Table 2 -Performance outcome of spatial strategies (1)

 2

		Random-effects models for the average monthly income per outlet
		(1)	(2)	(3)	(4)	(5)	(6)
		(3 clusters)	(3 clusters)	(7 clusters)	(7 clusters)	(9 clusters)	(9 clusters)
	Location Strategy	-1.839*	-3.304 ***	-1.840 ***	-0.572*	-1.173 ***	-0.724 ***
		(1.011)	(0.840)	(0.304)	(0.298)	(0.205)	(0.205)
	Foreign		-26.71 ***		-26.83 ***		-25.92 ***
			(3.718)		(3.980)		(3.927)
	ABF label		1.547 **		1.559 **		1.664 **
			(0.704)		(0.701)		(0.709)
	Sector dummies	no	yes	no	yes	no	yes
	Year dummies	yes	yes	yes	yes	yes	yes
	Constant	77.70 ***	92.38 ***	80.22 ***	84.99 ***	79.66 ***	86.20 ***
		(2.645)	(2.439)	(1.232)	(1.145)	(1.165)	(1.186)
	N	2010	2010	2010	2010	2010	2010
	Wald chi2	124.62***	883.62***	191.77***	954.71***	188.93***	950.88***
	Standard errors in brackets

* p < 0.05, ** p < 0.01, *** p < 0.001

Table 3 -Performance outcome of spatial strategies (2)

 3 Summary of additional estimation resultsRandom-effects models for the average monthly income / outlet

	Mean HDI of the network location area	+	***
	Mean population of the network location area	+	***
	% of network outlets in shopping malls	+	***
	Network geographic dispersion	_	***

  Random effects models for the average monthly income per outlet p < 0.05, ** p < 0.01, *** p < 0.001

		(7)	(8)	(9)	(10)
	Network Geo Dispersion	-0.321*	-0. 450*	-0. 141*	-0. 078 **
		(0.269)	(0. 277)	(0.0846)	(0.00349)
	% of network outlets in	8.096 ***	7.634 ***
	shopping malls
		(2.296)	(1.955)
	Dispersion x Age			-0.0170
				(0. 221)
	Dispersion x Owned units				0.194
					(0. 124)
	% of company-owned units				-2.075
					(1.742)
	Mean GDP of the network	-0. 276 ***
	location areas	(0.00492)
	Mean HDI of the network		241.2 ***	190.6 ***	175.8 ***
	location areas		(39.79)	(36.00)	(49.76)
	Mean population of the	0. 139 ***	0.0172 ***	0.0259 ***	0.0268 ***
	network location areas	(0.0210)	(0.00301)	(0.00304)	(0.00451)
	Network age	0.448 ***	0.465 ***	0.406 ***	0.443 ***
		(0.0551)	(0.0517)	(0.0471)	(0.0461)
	Brand value	0.563 **	0.645 **	0.279	0.519 **
		(0.238)	(0.215)	(0.232)	(0.236)
	Foreign	-26.24 ***	-28.63 ***	-24.63 ***	-26.50 ***
		(4.196)	(4.319)	(3.776)	(4.107)
	Sector dummies	yes	yes	yes	yes
	Year dummies	yes	yes	yes	yes
	Constant	48.43 ***	-127.9 ***	81.59 ***	83.73 ***
		(3.631)	(31.44)	(1.051)	(0.925)
	Number of networks	335	335	335	335
	Wald chi2	712.49***	877.87***	790.55***	996.18***
	Standard errors in brackets

*

To calculate the total sales (income) of the networks associated to the ABF (and therefore of the sample chains), we computed the average income per store, which is multiplied by the total number of stores. We treated the missing values using the average value for each segment.

To split the data and to determine the appropriate number of clusters for each chain, we used the "R" package "NbClust" and the "Kmeans" R function.

The whole descriptive statistics are available upon request.

Regarding the two variables "Foreign" and "ABF label", the instrumental variables methodology cannot be used. Indeed, our dataset does not provide relevant instruments for these two variables. However, removing them from the models (step-by-step approach), we observe that the estimation results remain qualitatively similar. For this reason, we conclude that there is no endogeneity problem with these variables.

We perform Hausman tests to compare the random effects model with a model including instrumental variables for the suspected endogenous variables.

Acknowledgements:

This research has received funding from the University of São Paulo, Brazil, and from the University of Lyon, France. We would like to acknowledge our respective institutions. We also wish to thank the Brazilian Franchising Association, more particularly Ricardo Camargo, President for the period 2010-2011, Rogério Feijó, Executive Director, and Lilian Greziou, Market Analyst, for their valuable help regarding the construction of our dataset.

We are grateful to Gérard Cliquet and Josef Windsperger for their insight and support. Ms. Bianca Maria Silva provided excellent research assistance. Additional thanks to the participants of the franchise session of the 7 th International Conference on Economics and Management of Networks -EMNet 2015, Cape Town, South Africa, December 3-5, for interesting feedback. All errors are ours.

With short periods panels, as with the sample, the random effects model may produce better estimators than the fixed effects model (Heckman, 1981). In addition, the random effects model is consistent in the presence of time-invariant variables [START_REF] Greene | Econometric Analysis[END_REF]. This is not the case of the fixed effects model. Indeed, time-invariant variables can be perfectly collinear with the fixed effects, while most of the contract variables are by nature almost time-invariant.

The Hausman test confirms our intuition, and shows that the random effects model is more appropriate to the data (χ 2 : 1.44, p-value: 0.487) Additional checks are performed, which confirm the choice for the random effects model.

We use the Lagrange multiplier test to see if the variance across the franchised networks is zero. This test supports the random effect model, since it provides evidence of significant differences across the networks (χ 2 : 3228.64, p-value: 0.000).

Using again the Hausman test, we check for potential problems of endogeneity, since the regressors may indeed raise endogeneity problems, because they are geographical characteristics from where the outlet is located deriving from the franchisor's choice. We compare an instrumental model including as instrument the lagged variable, with the previous results. The results presented in Appendix 4 show that there is no problem of endogeneity.

In addition, we perform a likelihood-ratio test regarding heteroskedasticity at the panel level.

The results (χ2: 3307.8, p-value: 0.000) confirm that the data in the sample do not have a common disturbance variance, providing thus another support for the random effect model. We also test for autocorrelation. The results (χ2: 13.23, p-value: 0.000) show that we have to correct this problem.

In order to correct these different problems we use the generalized least squares method (GLS). This method enables us to estimate the unknown parameters of a linear regression model.

The GLS is applied when the variances of the observations are unequal (heteroscedasticity problem), or/and when there is a certain degree of correlation between the observations. It is well known that in both cases the ordinary least squares (OLS) can be statistically inefficient, or even provide misleading inferences.

Finally, we test if all year coefficients are not jointly equal to zero. The results (χ2: 215.11, pvalue: 0.000) show that the time-fixed effects are needed.

All the results of the specification tests are presented in Appendix 4.

Appendix 2. Summary of clustering analyzes


Sébastien Ménard
email: sebastien.menard@univ-lemans.fr

Coralia Quintero
email: coralia@ugto.org

Absenteeism and productivity: the experience rating applied to employer contributions to health insurance

Keywords: Health Insurance, experience rating, productivity. JEL Classification:I13, I18

In this paper we analyze the effects of introducing experience rating on the employer contributions to health insurance. Generally, theoretical literature explains absenteeism by the workers' behavior. However, working conditions also has an effect on the use of sick leaves. As a result, Firms proposing good working conditions support the costs generated by the other firms. This implies a reduction of the good quality jobs on the benefit of the bad quality jobs. In this paper, we propose to introduce a modulation of employer contributions to health insurance based on historical rates of absenteeism. We show that the experience rating improves the productivity of the economy and welfare, when the unemployed are able to direct their research towards the good-quality jobs.

INTRODUCTION

Absenteeism, that is the employee's habitual absence from work, is expected to have a negative impact on productivity given the costs associated to it, for instance: wages paid to absent employees, costs of replacement workers, administrative costs of managing absenteeism, etc. People miss work for a variety of reasons, but illness and injuries are two major and legitimate causes of absenteeism directly linked to job conditions.In point of fact, statistics on occupational diseases, sickness absence, and disability pensions, show that there is still a need to improve safety and health at work (Kankaanp??, 2010). To this goal, incentives have been used in several countries as a policy tool for the promotionof safety and health at the workplace.

The economic rationale behind this is that most resource allocations in society relies on the functioning of the market, but markets function well only in very specific circumstances guaranteeing optimal allocations. Otherwise, it is necessary to look for actions to correct the market failure.On the safety and health at work context, the market does not reach the optimal solution. In part due that unsafe working conditions usually also result in costs uncovered by employers. These costs or negative externalities then must be borned by third parties, such as families and society at large. Moreover, as is pointed out by Kankaanp?? (2010), in the labor market workers usually have insufficient information about risks at work. Also employers lack information about ways and methods to reduce risks or improve working conditions. Then, the introduction of incentives may be an option to correct these failures as long as they can induce the desired behavior.

The experience rating has already been implemented for unemployment insurance 1 . In this more common context, the general method of introducing experience rating is to adjust employers? premiums according to their ex-employees? reliance on benefits, a method that is most commonly found in systems where all premiums are assessed to employers (de Raaf, [START_REF] De Raaf | A Literature Review of Experience-RatingEmployment Insurance in Canada, Social research and demonstration corporation (srdc) Working Paper Series[END_REF].

On the safety and health side, Mansfield et.al. (2012) point that since the late 1970s, this approach has become increasingly prevalent in several countries, including Canada, the United States, Australia and New Zealand. The premise of experience rating is that employers who maintain safer workplaces should be rewarded with lower premiums, while those with more workplace accidents should be penalized with higher premiums. The approach is meant to remedy deficiencies in flat-rate or manual-rated systems by adjusting premiums on the basis of injury costs, thereby providing incentives for employers to invest in health and safety. Similarly, [START_REF] Lengagne | Workers Compensation Insurance: Incentive Effects of Experience Rating on Work-related Health and Safety[END_REF] present a survey on empirical literature on the incentive effects of experience rating in the field of work-related health and safety. The author finds that several studies indicate that experience rating has an effect in reducing the frequency of workplace injuries and the duration of injury-related sick leave. Similarly, a number of empirical papers focuses on working conditions. This is the case of [START_REF] Valssenko | Absentéisme: le poids des facteurs collectives[END_REF], [START_REF] Strauss | Health, nutrition and Economic development[END_REF], [START_REF] Kuhn | The public health costs of job loss[END_REF], Browning, Dano and Heinesen (2009). For [START_REF] Ose | Working conditions, compensation and absenteeism[END_REF], absenteeism can be attributed to a deterioration of health capital. Using French data, Afse and Givord (2009) highlight a link between irregular schedules of working and absenteeism.

Then, conversely toprior theoretical literature on the link between health and employment usually focused on the behavior of workers,in this paper we consider the experience rating as a financial incentive addressed to firms, provided that the employer premiums are not based on average costs 2 . Instead, each employer will be charged based on its own record of claims. We expect that this toolwould improve the labor market outcomes regarding health 1 The experiencerating in the unemployment insurance system consists on taxing companies based on their historical layoffs. On this topic, Fern and Margolis (2000) and de Raaf et.al. (2005) present a review of the literature, whereas Cahucand Malherbet (2001) develop a canonical model of experience rating applied to a European type economy with minimum wage. They show that this economic tool is likely to improve the level of employment.

2 See, for instance, [START_REF] Ehrenberg | Absenteeism and the overtime decision[END_REF] and [START_REF] Allen | An empirical model of work attendance[END_REF] who are pioneers on this issue. Allen explains absenteeism by the classic trade-off between consumption and leisure. The absenteeism corresponds then to variations in the marginal utility unanticipated in the labor contracts. For [START_REF] Shapiro | Equilibrium unemployment as a worker discipline device[END_REF], the rate of absenteeism depends on the difference between the salary and the daily allowances in an environment with moral hazard and efficiency wages. For these authors, the workers behavior is the causative of the spending linked to sickness leaves.

insurance, since we assume that when agents are incentivized, they will take actions to reduce risks at work and improve the quality of working life.

In order to analyze the effects of modulating employer contributions based on absenteeism rates, we develop a matching model á la Pissarides. We assume that the economy consists of two segments that differ in their use of absenteeism. This difference can be explained by the working conditions of each segment. A higher absenteeism rate implies (i) lower average productivity and (ii) an indirect subsidy from the low-absenteeism-rate segment to the highabsenteeism-rate segment through the public health insurance. Indeed, since the costs of the disease are not supported neither by firms nor by employers, the economic equilibrium is characterized by high levels of bad jobs at the expense of good jobs.

It is then possible to internalize this costs by adjusting employer contributions based on absenteeism rates. In our model, wages and supplementary health assurance of each segment result from a Nash bargaining between firms and employees. The existence of a complementary health insurance is explained by the fact that the absenteeism is at the origin of a greater surplus than the surplus associated with the destruction of the job. Thus, we can analyze the effects of a modulation of the employer contributions on salaries, allowances diseases and productivity of the economy.

In our model, according to previous studies, part of absenteeism comes from jobs, not from employees. Employees are identical and there is no moral hazard. However, we assume that on certain positions sick leaves are more frequent so that those jobs are on average less productive. Although they representa health risk, these positions offer a positive profit and an income higher than the unemployment income. This explains why these positions exist at equilibrium. However, the presence of a public health insurance indirectly encourages the creation of this kind of posts, with high risk. Indeed, part of the absenteeism generated by high risk firms is supported by low risk and low absenteeism firms, through the financing of health insurance. Then, it seems pertinent to wonder about the possibility of improving the productivity and the welfare of the economy by adjusting the employer contributions based on the firms rates of absenteeism. Finally, we analyze in particular the effects on wages, social protection and productivity. We will distinguish two cases. In the first one workers cannot move between the different segments of the economy. In the second one, workers can orient their job search.

The remaining of the article is organized as follows: In Section 2, we present the model assumptions and the equilibrium. Calibration is detailed in Section 3. Section 4 shows our numerical results and Section 5 concludes.

THE MODEL

The model is built from the analytical framework proposed by [START_REF] Pissarides | Equilibrium Unemployment Theory[END_REF]. It allows to study (i) wages formation, (ii) health coverage offered by firms and (iii) the effects on the productivity of a modulation of employer contributions to health insurance. We consider an economy with a constant active population normalized to unity and the time is continuous. Workers are identical: they are subject to the same risks of unemployment and sickness. Agents are risk neutral with discount rate r. This rate measures the interest rate and the preference for the present.

There are two segments in the labor market but unemployed workers are allowed to look for employment in both segments. Segments are distinguished by the level of health risks of jobs: positions with high health risks are in segment B whereas positions with low health risks are in segment G. This implies higher absenteeism rates for type B jobs than for type G jobs. We note λ i (i = B, G) the probability of becoming sick and by ψ i (i = B, G) the probability of healing. Then, we have λ B ≥ λ G and ψ B ≤ ψ G . Absenteeism causes a loss of production for the firm, a loss of income for the worker and an higher burden for the insurance fund. This implies that when there is just a pool insurance fund for both types of jobs, the lower risk jobs G subsidize the higher risk jobs B through the health insurance fund.

The matching and the flows in the labor market

The two segments of the labor market are accessible to all workers. However, in each period, an unemployed is allowed to seek employment only on one segment of the market. At time t, the probability of seeking employment on the type G jobs at time t + 1 is denoted π. This probability is the same for all unemployed workers. In the discussion of the model, we will distinguish two cases: the one where this probability is exogenous and the other where this probability results from the maximizing behavior of unemployed workers.

Meetings between the unemployed and employers take time and effort, so they are not instantaneous. The search process on each segment of the labor market is represented by a matching function M i = M (U i , V i ) which links the number of new hires on each segment, M i , to the number of unemployed workers, U i and the disposable vacancies, V i . The matching technology fulfill the assumptions usually adopted in the literature: The function M i (U i , V i ) is increasing, continuously differentiable, and homogeneous of degree 1. It satisfies the Inada conditions and

M i (0, V i ) = M i (U i , 0) = 0 ∀ V i , U i ≥ 0.
The assumption of homogeneity allows us to write the probability q i of filling a vacancy as a function of the labor market tightness θ i = Vi

Ui . Thus, a position is fulfilled with probability

q i = M i (U i , V i )/V i = m i = (θ i ).
Similarly, the probability of finding a job for an unemployed worked in segment i is

p i = M i (U i , V i )/U i = θm i (θ i ).
The above assumptions for the matching function imply that ∂qi ∂θi ≤ 0 and ∂pi ∂θi geq0, so that the existence of congestion effects on the labor market is reproduced.

Once a worker is recruited on segment i, he suffers a health risk. This risk involves periods of absenteeism during which the agent is not able to produce. In fact, the health risk is similar to a transitory shock on worker's productivity. Matter of simplicity, we assume that there is no moral hazard. That is, the employer perfectly observes the health status of individuals. Thus, it is not possible for workers to be absent and healthy. We consider λ i the sickness probability in segment i and ψ i the cure probability. It is assumed that absenteeism follows a Poisson process which means that the average span between two periods of absenteeism is 1/λ i and that the average duration of a period of healing is 1/ψ i . Workers are identical. Thus, the gap λ G -λ B ≥ 0 is only due to the differences between firms. This assumption may reflect sectoral differences (ie. services vs. industry) or differences in the working conditions. Finally, the exogenous job destruction rate is noted s. This probability is the same in both segments and applies to occupied jobs as well as to unoccupied jobs because of absenteeism. We assume that the average span of absenteeism is never long enough to cause a lay-off. Therefore, the unique source of dismissal is the exogenous job destruction rate s.

The labor force is normalized to unity and is composed of the individuals from each segment of the labor market: the individuals from segment G, I G , and the individuals from segment B, I B . That is: I G + I B = 1. Transitions between segments can take place only during the unemployment spells. For an unemployed worker, the probability of transiting or stay on the segment G is π. At steady state, the balance of flow between the two segments is given by:

I G (1 -π)u G = I B πu B (1)
with u i the unemployment rate in sector i. Inside each sector, population is composed by unemployed workers, u i , employees, l i and absent workers because of sickness, a i , so that u i + l i + a i = 1. The equilibrium of flows is then described as follows:

s(1 -u i ) = p i u i
(2)

λ i l i = (ψ i + s)a i (3)
p i u i + ψa i = (s + λ i )l i (4)
From this, we deduce the rates of unemployment, employment and absenteeism in segment i, as well as the weight I G of sector G in the economy:

u i = s s + p i
(5)

l i = (ψ + s)p i (λ i + ψ i + s)(s + p i ) (6) a i = λ i p i (λ i + ψ i + s)(s + p i ) (7)
I G = π(s + p G ) (1 -π)(s + p B ) + π(s + p G ) (8)

Workers

We consider an incomplete markets economy in which agents do not have access to capital markets. Therefore, they cannot self-insure against the risk of income fluctuations associated to unemployment or illness. Instead, public authorities offer coverage against these risks. The lump-sum unemployment allocation b is paid to all unemployed unconditionally and is the same for both segments. Absent workers also receive public support. The daily lump-sum allowance zp is paid to all sick workers. Funding for public insurance is the responsibility of employers. This pooling of funding of the insurance fund means that the firms in segment G finance the surplus of absenteeism of segment B firms.

In case of absence, productivity is zero. But unlike the unemployment, absenteeism is not a breakdown of the employment relationship between the firm and the worker. The company can therefore elect to pay additional health benefits, zf i , to sick workers. This compensation is a form of deferred compensation to avoid the job destruction, that is, the time and effort of looking for a new job for the worker and the search for a new worker for the firm. Workers are risk neutral: they maximize their intertemporal flow income. Therefore, the existence of a complementary health compensation is not due to the need of smoothing the workers income over the full period of employment. Instead, it is explained by the mutual interest of workers and firms to maintain the job relationship. As for wage w i paid to employees, compensation zf i results from a bargaining process between the firm and the sick worker. The amount depends on the surplus created in the absent worker situation. Let's consider V (l,i) and V (a,i) as respectively the intertemporal utilities of present and absent workers in segment i, then Bellman equations are written as:

rV (l,i) = w i + λ i [V (a,i) -V (l,i) ] + s[V (u,i) -V (l,i) ] (9) rV (a,i) = zp + zf i + ψ i [V (l,i) -V (a,i) ] + s[V (u,i) -V (a,i) ] (10)
An employee receives a wage w i . With probability λ i that he will get sick. In that case, he will suffer a loss of welfare worth to V (a,i) -V (l,i) . Instead, with probability s, a dismissal will occur. In that case, the loss is worth to V (u,i) -V (l,i) . Similarly, an absent worker receives a state compensation zp and a employer complementary health compensation zf i . He can heal, with probability ψ, or be laid-off with probability s.

On the other side, the unemployed workers are allowed to look for employment in both segments of the labor market. Since the only difference between segments is the higher absenteeism rate in segment B jobs, it follows that the surplus is more important in segment G. Therefore, the welfare of the type G unemployed workers is always higher than the one of type B unemployed workers. However, the probability π(e) of becoming or remaining a type G unemployed requires an amount of effort e > 0. We will assume that the disutility of effort C(e) is an increasing and convex function (C > 0 and C > 0) additively separable in revenues. Thus, the Bellman equations for the two type of unemployed are written as:

rV (u,G) = max e {b -C(e) + p G [V (l,G) -V (u,G) ] + (1 -π(e))[V (u,B) -V (u,G) ]} (11) rV (u,B) = max e {b -C(e) + p B [V (l,B) -V (u,B) ] + π(e)[V (u,G) -V (u,B) ]} (12)
with π(e) = φe, where φ is a parameter to calibrate in order to reproduce the unemployment rate. Type G and type B unemployed workers receive a benefit b. A type G unemployed worker can find a job on the same segment with probability p G , which positively depends on the tightness θ G , or else becomes job seeker on the segment B with probability 1 -π(e).

Similarly, a type B unemployed worker finds a job on the same segment with probability p B , or else becomes job seeker on the segment G with probability π(e). The optimal level of effort is given by the resolution of maximization programs 11 and 12:

C (e) = φ[V (u,G) -V (u,B) ] (13)
Thus, the marginal cost of effort is equal to the earnings φ[V (u,G) -V (u,B) ].

Firms

The economy consists in a large number of neutral firms with respect to the risk which discounts future at rate r. Firms may have occupied or vacant positions, type G or type B. A type i vacancy costs to the firm cy i each period, with y i the productivity of a type i position and c > 0. A vacancy type i can be filled with probability q i = m i (θ i ). We denote Π (v,i) the value of a vacant job and Π (l,i) the value of an occupied job in segment i. Then the Bellman equation for a vacant job is written as:

rΠ (v,i) = -cy i + q i [Π (l,i) -Π (v,i) ] (14)
Once the vacancy is filled, the productivity is worth y i and the firm provides an income w i to the worker. Each job is then destroyed with an instantaneous probability s. Employment can also cause a work stoppage with probability λ i . In this case, the job productivity is zero and the company pays to employee a supplementary health income zf i . All incomes paid by firms are subject to a proportional taxation τ i in order to finance the public mechanisms of unemployment and health insurances. We consider Π (a,i) as the present value of an unoccupied position because of illness and ψ i the healing probability of workers. Then, the Bellman equations are:

rΠ (l,i) = y i -w i (1 + τ i ) + λ i [Π (a,i) -Π (l,i) ] + s[Π (v,i) -Π (l,i) ] (15) rΠ (a,i) = -zf i (1 + τ i ) + ψ i [Π (l,i) -Π (a,i) ] + s[Π (v,i) -Π (l,i) ] (16)
There is free entry into the labor market. Therefore, job creation is given by the free entry condition Π (v,i) = 0. This assumption means that new positions are created on each segment of the labor market as long as positive rents exist. At equilibrium, firms are thus indifferent between type G and type B vacancies. We have:

Π (l,i) = cy i q i (17)
Using equations 15 and 16, we obtain the equation for job creation for each segment i:

(r + ψ i + s)(y i -(1 + τ i )w i ) -λ i (1 + τ i )zf i (r + λ i + s)(r + ψ i + s) -λ i ψ i = cy i q i (18)
The left side of this equality is the average cost of holding a vacancy while the right one is the expected gains from an occupied position. This expression, which exhibits a decreasing relationship between workers' incomes (w i and zf i ) and the market tightness θ i , corresponds to the labor demand in each segment.

Wages

Wages and the complementary health insurance are determined by a continuous negotiation between firms and employees. That is, they solves the maximization of the generalized Nash criterion:

max wi < β ln[V (l,i) -V (u,i) ] + (1 -β) ln[Π (l,i) -Π (v,i) ] > (19) max zfi < β ln[V (a,i) -V (u,i) ] + (1 -β) ln[Π (a,i) -Π (v,i) ] > (20)
From equations 9, 10, 15 et 16, we can express V (l,i) -V (u,i) and V (a,i) -V (u,i) as functions of surpluses S (l,i) and S a,i :

V (l,i) -V (u,i) = β 1 + τ (1 -β) S (l,i) (21) V (a,i) -V (u,i) = β 1 + τ (1 -β) S (a,i) (22)
where

S (l,i) = Π (l,i) -Π (v,i) + V (l,i) -V (u,i) and S (a,i) = Π (a,i) -Π (v,i) + V (a,i) -V (u,i) .
Thus, the share received by workers in the wage negotiations is an increasing function of the bargaining power β and the surplus S (l,i) . In case of illness, the firm and the worker can decide whether or not to end the employment relationship. In case of destruction of the post, the firm may propose a vacancy and the worker experiences an unemployment span. The trade-off therefore depends on the expected duration of the sick leave. The post will be destroyed only for long periods of leave. In our model, it is assumed that there is no heterogeneity in the duration of the sick leave: This span is always equal to 1/ψ i . Moreover we assume that it is always shorter than the time required to fill a vacancy. Consequently, S (a,i) is always greater than zero. Thus, since absenteeism prevents a new search, it is preferable for both the firm and the worker. Thus, the existence of a positive surplus when there is absenteeism explains the existence of a complementary health insurance.

Using this surplus sharing rule, 9, 10, 15 and 16, and the free entry condition Π (v,i) = 0, we get the expressions for wages and complementary health benefits:

w i = βy i 1 + τ i + (1 -β)rV (u,i) (23)
zf i = (1 -β)(rV (u,i) -zp) (24)
These are classical results. The wage is an average of the job productivity and the reservation utility of workers, ie. the value of unemployment. The sharing of surplus depends on the bargaining power β, which increases wages, and on taxes which reduce them. Thus, in the bargain, the firm enforce workers to support a portion of taxes through lower wages.

Complementary health benefits depend negatively on the daily public allowance. In other words, any increase in government allocations is in part received by firms which reduces the amount of zf i .

Optimal research effort et the reservation utility

To characterize the equilibrium of the model, we must determine the optimal effort and then the value V (u,i) . From 11 and 12 we get the expression for the difference between the value of type G unemployment and the value of type B unemployment:

V (u,G) -V (u,B) = p G [V (l,G) -V (u,G) ] -p B [V (l,B) -V (u,B) ] r + 1 (25)
Using the free-entry condition Π (l,i) = cyi qi and the expression for the surplus

V (l,i) -V u,i = β (1+τi)(1-β) Π (l,i)
, we get:

V (u,G) -V (u,B) = βθ G cy G (1 + τ G )(1 -β)(r + 1) - βθ B cy B (1 + τ B )(1 -β)(r + 1) (26)
Assuming that C(e) = e 2 2 , we obtain the expressions for the value of type G unemployment, the value of type B unemployment, and the optimal level of effort, e * :

rV (u,G) = b - e * 2 2 + (r + π(e * )) βθ G cy G (1 + τ G )(1 -β)(r + 1) + (1 -π(e * )) βθ B cy B (1 + τ B )(1 -β)(r + 1) (27) rV (u,B) = b - e * 2 2 + π(e * ) βθ G cy G (1 + τ G )(1 -β)(r + 1) + (r + 1 -π(e * )) βθ B cy B (1 + τ B )(1 -β)(r + 1) (28) e * = φβc (1 -β)(r + 1) θ G y G (1 + τ G ) - θ B y B (1 + τ B ) (29)
Thus, the choice to seek employment in segment G depends, on the one hand, on the tightness gap between segments and, one the other hand, on the tax gap. Expressions 23 and 24 then lead us to the wage and the complementary health income equations:

w G = β y G 1 + τ G + (r + π(e * ))cy G θ G (r + 1)(1 + τ G ) + (1 -π(e * ))cy B θ B (r + 1)(1 + τ B ) + (1 -β) (b -C(e * )) (30) w B = β y B 1 + τ B + π(e * )cy G θ G (r + 1)(1 + τ G ) + (r + 1 -π(e * ))cy B θ B (r + 1)(1 + τ B ) + (1 -β) (b -C(e * )) (31) zf G = β (r + π(e * ))cy G θ G (r + 1)(1 + τ G ) + (1 -π(e * ))cy B θ B (r + 1)(1 + τ B ) + (1 -β) (b -zp -C(e * )) (32
)

zf B = β π(e * )cy G θ G (r + 1)(1 + τ G ) + (r + 1 -π(e * ))cy B θ B (r + 1)(1 + τ B ) + (1 -β) (b -zp -C(e * )) (33)

Endogenous taxation and balanced budget

To conclude the presentation of the model, we present the balanced budget. The only difference between the two labor market segments are health risks. We have λ G ≤ λ B and ψ G ≥ ψ B . These differences just come from the position characteristics and not from workers. Thus, the absenteeism rate is higher in segment B and thereby the average productivity of these positions is reduced and the unemployment rate is increased. The existence of public unemployment and health insurances means that firms in segment G indirectly subsidize the firms in segment B. Indeed, some of the expenses generated by firms in segment B is supported by taxes payed by firms in segment G. Thus, in order to internalize these costs, we will assume that the tax system is characterized by two taxes: (i) a τ tax charged to all firms and (ii) a T tax only charged to firms in the segment B of the market where absenteeism is higher. Therefore, we have τ G = τ and τ B = τ + T . The budget constraint is then:

τ = b(u G + u B ) + zp(a G + a B ) -T (w B l B + zf B a B ) (w G l G + w B l B + zf G a G + zf B a B ) (34)
It appears that for a given population and income structure, an increase of T implies a decrease of τ . In the following section, we propose numerical applications to analyze the consequences of modulating contributions depending on the employer's type.

CALIBRATION

The reference period in the model is the journey. In France, the absenteeism rate is around 4.5%, which corresponds to 16.5 days of absence per year. We assume that each sick leave lasts 7 days (ψ i = 1/7). In order to reproduce this absenteeism rate, we set λ G = 1/200 λ B = 1/100. Thus, we assume that the type B positions originates two times the sick leaves caused by type G positions. Production is normalized to y i = 1. Then the differences in productivity between segments are only due to absenteeism. For the calibration, we assume that the experience rating tax T is equal to 0. We retain a conventional calibration for the matching function:

M i (U i , V i ) = mU 0.5 i V 0.5 i ( 35
)
with m = 0.01 and c = 2 so as to reproduce an unemployment rate of 12%. The bargaining power β is equal to 0.5 and the interest rate r is set at 0.000125, that is 4.5% annual. Finally, we set b = 0.5 and zp = 0.5 which reproduces a replacement rate of 60 % and sickness coverage (both public and complementary health insurances) of 78 %. The rate of type G positions is set at 25% before the introduction of the experience rating.

MODULATION OF THE EMPLOYER CONTRIBU-TIONS

We are now able to study the effects of the employer's modulating contributions based on the mobility of unemployed from one segment to another.

The lack of mobility

First, we assume that the unemployed workers can not choose the segment in which they are seeking a job. It is equivalent to fix the value of Π(e). In this case, the introduction of the experience rating allows to transfer a part of the financial burden from type G jobs to the type B jobs. This is worth a rebalancing since as we said before, imposing the same tax implies that the sick leaves of firms in segment G are subsidized by firms in segment B. It appears that when the unemployed can not choose their research effort, the experience rating slightly increases unemployment rate. More specifically, the unemployment rate in segment G decreases due to the lower tax burden. Conversely, the unemployment rate in segment B increases. The latter effect dominates insofar this policy has the effect of increasing the labor market tightness in segment G which already is the tightest. Note that the share of type G individuals increases slightly. This increase is not due to directing research towards segment G, rather it is explained by the fact that the unemployed go out faster to type G jobs than before the experience rating.

The fact that unemployment rate increases does not imply the rejection of this policy. Indeed, graphics 1 and 2 show (i) a rise in wages and a reduction of absenteeism rate in segment G. The reduction of the the tax burden in segment G enhances the surplus. Therefore, wages, welfare of workers (that is, their expected consumption) and profit of firms all increase. This implies a more important creation of type G positions relative to type B positions, so that absenteeism decreases. Thereby, the higher unemployment rate in segment B may be interpreted as a substitution from absenteeism by unemployment. Regardless of destruction of jobs in segment B, both the jobs creation in segment G and the reduction in absenteeism dominate. This is in part explained by our calibration (before the experience rating the market tightness is already heavy in segment G), but also by the fact that unemployed workers are not allowed to direct their job search. However, the increase in wages in segment G together with the falling of wages in segment B should encourage unemployed workers to direct their research towards the segment G. To explore this intuition, in next section the search effort of type G positions is endogeneous.

The case with mobility: Directed search

Graphics 4 show the different rates of unemployment when the search effort is endogenous, that is when unemployed workers can direct their job search towards any type of jobs. In this case, the unemployment rate in the economy declines. This result is explained by the In this context, the experience rating is to make the firms which are responsible of higher absenteeism rates finance the health insurance expenditures. This policy implies a rise in earnings (wages and complementary health benefits) in the segment G where taxation decreases. In parallel, the recomposition of employment permits a better utilization of the labor resource and thus works up productivity. This is in part due to the decline in the unemployment rate (since type of jobs G are more profitable) but also by the lowering of absenteeism rate from 5% to 3.5%. Naturally, this implies an increase in the welfare of workers which in our model is measured as the expected consumtion each period.

Public health insurance vs Complementary private health insurance

The issues discussed in the previous sections are based on the existence of sick leaves financed by all firms. Firms in segment B pass over firms in segment G part of the health spending which they are responsible for. Moreover, universal social protection allows the unemployed workers to accept jobs with higher risks for health. However, we have seen that firms offered complementary health insurance. Indeed, absenteeism is associated with a positive surplus as it prevents the company from finding a new worker and the worker from finding a new job. Thus, the lack of public insurance does not mean the lack of social protection. Substituting public insurance by a complementary health insurance financed by firms may be a way to reduce the externalities between the two segments. Graphics 7 show the effects of the amount of daily allowances on the unemployment rate. It clearly appears that an increase in compensation leads to an increase in global unemployment. Daily allowances indirectly subsidize the posts with high health risks. Thus, we note that an increase in allowances is accompanied by an increase in the number of type B positions and by a reduction of the unemployment rate in this segment.

This policy is therefore accompanied by a decline in productivity due to a change in the structure of employment in favor of segment B. In parallel, the financing of allowances involves higher taxes. Thus, the surplus generated by the creation of an occupied job decreases, which results in a reduction in both remuneration (wages or complementary health benefits) and profits. Then welfare is decreasing with respect to the amount of daily allowances. This comes from the fact that the lack of indemnities does not mean the lack of insurance coverage since firms propose a complementary health insurance. Reductions in public insurance are offset by increases in the complementary health insurance.

We note that in the absence of public benefits, the amount of complementary benefits is 0.39, which is 45% of wage. However, this value still remain lower than the benchmark equilibrium value where the level of social protection (public insurance and complementary insurance) reached 75% of wage. Thus, in terms of welfare, the experience rating remains more efficient than the privatization of social protection. It allows to reach high levels of productivity (85.25 for T = 0.05 vs. 84.5 for zp = 0) in order to fund a more generous health coverage.

CONCLUSION

In this article, we focus on the modulation of employers' social contributions for health insurance. This system already exists in the United States to finance unemployment insurance. It is based on the idea that some companies may externalize some of their costs toward the social system. In our model economy, firms may create risky positions by making other firms bear part of their cost due to absenteeism via the public health insurance. We then show that the modulation of employers' social security contributions based on the firm's absenteeism rates allows to improve economic productivity by limiting externalities. Furthermore, the experience rating promotes the creation of high productivity jobs with low absenteeism rates. This improvement in economic productivity allows to maintain a generous health coverage, which is more favorable to the welfare of workers than the privatization of the health insurance system.

Figure 1 :

 1 Figure 1: Unemployment in lack of mobility

Figure

  Figure 2: Wages in lack of mobility

Figure

  Figure 6: Absenteeism and productivity with mobility

Figure 7 :

 7 Figure 7: Public insurance and unemployment

moving of a portion of workers towards the type G positions. Thus, the share of type G jobs changes from 25% to 75%. This mobility of workers stimulates the creation of many vacancies in segment G without affecting the market tightness in this segment. www.tepp.eu