Irina Peaucelle

Dynamic analysis of bankruptcy and economic waves

Intoduction

For a long time the relation between production of goods and

This one-dimensional score represents the temporal quality of firm (in a sense, it's a fundamental for hedonic price). Finally, the researcher reveals into the set of firms' scores some homogenous classes by descretizing the quantitative scores. For that she/he determines the thresholds, which disjoin firms in function of their score. Now the firms are scored and classified by different institutions and for different reasons and purposes. For example, the French agency VIGEO scores 500 000 firms around the world accordingly to social criterion of "responsible investment" [START_REF] Notat | participant de la table ronde Vers Une Nouvelle Ethnique, au Rencontres « 2010 Quelle place financière de Paris dans quelle économie internationale ?[END_REF]). In this paper the classes are created accordingly to default probability of firms. The average values of characteristics of firms in each class express the characteristic of representative agent.

Since, creditor accords credits to firms in function of their score and the performance of a firm depends, among other thinks, on condition of financial equilibrium of enterprise, I analyse here the credit policy which would avoid the representative firms serial default, except some eventual situations, when restructuring is necessary and selective bankruptcy must be realised.

Along these lines, the dynamic of solvency, insolvency and risk transition is analysed.

New rules are currently introduced in many countries to control the risk taken by the firms; in particular, to define the capital required to hedge a risky credit portfolio. It becomes possible to analyse the firm default risk and its expected evolution. The agencies report regularly summary statistics of the rating histories under the form of transition matrices providing the migration probabilities between given rating classes for different years and sectors of economic activity. The aim is to verify if the observed migration probabilities can be used as leading indicators for business cycles, recession and growth trends in place of other standard leading indicators as unemployment or inflation.

The bankruptcy principles and the financial regulation are presented in section 2. Then, in section 3, the data sets are discussed and some typical evolution of risk probabilities is reported. The data of firms' migration through the classes of risk are often analysed in the literature by means of an ordered qualitative model with observable or unobservable factors. This model is reviewed in section4, and especially its dynamic properties, when some factors represent the cycles. In section 5 the dynamics of up-grade and down-grade migration probabilities data are compared with the evolution of the GNP. Some results of causality analysis of links between risk of default and some financial variables are described. Finally, in section 6 examples of control methodology are agreed. The goal of the control is the selection of a policy for avoiding systemic risk.

The bankruptcy laws and the financial regulation

Operating firm must be solvent. According to accounting principles it signifies that it can serve and refund all its debt's becoming due. Insolvency is the situation when the firm's debt is greater than its asset value including: stocks, accorded credits, real estates, machines and other assets. In a situation of insolvency bankruptcy occurs. It is the pattern for resolving disbursement problems of firm owners. Moreover, bankruptcy, as an institution of regulation, implicates some general economic issues of capitalism such as the production of wealth (analysing by whom the wealth has been produced, in conformity with which objectives) and the outcome sharing. For example, the bankruptcy regulation is needed in Russia since the economic liberalisation and the massive privatisation in 1992. Before, the unique owner -the State -was not faced with the problem of firms' insolvency, because he valorised them throughout the criteria of national usefulness and the mechanism of equalization of assets among firms. The restructuring, moving or dismantling occurred without unemployment and without revenue losses for individuals (I will not discuss the overall economic efficiency of Soviet mechanism of reproduction and accumulation.) Historically, bankruptcy consists in three stages: 1) to withdraw publicly the bankrupt from operating;

2) to gather all information about creditors and to estimate assets;

3) to settle the investors' failure (they lose for this reason their property rights), to sale assets in order to indemnify the creditors, to quash the marginal debts and to arrange the firm's liquidation.

The entrepreneur observing insolvency can seek at short run to realise some very risky activity. Therefore bankruptcy legislation traditionally (since 17 century) seeks to regulate the enter/exit rules of operating in order to protect the public interest (or total efficiency) from excessively risky firms.

For several reasons firms face debts, and are unable to repay them in some circumstances. The bankruptcy procedure is required to explain and to resolve the problems rising in such situations. The most important goals of the bankruptcy can be enumerated: It should provide a not wasteful outcome that is the maximal sum available to be shared between debtors, creditors and other concerned participants, such us, employees. It should preserve the bonding role of debt by penalising the managers and shareholders according their faults. The bankruptcy and non-bankruptcy states must be treated with similar attention concerning the contractual obligations within the firm.

Two principal forms of bankruptcy procedures exist: an asset sale and a structural bargaining. The sale of the firm's assets is usually supervised by a trustee, or a receiver. Such procedures and supervision are not as evident as it seems from the old capitalist world. For example, the Russian government postponed decisions of restructuring the industrial sector after the privatisations in earlier 1990. It did not force insolvent firms into bankruptcy, even when it was their largest creditor. The government, particularly at the regional level, often interferes in bankruptcy proceedings to prevent job-losses. After all, the lack of a credible threat of bankruptcy has meant that managers did not seek to avoid insolvency. As a result the country was facing an increase of firm insolvency with a huge accumulation of unpaid debts. Recognising that large-scale initiation of legal proceedings of bankruptcy as asset sale is impossible; one seeks other means and ways.

In the case of structured bargaining the claimants are encouraged to bargain about the future of the firm. Indeed it can be liquidated or restructured, and in both cases the rules should be negotiated and determined. For example, the bankruptcy law in France give to the court, through an administrator, the power to accept a restructuring plan without the approval of creditors (or workers) if it guarantees the maintenance of employment and the repayments of creditors. Some problems arise in connection with structured bargaining procedure, since it follows two objectives at the same time that are: the task to decide for the firm future and who should get what in the event of a restructuring of claims. The bankruptcy reforms are in progress in many countries in order to make the procedures more transparent and efficient (see [START_REF] Hart | Different approaches to bankruptcy[END_REF]. Thus, the goal of an appropriate bankruptcy law is to reduce the systemic risk and overall financial instability. But the regulation of financial system, with the prudential rules is another way.

Bankruptcy of an individual financial institution or micro-prudential accident is a consequence of disruption of one or more indicators of the institution's health, such as: capital adequacy, asset quality, management soundness, earnings, liquidity, and sensitivity to risk. The widespread financial distress may come from the failure of individual institutions and the spread trough different contagion mechanisms to the financial system in general [START_REF] Gourieroux | Diffusion et effet de vague[END_REF]). The objective of a macro-prudential approach to regulation is to limit the risk of financial distress with its significant losses in terms of GDP. The strengthening of the macro-prudential mechanism needs a closer cooperation between supervisory authorities and central banks, that why new rules of macro-prudential regulation have been elaborated by Basle Capital Accord.

Available data for default analysis

The objective of the New Basle Capital Accord II (2003II ( -2004) ) is to allow banks to manage their risks with a dynamic approach of capital adequacy. The first internationally accepted standard was developed in 1988. These and following rules are introduced by the regulator (Central bank governors and the heads of bank supervisory authorities in the Group of Ten countries G10) to control the risk, in particular to define the capital required to hedge a risky credit portfolio [the so-called Value-at-Risk (V@R) that is the maximum expected loss over a given horizon period at a given level of confidence].

The implementation of this regulation requires a careful analysis of firm default risk and of its expected evolution. As a by product the rating agencies as Standard & Poor's (S&P), Moody's, Fitch, or some central banks, as the Banque de France (BdF), have been led to improve the quality of their proprietary rating data bases2 . Typically, they make public summary statistics of the rating histories under the form of transition matrices providing the migration probabilities between given rating classes for different years and economic sectors. These statistics are the dynamic measure of degrees of creditworthiness among operating firms.

The definition of the rating and the population of firms differ according to the rating agencies.

For instance the main rating agencies obtain information about the situation of the firms, generally when they are issuing bonds. This explains why their data bases concern large firms, mainly US companies, even if the proportion of European and Japanese firms represented in the bases has grown rapidly at the end of the eighties. The number of rated firms is around 10 000, with a proportion of missing data (alternative NR : not rated) between 10 and 20 %. These data are reliable since 1985 approximately, providing 17 years of observed transitions matrices. They use a rating with ten classes from the highest rating [AAA for S&P for instance] to the worst one D corresponding to default.

The data collected by the French Central Bank are of another type. They include the balance sheets of French firms, with sales larger than 762 000 Euros , or those with debts 5 times beyond the threshold of registration at Central of banking risks (the threshold since 1997 is 76 224 Euros). Consequently, the data are covering about 185 000 firms per year, 85% of workforces and 90% of distributed bank credits. In the French Central Bank case, the contribution of economic ratios on financial situation of a firm depends on the sector. For example, for Industry there are eight economic ratios that contribute to the score value. The score indicates the health of firms in report with the management ratios, such as: provider deadline, tax and social security creditor; rate of return and return on sales: rate of added value; solvency: burden of financial charges; debt: leasing liabilities, capital-debt ratio; and current liabilities: liquidity, bad or doubtful debt. Then the information included in the balance sheet is transformed into a quantitative score representing the risk level of defaulting.3 . After that the score is discretized to get a qualitative rating with ten classes of risk (average probability of default at the horizon of three years), noted D, 1 , ..., 10. The alternative " D" corresponds to default and the alternative "10" indicates a perfect financial situation (analogue of the AAA of the rating agencies).

The default in the French Central Bank rating signifies that the enterprise is under bankruptcy procedure. For example, in 2001 among industrial firms in France 20.4% of firms had a high probability of default in the future, 8.4% of firms were neutral, and 71.2% were healthy firms. The risk of default changes in time, and the score of any firm can maintain it in the same class of risk or switch into another class. The structure of migrations among the classes allows us to analyse the risk dynamic s. In France the data have been collected since 1992, which provides 11 years of transition matrices.

Example of transition matrix reported by the Banque de France is given in the table below. A lot of migration probabilities are rather small. The significant values are mainly around the main diagonals, which represents the proportions of firms keeping their previous rating class (the class of default probability) , and for default as arrival state (absorbing state). These matrices can be summarized by considering the probabilities of a down-grade [resp. an up-grade]. For instance for a firm rated "6" at the beginning of the year, the probability of an up-grade is the probability to migrate to one of the state 7,8,9 or 10. 4 .

In order to analyse the systemic default risk, it is important to consider the simultaneous rating migrations of firms with different indicators of risk in the same direction. Such migration is called migration correlation. The stochastic transition matrix, which assumes a common multivariate factor across firms, represents the migration correlation between different classes of risk.

Analysis of default dynamic: the ordered qualitative model with factor

The ordered qualitative model with factor is usually considered in the literature (see e.g. [START_REF] Albanese | Implied Migration Rates from Credit Barrier Models[END_REF], Bangia et alii (2002), Gupton et alii (1997), Crouhy et alii (2000)) as a convenient specification for stochastic transition matrices. Indeed it allows reducing the number of factors, which are driving the different migration probabilities, while keeping the model tractable with a reasonable number of parameters.

As usual the specification is based on a latent variable S i,t, , which can be interpreted as an underlying quantitative score, directly related to an expected probability of default at some horizon.

Typically the horizon is 3 years for the BdF score. Thus S i,t is the value of the score for firm i at date t.

It is assumed that the conditional distribution of variable S i,t given the information available at the beginning of period t depends on some factor Z t and on the most recent rating Y i,t -l . It is such that:

Latent model for the score

S i,t = α k + β k Z t + σ k u i,t , (1)
if

Y i,t-l = k, k = 0, ..., K -1,
where α k , β k , σ k are scalar parameters and u i,t are independent error terms, identically distributed with common distribution function G. Thus three parameters are introduced for each rating class: α k measures a level effect, β k is the risk sensitivity with respect to the factor 5 , whereas σ k is the idiosyncratic (firm specific) standard error.

Latent model for the factor

The factor has to be assumed non observable, to allow for migration correlation [see the discussion in [START_REF] Gagliardini | Stochastic Migration Models[END_REF]]. Loosely speaking, if the different sensitivity coefficients are nonnegative, a positive movement on Z t will imply a joint increase of the individual risks whatever the rating class of the ferms. Thus we will get a positive migration or up-grade correlation, if the future of the factor is not a priori known. It will be assumed that the evolution of the factor is independent of the values of the shocks u i,t , that they depend on the past by means of the most recent factor value (which is the Markov assumption), and that the transition factor density can be parameterized. This density major part of down-grades trend in ratings is the result of changing standards of scoring and rating by this agency 5 We have implicitly consided a one factor model for expository purpose.

will be denoted by:

), ( ] ) , ( [ 1 1 1 1 θ - - - ≅ = + ∈ t t t t t t t z z f z Z dz z z Z P dz (2)
for small dz.

Link between latent and observable variables

Finally the rating of period t is defined by discretizing the quantitative score:

Y i,t = l, if and only if a l < S it < a l+l , (3)
where: a 0 = -∞ < a l < ...< a K-1 < a K = + ∞ are fixed (unknown) thresholds.

Under the specification above it is easy to derive the migration probabilities given the factor value.

Since the factor is indexed by time only, these quantities are closed to the observed sample transition matrices, computed per year. We get:

p k,l,t = P [Y i,t = l|Y i,t-1 = k, Z t ] = P [a l < S i,t < a l+1 | Y i,t -1 = k, Z t ] = P [a l < α k + β k Z t + σ k u i,t < a l+1 | Z t ] = P       σ β - α - < < σ β - α - - t k t k k t i k t k k Z Z a u Z a 1 , l l = G . 1         - - -         - - + k t k k k t k k Z a G Z a σ β α σ β α l l
The model reduces to an ordered probit model with factor, if the common distribution G corresponds to the standard Gaussian distribution, and to a Cox model with stochastic intensity if exp u i,t follows an exponential distribution [see e.g. [START_REF] Lando | On Cox Processes and Credit Risky Securities[END_REF]]. The beta model assumes independent transition matrices, with independent rows, following beta distribution (the beta distribution is the basic specification used in probability and statistics for the law of a stochastic discrete distribution).

Different specifications of the factor dynamics can be retained in practice. Feng et alii (2003) assume a Gaussian vector autoregressive factor. When business cycle i s specified by means of a hidden Markov chain , it seems natural to consider a factor with discrete state space {0, 1}, where "0" represents "recession" and "1" represents "expansion". The factor dynamics is summarized in this case Markov chain, with some recursivity in the joint transition matrix [START_REF] Gagliardini | Stochastic Migration Models[END_REF]).

Credit migration and economic growth

The relationship between firm default and general economic dynamic has been advocated since a long time in the economic literature. During a recession period, the firms have more difficulty to sell their productions, which can deteriorate their balance sheet, their probability of failure increases, as well as the credit rate, offered by their lender. Conversely, if the probability of failure of a firm increases, it has more difficulty to find credit at a small rate, which can increase the amount of regular reimbursement and reacts negatively on its situation. This creates an accelerated movement towards default, with the usual consequences on employment, growth, deflation… The new existing databases on credit histories allow for a better understanding of the relationship between the business cycle and the factors influencing credit risk and credit migration. A few number of studies have already been done on this topic [see [START_REF] Nickell | Stability of Rating Transitions[END_REF], Bangia et alii (2002)], and especially with proxies of the business cycle , such as the NBER indicator. They essentially concern the US business cycle at a general level, and do not take into account the effect specific of a sector structure of economy. Gagliardini and Gourieroux (2004), [START_REF] Boussyguine | Contrôler la croissance et la Restructuration[END_REF] analyse the French rate of GDP evolution, and its impact on risk migration in some sectors of French economy.

The evaluation of migration probabilities of firms in France shows clearly some common feature, with at most two underlying patterns : 1) the evolutions for up-grade are in the inverse directions of the evolutions for down-grade, the up-grades have an ascending trend in each class of risk on the period between 1992-2001, and the down-grades feature has inverse declining general trend (except the class 1 of high default risk); 2) the evolutions for three sectors (industry, wholesale and retail trade) are very similar. This pattern is compared with the French growth rate, and the comparison shows the strong link between migration probabilities and growth rate. The dynamic linear link between the down-grade series and the GDP, using a causality analysis, indicates for analysed sectors that, on one hand, for the cla sses of low risk the GDP is a leading indicator of the down-grade risk migration, but on other hand, the ordering between both measures is reversed in the very risky classes, where the down-grade probabilities can be considered as leading indicator of the economic growth with a lead of two and three years. Besides, the down-grade tendency is more reactive than the up-grade one to GNP modification.

Such are recent empirical investigations concerning the dynamic analysis of default risk in some sectors of French economy and of economic growth of this country.

The firms' scoring determines the class of risk to which it belongs and consequently the condition of credit (amount and term) it can count on. In any case the "health" of operating firm depends on quality of credit it gets.

In [START_REF] Boussyguine | Contrôler la croissance et la Restructuration[END_REF] the causal relation between the trends of upgrade and downgrade in French industrial sector and the spread evolution, as well as with evolution of treasury bonds are analysed. It is shown that the rate of bonds remuneration is an advanced indicator for downgrade movement in one risky class (2 class) and in no risky classes (6,7,8,9). It is also leading indicator for upgrade movement in relatively neutral to risk classes (4,5,6 and 7). The causal impact of spread is observed only for two classes of risk (5 and 7) and it is statistically significant for upgrade trend as well as for downgrades.

Risk management or economic growth control

Some interesting works have been done recently in the domain of risk management and control.

The majority concern idiosyncratic shocks that provoke the defaults. In such case the optimisation programme has to solve either the creditor problem, or the borrower portfolio problem looking for the optimal allocation of in vestment between liquidity, stocks or credit subject to an exogenously specified V@R control condition. In the recent article by [START_REF] Yiu | Optimal portfolios under a value-at-risk constraint[END_REF] the V@R is imposed as a dynamic constraint in the optimisation of portfolios problem. Thus, at each period the V@R i s estimated and it has an effect on the investment decision. The author finds that in such model the investments in risky assets are reduced whenever the V@R constraint becomes binding. Besides, when V@R is the risk control, consumption and expected utilit y are not considerably affected for certain choices of parameters. This result confirms more general statement that system safety could not be a very strong constraint and certainly not the goal. Indeed, any system with some degree of probability at some instant reaches the attractive position of "catastrophe", like bankruptcy in the case of financial institution. If one hypothesises that safety is the aim of an operating system than the solution is obvious and consists in breaking off the system. If an existing system is considered as useful, than the problem of its safety must be analysed in the context of some incentives to operate it.

My fields of interest are the investigation in the systemic risk prevention and the adaptive control of interconnections that exist between business cycle and heterogeneous risk aversion of the firms. In particular I want to consider the stabilisation of complex chaotic systems through feedback management. The aim is not to come across the most effective means to achieve the goal, but rather to explore the principal possibilities of its' achievement and to analyse the class of potential movements of the system under control. For example, the migration matric es characterise the "health" of financial and real economy (as a system), and they can be used to feedback impulses (regulation) on it. The regulation consists in credit policy addressed to firms regarding the general rate of economic growth.

In general the realistic model of complex system cannot be solved analytically, and researchers combine simulation with optimisation tools for control and optimal design. Typically our problem of interest leads to complex optimisation problems whose criterion function admits no analytically tractable form. In such cases the estimation of the values of criterion function by simulation and the search for an optimal solution by genetic algorithms [START_REF] Köchel | Planning recovery in global economy[END_REF]) or evolution strategies can be performed.

Instead of conclusion, I prefer to describe the methodological scheme for future development of control analysis (prescriptive proposal) of the dynamic relation between risk evolutions and economic growth using the results of empirical investigations (descriptive proposal) reported in previous sections6 .

To formulate a control problem signify to design an interested subject, who has some concerns visà-vis the system, and such subject may be Basle Capital Accord of G10 or Central Bank, called CB.

The object of concern can be systemic risk avoiding (prevention of generalised down-grading) and sustain ing of economic growth. Such aim is interesting to study since till now one frequent criticism of the current Basel Capital Adequacy frame (determining the following risk components: default probability, loss given default, exposure at default, effective maturity) is that it increases procyclicity with a negative consequence on firm's operating.

Then it is necessary to describe the relationships between CB and the object that is the structure of interests, the dynamic properties of the object (revealed for the moment for three sectors of French firms by empirical analysis), and the possibilities and methods of concerns' achievement. The problem can be formalised by introducing a system of axioms that circumscribes a class of utility-oriented systems, which have the unique subject, CB, of concerns, but this subject has the concerns of multiperspective types. The object of interests is passive7 , dynamic and stochastic system. Its structure is not determined precisely and the decision maker, CB, can construct it. The control aim is not postulated a priori, and the control motivation is in relation with the set of concerns (interests).

It is postulated that dynamic is described through a Markovian process. Three types of interests are provided concerning: a) the control of system evolution, b) the choice of its structure, c) the diagnosis of situations , in which the process of interests' realisation can be situated. The axioms are used to formulate the premises of decision making oriented to control the process of interests achievement in the course of operating and avoiding the systemic default.

The premises of decision making are the following:

1.

The unplanned evolution of the states of the elements of risk migration matrix (object of concerns) is described by a Markovian process. The set of states S encloses the attractor D (default). ß(S) is an a priori distribution of probabilities on the set S.

2.

X is a finite set of situations. The situations require diagnosis, which consists in the selection of situation in function of the state. Let X s ⊆X the constraints, which determine the acceptance of situations as alternatives for diagnosis, depending on the stats s∈S.

4.

The structure of the object is not fixed and can be "selected" among the structural alternatives G (since a residual heterogeneity exists in any class of risk, see equation ( 1)).

The structural alternative is selected dependently on states and situations (scoring and rating); and especially on their common parameter (factor Z t ). If structural alternative is chosen consequently in any moment it is called tactical option, if it is constant at all horizon of interests existence it is called strategic option.

5.

The utilisation of control impulses generates a discrete Markovian control process with values belonging to the set S of states. The transition function of this process is given by: q g (SS×C), where parameter g∈G is a structural alternative.

6.

Then it is necessary to introduce the utility function w g (C×S×X) →ℜ 1 , which determines the a priori preferences on the set of alternatives control signals C, where c'>c ⇔ w g (c',s,x)>w g (c,s,x). (For example, supervisory review of banks' internal assessments of their overall risks must ensure that bank management is exercising good judgement of situation for crediting).

7.

The control is performed according to the scheme of situational control: at discrete moments one observes the state, depending on this state a diagnosis of situation is selected, and accordingly to the result of diagnosis one makes a decision about the control impulses.

The postulates of decision making (1-7) determine the bearer of information a priori about the condition of decision making, generating the "information structure" of basic data a priori:

I={S, ß(S),X, [X s ⊆X, s∈S],C, [C x ⊆C, x∈X],G, q g (S/S ×C), w g (C×S×X), g∈G}.

Accordingly to the information structure I, one develops the methodology of control formalisation based on the principles of: a) splitting of concerns (interests), b) equilibrium solutions, c) structural transformation. The following methodological positions describe the content of these principles:

1. The multi-perspective concerns are decomposed into some components. Each aspect is confronted to "virtual concerned segment" (class of risk) and corresponding set of alternatives. It is supposed that for each segment one criterion of quality among alternatives can be determined; at the same time criterions are independent, but not given a priori explicitly.

2. Each segment (firms of each class of risk) has the possibility to make a choice individually, but it is constrained by the necessity to respect the common interests of the subject, CB. Because of constrains the interests of different segments are consistent under these conditions, more, they are of cooperative type.

3. The problem has game theory content with latent cooperative concerns (interests).

4. The solution of the problem consists in researching of a stable compromise which cannot be improved. Such compromise is a cooperatively efficient equilibrium.

5. The criterions of alternatives' quality of virtual segments must be elaborated using the structural transformations of initial information structure I, into the necessary information structure.

The model of decision making describes:

-the initial hypotheses;

-the strategies of: control, diagnosis and structural choice;

-the criterions of: strategic control quality, structural choice quality, and quality of strategic diagnosis, which can be an average "risk";

-the dynamic equilibriums.

Than, it is necessary to explain the way to achieve the dynamic equilibrium: the necessary and sufficient conditions, as well as local equilibriums. The model of dynamic equilibriums presupposes that they are asymptotically stationary, and for this the estimates of closeness (operator of compression) to stationary equilibrium have to be demonstrated.

The computational construction of dynamic equilibrium by V. [START_REF] Baranov | Models and methods of decision making in the utility oriented systems accordingly to criterion of utility, risk and technical safety[END_REF] consists in the algorithm of dynamic equilibrium approximation and in the algorithm of local equilibrium. The last one needs the formulation of information structures concerning the "utility" and the "risk". Finally, the algorithms of configuration of information structures respectively for "utility" and for "risk" are described.

The procedures presented previously provide a dynamic apparatus of decision making in

.

  For this model the joint process (Y 1t , ..., Y nt , Z t ) defines a

  set of control signals, which are chosen depending on situation x∈X. The constraints C x ⊆C are given concerning the acceptance of control alternatives in function on situation x∈X. The set C contains the control signals which pull the system out of attractor state D. In our problem, on one side, the new entries in different classes of risk, for example in share proportional to the population of each class, can be interpreted as such signals , on other side, spreads are usual price signals in controlling economic systems.

Table 1 . Migration probabilities "Industry", between 1999 and 2000 (in %)

 1

		10	9	8	7	6	5	4	3	2	1	D	NS
	10	72,38	15,91	1,34	1,51	0,46	0,17	0,41	0,24	0,05	0	0,05	7,49
	9	12,47	57,58	13,56	5,75	0,92	0,59	0,72	0,98	0,1	0,06	0,09	7,17
	8	1,28	26,67	35,74	23,35	1,77	0,66	1,12	2,04	0,43	0,05	0,17	6,72
	7	0,39	4,88	16,16	50,57	8,71	2,94	2,13	4,21	1,21	0,54	0,48	7,79
	6	0,26	1,9	3,01	33,61	23,3	10	6,96	6,76	2,24	1,42	1,45	9,09
	5	0,26	1,94	2,51	17,21	20,92	16,16	14,07	9,94	3,71	1,94	1,78	9,57
	4	0,25	2,04	3,05	12,98	12,53	12,83	17,52	14,56	4,68	4,18	2,85	12,53
	3	0,08	1,62	3,05	13,64	9,3	5,89	11,61	21,11	7,11	6,21	4,34	16,04
	2	0,11	0,78	1,56	8,16	8,6	5,81	10,61	16,54	12,74	9,5	7,37	18,21
	1	0	0,24	0,82	2,83	4,59	3,53	6,48	12,96	8,48	24,5	15,31	20,26

See e.g.Brady et alii (2003) for a description of S&P data base,[START_REF] Carty | Moody's Rating Migration and Credit Quality Correlation 1920-1996 : Special Comment[END_REF] for the Moody's data base,Foulcher et alii (2003),[START_REF] Bardos | Les scores de la Banque de France. Méthodes, Résultats, Applications[END_REF], for a description of the Banque de France data base.

For example, in the article byBardos & ali (2004) the risk level of default is revealed by a discriminant analysis technique.

As usual, in empirical studies it is important here to be careful with interpretation of estimation results. For example, the study of Moody's ratings of U.S. corporates shows that the number of downgrades in corporate bond has exceeded the number of up-grades, leading to think that the credit quality of U.S. corporate debt has declined. The article byBlume and alii (1998) suggests however that a

I acknowledge V.[START_REF] Baranov | Models and methods of decision making in the utility oriented systems accordingly to criterion of utility, risk and technical safety[END_REF] who suggested me to consider the problem in this way.

Regulator admits the hypothesis of passivity of migration matrix, but the researcher has to remember that each matrix is an aggregation of operating firms and an abstract of decision making of thousands of firms.


The Void at the Heart of Rules: Routines in the Context of Rule-Following Observations from a Workshop of the Paris Metro

Keywords: Rules, Routines, Rule-Following, Incentives, Salary bonus JEL Classification: D70, D73, J33, J5

This paper is an attempt to understand how rules operate in organisations. I focus on the links between organisational routines and rules that are defined as incomplete since they come to their application. I analyse the role of routines in managing the incompleteness of rules. I present a case study where management introduced a productivity bonus in the middle of 1992. This allows to study in what extent the new rule modifies the prevailing routines of work organisation. Based on team observations, interviews, and statistics that I carried out over a period of nine years (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000), I show that in an initial period, the productivity bonus has partially biased the tasks selection process. In a second period -'the normal period'-our observations indicate that following the rules consists in translating the abstract rules into concrete reference points, and adding in what the rules have not specified. The translation process conducts to a routine since the interpretation is stabilised. Routines provide a pragmatic, local, and temporary solution to the incompleteness of rules. Since routines emerge only in the course of action, they come with no guarantee of success.

That constitutes their dynamic.

Introduction

Much of organisation theory has been concerned with how to coordinate the activities of individuals in organisations [START_REF] March | Organizations[END_REF][START_REF] Stinchcombe | The Sociology of the organization and the theory of the firm[END_REF][START_REF] Stinchcombe | Information and Organizations[END_REF]. Rules and organisational routines are two main forms of coordination used in organisations 1 . On the one hand, some scholars [START_REF] Blau | The Dynamics of Bureaucracy[END_REF][START_REF] March | Organizations[END_REF][START_REF] March | Decisions and Organizations[END_REF][START_REF] March | A Primer on Decision Making[END_REF][START_REF] March | The Dynamics of Rules. Change in Written Organizational Codes[END_REF][START_REF] Schulz | Limits to bureaucracy growth: the density dependence of organizational rules birth[END_REF][START_REF] Schulz | Impermanent institutionalization: The duration of dependence of organizational rule changes[END_REF][START_REF] Zhou | The Dynamics of organizational rules[END_REF][START_REF] Zhou | Organizational decision making as rule following[END_REF] focus on rules. In a broad perspective, rules are similar to the 'bureaucratic procedures' defined by Blau (1955: 23): 'A bureaucratic procedure can be defined as a course of action prescribed by a set of rules designed to achieve a given objective uniformly.

Agency-wide rules must be abstract in order to guide the different courses of action necessary for the accomplishment of an objective in diverse situations.' In the 1940s and 1950s, scholars built the bureaucratic theory of vicious circles in which rules, considered as potential sources of organisational dysfunction, are the main pillars [START_REF] Merton | Bureaucratic structure and personality[END_REF][START_REF] Gouldner | Patterns of Industrial Bureaucracy[END_REF][START_REF] Blau | The Dynamics of Bureaucracy[END_REF][START_REF] Crozier | The Bureaucratic Phenomena[END_REF]. To Gouldner, bureaucratic rules are used to substitute for the managerial supervision. As Zhou (1997: 260) emphasises, 'Rules become substitutes for direct authority relationships.' During the same period, Simon developed an administrative decision theory (1945), and later with March a decision theory in which rules are essential building blocks [START_REF] March | Organizations[END_REF]. In his further researches, [START_REF] March | Footnotes to organizational change[END_REF][START_REF] March | Decisions and Organizations[END_REF][START_REF] March | A Primer on Decision Making[END_REF] claims that much of organisational behaviour involves rule-following that consists in matching a set of rules to a situation by criteria of appropriateness. Rules are procedures that people follow to fulfil their identities (March, 1994: 57). Individuals try to match appropriate rules to identities: 'An identity is a conception of self organized into rules for matching actions to situations' (March, 1994: 61). Rule-following process refers to the logic of appropriateness rather than calculation of consequences [START_REF] March | Footnotes to organizational change[END_REF](March, : 565, 1988: 8): 8).

Then, the recognition that rule-following behaviour is a central process of the ongoing organisations (March, 1981: 565) directs attention to how rules are founded and changed [START_REF] Blau | The Dynamics of Bureaucracy[END_REF][START_REF] March | Footnotes to organizational change[END_REF]March, 1888: 8;[START_REF] Levitt | Organizational learning[END_REF][START_REF] March | The Dynamics of Rules. Change in Written Organizational Codes[END_REF][START_REF] Zhou | The Dynamics of organizational rules[END_REF], 1997).

On the other hand, other scholars adopt a micro-micro level of analysis, that of organisational routines [START_REF] Cyert | A Behavioral Theory of the Firm[END_REF][START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF][START_REF] Cohen | Individual learning and organizational routine: emerging connections[END_REF][START_REF] Cohen | Organizational routines are stored as procedural memory: evidence from a laboratory study[END_REF]Pentland and Rueter, 1994;[START_REF] Cohen | Routines and other recurring actions patterns of organizations: Contemporary research issues[END_REF][START_REF] Feldman | Organizational routines as a source of continuous change[END_REF][START_REF] Feldman | A Performative perspective on stability and change in organizational routines[END_REF][START_REF] Feldman | Reconceptualizing organizational routines as a source of flexibility and change[END_REF]. As Becker (2004: 643) emphasises, 'Many ambiguities and inconsistencies in 1 Plans, scripts, and procedures are other forms of coordination.

the literature dealing with routines prevail still today. ' Becker uses the word 'ambiguity', but this is an understatement. Among the different meanings given to the notion of routine there is a dividing line between scholars who consider routines and scripts as mindless repetitions [START_REF] March | Organizations[END_REF][START_REF] Ashforth | The mindlessness of organisational behaviours[END_REF], and those who use the grammatical analogy to think of routines as a set of actions people can choose (Pentland and Rueter, 1994). Performing a routine is an 'effortful and ongoing accomplishment' [START_REF] Feldman | Organizational routines as a source of continuous change[END_REF](Feldman, : 613, 2003;;[START_REF] Feldman | Reconceptualizing organizational routines as a source of flexibility and change[END_REF]. The respective issues that arise from these two opposite views differ radically. The former studies the lack of change. The latter analyses the change processes. Finally, in this rather confusing and contradictory literature, it will be a major challenge to arrive at a definition of organisational routines that will fit the conception of rule I adopt.

Whether focusing on rules, or on organisational routines, the two approaches emphasise only one aspect of the organisation where they are applied. On the one hand, the routines-based analysis focuses on strategies adopted by individuals to achieve organisational goals. However, almost no research attempts to link the organisational routines to more general principles such as rules. On the other hand, in the rules-based perspective, researchers pay attention to the cohesion of the organisation [START_REF] March | Organizations[END_REF], to the reasons why people follow rules [START_REF] March | Decisions and Organizations[END_REF], and to the ability of organisational rules to deal with external and internal shocks [START_REF] March | The Dynamics of Rules. Change in Written Organizational Codes[END_REF]. Nevertheless, the unanswered question is to understand how rules operate in organisations or rather, how workers follow rules. I argue that a misunderstanding of what rules are is causing the gap between these two approaches in the research landscape. A majority of scholars denies the incompleteness of rules when it comes to their application. Yet, agreement on this property would bring about a new way of understanding the relationships between rules and routines.

The paper is organised as follows. Section 2 provides theoretical considerations on rules and routines. They highlight the novelty of my approach. Section 3 presents the case study, the Electronic Equipment Maintenance Workshop of the Paris Metro (hereafter: the Workshop). This fieldwork was part of a larger study relating to rules dynamics, which I published in [START_REF] Reynaud | Operating Rules in Organizations[END_REF] 2 . Among the different issues I have explored, I focus in this paper on the relationships between rules and routines. As management introduced a productivity bonus in the middle of 1992, this gives the opportunity to study in what extent the new rule modifies the prevailing routines of work organisation. I draw on team observations, interviews and statistics that I carried out over a period of nine years (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000). First, I show that in an initial period, the productivity bonus has 2 Reynaud, B. (2002), Operating Rules in Organizations. Macroeconomic and Microeconomic Analyses. Palgrave, Macmillan.

partially biased the tasks selection process. The fact that the new rule contains negative externalities supports this evidence. Some tasks that pay more than the others do are no longer a shortterm priority for the Workshop. The application of the rule itself stops this process. Then, I offer a new insight of how usually workers follow rules governing tasks selection, after this distressed period. Section 4 concludes.

Defining Rules and Routines

From Rules to their Practices: the Emergence of Rules Incompleteness

Chester Barnard, in his seminal work The Function of the Executive (1938), emphasised that personal contacts and interactions develop within formal organisations. He considered the fact that people fail to conform to the prevailing rules a necessary condition to the ongoing of organisations (1938: 2): 'Informal organizations are necessary to the operations of formal organizations as a means of communication, of cohesion, and of protecting the integrity of the individual.' [START_REF] Blau | The Dynamics of Bureaucracy[END_REF] exploited this idea. In his study of a state employment agency, he analysed the process of rules modification that occurs when workers interpret and apply rules in particular situations. Blau highlighted three forms of rules transformation: The adjustment of the procedure, which does not imply a modification of the organisational objectives; the modification or redefinition of the procedure, characterised by a redefinition of the objectives, and the amplification (expansion) of the procedure. However, Blau has a narrow conception of rules application, which only happens with changes in the context. His major contribution consisted in showing that bureaucratic structures continually create conditions that modify these structures. In this perspective, rules are one piece of the organisation's puzzle. I go further than Blau's conception of rules application. I claim that rules application (or interpretation 3 ) is coextensive to an essential rules property. They are incomplete because each one needs to be applied in the light of knowledge, of information contained in the other rules, as well as custom, and practice, and context. A rule in itself, neither strictly determines individual choices and behaviours, nor guides them. Rather than being autonomous, rules form a system. If a majority of scholars shares this view, it lies on the ambiguity of the statements: rules incompleteness and 'rule-following'. For some scholars, the incompleteness of rules arises from a lack of information which is seen, either as a technical problem (contacts theory), or as a deliberate strategy of employers to prevent workers from minimising their effort [START_REF] Gouldner | Patterns of Industrial Bureaucracy[END_REF]. Gouldner 3 We consider the two terms as synonymous.

considers the incompleteness of rules as a voluntary lack of information that occurs as rules operate. He confuses the formal level with the practical level. The former deals with rules statements, the latter concerns operating rules. In my framework, the incompleteness of rules is structural.

Rules are explicit and public statements that trigger an action with a certain degree of predictability, but do not determine it. My perspective lays in a conception of rules that first draws a distinction between formal rules and applied rules, and secondly attributes to each one of them a specific property. The former is complete, but at a general and a syntax level. The latter is incomplete because rules must be abstract and general since they are designed for a diversity of concrete cases. Moreover, they have to deal with new elements that arise in the course of operations.

Although most of continental law scholars 4 share this point, I underline it to draw on another property of rules: the distance between rule and solution. This is the reason why one has to interpret rules. Indeed, rules make it possible to find a solution to a problem 5 , but they do not provide that solution in any detail (Atias, 1982: 216): 'If the content of the rule corresponded exactly to the actual hypothesis, the prescription would be valid only for the very limited number of hypotheses expressly considered. Even the slightest difference in circumstances would make it impossible to infer the solution from the rule'. Otherwise, there should be as many rules as problems to solve, which would destroy the rules distinctiveness in favour of another category that continental law calls decision 6 : 'It uses up its effect in an instant even though its consequences may be lasting. In contrast to norms (or rules), which can be applied in a limitless number of cases through the effect of a single edict, decisions only exert their effects gradually' (Jeammaud and Lyon-Caen, 1982: 57). In other words, the incompleteness of rules refers to an uncertainty of rules effects, which is distinct from rules uncertainty. This perception of rules as involving incompleteness is close in some respects to the notion of 'rule implementation', developed by [START_REF] Baier | Implementation and Ambiguity[END_REF], [START_REF] March | Understanding how decisions happen in organizations[END_REF], [START_REF] Zhou | Organizational decision making as rule following[END_REF], [START_REF] March | The Dynamics of Rules. Change in Written Organizational Codes[END_REF]. 'Rules are ambiguous; more than one rule may apply in a particular situation; and the behaviour required by the rule may be shaped through interpretation' (March, 1997: 20) 7 . For March et al. (2000: 22), rule implementation refers to 'the complications involved in translating rules into action'. Nevertheless, they do not explore this problem in their book (March et al. 2000: 202). Knowing the March's (1997: 19-20) hard criticisms addressed to scholars who consider 'rules implementation as taken for granted', this abandon is quite surpris-4 See Virallly (1960), Carbonnier (1985), and for a recent synthesis, de Béchillon (1997).

5 Reaching an objective is considered here as a kind of problem solving.

6 This meaning of decision is distinct from the notion of decision as rules-based action, developed by March (1997: 17-18). 7 Before March's work, [START_REF] Pressman | Implementation[END_REF] developed the problem of rule implementation.

ing. However, for the authors rule-following refers to a behaviour that is either pre-programmed by implicit rules, or based on explicit rules (Zhou, 1997: 258), their position is consistent 8 .

In fact, the novelty of my perspective consists in grasping the incompleteness of rules in the rule-following process. As rule-following is not a 'pre-programmed' behaviour, nevertheless, I do not share the view of some philosophers such as Saul [START_REF] Kripke | Wittgenstein on Rules and Private Language[END_REF] who claim that rulefollowing behaviour may lead to a regression of rules to infinity: one rule needs another one, which determines its condition of application. In turn, that rule also needs another rule to operate, and so on. This problem called the 'Kripke-Wittgenstein paradox' is only a logical problem. In practice, the regression process does not occur since rules are embedded in a context shaped by custom and practices. As Bouveresse (1976: 551) writes, 'the notion of usage is irreducible.' The following example shows the meaning of the incompleteness of rules. Taking Taylor's differential piecework as an example, the hypothesis that rules can regress to infinity is untenable, as it comes up against the power of usages. Taylor built this wage rule on an assessment of the exact time allowed for each task. In his view, one has to measure the work rate of the average worker, which in fact does not exist. However, it is possible to assess the work rate of the average worker in an indirect fashion, by means of rules. To obtain the average work rate, Taylor (1911: 168) takes that of the excellent worker as a starting point, to which he applies a standard deduction: 'Perhaps the greatest difficulty rests upon the fact that no two men work at exactly the same speed. The writer has found it best to take his time observations on first-class men only, when they can be found; and these men should be timed when working at their best. Having obtained the best time of a first-class man, it is a simple matter to determine the percentage which on average he will fall short of this maximum'.

To apply the deduction rule, the rate-fixer refers to his subjective judgement. Taylor or Brown's description of rate fixing has become a byword for the intractability of this problem. Brown (1962: 29-33) Measurement is not to be confused with guessing, counting, appraisal, evaluation or assessment'.

If however the rate-fixer supplements his measurement with 'his assessment as to whether the individual timed is working at normal pace and, on the basis of that measurement and that as-8 See also [START_REF] March | Decisions and Organizations[END_REF], [START_REF] March | Understanding how decisions happen in organizations[END_REF].

sessment, he states a time target in units of minutes, he has not produced that target by measurement. (…) Rate-fixers can measure the time, which physical work takes to perform, with a high degree of consistency (…), but they are measuring one aspect of the work, its physical manifestations which can be observed with the eye. They are not measuring the degree of responsible judgement shown by an operator in doing work. 9 ' Brown emphasises the intuition the rate-fixer requires to ascertain whether an operative is working at a normal pace and to assess his physical and mental concentration. The risk is that the average observed by the rate-fixer merely reflects the minimum work rate required to complete a given task, since workers are likely to be indulging in 'systematic soldiering'. In order to minimise this risk, the rate-fixer has recourse to a 'coefficient of reduction'. This is not an explicit rule, enshrined in some written document. The coefficient selected is the result of the rate-fixer's past experience and of his knowledge of current practices in respect of work rates.

This example helps to specify the research question. How do rules operate in a framework characterised by an incompleteness of rules? In the following, I will highlight the specificity of the incompleteness of rules relating to closed concepts.

Specificity of the Incompleteness of Rules Relating to Closed Concepts

On the one hand, the incompleteness of rules is not reducible to uncertainty. Some theorists [START_REF] Thompson | Organizations in Actions[END_REF][START_REF] Galbraith | Design Complex Organizations[END_REF][START_REF] Egelhoff | Information-Processing theory and the multinational enterprise[END_REF] consider uncertainty in organisations to result from the information process 'defined as including the gathering of the data, the transformation of data into information, and the communication and storage of information in the organization' (Egelhoff, 1991: 343). Moreover, for [START_REF] Galbraith | Design Complex Organizations[END_REF], uncertainty is the difference between the amount of information required to perform the task and the amount of existing information. Among the different ways of absorbing uncertainty, Galbraith listed rules and programs (Galbraith, 1973: 15). While in my perspective, the incompleteness of rules creates uncertainty that a new rule cannot diminish, Galbraith's theory claims the opposite.

On the other hand, economic literature suggests three characteristics of competenciestacitness, complexity, and specificity -that can be simultaneously sources of advantage and of ambiguity. In my perspective, the incompleteness of rules implies that workers develop a 'tacit knowledge', which consists in completing by the observation of concrete situations what rules do not specify. [START_REF] Polanyi | The Tacit Dimension[END_REF] defines tacit knowledge as an accumulation of experience that practices redefine. For workers it entails an inability to codify rules of decision that underlie their 9 The words underlined are in italics in the original text. work performance. For [START_REF] Reed | Causal ambiguity, barriers to imitation, and sustainable competitive advantage[END_REF], tacit knowledge associated with complexity and specificity of the competencies may be a source of 'causal ambiguity'.

Defining Routines

In analysing the case study, I will argue that routines contribute to managing the incompleteness of rules. Therefore, it is essential to present an overview of routine in the literature and its intellectual context to specify our own concept. Historically, the notion of routine comes from artificial intelligence. It is to Hayek and, in particular Simon 10 , that we owe its introduction into the social sciences. Simon is not only a theorist of organisations, but also a specialist in artificial intelligence and cognitive psychology 11 . As for Hayek, he is one of the founders of cybernetics. We underline this point since it explains their conception of routines as mindless repetitions 12 .

A reading of the principal texts on the topic (March and Simon, 1958; Cyert and March, 1963; Nelson and Winter 1982; Cohen, 1991; Dosi, Teece and Winter, 1992; Cohen and Bacdayan, 1994, Cohen et al. 1996 13 , Pentland and Rueter, 1994; Feldman, 2000, 2003, etc.) reveals two possible points of entry into the notion of routine.

In the first, routines are patterns of behaviour, or action or interactions. The content of the patterns differs among the scholars 14 . For [START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF], routines are 'patterns of regular and predictable behaviours'. Egidi (1993: 1) defines routines as 'sequences of patterns of actions that lead to the realization of a final goal'. Dosi, Teece and Winter (1992: 191) consider routines as 'patterns of interactions which represent efficient solutions to particular problems'.

Another ambiguity in the literature deals with the level at which the concept is applied. Does it apply to individuals, organisations, or to both? In that case, one has to spell out the passage from the individuals' level to the organisations level. Cohen et al. (1996: 683) gave an example in which both individual and collective levels interplay. They define a routine as 'an executable capability for repeated performance in some context that has been learned by an organization in response to selective pressures.' For Nelson and Winter (1982: 97) 11 See [START_REF] Newell | Human Problem-Solving[END_REF].

12 I will develop this point in the following paragraph. 13 Cohen et al. refer to a scholars' group that met at The Santa Fe Institute in 1995. Industrial Corporate Change published the group's report in Cohen et al. (1996): 1996, 5, no 3: 653-698. 14 As Becker (2004: 645) emphasises, there are differences between these terms. Behaviour is a subset of action. Moreover, behaviour is observable, while action is not observable. Interaction is a subset of action, and refers to a collective level. such as [START_REF] Cohen | Organizational routines are stored as procedural memory: evidence from a laboratory study[END_REF], who specify that skills refer to individuals, while routines are organisational.

The second point of entry defines a routine as a capacity to learn, which in fact contains two essential and linked questions. How does learning defined? Are routines mindless repetitions, or effortful accomplishments? Learning as a capability to replicate a task fits with routines as mindless repetitions. Likewise, learning considered as a capability to increase his (her) knowledge fits with routines as effortful accomplishments. Stinchombe (1990: 63) describes the mindless vision of routines as follows: 'The parts of an individual's skill which are completely routinized are the parts that he or she does not have to think about -once a routine is switched on in the worker's mind, it goes on to the end without further consultation of the higher faculties'. This position argues the efficiency of repetitive tasks that prevail in forms of management and of work organisation (assembly line). For March and Simon (1958: 142), a behaviour becomes a routine when it has reached the highest degree possible to develop a fixed response to a given stimuli. The authors describe routines as automatic skills, which they compare to computer programs. Routine has the historical meaning of computation theory. [START_REF] Cyert | A Behavioral Theory of the Firm[END_REF], [START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF] have also likened organisational routines to computer programs and subprograms. Workers perform such tasks as standard operative procedures [START_REF] Blau | The Dynamics of Bureaucracy[END_REF][START_REF] Cyert | A Behavioral Theory of the Firm[END_REF] or as habitual responses to familiar situations [START_REF] Weiss | Routinized behaviour in organisations[END_REF]Gersik and Hackman, 1990).

Other researchers have challenged the traditional understanding of organisational routines, for which routines are mindless repetitions, fixed behaviours, and a source of inertia. Pentland and Rueter (1994) and Pentland (1995) did the pioneering work, introducing the idea that routines evolve and change. In the first paper, the authors claim that organisational routines operate as grammars. This insight entails a new understanding of routines. Routines are a set of possibilities called 'repertories of actions'. 'A grammar does not specify a fixed outcome; it defines a set of possibilities among which members accomplish specific sequences of action ' (1994: 485).

The choice among them depends on previous actions and the grammar or rules that fit actions together. In a similar approach, [START_REF] Feldman | Organizational routines as a source of continuous change[END_REF] emphasises that 'change is more than choosing among a repertoire of responses, and that the repertoire itself, and the rules that govern choice within a repertoire, can also change ' (2000: 613). Scholars use the terms 'routines as effortful accomplishments' to sum up this new understanding. However, I will call it 'routines as sense making repetitions' alluding to Weick's book (1995), Sensemaking in Organizations. It offers a better contrast to the traditional view, 'routines as mindless repetitions.' This divided line -mindless routines versus 'sense making routines' -partly match up with another opposition between static and dynamic routines. 'Static routines embody the capacity to replicate certain previously performed tasks. Needless to say, routines are never entirely static, because with repetition routines can be constantly improved'. Learning curves concretely display the operation of this type of routine. Dynamic routines, on the other hand, 'are explicitly directed at learning' (Dosi, Teece and Winter, 1992: 192).

I propose to combine these two distinctions -individual/organisational and mindlessness /sense making -to highlight four meanings of the notion of routine. Each of the numbered cells in the table I have constructed shows the concept that best characterises each of the four pairings of one row and one column. Note that I have not sought to provide a unified vision of the notion of routine (no such thing exists). Feldman & Rafaelli ( 2002) [START_REF] Feldman | Organizational routines as a source of continuous change[END_REF][START_REF] Feldman | A Performative perspective on stability and change in organizational routines[END_REF] Cell (I): Mindless learning capacity at the individual level is best characterised as skills. They express a capacity to execute the same task repeatedly. [START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF] devoted an entire chapter to routines as skills that define the capacity for coordination in a normal situation. Routines have another property: they are a form of tacit knowledge. As Polyani (1967: 4) notes: 'We know more than we can tell'. Thus, routines form a set of implicit arrangements that individuals, who adhere to them, do not recognise as such.

Cell (II): Mindless learning capacity governing the organisation level defines the 'standard operating procedures' or 'rules of thumb' [START_REF] Blau | The Dynamics of Bureaucracy[END_REF]Cyert and March, 1963: 101;Nelson and Winter, 1982: 17). These are simple decision-making rules adopted by the firm that need minimal information. For example, standard operating procedures make it possible to establish the output level of the firm in various contexts (Nelson, 1995: 69). They constitute 'an organisation's memory' (Cyert and March, 1963: 101;Nelson and Winter, 1982: 99). (1982: 171-172) underline that search defines the capability to advance through a process of trial and error. Search makes use of heuristics to provide a common framework to solve similar problems (Winter in Cohen et al., 1996: 663).

Cell (IV):

This cell describes a new insight among a few scholars since ten years. Organisational routines are patterns of behaviours operating at the organisational level and involving 'sense making' learning capacity. Indeed, they operate as grammars that express a set of possibilities, called 'repertories of actions' (Pentland and Rueter: 1994). The novelty consists in underlying the change ability of organisational routines. This change comes from either, a change of the repertory, or of the rules governing the repertory [START_REF] Feldman | Organizational routines as a source of continuous change[END_REF].

The Contrast between Routines and Algorithms

In a first approach, I define routines as a transformation devices based on cognitive resources to reach a particular result. Cognitive resources are both internal (the capability of adaptation) and external (the ability to make use of reference points). Therefore, routines are located devices, embedded in particular contexts, since the problems they should solve are susceptible only to local exploration: individuals do not have full knowledge of the world. This is perhaps a point on which I beg to differ with Egidi (1992: 170, note 4), for whom 'routine' is here a synonym of 'not completely specified procedure', which might lead one to think that a complete specification were possible. I also disagree on this point with Dosi, Teece and Winter (1990: 243 and1992: 192), for whom the complexity of individual behaviour stands in the way of a codification of routines and their transformation into rules.

Procedure or algorithm 15 is both close to and opposite of individual routine. Algorithm is close to individual routine in the extent where they contribute to the decision process. Nevertheless, they act in very different ways: implicitly for routines and explicitly for procedures. They are opposed in several other points. For Lassègue (1994: 49), 'An algorithm is a finite list of instructions that have to be followed in a given order. By following the instructions gradually, one should arrive at a result after a finite number of steps. The result should be reproducible in the infinitude of individual cases that are all dealt with in the same manner.' A computer program is an example of an algorithm.

I distinguish between these notions according to the nature of reasoning required to apply them. The reasoning may be either entirely made of cognitive elements -calculation, selection, search for an algorithm, and so on (hypothesis H 1 ) -or wholly made of located dimensions. In that case, the context leaves so little choice that the application is almost over-determined (hypothesis H 2 ). The former is an algorithmic procedure. The latter defines a routine. Under hypothesis H 1, agents are purely cognitive beings who make their calculations in a world without context. H 1 does not fit with real individuals. Hypothesis H 2 means that agents react to a context characterised by a limited number of choices. Among all the options, theoretically available, very few of them are applicable. H 2 implies that agents are pseudo-reactive beings.

Procedures and routines differ in other respects. The decisive reasoning with regard to future action is performed at different points in time: before the execution of a procedure and in the course of the application of a routine. Procedures are explicit and codified, routines are tacit.

The execution of a procedure does not require any interpretation given that it takes place in the domain of syntax and of calculable. This kind of rationality is procedural in Simon's sense of the term (1976). On the contrary, routines are based on 'making sense' since they operate in an area that is pre-delimited by an interpretation that has already been done. That is the reason why routines are governed by an adaptive rationality that puts the emphasis on the experimental learning undertaken by individuals and groups [START_REF] Cyert | A Behavioral Theory of the Firm[END_REF]. By contrasting routines with algorithms, one may grasp their respective degree of cognition. While algorithms are mindlessness, routines do not present this property. They are sense making. On this point, I agree with 15 I consider these terms as synonymous. In that point I agree with Egidi, who writes: "I use the word 'procedure' in the precise sense of algorithm, which (by Church's thesis) can be represented by means of a Turing Machine and mechanically executed" (1992: 170, note 4). [START_REF] Feldman | Organizational routines as a source of continuous change[END_REF] thesis that considers routines as effortful and ongoing accomplishments. Table 2 sums up these differences.

Table 2: Procedures and routines PROCEDURE (OR ALGORITHM) ROUTINE

-A finite list of instructions to be followed in a given order and leading to a reproducible result.

-A routine is a mechanism for effecting transformations with a view to obtaining a result. A routine is a way of acting.

-Non-context bound, since one has explored the all possibilities.

-Context-bound, since one has explored locally the problem.

-The solution is guaranteed, either with a certain probability (probabilistic algorithm), or with certainty (deterministic algorithm).

-A solution is not guaranteed by the application of a routine.

-The problem has been explored systematically, at least to a certain point.

-The problem is explored pragmatically: in adopting routines, the solution may be found. One cannot find the solution in advance.

-Explicit, codified character of the procedure.

⇒ Transferable or reproducible.

-Tacit, non-codified nature of the routine.

⇒ Not transferable from one firm to another, unless the contexts are very similar.

-Carried out automatically (mindless).

-'Making-sense' is required for the selection of a routine.

-Procedural rationality 16 [START_REF] Simon | From substantive to procedural rationality[END_REF].

-Adaptive rationality [START_REF] Cyert | A Behavioral Theory of the Firm[END_REF].

This outline of the multiple meanings of the notion of routine in organisation and evolutionary theories conveys the impression that routines are everywhere and therefore nowhere, in economic life. How can we make sense of this? The radical difference between our concept of routines and the algorithm of a Turing machine highlights that routines and rules application are closely linked. My approach to routines is quite different from that of evolutionary theorists, and 16 Procedural rationality and adaptive rationality are not radically different from each other; see March andSimon (1958), chapter 7, and[START_REF] March | Decisions and Organizations[END_REF].

The Work Process

The Workshop is responsible for the maintenance of the electronic and micro-mechanical equipment and the relays of the Paris Metro 19 . The operatives of the Workshop are required to deliver the repaired equipment without any delay to the 'line operators' of each Metro line. In the following, I will often refer to the latter as 'lines'. As I will explain, the delivery of the components at the due date is a rather complex activity. Before analysing this issue, an outline is required of the operatives' organisation, and of the rules, they have to follow.

The 122 operatives are divided into eight teams: five of them are specialised in repair and maintenance, two are in charge of logistics, and one constitutes the engineering and design department. However, for my purpose, I will concentrate on the five repair teams that are responsible for maintenance of the electronic circuit boards, power electronics, micromechanical equipment, and relays used in critical failure mode on the various Metro lines. One of the difficulties of the work results from the fact that electronic operatives have to repair three generations of equipment, dating from 1955 to today. Therefore, operatives must deal with a multiplicity of models (around 500 models in electronics), which requires extended knowledge. While operatives are members of a same team, the tasks performed are individual.

The line operators' tasks consist in inspecting the state of the trains and then removing the faulty equipment; these tasks constitute curative operations or correctives procedures. The 18 It was obviously necessary to reconstitute these data for all the teams in order to assess the degree of diversity within the results as a whole, in terms of both productivity and work quality. I did it in [START_REF] Reynaud | Operating Rules in Organizations[END_REF]. 19 In September 2000, there were 162 employees: 8 managers, 35 supervisors, and 122 operatives.

lines are the sole judges of which items of the equipment should be removed for repair. For example, they decide to remove either a single faulty circuit board or all the boards in a train. Electronic equipment undergoes only corrective procedures. Conversely, as micromechanics and relays are subject to wear and tear, the lines apply security rules that govern the cycles of maintenance procedures. They depend on the number of kilometres travelled. However, these are twofold: the major services every 25,000 kilometres consist of technical inspections that involve dismantling, cleaning, and removing the grease marks of the units. The standard services, which include safety inspections every 8,300 kilometres, are more superficial. To sum up, corrective procedures are random while preventive operations are scheduled.

The logistics builds two rules dealing with the organisation of work. First, the schedule for the major services and the standard services, based on the number of kilometres travelled, has a time horizon ranging between one and three months. Secondly, logistics writes down, updates, and displays the so-called 'debt sheet' for the corrective tasks, based on the state of the rolling stocks, and the removed equipment. The 'debt sheet' is a listing that shows operatives on a twiceweekly basis the amount of the various units and electronic circuit boards required. The expression 'debt sheet' refers to different kind of delay that a team may encounter. The first one is a delivery delay to the logistics, which is in charge of sending back the items to the line operators. This delay involves a store debt 14 that arises if the logistics does not have enough stock of a given part to meet the needs of the line operators. The store debt makes up a safety margin, ensuring that logistics can always meet demand from the lines. It acts as an alarm signal. The logistics technicians determine the level of debt, which depends on the existing stock, frequency of breakdowns, and the age of the equipment (and so on), and therefore varies from component to component.

The second delay is more serious. A line debt arises when the line operator makes a train out of service because he cannot replace the faulty unit by a new one. During the strikes in 1988, line debts were frequent.

The Definition of the Productivity Bonus

In the following, I present the productivity bonus that management introduced in the middle of 1992 to increase labour productivity. Before, the direction's Workshop considered as normal that work hours could vary between an upper and lower threshold, respectively 6.50 hours and 5.80 hours, the working time being of 7.60 hours. The former, called the 'statutory working time', is calculated by subtracting from the 'legal working time' (7.60 hours), the 1.1 hours spent 14 The 'store debt' refers to the store of the logistics team.

on changing, showering, being paid, cleaning the work stations weekly, and statutory absences.

The latter, called the 'normal or average working time', resulted from management evaluation.

The difference of 12% originated in the various lost hours tolerated by management. Officially termed 'recuperation time', they amounted to a production loss (see Table 3). In setting up the new pay rule, the direction no longer considered working less than 5.80 hours as normal. Essentially, the 'PB' aimed at increasing the intensity of work by reducing the difference between statutory and real working times.

Table 3: Working times -"Normal" and Statutory Hours -according to the Workshop rule -7.60 hours spent at work: legal working time -6.50 effective hours of statutory time (5.8 x 1.12) => "PB max" -6.34 effective hours by team 1 -5.80 minimum "normal" hours => "PB min"

For these two thresholds, production equivalents were defined, since the 'PB' was to be obtained, not by staying a certain hours at work, but by achieving an output equal in terms of quantity and quality to some fixed minimum. The average number of effective work hours was reckoned to be at such a feeble level that management decided to fix the equivalent in output terms of the lower threshold of 5.80 hours as a minimal objective. In the same way, the equivalent input of the upper threshold of 6.80 hours is the maximal objective. In table 3, team 1 that works a average of 6.34 effective hours, has only to improve its production to an amount of 0.16 hour to get the 'PB max' if the quality indicators had reached the top level.

Half of the bonus depends on output volumes. Since the time spent to repair each unit is very different from the others, management decided to apply a unique 'weighting coefficient' to each team activity. Thus, the output has one measure, the 'Weighted Output Unit'20 . It is obvious that many inequalities remain21 . First example: corrective maintenance procedures, equipment modifications, and preventive maintenance operations have the same 'weighted coefficient'. This means one considers them as equal outputs. Indeed, they take very different lengths of time to complete. Second example: the shortest corrective operation takes half an hour, while the preventive maintenance of some parts may require 13 hours' work.

The other half of the bonus depends on work quality that has two aspects. Internal quality is a measure of the ability of each team to carry out repairs within the times allotted. The level of the team debts to the logistics evaluates this capability. External quality depends on client satisfaction. This is a function of the failure rate of repaired equipment, defined by a breakdown in the six months following the corrective procedure 22 . The productivity bonus varies linearly between two intervals. If the team attains only the 'PB min' the bonus is nil; it is maximal (around 8% of the operative's salary) if the team attains or goes over the 'PB max'.

How the new rule modifies the prevailing routines of tasks selection?

Before examining in what extend the new rule modifies the tasks selection routines, let us first observe how, and in what environment, an operative visualises the work to do. Every morning, the logistics brings in the equipment and places it on different shelves depending on the type of procedure required, or puts it on racks in the case of identical units. The operative takes note of the equipment waiting for repair or maintenance, and sees the colour of the tags attached to the equipment awaiting his attention: white for corrective procedures and yellow for major services and standard services. These tags indicate the due date of the equipment to the logistics. The operative also sees the debt sheet brought to him twice a week by the logistics. This listing does not give the precise order of repairs to be done, but indicates the quantity of each item that has to be repaired before the next debt sheet arrives.

I studied in detail the strategies of the same three teams I observed before. In a first period, two of them -control electronics (EK1) and power electronics (EK3) -changed their prevailing routines. The third one (micromechanics) had no choice that following the scheduled work since the entire activity consists of major and standard services.

Shortly after the introduction of the productivity bonus scheme, the operatives of the team, called EK1, gave priority to the procedures that generated the most 'Weighted Output Units' in a minimum of time, by repairing the single circuit boards rather than whole units, etc.

This strategy, adopted during the first two six-month (November 1992-October 1993), immediately proved to be profitable. Labour productivity reached an output figure 11.3 per cent above that triggering the maximum bonus while debt levels and fault recurrence rates were also good. Thus, the operatives received the full bonus. Obviously, maximising the output is no longer compatible with quality standards, whether external (fault recurrence rates), or internal (debt levels). First, the productivity strategy reduces the reliability of repairs that increases the fault recurrences and 22 However, an item could be 'shipped' only well after this period of 6 months, because lines often hold stocks of the different items during a period of over 6 months.

as a consequence, the debts levels. This effect is particularly strong is the team EK1 where the equipment is ageing. It is the reason why the fault recurrence rate rises very sharply, which leads to massive indebtedness. Secondly, maximisation of the output is no longer compatible with adherence to the priorities detailed on the debt sheets. This is the second factor that contributed to the massive indebtedness from May 1994 onwards (see Figure 1 in the Appendices). The team found itself in a critical situation that forced it to follow all rules constituting the 'PB'.

The other team, EK3, followed suit. The strategy of maximising labour productivity by concentrating on procedures that take little time came into conflict with the rule imposed by the debt sheet and telephone calls from the line operators. When debts and productivity in volume increase simultaneously, as it did between April 1994 andApril 1996, this means that operatives select the easiest tasks (see Figure 2 in the Appendices). In other words, they are not continuously adhering to the priorities imposed by the debt sheets otherwise debt levels would have declined significantly, as labour productivity rose. After this period, a new supervisor takes over the management of the team and implicitly forced operatives to follow all rules defining the 'PB'.

These two examples show how a new rule may change the prevailing routines, even if it is not the management interest. However, the 'PB' may play its incentive role, if some authority uses the existing rules to call back the deviating routines.

Following the Rules that Govern Tasks Selection in the Workshop

For an economist-observer, one of the unresolved questions is to know how, in a normal period, the operatives follow the complex rules of tasks selection without any delay. Our observations indicate that following the rules consists in translating abstract rules into concrete reference points, and adding in what the rules have not specified. In so doing, operatives rely on existing usage or routines in the broad sense of 'a way of doing things' (Winter, 1986: 165). I observed two examples of usage. First, maintenance procedures need to be anticipated for any equipment that has been withdrawn for corrective procedure, and that has reached two-thirds of its kilometre service. There is no written trace of this usage. However, all operatives know it, and have to take it into account as well as the explicit rules. Second, in order to avoid any temptation to choose the easiest procedures, an old usage, a working practice established a long time ago, consists in taking the equipment to repair first, and only afterwards looking at the tag attached to it. The aim of this practice is to dispel finally the notion that unfair work strategies are acceptable in order to preserve a good working atmosphere. According to one operative, 'it's an implicit rule that new re-cruits apply instinctively'. 23 The fact that new operatives work alongside an experienced hand for about six months makes it easier to pass on such practices. These two examples deal with routines as tacit knowledge that explains behaviour patterns.

Moreover, the necessity to add in what the rules do not specify means that the operatives have to anticipate the future in several respects. The operatives cannot select the items to repair in a random order. If they did, there would surely be a delay. They have to take into account their anticipation of several events, such as the breakdown of a test bench, the lack of a component or of a spare part, and so on. Each operative has to determine the sequence of procedures to select, based on anticipation dealing with their work environment. Moreover, each operative also has to anticipate which items will soon be in deficit, since the debts notified on a Tuesday will have to be discharged by Thursday, and so on. The reason is that operatives have a better sense of the stock statement than the logistics. The line operators do not plan for these contingencies. For example, in one team, an operative carries out a daily inspection of all the drawers containing the components required for repairs -the so-called advance stock -and goes down to the logistics in order to obtain fresh supplies.

Finally, the operatives have to draw on a number of very different resources. First, they rely on explicit knowledge contained in other rules. Secondly, tacit knowledge is gained through personal experience: knowledge about the state of the rolling stock, wear and tear on machinery, quantities of spare parts held in stock, and so on. Finally, they use of existing usages and practices encapsulated in phrases such as -'We don't look at the tag before taking the unit to be repaired'

and 'we like to build up as much advance stock as possible'. Thus, the repetition of certain patterns of behaviour, such as glancing at the shelves in order to assess debt levels, is an example of a routine: a gesture of which an operative is not aware, and which in reality is a rule already interpreted.

In fact, operatives follow a whole system of rules governing work organisation, safety, and so on. One important property of rules emerges from this: they form a structure made up of several interlinked subsets, somewhat like a network. Thus explanations, which supplement the previous ones, such as -'We check out the MS (major services) shelves. If the parts are piling up, they have to be done; the debts will have to wait' or 'we glance briefly at the shelves' -reveal in very concrete terms how the operatives follow rules. They have found tangible reference points that equate with the written instructions that all these rules constitute. This key element in this particular situation enables them to dispense with formal rules as new information or problems 23 The term 'implicit rule' was used by the operatives; from my point of view, a rule is always explicit. appear. In this example, the operatives have created for themselves a rule governing task selection: rising demand for major services, which is all too evident from the growing piles of parts on the shelves, triggers a decision to give priority to preventive maintenance procedures over corrective procedures. Such a rule governing task selection is not self-evident: the operatives could have chosen to ignore the growing piles of parts requiring major services in favour of corrective procedures, which are often more profitable in terms of bonus payments. This clearly represents the stabilisation of an interpretation of the reference point, which we denote by the term routine. It would be particularly misleading to think that the act of 'glancing briefly at the shelves' constitutes a rule. Such a gesture, made without being aware of it, is a routine.

4. Routines and 'the void at the heart of rules' 24

Let us take the following example. An operative, who is repairing a printed circuit board, solves the problems himself by applying, for example, the rules of basic electronics. The operative does not need to draw on all the rules of electronics, electricity etc., which he knows, but just on those he considers necessary as the repair proceeds. Consequently, his action is governed by a restricted set of rules that summarise the relevant interactions between the tasks to be performed and the set of appropriate actions. The operative's mental processes consist in recognising the models that trigger the appropriate action, the repetition of which leads to an apparently 'routinised' pattern of behaviour. However, the 'routinisation' is only apparent, since the operative must be able to change rules when he encounters radically new problems. This means that routines are not mindlessness, but sense making repetitions. In such processes, routines appear to be interpreted rules or pragmatic, interpretative working practices. This point highlights the thin line that separates the act of following rules from that of adopting routines.

In my view, the first difference between rules and routines is that the former are arrangements awaiting interpretation, while the latter are rules already interpreted. The second difference is that rules are explicit while routines are more often implicit. The third difference lies in the distinction between the theoretical and the pragmatic. Since the fundamental characteristic of rules is their general nature (which explains their distance from the solution 25 ), routines are a form of pragmatic resolution that can be applied to a problem to which rules give only a theoretical, abstract and general response. Thus, in my observations, routines emerge as one of the ways of following rules. To force the point a little, one can say that it is through routines that 24 The expression is borrowed from Pierre Bourdieu. Cf. [START_REF] Bourdieu | The Social Structures of the Economy[END_REF]: 160.

25 Since rules help in the search for a solution, but do not provide it. See [START_REF] Reynaud | Le Salaire, la règle et le marché[END_REF], Chapter 2.

rules operate. Rules constitute the background for routines. In other words, routines are rulebased patterns of behaviour, as Egidi points out (in Cohen et al., 1996: 687). The distinction that Argyris and Schön (1974: 7) make between the 'theory-in-use' and the 'espoused theory' of the members of an organisation helps to clarify the difference between rules and routines. 'The 'espoused theory' is the theory to which an actor gives allegiance and which he communicates to others when they ask. On the other hand, the theory that governs his actions is his 'theory-inuse', which may or may not be compatible with the 'espoused theory'. Moreover, the agent may or may not be aware of the compatibility between the two theories.' Rules reflect the organisation's 'espoused theory', while routines reflect the actors' various 'theories-in-use'.

It is the development of certain modes of behaviour, which, through repetition, creates routines. In a sense, routines provide a pragmatic, local, and temporary solution to the incompleteness of rules. Since routines emerge only in the course of action, they come with no guarantee of success. That constitutes their dynamic. This analysis of the role of routines in managing the incompleteness of rules is very close to what Bourdieu (2005: 160) says with regard to the way rules operate: 'It is habitus that fills the void at the heart of rules'. 26

26 Pierre Bourdieu has expressed similar ideas on the incompleteness of rules and the scope that exists for interpreting them. Cf. in particular, [START_REF] Bourdieu | The Logic of Practice[END_REF][START_REF] Bourdieu | The Social Structures of the Economy[END_REF], Chapter 3: 156-165.

Appendices

Figure

  devotes a whole chapter to 'The inaccuracy of rate-fixing': '… neither piecework prices nor time allowances are the result of measurement (…). Both result from the use of judgement by rate-fixers'. He defines what measurement is: 'Measurement is the process of ordering data or observations to a scale of length by means of objectively definable operations.

  routines may 'refer to a repetitive pattern of activity in an entire organization, (or) to an individual skill'. Rare are those, 10 Both are Nobel Laureates in Economics.

  Cell (III): 'Sense making' learning capacity operating at the individual level deals with an individual's ability to solve new problems without undermining the general functioning of the organisation. The terms search and individual learning match up closely to this notion. Nelson and Winter

  in particular, from Nelson and Winter for whom routines are a 'catch-all' notion, asWinter himself recognises (1986: 165): 'Nelson and I use the word routine17 as the generic term for a way of doing things. It is simultaneously the counterpart of a wide range of terms employed in everyday life and in various theoretical languages, including those of orthodox and behavioral economic theory; among these terms are decision, rule, technique, skill, standard operative procedure, management practice, policy, strategy, information system, information structure, program, script and organization form.'3. The Case Study: Revisiting Rules and Routines3.1. The Data GatheredThe fieldwork is the Electronic Equipment Maintenance Workshop of the Paris Metro that I studied shortly after the introduction of the productivity bonus in July/August 1992, from February 1993 until June 2001. I obtained straightaway the agreement of management. However, the research could not start without the agreement of shop stewards and operatives on the objectives and method of my research. Workers were sceptical of the observations at work. Shop stewards thought I was a direction's agent in charge of controlling them. Nevertheless, the fact that management did not paid me played in my favour. At the end of a long meeting, they agreed to my proposal. Then, I gathered data in three stages. Each of them was useful -sometimes partiallyfor the purpose of this paper.First, between February and April 1993, I involved five interviews with management and thirty with workers. I asked managers how the new pay rule lies within the policy framework of the Workshop. I asked workers what their understanding of the productivity bonus (hereafter abbreviated as 'PB') was, and for which reasons they either agreed or not the 'PB'.Secondly, I carried out observations during a period of three months (December 1994 to February 1995) with an ergonomist from the National Agency for the Improvement of Working Conditions (ANACT). Together we observed three teams, each of them working with a different technology (control electronics, power electronics, and micromechanics). In each team, we did an immersion of two days during which our working day extended over the longest time slot worked by the operatives (7 AM -7 PM). We observed them at work and questioned them about what they were doing, how and why, in what order, and so on. Our attention was concentrated on the nature of the cooperation between the operatives, and on the methods of tasks selection. We kept our 17 Words underlined are in italics in the text. field notes. Our reports came up for discussion with operatives who validated them. Afterwards, they handed them to management.The last stage consisted in reconstituting from 1992 until 2000 monthly statistics related to output, labour productivity, fault recurrence rates, and debt in volume terms for the three teams whose strategies I examined in detail (EK1, EK3 and micromechanics)18 . These teams are those for which I did observations between December 1994 and February 1995. Moreover, they are representative of the Workshop activity. Taking these monthly figures as a starting point, I calculated the quarterly figures corresponding to the bonus payment periods (six months). I also gathered the percentage of the maximum bonus obtained by each team at the end of each bonus period. From these indicators, I inferred team routines that I exposed to management and to the supervisor concerned. After discussions, which sometimes led me to change some interpretations, they validated my conclusions.

  1: EK1-Evolution of labour productivity, debts, and fault recurrence rates(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)

		700															160
		600															140
	Productivity in volume terms	200 300 400 500															40 60 80 100 120
		100															20
		0															0
		Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.
		93	93	94	94	95	95	96	96	97	97	98	98	99		99	00	00
		Labour productivity in volume tems		Debts in volume terms	Fault recurrence rates
	Figure 2: EK3 -Evolution of labour productivity, debts, and fault recurrence rates (1993-2000)
		700															25
		600
	Labour productivity and debts	200 300 400 500															5 20 10 15	% Fault reccurence
		100
		0															0
		Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.	Apr.	Oct.
		93	93	94	94	95	95	96	96	97	97	98	98	99		99	00	00
		Labour productivity in volume tems		Debts in volume terms	Fault recurrence rates

The 'Weighted Output Unit' is the product of one intervention pondered by the 'weighted coefficient' of the team.

In each team, breakdowns are not equally difficult to repair: some are simple, other are complex.