# Heterogeneity matters: labour productivity differentiated by age and skills

Muriel Roger, Malgorzata Wasmer

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Muriel Roger, Malgorzata Wasmer. Heterogeneity matters: labour productivity differentiated by age and skills. 2011. hal-05483880

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Direction des Études et Synthèses Économiques

G 2011 / 04

Heterogeneity matters: labour productivity differentiated by age and skills

Muriel ROGER et Malgorzata WASMER

Document de travail

<figure><img src="image_2.png" /></figure>

Institut National de la Statistique et des Études Économiques
INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES

Série des documents de travail
de la Direction des Études et Synthèses Économiques

G 2011 / 04

Heterogeneity matters: labour productivity differentiated by age and skills

Muriel ROGER* et Malgorzata WASMER**

FÉVRIER 2011

The data analysis has been completed during the research stay of Malgorzata WASMER at the Institut National de la Statistique et des Études Économiques in Paris. We would also like to thank Sébastien ROUX, Anthony BRIANT and Didier BLANCHET for their fruitful remarks as our work was progressing and to Virginie RÉGNIER for her assistance in the dataset construction. Helpful comments were received from participants of the internal INSEE seminar, the 57th Congress of AFSE (French Association of Economic Science), 26th JMA (Journées de Microéconomie Appliquées), EEA-ESEM 2009 and EALE 2009.

<footnote>* Département des Études Économiques d'Ensemble - Timbre G201 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF and Paris School of Economics (INRA), 48 Bd Jourdan, 75014 Paris, France, e-mail: muriel.roger@ens.fr</footnote>

<footnote>** Corresponding author. University of Fribourg and Université Lumière Lyon 2, GATE/CNRS. Adresse: University of Fribourg, Economics Department, Bd de Pérolles 90, O ce G 510, 1700 Fribourg, Switzerland, tel: +41 (0) 26 300 82 22, e-mail: malgorzata.wasmer@unifr.ch</footnote>
# Heterogeneity matters: labour productivity differentiated by age and skills

## Abstract

This study aims at evaluating the actual profile of marginal productivity across age groups within the workforce. As age-productivity profiles might differ between occupations, we differentiate the workforce simultaneously by skills (low-skilled, high-skilled) and by age (young, middle-aged, old). Estimating a production function with a nested constant-elasticity-of-substitution (CES) specification in labour allows imperfect substitution between different categories of workers. We use French datasets for manufacturing, services and trade sectors. Labour productivity is found to be the lowest for the low-skilled older workers while high-skilled senior employees in manufacturing and trade are the most productive group. Throughout the sectors, wage rates vary considerably less than productivity and wage profiles are steeper for high-skilled workers. The relative productivity/wage ratio is found to be sector-specific. It is the highest for young workers in manufacturing while in services and trade it is the highest for the middle-age employees.

**Keywords:** ageing, older workers, labour productivity, CES production function, endogeneity

# La productivité du travail selon l'âge et selon les qualifications

## Résumé

Cette étude vise à évaluer le profil de productivité marginale selon l'âge. Les profils âge-productivité pouvant être différents selon les professions, nous considérons la main-d'œuvre à la fois par qualification (peu qualifiés, hautement qualifiés) et par âge (jeunes, âge moyen, âgés). Nous spécifions et estimons sur données françaises d'entreprises une fonction de production de type CES emboîtée qui autorise une substitution imparfaite entre les différentes catégories de travailleurs. Les estimations sont effectuées séparément sur les secteurs de l'industrie, des services et du commerce. Nous trouvons que la productivité du travail est la plus basse pour les travailleurs âgés peu qualifiés, alors que les employés âgés hautement qualifiés dans l'industrie et le commerce sont les groupes les plus productifs. Dans l'ensemble des secteurs, les salaires varient considérablement moins que la productivité et les profils salariaux sont plus accentués pour les travailleurs hautement qualifiés. Le ratio productivité relative sur salaire relatif dépend fortement du secteur. Il est maximal pour les travailleurs jeunes dans l'industrie. Par contre, dans les services et le commerce, il est le plus élevé pour les travailleurs d'âge moyen.

**Mots-clés** : vieillissement, travailleurs âgés, productivité du travail, CES

**Classification JEL** : J24, J31, J41
# Contents

1 Introduction

2 Age, wage and productivity: a review

2.1 Theoretical background

2.2 Empirical evidence

3 The model: production function with labour as nested CES

4 The method

5 Data and summary statistics

6 Results

6.1 Econometric results

6.2 Age-productivity and age-earnings profiles: general pattern

6.3 Density estimations

6.3.1 Productivity

6.3.2 Earnings

6.3.3 Productivity/earnings ratio

7 Conclusions

8 Appendix

References
<figure><img src="image_3.png" /></figure>
# 1 Introduction

An ageing population bears important consequences for labour markets. Policy makers and an increasing number of individual organisations as well as private firms realise that early retirement of older employees deprives companies of valuable expertise and creates a shortage of qualified employees. Thus, the trend towards early retirement policies starts being reversed.

Nevertheless, the available evidence indicates that in many countries older workers continue to confront unfavourable labour market conditions compared to other age groups. Despite the increasing need for working life extension as well as the age diversity enabling the transmission of skills and know-how, the employment and hiring rates of older workers stay at a very low level in many developed countries. Employers' negative perceptions about the adaptability and productivity of older employees are among the reasons. An increase in the workforce's average age is frequently associated with higher labour costs as well as greater resistance to technological developments and only rarely with an expected increase in productivity (Remery and al., 2003). Although employers appreciate older employees' experience, loyalty and low turnover, nevertheless younger workers are preferred when it comes to actual hiring decisions (Guest and Shacklock, 2005).

Actually, the distribution of productivity across age groups is not a priori determined. It can be higher for older workers due to longer experience acquired and higher level of job-specific knowledge. On the other hand, the older workers' efficiency might become deteriorated as a result of the structural changes in the labour market, e.g. accelerating technological progress and less training offered (Daveri and Maliranta, 2007; Maurer, 2001). Interestingly, age-productivity profiles might differ between occupations. Older employees can remain highly productive in the domain that they know well and where relatively long experience is important. Thanks to tacit knowledge, older managers may perform as well as younger ones (Colonia-Willner, 1998). On the other hand, reduction in productivity of seniors appears to be the strongest in jobs where speed, spatial orientation and learning new materials are important (Skirbekk, 2004).

More generally, the situation of older workers on the labour market may be undermined when aging drives a negative wedge between the workers' productivity and earnings. The increasing age-earnings pattern characterised by lower wages for young workers and higher wages for older workers is widely observed (Loewenstein and Sicherman, 1991). This fact combined with doubts about the true productivity of older workers raises an important question on the relations between productivity and earnings across the age groups. There exists some empirical evidence against the paradigm of wage and marginal productivity equality. Frank (1984) as well as Campbell and Kamlani (1997) have found that wage rates vary substantially less than do individual productivity values. Even if a wide discrepancy in productivity among individual workers exists, many firms continue to follow strict remuneration schemes based on education,
experience and tenure length. As a result of rigid remuneration systems, in response to
a negative productivity shock, employers instead of adjusting wages, adjust their em-
ployment structure. Consequently, the least productive workers are the first to become
redundant. Likewise, the employment opportunities of workers whose wages exceed
their productivity levels become reduced.

The present study aims at evaluating the actual profile of marginal productivity across
the age classes within the workforce. The comparison with earnings profiles allow
us to analyse the relative productivity and test whether differences in wage shares
across groups of workers are justified by proportional productivity contribution. Since,
as mentioned above, age-productivity profiles might differ between occupations, the
workforce has been differentiated not only by age (young, middle-aged, old), but also
by skills (low-skilled, high-skilled). The simultaneous differentiation by age and by
skills is of high interest in the perspective of possible dissimilarities among different
categories of workers with respect to the sensitivity to work effort incentives, training
offered, etc.

Although there is a growing research interest in the relation between age and pro-
ductivity, the empirical analyses so far have often been focused on the estimation of
Cobb-Douglas production functions specification in capital and labour. The firm-level
labour productivity itself is treated as a simple summation of productivities of individ-
ual workers (Hellerstein et al., 1999; Crépon et al., 2003; Aubert and Crépon, 2003).
Thus, the existing studies are characterised by an assumption of perfect substitutabil-
ity between different categories of workers. In this study, we refer to the production
function estimation as well. However, in contrast to the previous studies, the use of the
less restrictive, constant-elasticity-of-substitution (CES) functional form is proposed
at the level of labour input. This more general form, thanks to smaller number of
constraints imposed on the production technology, allows the imperfect substitution
between different categories of workers.

The dataset used in this study (DADS-BRN) covers the French manufacturing, services and trade sectors. French data are particularly interesting in the perspective of our study. Actually, among all OECD countries, France is characterised by the highest employment rate of people aged 25-54 (83 % in 2008) and at the same time one of the lowest employment rate of people over 55 (38 % in 2008). In fact, workers over 50 are often affected by long-term unemployment. In particular, the low-skilled workers face problems to stay employed and once unemployed hardly find a new job.

Differentiating the workforce simultaneously by age and skills allows us to observe the
differences in the age-productivity and age-earnings profiles separately within each skill
group. We find that this differentiation is, in fact, very important. The productivity
profile observed across different age groups seems actually to depend on the skill level.
Among the main findings of this study, labour productivity is found to be the lowest
for the oldest low-skilled workers. In the high-skilled manufacturing labour, the mean
productivity stays quite stable across the age groups, being the highest for the workers
over 50. In trade, the high-skilled oldest employees are clearly the most productive
group. Moreover, we observe a very similar age-earnings pattern across the sectors. Wage rates vary considerably less than productivity in both skill groups. The wage profile is however steeper for the high-skilled workers.

The results for the manufacturing sector show that the age-productivity and age-earnings profiles are compatible with a deferred compensation system. It might indicate that the effort incentive problem has been regulated in practice by many firms by offering at the start of the career wages under the workers’ marginal productivity and compensating this difference in the later periods. On the other hand, in services and in trade, we observe the combined relevance of specific human capital and deferred compensation.

Though, the most interesting aspect is the workers’ productivity in relation to their cost. It is particularly important as it may present for the employers an incentive to exclude some age groups from the labour market and to give preference to the others. In our study, the relative productivity over cost in manufacturing sector has been found to represent a similar pattern in both skill groups, being the highest for the young, followed by middle-aged and old workers. In both skill groups in services and for low-skilled trade employees the productivity/earnings ratio is the highest for the middle-aged, followed by young and senior workers. This discrepancy between productivity and wage can be a source of employment difficulties particularly for the older low-skilled workers.

The remainder of the paper is organised as follows. Section 2 discusses the existing theoretical literature as well as empirical evidence on the relation between age, wage and productivity. Section 3 shows the model. In the fourth part an econometric estimation method is presented. The dataset used in this study has been described in part 5. The estimation results are analysed in section 6, followed by the conclusions.

# 2 Age, wage and productivity: a review

## 2.1 Theoretical background

From an employer’s perspective, the actual distribution of productivity and earnings across different age groups of the current workforce is very important. While deciding on the production level, a firm has to choose the optimal level of labour input needed to generate the given output. From the economic point of view, “there is an incentive to find the age mix of the workforce that can produce a given output at the least cost. This will be the age mix that yields the highest labour productivity and is described as the optimal age mix of the firm’s workforce” (Guest and Shacklock, 2005). Although the first aspect, dispersion of earnings, is usually easy to verify, there exists still large uncertainties regarding the productivity distribution across age categories.

Over the 70s and 80s, the relationship between workers’ age, wage rates and their productivity has attracted the attention of many researchers. Observations of wage
tending to grow with worker's seniority in the firm brought questions on the link be-
tween this phenomenon and the evolution of worker's productivity. There exists two
important approaches that predict a possible relation between age, wage and produc-
tivity: 1) human capital theory suggesting that wage profiles are either equivalent to
or flatter than productivity growth over the life cycle and 2) deferred compensation
models justifying the need for a wage profile steeper than productivity.

An explanation yielded by human capital theory is based on the idea that wages increase over time due to investments in human capital, particularly investments in the job training (Mincer, 1974; Becker, 1975). Older workers are therefore paid more since they have accumulated more firm-specific human capital and thus they are more productive. The general human capital theory is founded on the assumption that at any point in time workers' wage indicates their productivity. Wages rise over the life cycle at a decreasing rate until depreciation exceeds the level of skill acquisition, yielding a concave earnings profile. According to specific human capital theory, the firm and the worker are assumed to share the investment in worker's training during an initial period. While being trained, workers receive a wage that is lower than wages offered otherwise but still higher than their productivity. Thanks to training, workers become more productive and in later periods gain the returns from the investment through higher marginal products and higher wages. The second period wage, although higher than in the previous period, lies below the value of marginal productivity. In fact, the employer and the employee set the second period wage so as to split the quasi-rents generated by specific training. In this case, the resulting wage profiles will be flatter than the productivity path (Hashimoto, 1981).

On the other hand, deferred compensation models underline the possibility of incentive based compensation schemes. A good example of such model is the agency model by Becker and Stigler (1974) and Lazear (1979, 1981). In order to discourage workers' shirking, the firm pays young workers below their marginal productivity and later in their career remunerates them over their marginal product. Senior workers receive high salaries, not due to relatively higher productivity but because it creates the appropriate wage incentives for them and for their younger co-workers (Lazear, 1981). Consequently, a steeper wage profile increases workers' effort. In particular, the young workers who hope to stay in the firm are induced to perform at the optimal level. The efficiency wage models (Yellen, 1984; Shapiro and Stiglitz, 1984; Bulow and Summers, 1986) point out the importance of the payment above market clearing wages as a mechanism to elicit more effort from the worker when it cannot be fully observable. The fact that wages do not reflect the actual productivity but increase with seniority may result in raised employment difficulties for older workers. Indeed, the deferred compensation contracts may constitute a form of fixed costs for the employer. We observe that for certain jobs many firms employ, but tend not to hire older workers (Hutchens, 1986).

According to the arguments mentioned above, it takes time for workers to accumulate
education, experience and skill through learning-by-doing. Thus, older workers seem
to be more productive than younger ones. However, searching for an optimal age
composition of a given workforce, one should not forget that younger cohorts of workers
today have much higher education levels than their predecessors. Moreover, within the
given enterprise, workers of different age might be less than perfectly substitutable
as it is usually assumed. Hence, the optimum age composition of a given workforce
might in fact depend on two elements: relative marginal productivity and the degree
of substitutability between workers of different age (Lam, 1989).

## 2.2 Empirical evidence

In the empirical literature, there is relatively little research aiming at productivity and wage data comparison and their correlation with workers’ age. Among the recent studies, the contribution of Hellerstein and al. (1999) is worth being mentioned. Using a cross-section plant-level matched employer-employee dataset, the authors analysed the relationship between productivity and wage differentials among manufacturing workers distinguished by different demographic characteristics such as gender, race, marital status, age, education and occupation. In this purpose, a translog production function was jointly estimated with earnings equation. Different categories of workers were assumed to be perfectly substitutable but have potentially different marginal products. The condition of perfectly competitive market was not imposed. The authors allowed possible inequality between relative marginal productivity and relative wage for different groups of workers, which could be then interpreted as an indicator of long-term incentive contracts or discrimination. As a result of their analysis, the authors claimed that in fact wage differentials reflect actual differences in marginal products for most types of workers, particularly for the age category. Consequently, and as underlined by authors, this finding is coherent with the general human capital model by Mincer (1974) mentioned above.

Opposite results have been obtained by Crépon and al. (2003) who expanded the approach by Hellerstein et al. Using the French matched employer-employee panel data set they estimated the Cobb-Douglas production function. The assumption of perfect substitutability between different types of workers was also made. However, instead of parallel estimation of production function and earnings equation as had done Hellerstein et al., only one equation was estimated here. The authors made use of disaggregated data on wages that were not available to Hellerstein et al. The production function was modified in a way to contain directly a ratio of hourly productivity to wage for different workers categories. Among the findings, the authors stated the existence of a wage productivity gap which tends to expand with age. The wages continue to increase with workers’ age whereas the productivity stops rising at one point or even declines. It is though unclear whether the old workers are overpaid or the young ones underpaid, or if both events take place. However, the authors pointed out that increase in wages for workers over 35 cannot be interpreted as reflecting human capital accumulation.

Expanding on the previous methodologies, Aubert and Crépon (2003) made use of the French panel data decomposing the labour force into thinner age groups. Through
the estimation of the Cobb-Douglas production function, they found that productivity tends to grow with age up to age of 40 and stabilises afterwards. In all sectors, workers aged 35-39 appear to be slightly less productive than those over 40 and around 15 to 20% more productive than young workers under 30 years old. At the same time, the authors found no evidence of a significant difference between wage and productivity that could explain the lower employability of older workers. Although for workers older than 55 a slight decrease in productivity is observed, this result is not statistically significant.

Again, quite different results have been obtained by Hellerstein and Neumark (2007) who extend the analysis of their previous article (Hellerstein et al., 1999). They used the same specifications and sample selection criteria but used larger and more representative dataset. The estimated age profiles suggest that the most productive group are prime-age workers (35-54), followed by the younger ones and the seniors (over 55) as the least productive. Furthermore, the wage profile appears steeper than productivity profile, a result consistent with the deferred compensation model à la Lazear. Finally, the authors strongly rejected the hypothesis of productivity and wage differentials equality.

Overall, it is evident from this literature review that no clear conclusion can be drawn from earlier research. The current paper continues to investigate the productivity and wage relationship across different age categories of labour trying to overcome one common limitation of previous studies. In our analysis, we introduce the possibility of imperfect substitutability between different categories of workers. In previous empirical works, regardless of the choice of the production function specification in labour and capital (Cobb-Douglas or translog), different workers types were simply summed up under the assumption of perfect substitutability.

## 3 The model: production function with labour as nested CES

The assumption of perfect substitutability between workers with different characteristics implies that employing one worker while dismissing another one will not lead to any change in the marginal products of either of them as one is perfectly substitutable for another. However, it has been noticed that actually there might arise an interaction of workers within a firm (Lengermann, 2002). The productivity of a certain employee might be affected by co-worker's characteristics. It might matter whether the employee works together with a colleague with the same level of skills, similar age, etc. In particular, there exists empirical evidence that the human capitals of young and older workers are imperfect substitutes (Kremer and Thomson, 1998). Hence, labour is not necessarily as easily substitutable as it seems at first glance. This study tries to take into account this possibility by choosing such a form of the production function that would take into account the potential imperfect substitutability within the workforce - between high-skilled and low-skilled workers and between different age categories within each skill group. For this purpose, we estimate the Cobb-Douglas production function
specification in capital (K) and labour (L) whereas the labour input itself takes the form of the nested constant-elasticity-of-substitution (CES) function.

Since Arrow and al. (1961) have formulated the CES function, numerous studies have aimed at estimating its parameters, but not so far in the context of the labour productivity analysis. As mentioned before, most of research on age-productivity pattern has been based so far on the estimation of the production function. However, by imposing the additive functional form for different categories of labour inputs, they assumed a perfect substitution between them.

<figure><img src="image_4.png" /><figcaption>Figure 1: Scheme of the production structure</figcaption></figure>

Our benchmark (see Figure 1) takes into account two skill groups (low-skilled ($L_l$) and high-skilled ($L_h$)) and within each skill category - three age groups of workers (young ($L_y$), middle-aged ($L_m$), old ($L_o$)). The labour input is allowed to be heterogeneous across but homogeneous within closely defined groups of workers. Thus, it is assumed that the employees belonging to the same skill-age group (e.g. young low-skilled) are perfectly substitutable.

At the “highest level”, our production function takes the Cobb-Douglas form given by:

$$Y = f(K, L) = AK^{\alpha}L^{\beta}$$

where K denotes capital, L stands for labour and A is a Hicks neutral technological progress.
At the “second level” the labour aggregate is defined as a CES function of high-skilled and low-skilled workers:

$$L = \left( \sum_{i} \delta_{i} L_{i}^{\rho_{i}} \right)^{\frac{1}{\rho_{i}}} \qquad (1)$$

where i indicates the skill category. Finally, each skill group of workers is a CES function by itself:

$$L_i = \left[ \sum_j \delta_{ij} L_{ij}^{\rho_{ij}} \right]^{\frac{1}{\rho_{ij}}} \qquad (2)$$

where the age category is denoted by j.

Based on this choice of production function, we aim at estimating the distribution parameters: $\delta_i$, $\delta_{ij}$ as well as the substitution parameters: $\rho_i$ and $\rho_{ij}$. The elasticity of substitution is defined as $\sigma = \frac{d \ln(x_1/x_2)}{d \ln(\frac{\partial Y}{\partial x_1} / \frac{\partial Y}{\partial x_2})}$ and is a measure of the percentage

change in factors demand due to a percentage change in the marginal rate of technical substitution so that the output remains constant. For the case of constant returns to scale it takes the form: $\sigma = \frac{1}{1-\rho}$. The inverse of sigma ($\frac{1}{\sigma}$) denotes a change in the marginal rate of technical substitution due to a change in factor proportions so that output remains constant.

## Labour productivity contribution

Given the estimate value of the production function parameters, we compute the marginal product of labour for different categories of labour. Since, in our setting, constant returns to scale are assumed at the level of labour input, we can make use of Euler's theorem to specify the function of labour. According to Euler, if a function is homogeneous of degree 1, it can be represented as a sum of its inputs multiplied by their marginal products. Thus, our labour function takes the following form:

$$f(L_1, L_2, ..., L_n) = L_1 \frac{\partial f}{\partial L_1} + L_2 \frac{\partial f}{\partial L_2} + ... + L_n \frac{\partial f}{\partial L_n} \qquad (3)$$

Consequently, the labour production can be entirely explained by the sum of the marginal products of different labour categories multiplied by their employment level.

## Skill differentiation

The marginal product of a particular labour input is defined as the partial derivative of the production function with respect to the specific category of labour. For the given skill group, it takes the following form:
$$MP_i = \frac{\partial Y}{\partial L} \frac{\partial L}{\partial L_i} \qquad (4)$$

$$MP_i = AK^{\alpha\beta} \left( \sum_i \delta_i L_i^{\rho_i} \right)^{\frac{\beta}{\rho_i} - 1} \delta_i L_i^{\rho_i - 1} \qquad (5)$$

The marginal rate of technical substitution depends not only on the factor intensity and the distribution parameter but also on the level of substitution between different labour categories. It shows the rate at which one input may be substituted for another, while maintaining the same level of production. The relative marginal product of labour for workers differentiated by skills is given by:

$$\frac{MP_1}{MP_2} = \frac{\partial L/\partial L_1}{\partial L/\partial L_2} = \lambda = \frac{\delta_1}{\delta_2} \left(\frac{L_1}{L_2}\right)^{\rho_1 - 1} \qquad (6)$$

In order to compare productivity contribution over different skill categories, we compute for each firm ratios of marginal products of workers belonging to certain skill group in relation to the average marginal product of labour. For two categories of skills, the ratios take the following form:

$$\frac{MP_1}{MP_{av}} = \frac{L}{L_1 + \lambda^{-1}L_2} \quad \text{and} \quad \frac{MP_2}{MP_{av}} = \frac{L}{\lambda L_1 + L_2}$$

where $MP_{av}$ is the average marginal product of total labour.

### Age differentiation

The marginal product of labour for a given age group in a specified skill category is defined as:

$$MP_{ij} = \frac{\partial Y}{\partial L} \frac{\partial L}{\partial L_i} \frac{\partial L_i}{\partial L_{ij}} \qquad (7)$$

$$MP_i = AK^{\alpha\beta} \left( \sum_i \delta_i L_i^{\rho_i} \right)^{\frac{\beta}{\rho_i} - 1} \delta_i L_i^{\frac{\rho_i}{\rho_j} - 1} \delta_{ij} L_{ij}^{\rho_{ij} - 1} \qquad (8)$$

The relative marginal product of any two age groups of workers in a given skill group is:

$$\frac{MP_{i1}}{MP_{i2}} = \frac{\delta_{i1}}{\delta_{i2}} \left(\frac{L_{i1}}{L_{i2}}\right)^{\rho_{i1} - 1} \qquad (9)$$

In our setting, we define relative marginal products as: $\frac{MP_{iY}}{MP_{iM}} = \varphi$, $\frac{MP_{iY}}{MP_{iO}} = \gamma$ and $\frac{MP_{iM}}{MP_{iO}} = \eta$ (where Y - young, M - middle-aged, O - old). The productivity contribution
of each age group is given by the ratio of marginal product of respective age group over the average labour marginal productivity of a specific skill group:

$$ \frac{MP_{iY}}{MP_{av}} = \frac{L_i}{L_{iY} + \varphi^{-1}L_{iM} + \gamma^{-1}L_{iO}} \qquad (10) $$

$$ \frac{MP_{iM}}{MP_{av}} = \frac{L_i}{\varphi L_{iY} + L_{iM} + \eta^{-1} L_{iO}} \qquad (11) $$

$$ \frac{MP_{iO}}{MP_{av}} = \frac{L_i}{\gamma L_{iY} + \eta L_{iM} + L_{iO}} \qquad (12) $$

## Wage share

Our dataset contains rich information on earnings. Hence, according to the procedure above, we compute the share of a distinct age group in the wage bill of the given skill category. Given the productivity contributions and the analogously constructed wage shares, we can compare an earnings-productivity pattern for different categories of workers.

# 4 The method

In the econometric estimation of the production function, one of the major problems we are confronted with is the possible endogeneity of inputs, which will result in inconsistency of direct estimators. In fact, the input demand might be correlated with the productivity shocks unobservable by the econometrician but observed or predicted by the firm (Marschak and Andrews, 1944). A profit maximizing (or cost-minimizing) firm facing positive productivity shocks will expand its production and thus increase the inputs level. Conversely, a consequence of the negative shocks will be a decrease in production and lower input usage. A particular concern about the endogeneity bias concerns the analysis of labour disaggregated by age. Aubert and Crépon (2003) draw attention to the fact that enterprise could respond to negative productivity shocks by postponing its hiring decisions. Then, one might observe a decline in production accompanied by ageing workforce. On the other hand, positive shocks could encourage the firm to hire some young workers. As a result, the rise in output would be associated with a relatively younger workforce. The causality problem that appears in such case is whether firms employing relatively older workforce are less productive or if firms employ relatively older workforce because they are less productive.

In order to obtain consistent estimates of the production function parameters, we use the method developed by Levinson and Petrin (2003). The procedure consists in
including in the estimation equation a proxy for the productivity shocks potentially observed by firms while making input decisions<fnref n="1" />.

We consider the following value added production function:

$$y_{it} = \beta_0 + \alpha k_{it} + \beta \ln \left( \left( \sum_i \delta_i \left( \sum_j \delta_{ij} L_{ijit}^{\rho_{ij}} \right)^{\frac{\rho_i}{\rho_{ij}}} \right)^{\frac{1}{\rho_i}} \right) + \omega_{it} + \eta_{it} \quad (13)$$

The error term is composed of 2 elements: $\omega_{it}$ denoting productivity shocks likely to be observed by the firm and $\eta_{it}$ having no impact on the firm's inputs decisions. $y_{it}$ is the natural logarithm of value added and $k_{it}$ denotes the natural logarithm of capital.

Following LP, we assume that firms decide on the level of capital at $t-1$, thus capital is a dynamic input. Labour and the intermediate inputs (materials) $m_{it}$ are chosen at time $t$. The productivity shock $\omega_{it}$ is assumed to follow a first order Markov process:

$$p(\omega_{it} | I_{it-1}) = p(\omega_{it} | \omega_{it-1}) \quad (14)$$

where $I$ is firm's $i$'s information set at $t$.

The approach adopted in the current work consists in using intermediate input as a proxy for the unobservable productivity shocks. Hence, materials control for the part of the error term correlated with inputs. Given the above timing assumptions, the firm's demand for the intermediate input $m_{it}$ is assumed to depend on the state variables $k_{it}$ and $\omega_{it}$.

$$m_{it} = f_t(k_{it}, \omega_{it}) \quad (15)$$

The assumption that intermediate input is strictly monotonic in the productivity shock allows inversion of materials demand function for $\omega_{it}$.

$$\omega_{it} = f_t^{-1}(k_{it}, m_{it}) \quad (16)$$

Substituting it into the production function leads to the following first stage equation:

$$y_{it} = \beta \ln \left( \left( \sum_i \delta_i \left( \sum_j \delta_{ij} L_{ijit}^{\rho_{ij}} \right)^{\frac{\rho_i}{\rho_{ij}}} \right)^{\frac{1}{\rho_i}} \right) + \phi_{it}(k_{it}, m_{it}) + \eta_{it} \quad (17)$$

<footnote n="1">¹An alternative approach toward endogeneity bias has been developed by Arellano and Bond (1991) and consisted in estimating an equation in first-differences with appropriately lagged levels as instruments. However, since lagged variables in levels are often weak instruments for contemporaneous differences, in case of highly persistent data, the method appeared to suffer from finite sample bias and poor precision of the estimates. This problem has been further addressed by Blundell and Bond (1998), Blundell and Bond (2000), Blundell, Bond and Windmeijer (2000) and Windmeijer (2000). Within this framework lagged levels are used as instruments for contemporaneous differences and lagged differences as instruments for contemporaneous levels.</footnote>
where $\phi_{it}(k_{it}, m_{it}) = \beta_0 + \alpha k_{it} + \omega_{it}(k_{it}, m_{it})$.

By substituting a third-order polynomial in $k_{it}$ and $m_{it}$ to $\phi_{it}(k_{it}, m_{it})$:

$$y_{it} = \delta_0 + \beta \ln \left( \left( \sum_i \delta_i \left( \sum_j \delta_{ij} L_{ijit}^{\rho_{ij}} \right)^{\frac{\rho_i}{\rho_{ij}}} \right)^{\frac{1}{\rho_i}} \right) + \sum_{j=0}^{3} \sum_{n=0}^{3-j} \delta_{jn} k_{it}^j m_{it}^n + \eta_{it} \quad (18)$$

we can consistently estimate parameters for labour using the non-linear least squares method.

Identification of the input coefficients according to the method by Levinsohn and Petrin has been questioned recently. Bond and Soderbom (2005) argue that production function parameters are not identified from cross section variation when inputs are perfectly flexible and chosen optimally, and input price are common to all firms. However, their result holds on the property that Cobb Douglas optimal capital and labour inputs demand can be expressed as log linear functions of real input prices. This is not the case in our model where labour input takes a form of a CES production function. Moreover, we do not impose the condition of an optimal input choice implying wage and marginal productivity equality.

On the other hand, Ackerberg, Caves and Frazer (2006) pointed out the potential problem with the identification of labour input coefficients in the first stage of the Levinsohn and Petrin method. The authors raise the question of collinearity issues. They claim that the simultaneous choice of labour input and material induces collinearity between the variables in the first step regression. Considering their statement, the identification of the labour parameters in our model is relying on the non-linearities of the production function<fnref n="2" />.

The second stage of the procedure helps us identify the coefficient for capital.<fnref n="3" /> It starts with the computation of the estimated value for $\phi_{it}$:

<footnote n="2">²Ackerberg, Caves and Frazer (2006) propose an alternative procedure to estimate production functions. In their approach, all input coefficients are estimated in the second stage. Their procedure draws on the Levinsohn and Petrin method. Intermediate input demand is indeed used as a proxy to net out an error term of the production function. The main difference is that the firm's demand for the intermediate input is assumed to be a strictly monotonic function of the productivity shock and all the input variables, i.e. capital and all types of labour. In the more complex model that we propose, the firm's demand for the intermediate input is thus a function of 8 arguments. When substituting the productivity shock with a third order polynomial depending on materials and other inputs, identification became really fragile with our data. We thus privileged the Levinsohn and Petrin method in our context.</footnote>

<footnote n="3">³Even if we consider only marginal labour productivity in the sequel, we implement the two steps of the estimation procedure.</footnote>
$$ \hat{\phi}_{it} = \hat{y}_{it} - \hat{\beta} \ln \left( \left( \sum_{i} \hat{\delta}_{i} \left( \sum_{j} \hat{\delta}_{ij} L_{ij it}^{\hat{\rho}_{ij}} \right)^{\frac{\hat{\rho}_{i}}{\hat{\rho}_{ij}}} \right)^{\frac{1}{\hat{\rho}_{i}}} \right) = \hat{\delta}_{0} + \sum_{j=0}^{3} \sum_{n=0}^{3-j} \hat{\delta}_{jn} k_{it}^{j} m_{it}^{n} \quad (19) $$

For any candidate value $\alpha^*$, we can compute the prediction for $\omega_{it}$ for all periods $t$:

$$ \hat{\omega}_{it} = \hat{\phi}_{it} - \beta_{0}^{*} - \alpha^{*} k_{it} \quad (20) $$

Given these values, we regress $\omega_{it}$ on its lagged term $\omega_{it-1}$:

$$ \hat{\omega}_{it} = \gamma_{0} + \gamma_{1}\omega_{it-1} + \gamma_{2}\omega_{it-1}^{2} + \gamma_{3}\omega_{it-1}^{3} + \epsilon_{it} \quad (21) $$

in order to get the residual $\xi_{it}$ and the conditional expectation $E[\omega_{it} | \omega_{it-1}] = \omega_{it} - \xi_{it}$.

Given labour coefficients, a starting value for $\alpha^*$ and $E[\omega_{it} | \omega_{it-1}]$, we can find a consistent estimate of a parameter for capital through the minimisation of a squared sum of a residuals of our production function:

$$ \min_{\alpha^*} \sum_t (\eta_{it} + \xi_{it})^2 = \min_{\alpha^*} \sum_t \left( y_{it} - \hat{\beta} \ln \left( \left( \sum_i \hat{\delta}_i \left( \sum_j \hat{\delta}_{ij} L_{ij it}^{\hat{\rho}_{ij}} \right)^{\frac{\hat{\rho}_i}{\hat{\rho}_{ij}}} \right)^{\frac{1}{\hat{\rho}_i}} \right) - \alpha^* k_{it} - E[\omega_{it} | \omega_{it-1}] \right)^2 \quad (22) $$

The asymptotic standard errors for estimated parameters can be constructed using a bootstrap approach.

# 5 Data and summary statistics

The dataset used in this study covers a short panel of data for years 2003 and 2004 for manufacturing, services and trade sectors in France. It comes from merging two different data sources: *Bénéfices Réels Normaux* (BRN) and *Déclarations Administratives de Données Sociales* (DADS). They both constitute mandatory employers' reports to the Fiscal Office. The BRN consists of firms' balance sheets and provides important information on the employers' output, capital stock and economic sector. The DADS contains rich data on the characteristics of the workforce. The number of hours worked is decomposed by workers' age and occupation. The valuable information on earnings allows measuring the share of a distinct labour category in the total wage bill. However, the dataset is not without imperfections: unfortunately, the DADS does not contain any information on workers' education level and tenure.

In order to distinguish among workers according to the level of skills, we make use of the available decomposition by occupation. The DADS employment data are arranged by
occupation according to the French socio-professional classification. This classification is used in collective agreements for wage determination. A higher level of education places a worker directly on the "higher starting point" and experience then allows further wage increases. However, as emphasised by Thesmar and Thoenig (2000), this classification, based on the mix of education and experience, contains no information about the task-assignment. Therefore, the executives ("Cadres") may include high-ranked directors as well as e.g. consultants without any supervision duty. Using this occupation classification, we distinguish two skills categories of workers: high-skilled and low-skilled. The high-skilled correspond to employers, the senior and intermediate personnel. The office and sales employees as well as blue collar workers are included in the low-skilled category. For details, see Table 1.

<table><caption>Table 1: Skill classification</caption><thead><tr><th>High-skilled labour</th><th>Low-skilled labour</th></tr></thead><tbody><tr><td><em>Employers</em><br>Craftsmen<br>Traders<br>Employers (of 50 or more employees)</td><td><em>Non-manual workers</em><br>Office employees<br>Sales workers</td></tr><tr><td><em>Liberal professions, senior and executive personnel</em><br>Liberal professions<br>Professors and scientific professions<br>Artistic professions<br>Senior administrative personnel<br>Engineers and senior technicians</td><td><em>Manual workers</em><br>Skilled industrial manual workers<br>Skilled craftsman<br>Drivers<br>Skilled handling, storage and transport workers<br>Unskilled industrial workers<br>Unskilled artisans</td></tr><tr><td><em>Intermediate personnel</em><br>Medical and social services<br>Intermediate administrative personnel<br>Technicians<br>Foreman, supervisors</td><td></td></tr></tbody></table>

Regarding labour force composition, three age groups are considered within each skill group. We define young workers as those who are under 30 years old, the middle-aged workers between 30 and 50, and the senior employees as those over 50. The reason why we choose these age groups is twofold. Firstly, since we keep only firms where all age categories are present, the condition for having sufficient number of observations within each age group is verified. Secondly, the data analysis revealed that the employment level is much more heterogeneous among the young (up to 30) and among seniors (over 50) compared to the middle-aged (30-50) group. In particular, the lowest employment rates characterise the young under 25 and older persons over 55. Nowadays, many
young people decide to prolong their education and, thus, enter relatively late into
labour market. Similarly, an earlier exit from the labour market is still quite common
among the seniors.

For the purpose of our analysis, the volume of production is represented by value
added and the employment level is measured by the number of hours worked. It
allows distinguishing between part-time and full-time employees. Outliers have been
eliminated. Value added, capital, labour cost and employment are required to take
positive values. Only firms employing at least fifty workers have been considered. As
a result of these operations, the final dataset contains 15 992 observations.

As regards sectoral division, manufacturing, trade and services are distinguished according to NES16 (Nomenclature économique de synthèse en 16 postes). Agriculture, forestry and fishing as well as the construction sector (due to high ratio of seasonal workers) have been excluded from manufacturing. Administration and financial services have not been taken into account in the services sector.

Summary statistics for the main variables as well as the labour force composition by age and skills are represented in Table 2. We can observe substantial differences with respect to age-employment and age-earnings patterns of workers belonging to different skill groups.

### Employment pattern

First of all, we can see that in all three sectors, i.e. manufacturing, trade and services, workers between 30 and 50 years old account for around 60% of total hours worked. The employment share of the young and the seniors is considerably lower. If we look separately at each skill group, we can notice that among the high-skilled, the number of hours worked by older workers exceeds those of the young ones. In particular, discrepancies are the biggest in manufacturing. The opposite pattern characterises the low-skilled employees (with exception of manufacturing sector), where the youngs are more numerous than the seniors.

### Earnings pattern

We observe that hourly earnings are increasing with age, for both skill groups and in all sectors. The remuneration of young workers is the lowest and the oldest employees are paid the most. According to economic expectations, high-skilled workers are better paid than the low-skilled. Taking into account the desaggregation by skills, the profile of hourly earnings of the low-skilled looks considerably flatter - the differences between consecutive age groups are on the average of 15% and 4%. Interestingly, the respective mean differentials in salaries between the high-skilled age groups are of 40% and 30%. Consequently, the range of salaries in this skill category is wider.
<table><caption>Table 2: Sample statistics, DADS-BRN, 2004</caption><thead><tr><th rowspan="2">Variables*</th><th colspan="3">Manufacturing</th><th colspan="3">Services</th><th colspan="3">Trade</th></tr><tr><th>share</th><th>mean</th><th>sdv</th><th>share</th><th>mean</th><th>sdv</th><th>share</th><th>mean</th><th>sdv</th></tr></thead><tbody><tr><td>ln value added</td><td></td><td>-2.67</td><td>1.15</td><td></td><td>-3.01</td><td>1.26</td><td></td><td>-3.04</td><td>1.04</td></tr><tr><td>ln capital</td><td></td><td>-2.57</td><td>1.54</td><td></td><td>-3.32</td><td>1.85</td><td></td><td>-3.28</td><td>1.38</td></tr><tr><td>ln capital (t-1)</td><td></td><td>-2.61</td><td>1.57</td><td></td><td>-3.38</td><td>1.88</td><td></td><td>-3.34</td><td>1.39</td></tr><tr><td>ln materials</td><td></td><td>-2.81</td><td>1.63</td><td></td><td>-5.54</td><td>2.06</td><td></td><td>-6.81</td><td>2.15</td></tr><tr><td>ln materials (t-1)</td><td></td><td>-2.86</td><td>1.63</td><td></td><td>-5.59</td><td>2.03</td><td></td><td>-6.82</td><td>2.17</td></tr><tr><td colspan="10">Hours worked by age:</td></tr><tr><td>total</td><td>1.00</td><td>4.85</td><td>22.47</td><td>1.00</td><td>5.28</td><td>44.68</td><td>1.00</td><td>3.83</td><td>22.14</td></tr><tr><td>(Ly) young (&lt;30)</td><td>0.18</td><td>0.79</td><td>4.04</td><td>0.21</td><td>1.09</td><td>4.99</td><td>0.28</td><td>1.08</td><td>6.74</td></tr><tr><td>(Lm) middle-aged (30-50)</td><td>0.60</td><td>2.85</td><td>11.68</td><td>0.58</td><td>3.07</td><td>24.65</td><td>0.57</td><td>2.19</td><td>12.90</td></tr><tr><td>(Lo) old (&gt;50)</td><td>0.22</td><td>1.21</td><td>7.09</td><td>0.21</td><td>1.11</td><td>15.93</td><td>0.15</td><td>0.56</td><td>2.76</td></tr><tr><td colspan="10">Hours worked by skills and age:</td></tr><tr><td>(Ll) low-skilled</td><td>0.59</td><td>2.85</td><td>13.07</td><td>0.58</td><td>3.05</td><td>18.63</td><td>0.65</td><td>2.50</td><td>17.41</td></tr><tr><td>(Lly) young</td><td>0.18</td><td>0.52</td><td>2.61</td><td>0.25</td><td>0.74</td><td>3.57</td><td>0.34</td><td>0.86</td><td>5.88</td></tr><tr><td>(Llm) middle-aged</td><td>0.58</td><td>1.65</td><td>6.65</td><td>0.56</td><td>1.72</td><td>9.64</td><td>0.53</td><td>1.32</td><td>9.70</td></tr><tr><td>(Llo) old</td><td>0.24</td><td>0.68</td><td>4.05</td><td>0.19</td><td>0.59</td><td>6.24</td><td>0.13</td><td>0.32</td><td>1.99</td></tr><tr><td>(Lh) high-skilled</td><td>0.41</td><td>2.00</td><td>10.24</td><td>0.42</td><td>2.23</td><td>26.92</td><td>0.35</td><td>1.33</td><td>5.40</td></tr><tr><td>(Lhy) young</td><td>0.14</td><td>0.27</td><td>1.52</td><td>0.16</td><td>0.35</td><td>1.71</td><td>0.17</td><td>0.22</td><td>1.04</td></tr><tr><td>(Lhm) middle-aged</td><td>0.59</td><td>1.19</td><td>5.65</td><td>0.61</td><td>1.36</td><td>15.59</td><td>0.65</td><td>0.87</td><td>3.65</td></tr><tr><td>(Lho) old</td><td>0.27</td><td>0.53</td><td>3.27</td><td>0.23</td><td>0.51</td><td>9.94</td><td>0.18</td><td>0.24</td><td>0.86</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Variables</th><th colspan="3">Manufacturing</th><th colspan="3">Services</th><th colspan="3">Trade</th></tr><tr><th>share</th><th>mean</th><th>sdv</th><th>share</th><th>mean</th><th>sdv</th><th>share</th><th>mean</th><th>sdv</th></tr></thead><tbody><tr><td colspan="10">Hourly earnings by age:</td></tr><tr><td>total</td><td>1.00</td><td>15.66</td><td>3.93</td><td>1.00</td><td>14.65</td><td>5.84</td><td>1.00</td><td>14.36</td><td>4.42</td></tr><tr><td>(Ly) young (&lt;30)</td><td>0.14</td><td>12.00</td><td>2.46</td><td>0.20</td><td>11.74</td><td>5.51</td><td>0.22</td><td>10.70</td><td>2.42</td></tr><tr><td>(Lm) middle-aged (30-50)</td><td>0.60</td><td>15.70</td><td>3.98</td><td>0.58</td><td>14.90</td><td>8.04</td><td>0.58</td><td>14.87</td><td>4.52</td></tr><tr><td>(Lo) old (&gt;50)</td><td>0.26</td><td>18.99</td><td>6.75</td><td>0.22</td><td>17.90</td><td>7.70</td><td>0.20</td><td>18.58</td><td>7.57</td></tr><tr><td colspan="10">Hourly earnings by skills and age:</td></tr><tr><td>(Ll) low-skilled</td><td>0.52</td><td>12.13</td><td>2.44</td><td>0.51</td><td>11.20</td><td>2.12</td><td>0.50</td><td>10.63</td><td>1.92</td></tr><tr><td>(Lly) young</td><td>0.17</td><td>10.54</td><td>1.97</td><td>0.25</td><td>10.15</td><td>1.72</td><td>0.30</td><td>9.49</td><td>1.72</td></tr><tr><td>(Llm) middle-aged</td><td>0.60</td><td>12.35</td><td>2.53</td><td>0.56</td><td>11.46</td><td>2.39</td><td>0.55</td><td>11.03</td><td>7.49</td></tr><tr><td>(Llo) old</td><td>0.23</td><td>12.92</td><td>3.08</td><td>0.20</td><td>11.95</td><td>2.88</td><td>0.15</td><td>11.54</td><td>5.76</td></tr><tr><td>(Lh) high-skilled</td><td>0.48</td><td>22.13</td><td>4.84</td><td>0.49</td><td>19.94</td><td>6.96</td><td>0.50</td><td>20.62</td><td>5.32</td></tr><tr><td>(Lhy) young</td><td>0.11</td><td>15.05</td><td>4.52</td><td>0.16</td><td>14.58</td><td>6.44</td><td>0.11</td><td>14.28</td><td>0.36</td></tr><tr><td>(Lhm) middle-aged</td><td>0.59</td><td>21.73</td><td>4.86</td><td>0.58</td><td>19.88</td><td>7.14</td><td>0.62</td><td>20.36</td><td>8.54</td></tr><tr><td>(Lho) old</td><td>0.30</td><td>28.00</td><td>10.83</td><td>0.26</td><td>25.96</td><td>18.89</td><td>0.27</td><td>26.66</td><td>7.75</td></tr><tr><td>Number of observations</td><td></td><td>8185</td><td></td><td></td><td>4498</td><td></td><td></td><td>3309</td><td></td></tr></tbody></table>

<footnote>* All variables have been standardised (divided by 100 000 before taking logarithms)</footnote>
# 6 Results

We start our analysis with the estimation of the production function whose structure has been detailed in Part 3. Based on estimated parameters, we will generate and compare the age-productivity and age-earnings pattern for the low-skilled and for the high-skilled workers belonging to different sectors. First, on the basis of median values, we will present the general pattern. Afterwards, we will analyse the density estimations of inter-firm distributions of productivity and earnings. The detailed analysis will be carried out consecutively by skills and then by age within each skill group.

## 6.1 Econometric results

Our estimation procedure consists in estimating three successive models:

model (1) with labour differentiated by skills:

$$Y = AK^{\alpha} (\delta_s L_l^{\rho_s} + (1 - \delta_s) L_h^{\rho_s})^{\frac{\beta}{\rho_s}}$$

model (2) with labour differentiated by age:

$$Y = AK^{\alpha} (\delta_y L_y^{\rho_a} + \delta_m L_m^{\rho_a} + (1 - \delta_y - \delta_m) L_o^{\rho_a})^{\frac{\beta}{\rho_a}}$$

model (3) with labour differentiated simultaneously by age and skills:

$$Y = AK^{\alpha} \left( \gamma \left( \delta_{ly} L_{ly}^{\rho_l} + \delta_{lm} L_{lm}^{\rho_l} + (1 - \delta_{ly} - \delta_{lm}) L_{lo}^{\rho_l} \right)^{\frac{\rho_s}{\rho_l}} + \right. \\ \left. + (1 - \gamma) \left( \delta_{hy} L_{hy}^{\rho_h} + \delta_{hm} L_{hm}^{\rho_h} + (1 - \delta_{hy} - \delta_{hm}) L_{ho}^{\rho_h} \right)^{\frac{\rho_s}{\rho_h}} \right)^{\frac{\beta}{\rho_s}}$$

The estimation results of the production function for each sector are presented respectively in Tables 3 to 6⁴. The first column refers to results obtained according to the nonlinear least squares method. The second column reports the production function estimates based on the two-stages procedure by Levinsohn and Petrin (2003) controlling for the potential endogeneity. Since parameters enter into the function in a nonlinear way, estimators only have asymptotic validity. Standard errors have been constructed according to a bootstrap approach with 200 replications.

### Elasticity of substitution

<footnote n="4">⁴In order to check the validity and robustness of our results, in the appendix we present the results of the estimation of different models with sub-sector dummy variables in manufacturing and services sectors (Tables 17 and 18). The results confirm the robustness of the estimates after introducing the sub-sector controls.</footnote>
In models with labour differentiated by skills, the inter-skill substitution parameter $\rho_s$ has surprisingly been found to converge to 1 in all the sectors (see Table 3) which means perfect substitutability between workers belonging to different skill groups. We suppose that this result might come from the classification of low-skilled and high-skill workers. It is possible that, in fact, there are not much differences in skill levels for certain socio-professional categories. To try to overcome this problem, we have run the estimation with 3 skill groups, taking apart the intermediate personnel but it did not have much impact on the results. In the sequel, estimations are thus made directly under the constraint $\rho_s = 1$.

<table><caption>Table 3: Production function estimates for each sector, labour differentiated by skills, model (1)</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">Manufacturing</th><th colspan="2">Services</th><th colspan="2">Trade</th></tr><tr><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th></tr></thead><tbody><tr><td>c</td><td>-2.197***<br>(0.015)</td><td></td><td>-2.243***<br>(0.022)</td><td></td><td>-2.421***<br>(0.027)</td><td></td></tr><tr><td>α</td><td>0.187***<br>(0.005)</td><td>0.301***<br>(0.047)</td><td>0.234***<br>(0.006)</td><td>0.173***<br>(0.038)</td><td>0.118***<br>(0.008)</td><td>0.164***<br>(0.038)</td></tr><tr><td>β</td><td>0.829***<br>(0.008)</td><td>0.729***<br>(0.009)</td><td>0.743***<br>(0.011)</td><td>0.699***<br>(0.023)</td><td>0.903***<br>(0.012)</td><td>0.875***<br>(0.015)</td></tr><tr><td>δ<sub>s</sub></td><td>0.231***<br>(0.011)</td><td>0.207***<br>(0.015)</td><td>0.190***<br>(0.033)</td><td>0.163***<br>(0.043)</td><td>0.216***<br>(0.016)</td><td>0.216***<br>(0.019)</td></tr><tr><td>ρ<sub>s</sub></td><td>1.257***<br>(0.078)</td><td>1.327***<br>(0.093)</td><td>2.408***<br>(0.322)</td><td>2.649***<br>(0.512)</td><td>1.336***<br>(0.111)</td><td>1.328***<br>(0.118)</td></tr><tr><td>No of obs.</td><td>8185</td><td>8185</td><td>4498</td><td>4498</td><td>3309</td><td>3309</td></tr></tbody></table>

Notes: Bootstrapped standard errors in parentheses. *** Significant at 1%, ** significant at 5%, * significant at 10%.

The elasticity of substitution between workers differentiated only by age appears quite different by sector (see Table 4). The substitution parameter $\rho_a$ is not significantly different from zero in services, between zero and one in manufacturing and higher than unity in the trade sector. These results imply different work organization in each sector. They hold in the model with labour differentiated simultaneously by age and skills (see Table 5). There we observe that the substitution parameter $\rho_h$ in the services sector is not significantly different from 0. In trade, the respective parameter for both skill groups tends to converge to 1.
<table><caption>Table 4: Production function estimates for each sector, labour differentiated by age, model (2)</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">Manufacturing</th><th colspan="2">Services</th><th colspan="2">Trade</th></tr><tr><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th></tr></thead><tbody><tr><td>c</td><td>-1.947***<br>(0.022)</td><td></td><td>-2.067***<br>(0.036)</td><td></td><td>-2.287***<br>(0.039)</td><td></td></tr><tr><td>α</td><td>0.200***<br>(0.005)</td><td>0.278***<br>(0.038)</td><td>0.240***<br>(0.006)</td><td>0.186***<br>(0.037)</td><td>0.104***<br>(0.008)</td><td>0.159***<br>(0.038)</td></tr><tr><td>β</td><td>0.835***<br>(0.008)</td><td>0.726***<br>(0.010)</td><td>0.735***<br>(0.011)</td><td>0.691***<br>(0.021)</td><td>0.921***<br>(0.013)</td><td>0.879***<br>(0.016)</td></tr><tr><td>δ<sub>y</sub></td><td>0.314***<br>(0.018)</td><td>0.281***<br>(0.020)</td><td>0.221***<br>(0.027)</td><td>0.238***<br>(0.036)</td><td>0.070***<br>(0.019)</td><td>0.074***<br>(0.017)</td></tr><tr><td>δ<sub>m</sub></td><td>0.443***<br>(0.026)</td><td>0.491***<br>(0.032)</td><td>0.479***<br>(0.057)</td><td>0.540***<br>(0.084)</td><td>0.326***<br>(0.064)</td><td>0.357***<br>(0.072)</td></tr><tr><td>δ<sub>o</sub></td><td>0.243</td><td>0.228***<br>(0.017)</td><td>0.300</td><td>0.222**<br>(0.094)</td><td>0.604</td><td>0.569***<br>(0.074)</td></tr><tr><td>ρ<sub>a</sub></td><td>0.367***<br>(0.074)</td><td>0.246***<br>(0.094)</td><td>1.321***<br>(0.314)</td><td>0.955<br>(1.482)</td><td>1.912***<br>(0.340)</td><td>1.848***<br>(0.366)</td></tr><tr><td>No of obs.</td><td>8185</td><td>8185</td><td>4498</td><td>4498</td><td>3309</td><td>3309</td></tr></tbody></table>

Notes: Bootstrapped standard errors in parentheses. *** Significant at 1%, ** significant at 5%, * significant at 10%.
<table><caption>Table 5: Production function estimates for each sector, labour differentiated by age and skills, model (3)</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">Manufacturing</th><th colspan="2">Services</th><th colspan="2">Trade</th></tr><tr><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th></tr></thead><tbody><tr><td>c</td><td>-1.294***<br>(0.021)</td><td></td><td>-1.538***<br>(0.037)</td><td></td><td>-1.538***<br>(0.036)</td><td></td></tr><tr><td>α</td><td>0.186***<br>(0.004)</td><td>0.291***<br>(0.045)</td><td>0.222***<br>(0.006)</td><td>0.166***<br>(0.040)</td><td>0.112***<br>(0.008)</td><td>0.159***<br>(0.036)</td></tr><tr><td>β</td><td>0.833***<br>(0.007)</td><td>0.736***<br>(0.009)</td><td>0.759***<br>(0.011)</td><td>0.717***<br>(0.022)</td><td>0.911***<br>(0.012)</td><td>0.879***<br>(0.015)</td></tr><tr><td>γ</td><td>0.274***<br>(0.013)</td><td>0.254***<br>(0.015)</td><td>0.367***<br>(0.027)</td><td>0.357***<br>(0.023)</td><td>0.226***<br>(0.021)</td><td>0.215***<br>(0.026)</td></tr><tr><td>1-γ</td><td>0.725</td><td>0.746***<br>(0.015)</td><td>0.633</td><td>0.643***<br>(0.023)</td><td>0.774</td><td>0.785***<br>(0.026)</td></tr><tr><td>δ<sub>ly</sub></td><td>0.437***<br>(0.034)</td><td>0.395***<br>(0.032)</td><td>0.275***<br>(0.036)</td><td>0.282***<br>(0.030)</td><td>0.236***<br>(0.042)</td><td>0.263***<br>(0.046)</td></tr><tr><td>δ<sub>lm</sub></td><td>0.417***<br>(0.046)</td><td>0.458***<br>(0.052)</td><td>0.497***<br>(0.075)</td><td>0.558***<br>(0.068)</td><td>0.608***<br>(0.099)</td><td>0.673***<br>(0.124)</td></tr><tr><td>δ<sub>lo</sub></td><td>0.145</td><td>0.147***<br>(0.030)</td><td>0.227</td><td>0.159**<br>(0.065)</td><td>0.155</td><td>0.063<br>(0.121)</td></tr><tr><td>ρ<sub>l</sub></td><td>0.463***<br>(0.119)</td><td>0.372***<br>(0.120)</td><td>0.810***<br>(0.286)</td><td>0.574***<br>(0.186)</td><td>1.341***<br>(0.427)</td><td>1.039**<br>(0.518)</td></tr><tr><td>δ<sub>hy</sub></td><td>0.247***<br>(0.029)</td><td>0.242***<br>(0.031)</td><td>0.117**<br>(0.061)</td><td>0.134<br>(0.099)</td><td>0.209***<br>(0.032)</td><td>0.192***<br>(0.058)</td></tr><tr><td>δ<sub>lm</sub></td><td>0.405***<br>(0.036)</td><td>0.432***<br>(0.042)</td><td>0.372***<br>(0.103)</td><td>0.388**<br>(0.181)</td><td>0.421***<br>(0.049)</td><td>0.427***<br>(0.091)</td></tr><tr><td>δ<sub>ho</sub></td><td>0.347</td><td>0.326***<br>(0.026)</td><td>0.511</td><td>0.477*<br>(0.268)</td><td>0.370</td><td>0.380***<br>(0.054)</td></tr><tr><td>ρ<sub>h</sub></td><td>0.725***<br>(0.122)</td><td>0.594***<br>(0.132)</td><td>2.302***<br>(0.820)</td><td>2.065<br>(10.898)</td><td>0.789***<br>(0.169)</td><td>0.792**<br>(0.324)</td></tr></tbody><tfoot><tr><td>No of obs.</td><td>8185</td><td>8185</td><td>4498</td><td>4498</td><td>3309</td><td>3309</td></tr></tfoot></table>

Notes: Bootstrapped standard errors in parentheses. *** Significant at 1%, ** significant at 5%, * significant at 10%.

The results shown in Table 6 include already all these constraints on parameters $ρ_l$ and $ρ_h$. We observe that low-skilled services workers of different ages are closer substitutes than high-skilled ones. Interestingly, in manufacturing, high-skilled workers have been found more easily substitutable between each other than low-skilled ones.
<table><caption>Table 6: Production function estimates for each sector, labour differentiated by age and skills, constrained model (3)</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">Manufacturing</th><th colspan="2">Services</th><th colspan="2">Trade</th></tr><tr><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th></tr></thead><tbody><tr><td>c</td><td>-1.294***<br>(0.021)</td><td></td><td>-1.587***<br>(0.035)</td><td></td><td>-1.534***<br>(0.035)</td><td></td></tr><tr><td>α</td><td>0.186***<br>(0.004)</td><td>0.291***<br>(0.045)</td><td>0.222***<br>(0.006)</td><td>0.165***<br>(0.040)</td><td>0.113***<br>(0.008)</td><td>0.159***<br>(0.036)</td></tr><tr><td>β</td><td>0.833***<br>(0.007)</td><td>0.736***<br>(0.009)</td><td>0.751***<br>(0.011)</td><td>0.709***<br>(0.022)</td><td>0.910***<br>(0.012)</td><td>0.878***<br>(0.015)</td></tr><tr><td>γ</td><td>0.274***<br>(0.013)</td><td>0.254***<br>(0.015)</td><td>0.405***<br>(0.027)</td><td>0.387***<br>(0.024)</td><td>0.218***<br>(0.019)</td><td>0.213***<br>(0.022)</td></tr><tr><td>1-γ</td><td>0.725</td><td>0.746***<br>(0.015)</td><td>0.595</td><td>0.612***<br>(0.024)</td><td>0.782</td><td>0.786***<br>(0.022)</td></tr><tr><td>δ<sub>ly</sub></td><td>0.437***<br>(0.034)</td><td>0.395***<br>(0.032)</td><td>0.252***<br>(0.038)</td><td>0.263**<br>(0.030)</td><td>0.240***<br>(0.037)</td><td>0.262***<br>(0.037)</td></tr><tr><td>δ<sub>lm</sub></td><td>0.417***<br>(0.046)</td><td>0.458***<br>(0.052)</td><td>0.430***<br>(0.071)</td><td>0.505</td><td>0.668***<br>(0.085)</td><td>0.680***<br>(0.085)</td></tr><tr><td>δ<sub>lo</sub></td><td>0.145</td><td>0.147***<br>(0.030)</td><td>0.318</td><td>0.231**<br>(0.079)</td><td>0.092</td><td>0.058<br>(0.091)</td></tr><tr><td>ρ<sub>l</sub></td><td>0.463***<br>(0.119)</td><td>0.372***<br>(0.120)</td><td>1.062***<br>(0.324)</td><td>0.778***<br>(0.230)</td><td>1</td><td>1</td></tr><tr><td>δ<sub>ly</sub></td><td>0.247***<br>(0.029)</td><td>0.242***<br>(0.031)</td><td>0.081**<br>(0.028)</td><td>0.110</td><td>0.222***<br>(0.032)</td><td>0.201***<br>(0.056)</td></tr><tr><td>δ<sub>hm</sub></td><td>0.405***<br>(0.036)</td><td>0.432***<br>(0.042)</td><td>0.832***<br>(0.045)</td><td>0.802**<br>(0.052)</td><td>0.373***<br>(0.029)</td><td>0.385***<br>(0.038)</td></tr><tr><td>δ<sub>ho</sub></td><td>0.347</td><td>0.326***<br>(0.026)</td><td>0.085</td><td>0.087*<br>(0.034)</td><td>0.404</td><td>0.414***<br>(0.039)</td></tr><tr><td>ρ<sub>h</sub></td><td>0.725***<br>(0.122)</td><td>0.594***<br>(0.132)</td><td>0</td><td>0</td><td>1</td><td>1</td></tr></tbody></table>

Notes: Bootstrapped standard errors in parentheses. *** Significant at 1%, ** significant at 5%, * significant at 10%.

## Control for endogeneity bias

The nonlinear least squares estimates appear to suffer from the endogeneity bias implying existing correlation between productivity and input choices. Interestingly, the existing bias has different character in distinct sectors. In manufacturing and in trade, the NLLS method tends to underestimate the capital coefficient (α) and overestimate the labour coefficients (β). Such situation takes place if capital and labour are positively correlated and labour's correlation with the productivity shock is higher than capital's correlation. On the other hand, in services, both NLLS coefficients α and β
tend to be biased upwards. It might be the case when only labour responds to the
shock and at the same time capital and labour are positively correlated<fnref n="5" />.

We can also observe interesting results regarding the potential endogeneity bias within
the labour input. In the model with labour differentiated by skills (model (1) and
(3)), we observe that the coefficients of low-skilled workers are slightly biased upwards
in all the sectors. Among different age categories, the coefficients of old workers (as
well as young workers in manufacturing) are overestimated. Although these biases
are not statistically significant, they might however indicate that the correlation of
these categories of labour with the productivity shock is higher. It could imply that
a greater part of this labour category is hired/made redundant in response to the
positive/negative productivity shock.

Within the labour differentiated simultaneously by age and skills, in all the sectors, the NLLS estimates tend to underestimate the middle-aged workers coefficient. For other skill-age categories, the results are more sector-specific. Among the underestimated coefficients suggesting lower correlation with the productivity shock, we find those of young low-skilled workers in services and trade, those of old low-skilled workers in manufacturing, those of young high-skilled workers in services and those of senior high-skilled workers in trade. Nevertheless, these biases remain not very significant.

## 6.2 Age-productivity and age-earnings profiles: general pattern

According to the methodology presented in part 3, we construct the productivity contri-
butions and wage shares for different categories of workers. Thanks to the information
on earnings in the dataset, the share of a distinct age group in the wage bill of a given
skill category may be easily computed. Based on the estimated parameters values cor-
rected for the endogeneity bias (right columns of Table 6), we estimate the marginal
product of labour. Consequently, we can compare an earnings-productivity pattern for
different skill and age categories of workers in three different sectors.

A general tendency regarding productivity contributions and wage shares is presented
in Table 7 and is given by the median. In our case, where the data are not necessarily
symmetrically distributed, the median is a summary that gives a better idea of a general
pattern than given by the mean. In fact, if data are symmetrically distributed, using
either the mean or the median gives identical results. In case of skewed distributions
however, using the mean could be misleading as means are very sensitive to outliers.

<footnote n="5">⁵According to Levinsohn and Petrin (2003), these two cases might be the most relevant for short panels because between-firm variation often plays a dominant role in identification and, in this dimension, capital and labour tend to be highly correlated.</footnote>
<figure><img src="image_5.png" /><figcaption>Table 7: Age-productivity and age-earnings pattern
Manufacturing</figcaption></figure>
For the median firm, we observe throughout the sectors and for both skill categories of workers that wage shares vary substantially less than workers' productivity. In manufacturing, the age-productivity and age-earnings profiles are compatible with a deferred compensation system. It might indicate that, in this sector, the effort incentive problem has been regulated in practice by many firms by offering at the start of the career wages under the workers' marginal productivity and compensating this difference in the later periods. On the other hand, in services and in trade, we observe the combined relevance of specific human capital and deferred compensation. For young employees, the productivity profile is steeper than the wage profile suggesting that investments in specific human capital are important at the beginning of employees' careers. For older workers, the wage share is higher than the contribution of productivity, pointing rather to an incentive-based compensation scheme.

Interestingly, for high-skilled workers in manufacturing, there is not much difference in productivity across age groups. Though, it is the highest for the oldest employees. In trade, the productivity has a clearly increasing slope. Importantly, in both of these sectors, the profile of wage share of middle-aged and senior workers does not diverge much from the profile of productivity contribution.

At the same time, in the low-skilled category, the estimated workers' productivity is clearly the lowest for the oldest workers. However, this result may suffer from a selection bias: experience upgrade low-skilled workers qualification and they may move to high-skilled occupation as time is passing; thus, the senior workers who stay in the low-skilled jobs may be those who are not very productive. A reverse phenomenon could be also observed among the people in high-skilled occupations. Seniors working as highly-skilled experts are not an exception in certain jobs.

## 6.3 Density estimations

The results for the median firm are interesting but do not reflect all the complexity of variation in wage shares and productivity contributions of different labour categories across the enterprises. Since the estimated parameters (right columns of Table 6) allow calculating the marginal productivities of all labour categories in each firm, we can also analyse the shape of the inter-firm density functions of wage and productivity distributions. For this purpose, we make use of kernel density estimation which is a non-parametric way of estimating the probability density function. It is clearly smoother than some other density estimators such as histogram. The univariate kernel density estimator is computed using:

$$ \hat{f}(x) = \frac{1}{nh} \sum_{i=1}^{n} K \left[ \frac{x - X_i}{h} \right] \qquad (23) $$
where *K* is the Epanechnikov Kernel function and *h* is a smoothing parameter called the bandwidth [Parzen, 1962].

### 6.3.1 Productivity

The productivity contribution ($MP_{ij}/MP_{iav}$) is defined as the ratio of the marginal product of labour of a specific skill and age group (ij) over the average marginal product of labour of a given skill group (i). If the productivity of a certain age group is equal to the sector average, this ratio is equal to 1. In Tables 8 - 10, this case is expressed as a black vertical line. Since the distribution of productivity across the age groups is highly sector-specific, we analyse each sector separately as follows.

#### Manufacturing

In manufacturing, as shown in Table 8, the productivity of low-skilled workers across firms is characterised by higher variability than the one of high-skilled workers. In general, the median absolute deviations are higher and there are more positive outliers. If we look closer at different age groups, we can notice that in both skill groups a greater variability in productivity is observed among young and older workers. At the same time, the productivity contribution of the middle-aged group does not vary that much between the firms. Its values are well concentrated around the sector average.

Certain particularities can be observed within each skills category. Among the low-skilled, the young workers appear the most productive. Most of them have productivity contributions exceeding the sector average (>1) and we observe many positive outliers. On the other hand, the great majority of older workers have productivity below the average (<1). Though a few positive outliers occur.

The density estimations concerning the high-skilled workers are quite different. The productivity distributions of different age groups have much more symmetric shapes and the median values are quite close to the sector average. In this skill category, the older workers appear the most productive group. More than half of them are more productive than an average high-skilled person.

#### Services

Table 9 shows the pattern of the productivity distribution in the sector of services. In this case, a higher inter-firm variability can be observed for the high-skilled employees. Both, the median absolute deviations as well as positive outliers take much higher values for this type of workers.

Nevertheless, in this case the productivity profile across age groups is similar in both skill groups. The middle-aged workers are found clearly the most productive. Almost all of them have productivities that are higher than the sector average (> 1). In contrast, most juniors and seniors are characterised by a productivity below the mean. However, there are some positive outliers, especially among high-skilled workers.
<table><caption>Table 8: Share in average marginal productivity (manufacturing)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>1.75</td><td>0.48</td><td>0.73</td><td>44.44</td></tr><tr><td>middle-aged</td><td>0.95</td><td>0.07</td><td>0.77</td><td>3.88</td></tr><tr><td>old</td><td>0.61</td><td>0.13</td><td>0.33</td><td>16.18</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>1.03</td><td>0.17</td><td>0.63</td><td>7.55</td></tr><tr><td>middle-aged</td><td>0.99</td><td>0.05</td><td>0.89</td><td>2.77</td></tr><tr><td>old</td><td>1.09</td><td>0.16</td><td>0.76</td><td>8.96</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Table 9: Share in average marginal productivity (services)</figcaption></figure>

<table><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.76</td><td>0.05</td><td>0.68</td><td>1.96</td></tr><tr><td>middle-aged</td><td>1.21</td><td>0.07</td><td>0.99</td><td>3.74</td></tr><tr><td>old</td><td>0.72</td><td>0.06</td><td>0.62</td><td>2.53</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.62</td><td>0.27</td><td>0.13</td><td>47.11</td></tr><tr><td>middle-aged</td><td>1.36</td><td>0.19</td><td>0.83</td><td>27.85</td></tr><tr><td>old</td><td>0.44</td><td>0.18</td><td>0.09</td><td>119.00</td></tr></tbody></table>

<figure><img src="image_7.png" /></figure>
Trade

As can be seen in Table 10, in trade the productivity pattern is very different from those observed in other sectors. First of all, the productivity variability within narrowly defined age groups is much lower. Furthermore, there are large differences between skill groups. Among the low-skilled workers, the productivity distributions almost do not cross each other. The middle-aged workers are the most productive with the productivity contribution over the sector average in all the enterprises. The productivity of young and seniors is considerably lower, well below the sector mean.

A very different pattern is observed within the high-skilled category of workers. Here, seniors are the most productive group followed closely by middle-aged workers with very similar productivity distribution. The young high-skilled employees are significantly less productive.

<table><caption>Table 10: Share in average marginal productivity (trade)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.58</td><td>0.04</td><td>0.42</td><td>1.17</td></tr><tr><td>middle-aged</td><td>1.50</td><td>0.11</td><td>1.10</td><td>3.03</td></tr><tr><td>old</td><td>0.13</td><td>0.01</td><td>0.09</td><td>0.26</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.55</td><td>0.02</td><td>0.49</td><td>0.82</td></tr><tr><td>middle-aged</td><td>1.05</td><td>0.03</td><td>0.95</td><td>1.57</td></tr><tr><td>old</td><td>1.13</td><td>0.04</td><td>1.03</td><td>1.69</td></tr></tbody></table>

<figure><img src="image_8.png" /></figure>

------- young ; ------- middle-aged ; — old

6.3.2 Earnings

Distributions of wages over age and skill categories are presented in Tables 11, 12 and 13. The wage share ($W_{ij}/W_{iav}$) is defined as a ratio of earnings of a specific age group
(j) over the average earnings of a given skill group (i). The ratio equals to 1 (expressed in the tables by a black vertical line) if earnings correspond to the sector average.

In all the sectors we observe a very similar pattern. In general, wage rates vary substantially less than workers' productivity. This result is in line with empirical evidence rejecting the paradigm of wage and marginal productivity equality (Frank (1984), Campbell and Kamlani (1997)).

Looking separately at the two skill classes, we notice that wages of low-skilled workers are less variable than those of the high-skilled. In the low-skilled category, the middle-aged group of workers is characterised by the earnings distribution with the lowest variability, well concentrated around the mean. The earnings variability of young and older workers is very comparable.

Within the high-skilled group we observe more positive outliers, in particular for senior workers, possibly due to better remuneration offered to high-skilled employees with a long tenure. The distribution of earnings for the middle-aged workers is the least variable, followed by young and senior employees.

<table><caption>Table 11: Share in average wage (manufacturing)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.89</td><td>0.05</td><td>0.05</td><td>2.74</td></tr><tr><td>middle-aged</td><td>1.01</td><td>0.02</td><td>0.54</td><td>1.49</td></tr><tr><td>old</td><td>1.05</td><td>0.04</td><td>0.44</td><td>4.79</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.68</td><td>0.08</td><td>0.01</td><td>2.94</td></tr><tr><td>middle-aged</td><td>0.99</td><td>0.05</td><td>0.40</td><td>2.23</td></tr><tr><td>old</td><td>1.19</td><td>0.13</td><td>0.35</td><td>8.34</td></tr></tbody></table>

<figure><img src="image_9.png" /></figure>

------- young ; ------- middle-aged ; — old
<table><caption>Table 12: Share in average wage (services)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.92</td><td>0.04</td><td>0.24</td><td>1.43</td></tr><tr><td>middle-aged</td><td>1.01</td><td>0.02</td><td>0.78</td><td>1.80</td></tr><tr><td>old</td><td>1.05</td><td>0.05</td><td>0.34</td><td>3.52</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.75</td><td>0.08</td><td>0.02</td><td>5.02</td></tr><tr><td>middle-aged</td><td>1.00</td><td>0.05</td><td>0.31</td><td>2.23</td></tr><tr><td>old</td><td>1.20</td><td>0.15</td><td>0.28</td><td>37.84</td></tr></tbody></table>

<figure><img src="image_10.png" /></figure>

------- young ; ------- mid-age ; — old

<table><caption>Table 13: Share in average wage (trade)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.91</td><td>0.05</td><td>0.13</td><td>1.33</td></tr><tr><td>middle-aged</td><td>1.03</td><td>0.02</td><td>0.82</td><td>1.51</td></tr><tr><td>old</td><td>1.07</td><td>0.05</td><td>0.59</td><td>2.32</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.70</td><td>0.09</td><td>0.02</td><td>3.75</td></tr><tr><td>middle-aged</td><td>1.00</td><td>0.06</td><td>0.42</td><td>1.83</td></tr><tr><td>old</td><td>1.20</td><td>0.17</td><td>0.38</td><td>5.49</td></tr></tbody></table>

<figure><img src="image_11.png" /></figure>

------- young ; ------- mid-age ; — old
### 6.3.3 Productivity/earnings ratio

The most interesting aspect from the perspective of the employer is the workers' productivity in relation to their cost. It is particularly important as it may create an incentive for employers to exclude some age groups from the labour market and to give preference to the others.

It is possible that some workers having the same productivity are paid differently or that some others are paid equally but have different productivities. Therefore, apart from analysing the productivity distribution separately from wages, we consider also the inter-firm distribution of the productivity/earnings ratio with respect to all age and skill groups (see Tables 14, 15 and 16). We define it as $\frac{MP_{ij}}{MP_{iav}} = \frac{W_{ij}}{W_{iav}}$.

It appears that in manufacturing the relative productivity over the wage ratio is the highest for the young, followed by the middle-aged and the old. The possible explanation could be that the young are paid the least and at the same time they are highly motivated to work hard. If there exists incomplete information about the workers' ability at the beginning of their career, the young workers might exert much more effort in order to suggest high ability level and keep their current job (Grund and Westergård-Nielsen, 2008). The high variability in distribution for the young comes from the positive outliers.

This productivity/earnings ratio decreases with age for both skill groups. It means that the attractiveness of an employee for the employer decreases with age. Though, it is not so strong for the high-skilled workers. The distribution of the ratio shows higher variability for the older compared to the middle-aged workers. It has a lower median and a significant majority of observations are below the sector average.
<table><caption>Table 14: Ratio of relative productivity over relative wage (manufacturing)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>2.02</td><td>0.59</td><td>0.56</td><td>106</td></tr><tr><td>middle-aged</td><td>0.93</td><td>0.07</td><td>0.70</td><td>4.03</td></tr><tr><td>old</td><td>0.58</td><td>0.13</td><td>0.24</td><td>17.77</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>1.53</td><td>0.33</td><td>0.60</td><td>291</td></tr><tr><td>middle-aged</td><td>1.00</td><td>0.07</td><td>0.73</td><td>3.82</td></tr><tr><td>old</td><td>0.88</td><td>0.13</td><td>0.32</td><td>10.17</td></tr></tbody></table>

<figure><img src="image_12.png" /></figure>

------- young ; ------- mid-age ; ------ old

In the services sector, we observe lower variability of the ratio among the low-skilled workers. The high variability for the high-skilled comes, among others, from the positive outliers in this group. In both skill categories, the productivity/earnings ratio is the highest for the middle-aged, followed by young and senior workers. Thus, similarly to the pure productivity profile, the middle-aged workers are the most attractive employees. However, the biggest positive outliers are found among the junior workers.
<table><caption>Table 15: Ratio of relative productivity over relative wage (services)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td>low-skilled</td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.84</td><td>0.08</td><td>0.50</td><td>4.08</td></tr><tr><td>middle-aged</td><td>1.20</td><td>0.07</td><td>0.83</td><td>3.63</td></tr><tr><td>old</td><td>0.68</td><td>0.06</td><td>0.34</td><td>2.44</td></tr><tr><td>high-skilled</td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.85</td><td>0.40</td><td>0.13</td><td>223.53</td></tr><tr><td>middle-aged</td><td>1.36</td><td>0.21</td><td>0.82</td><td>35.50</td></tr><tr><td>old</td><td>0.36</td><td>0.14</td><td>0.09</td><td>67.48</td></tr></tbody></table>

<figure><img src="image_13.png" /></figure>

Contrasting results are found in the trade sector as shown in Table 16. For low-skilled employees, the productivity/earnings ratio is very dispersed across age groups. Likewise in services, middle-aged workers are the most attractive, followed by juniors and seniors. Among the high-skilled, for all age groups the distribution of the ratio converge closely around the mean and does not vary much. Again, the prime-age workers form the group whose majority has the higher ratio of productivity over cost higher. They are followed by the older workers, whose distribution is well symmetric around the mean.
<table><caption>Table 16: Ratio of relative productivity over relative wage (trade)</caption><thead><tr><th></th><th>median</th><th>median absolute<br>deviation</th><th>min</th><th>max</th></tr></thead><tbody><tr><td><em>low-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.64</td><td>0.06</td><td>0.37</td><td>3.67</td></tr><tr><td>middle-aged</td><td>1.44</td><td>0.10</td><td>0.95</td><td>2.97</td></tr><tr><td>old</td><td>0.12</td><td>0.01</td><td>0.05</td><td>0.26</td></tr><tr><td><em>high-skilled</em></td><td></td><td></td><td></td><td></td></tr><tr><td>young</td><td>0.80</td><td>0.10</td><td>0.14</td><td>29.40</td></tr><tr><td>middle-aged</td><td>1.06</td><td>0.05</td><td>0.67</td><td>2.75</td></tr><tr><td>old</td><td>0.95</td><td>0.14</td><td>0.23</td><td>3.02</td></tr></tbody></table>

<figure><img src="image_14.png" /></figure>

# 7 Conclusions

This paper revisits the question of the actual profiles of marginal productivity across age groups within the given workforce and its potential equality with profiles of earnings. Using French firm-level data, we estimated the parameters of the production function where the labour input, differentiated simultaneously by age and skills, takes a nested CES functional form. We controlled for the endogeneity bias according to the methodology developed by Levinsohn and Petrin (2003).

Among the main findings, workers of different ages appear to be imperfect substitutes in production. The elasticity of substitution for workers of different ages has been found considerably lower than implied by the additive functional form specification. Our results suggest that wages do not necessarily reflect the actual productivity. Consistent with study by Frank (1984) and Campbell and Kamlani (1997), the wage profile has been found less variable than productivity.

As regards labour productivity, its profile across distinct age groups is likely to depend on the skill category. It has been found the lowest for the low-skilled older workers. Senior high-skilled employees in manufacturing and trade are the most productive group. Results for the manufacturing sector show that the age-productivity and age-earnings
profiles are compatible with a deferred compensation system. It might indicate that the effort incentive problem has been regulated in practice by many firms by offering at the start of the career wages under the workers’ marginal productivity and compensating this difference in the later periods. On the other hand, in services and in trade, we observe the combined relevance of specific human capital and deferred compensation.

Relative productivity over wage ratio, an important aspect for the employer, has been found sector-specific. In manufacturing, it is the highest for the young workers. In services and trade, the ratio is the highest for the middle-aged employees. This discrepancy between productivity and earnings can be a source of employment difficulties particularly for the older low-skilled workers.
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# 8 Appendix

<table><caption>Table 17: Production function estimates for each sector, labour differentiated by age, sub-sector controls</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">Manufacturing</th><th colspan="2">Services</th></tr><tr><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th></tr></thead><tbody><tr><td>α</td><td>0.222<br>(0.005)***</td><td>0.284<br>(0.029)***</td><td>0.241<br>(0.006)***</td><td>0.189<br>(0.039)***</td></tr><tr><td>β</td><td>0.811<br>(0.008)***</td><td>0.679<br>(0.010)***</td><td>0.710<br>(0.011)***</td><td>0.642<br>(0.024)***</td></tr><tr><td>δ<sub>v</sub></td><td>0.325<br>(0.019)***</td><td>0.293<br>(0.023)***</td><td>0.275<br>(0.026)***</td><td>0.299<br>(0.030)***</td></tr><tr><td>δ<sub>m</sub></td><td>0.450<br>(0.027)***</td><td>0.508<br>(0.035)***</td><td>0.427<br>(0.048)***</td><td>0.425<br>(0.051)***</td></tr><tr><td>δ<sub>o</sub></td><td>0.224</td><td>0.198<br>(0.017)***</td><td>0.298</td><td>0.276<br>(0.051)***</td></tr><tr><td>ρ<sub>a</sub></td><td>0.345<br>(0.075)***</td><td>0.188<br>(0.099)*</td><td>0.935<br>(0.213)***</td><td>0.759<br>(0.176)***</td></tr><tr><td>sub-sector controls</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td></tr><tr><td>No of obs.</td><td>8185</td><td>8185</td><td>4498</td><td>4498</td></tr></tbody></table>

Notes: Bootstrapped standard errors in parentheses.

*** Significant at 1%, ** significant at 5%, * significant at 10%.
<table><caption>Table 18: Production function estimates for each sector, labour differentiated by age and skills, sub-sector controls</caption><thead><tr><th rowspan="3">Parameters</th><th colspan="2">Manufacturing</th><th colspan="4">Services</th></tr><tr><th colspan="2">no constraints</th><th colspan="2">no constraints</th><th colspan="2">ρ<sub>h</sub>=0</th></tr><tr><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th><th>NLLS</th><th>LP</th></tr></thead><tbody><tr><td>α</td><td>0.191<br>(0.005)***</td><td>0.283<br>(0.041)***</td><td>0.218<br>(0.006)***</td><td>0.167<br>(0.042)***</td><td>0.219<br>(0.006)***</td><td>0.167<br>(0.042)***</td></tr><tr><td>β</td><td>0.827<br>(0.008)***</td><td>0.714<br>(0.009)***</td><td>0.733<br>(0.011)***</td><td>0.668<br>(0.025)***</td><td>0.724<br>(0.011)***</td><td>0.660<br>(0.025)***</td></tr><tr><td>γ</td><td>0.279<br>(0.013)***</td><td>0.269<br>(0.016)***</td><td>0.331<br>(0.025)***</td><td>0.324<br>(0.023)***</td><td>0.364<br>(0.026)***</td><td>0.356<br>(0.026)***</td></tr><tr><td>1-γ</td><td>0.721<br>(0.016)***</td><td>0.730<br>(0.016)***</td><td>0.669<br>(0.023)***</td><td>0.675<br>(0.023)***</td><td>0.635<br>(0.026)***</td><td>0.643<br>(0.026)***</td></tr><tr><td>δ<sub>ly</sub></td><td>0.441<br>(0.033)***</td><td>0.404<br>(0.033)***</td><td>0.342<br>(0.038)***</td><td>0.371<br>(0.034)***</td><td>0.334<br>(0.038)***</td><td>0.365<br>(0.034)***</td></tr><tr><td>δ<sub>lm</sub></td><td>0.420<br>(0.046)***</td><td>0.465<br>(0.052)***</td><td>0.435<br>(0.071)***</td><td>0.451<br>(0.062)***</td><td>0.387<br>(0.066)***</td><td>0.409<br>(0.062)***</td></tr><tr><td>δ<sub>lo</sub></td><td>0.138<br>(0.029)***</td><td>0.131<br>(0.029)***</td><td>0.222<br>(0.055)***</td><td>0.177<br>(0.055)***</td><td>0.278<br>(0.060)***</td><td>0.226<br>(0.060)***</td></tr><tr><td>ρ<sub>l</sub></td><td>0.437<br>(0.117)***</td><td>0.323<br>(0.118)***</td><td>0.653<br>(0.234)***</td><td>0.473<br>(0.160)***</td><td>0.814<br>(0.248)***</td><td>0.608<br>(0.172)***</td></tr><tr><td>δ<sub>hy</sub></td><td>0.248<br>(0.029)***</td><td>0.246<br>(0.032)***</td><td>0.211<br>(0.041)***</td><td>0.214<br>(0.067)***</td><td>0.132<br>(0.028)***</td><td>0.144<br>(0.035)***</td></tr><tr><td>δ<sub>hm</sub></td><td>0.403<br>(0.037)***</td><td>0.435<br>(0.044)***</td><td>0.391<br>(0.067)***</td><td>0.361<br>(0.091)***</td><td>0.696<br>(0.045)***</td><td>0.664<br>(0.054)***</td></tr><tr><td>δ<sub>ho</sub></td><td>0.348<br>(0.027)***</td><td>0.318<br>(0.027)***</td><td>0.398<br>(0.132)***</td><td>0.424<br>(0.132)***</td><td>0.172<br>(0.037)***</td><td>0.191<br>(0.037)***</td></tr><tr><td>ρ<sub>h</sub></td><td>0.726<br>(0.124)***</td><td>0.581<br>(0.138)***</td><td>1.009<br>(0.288)***</td><td>0.984<br>(3.484)</td><td>0</td><td>0</td></tr><tr><td>sub-sector<br>controls</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td><td>yes</td></tr><tr><td>No of obs.</td><td>8185</td><td>8185</td><td>4498</td><td>4498</td><td>3309</td><td>3309</td></tr></tbody></table>

Notes: Bootstrapped standard errors in parentheses.

*** Significant at 1%, ** significant at 5%, * significant at 10%.
<table><tr><td>G 9001</td><td>J. FAYOLLE et M. FLEURBAEY<br>Accumulation, profitabilité et endettement des entreprises</td><td>Macro-economic import functions with imperfect competition - An application to the E.C. Trade</td></tr><tr><td>G 9002</td><td>H. ROUSSE<br>Détection et effets de la multicolinéarité dans les modèles linéaires ordinaires - Un prolongement de la réflexion de BELSLEY, KUH et WELSCH</td><td>G 9203<br>I. STAPIC<br>Les échanges internationaux de services de la France dans le cadre des négociations multilatérales du GATT<br>Jun 1992 (1ère version)<br>Novembre 1992 (version finale)</td></tr><tr><td>G 9003</td><td>P. RALLE et J. TOUJAS-BERNATE<br>Indexation des salaires : la rupture de 1983</td><td>G 9204<br>P. SEVESTRE<br>L'économie sur données individuelles-temporelles. Une note introductive</td></tr><tr><td>G 9004</td><td>D. GUELLEC et P. RALLE<br>Compétitivité, croissance et innovation de produit</td><td>G 9205<br>H. ERKEL-ROUSSE<br>Le commerce extérieur et l'environnement international dans le modèle AMADEUS (réestimation 1992)</td></tr><tr><td>G 9005</td><td>P. RALLE et J. TOUJAS-BERNATE<br>Les conséquences de la désindexation. Analyse dans une maquette prix-salaires</td><td>G 9206<br>N. GREENAN et D. GUELLEC<br>Coordination within the firm and endogenous growth</td></tr><tr><td>G 9101</td><td>Equipe AMADEUS<br>Le modèle AMADEUS - Première partie - Présentation générale</td><td>G 9207<br>A. MAGNIER et J. TOUJAS-BERNATE<br>Technology and trade : empirical evidences for the major five industrialized countries</td></tr><tr><td>G 9102</td><td>J.L. BRILLET<br>Le modèle AMADEUS - Deuxième partie - Propriétés variantielles</td><td>G 9208<br>B. CREPON, E. DUGUET, D. ENCAOUA et P. MOHNEN<br>Cooperative, non cooperative R &amp; D and optimal patent life</td></tr><tr><td>G 9103</td><td>D. GUELLEC et P. RALLE<br>Endogenous growth and product innovation</td><td>G 9209<br>B. CREPON et E. DUGUET<br>Research and development, competition and innovation : an application of pseudo maximum likelihood methods to Poisson models with heterogeneity</td></tr><tr><td>G 9104</td><td>H. ROUSSE<br>Le modèle AMADEUS - Troisième partie - Le commerce extérieur et l'environnement international</td><td>G 9301<br>J. TOUJAS-BERNATE<br>Commerce international et concurrence imparfaite : développements récents et implications pour la politique commerciale</td></tr><tr><td>G 9105</td><td>H. ROUSSE<br>Effets de demande et d'offre dans les résultats du commerce extérieur manufacturé de la France au cours des deux dernières décennies</td><td>G 9302<br>Ch. CASES<br>Durées de chômage et comportements d'offre de travail : une revue de la littérature</td></tr><tr><td>G 9106</td><td>B. CREPON<br>Innovation, taille et concentration : causalités et dynamiques</td><td>G 9303<br>H. ERKEL-ROUSSE<br>Union économique et monétaire : le débat économique</td></tr><tr><td>G 9107</td><td>B. AMABLE et D. GUELLEC<br>Un panorama des théories de la croissance endogène</td><td>G 9304<br>N. GREENAN - D. GUELLEC / G. BROUSSAUDIER - L. MIOTTI<br>Innovation organisationnelle, dynamisme technologique et performances des entreprises</td></tr><tr><td>G 9108</td><td>M. GLAUDE et M. MOUTARDIER<br>Une évaluation du coût direct de l'enfant de 1979 à 1989</td><td>G 9305<br>P. JAILLARD<br>Le traité de Maastricht : présentation juridique et historique</td></tr><tr><td>G 9109</td><td>P. RALLE et alii<br>France - Allemagne : performances économiques comparées</td><td>G 9306<br>J.L. BRILLET<br>Micro-DMS : présentation et propriétés</td></tr><tr><td>G 9110</td><td>J.L. BRILLET<br>Micro-DMS<br>NON PARU</td><td>G 9307<br>J.L. BRILLET<br>Micro-DMS - variantes : les tableaux</td></tr><tr><td>G 9111</td><td>A. MAGNIER<br>Effets accélérateur et multiplicateur en France depuis 1970 : quelques résultats empiriques</td><td>G 9308<br>S. JACOBZONE<br>Les grands réseaux publics français dans une perspective européenne</td></tr><tr><td>G 9112</td><td>B. CREPON et G. DUREAU<br>Investissement en recherche-développement : analyse de causalités dans un modèle d'accélérateur généralisé</td><td>G 9309<br>L. BLOCH - B. CŒURÉ<br>Profitabilité de l'investissement productif et transmission des chocs financiers</td></tr><tr><td>G 9113</td><td>J.L. BRILLET, H. ERKEL-ROUSSE, J. TOUJAS-BERNATE<br>"France-Allemagne Couplées" - Deux économies vues par une maquette macro-économétrique</td><td>G 9400<br>J. BOURDIEU - B. COLIN-SEDILLOT<br>Les théories sur la structure optimal du capital : quelques points de repère</td></tr><tr><td>G 9201</td><td>W.J. ADAMS, B. CREPON, D. ENCAOUA<br>Choix technologiques et stratégies de dissuasion d'entrée</td><td>G 9410<br>F. ROSENWALD<br>Suivi conjoncturel de l'investissement</td></tr><tr><td>G 9202</td><td>J. OLIVEIRA-MARTINS, J. TOUJAS-BERNATE</td><td>G 9411<br>J. BOURDIEU - B. COLIN-SEDILLOT<br>Les décisions de financement des entreprises</td></tr></table>

<table><tr><td>G 9312</td><td>L. BLOCH - B. CŒURÉ<br>Q de Tobin marginal et transmission des chocs financiers</td></tr><tr><td>G 9313</td><td>Equipes Amadeus (INSEE), Banque de France, Métric (DP)<br>Presentation des propriétés des principaux modèles macroéconomiques du Service Public</td></tr><tr><td>G 9314</td><td>B. CREPON - E. DUGUET<br>Research &amp; Development, competition and innovation</td></tr><tr><td>G 9315</td><td>B. DORMONT<br>Quelle est l'influence du coût du travail sur l'emploi ?</td></tr><tr><td>G 9316</td><td>D. BLANCHET - C. BROUSSE<br>Deux études sur l'âge de la retraite</td></tr><tr><td>G 9317</td><td>D. BLANCHET<br>Répartition du travail dans une population hétérogène : deux notes</td></tr><tr><td>G 9318</td><td>D. EYSSARTIER - N. PONTY<br>AMADEUS - an annual macro-economic model for the medium and long term</td></tr><tr><td>G 9319</td><td>G. CETTE - Ph. CUNÉO - D. EYSSARTIER - J. GAUTIÉ<br>Les effets sur l'emploi d'un abaissement du coût du travail des jeunes</td></tr><tr><td>G 9401</td><td>D. BLANCHET<br>Les structures par âge importent-elles ?</td></tr><tr><td>G 9402</td><td>J. GAUTIÉ<br>Le chômage des jeunes en France : problème de formation ou phénomène de file d'attente ?<br>Quelques éléments du débat</td></tr><tr><td>G 9403</td><td>P. QUIRION<br>Les déchets en France : éléments statistiques et économiques</td></tr><tr><td>G 9404</td><td>D. LADIRAY - M. GRUN-REHOMME<br>Lissage par moyennes mobiles - Le problème des extrémités de série</td></tr><tr><td>G 9405</td><td>V. MAILLARD<br>Theorie et pratique de la correction des effets de jours ouvrables</td></tr><tr><td>G 9406</td><td>F. ROSENWALD<br>La décision d'investir</td></tr><tr><td>G 9407</td><td>S. JACOBZONE<br>Les apports de l'économie industrielle pour définir la stratégie économique de l'hôpital public</td></tr><tr><td>G 9408</td><td>L. BLOCH, J. BOURDIEU, B. COLIN-SEDILLOT, G. LONGUEVILLE<br>Du défaut de paiement au dépôt de bilan : les banquiers face aux PME en difficulté</td></tr><tr><td>G 9409</td><td>D. EYSSARTIER, P. MAIRE<br>Impacts macro-économiques de mesures d'aide au logement - quelques éléments d'évaluation</td></tr><tr><td>G 9410</td><td>F. ROSENWALD<br>Suivi conjoncturel de l'investissement</td></tr><tr><td>G 9411</td><td>C. DEFEUILLE - Ph. QUIRION<br>Les déchets d'emballages ménagers : une analyse économique des politiques française et allemande</td></tr></table>

<table><tr><td>G 9412</td><td>J. BOURDIEU - B. CŒURÉ - B. COLIN-SEDILLOT<br>Investissement, incertitude et irréversibilité<br>Quelques développements récents de la théorie de l'investissement</td></tr><tr><td>G 9413</td><td>B. DORMONT - M. PAUCHET<br>L'évaluation de l'élasticité emploi-salaire dépend-elle des structures de qualification ?</td></tr><tr><td>G 9414</td><td>I. KABLA<br>Le Choix de breveter une invention</td></tr><tr><td>G 9501</td><td>J. BOURDIEU - B. CŒURÉ - B. SEDILLOT<br>Irreversible Investment and Uncertainty : When is there a Value of Waiting ?</td></tr><tr><td>G 9502</td><td>L. BLOCH - B. CŒURÉ<br>Imperfections du marché du crédit, investissement des entreprises et cycle économique</td></tr><tr><td>G 9503</td><td>D. GOUX - E. MAURIN<br>Les transformations de la demande de travail par qualification en France<br>Une étude sur la période 1970-1993</td></tr><tr><td>G 9504</td><td>N. GREENAN<br>Technologie, changement organisationnel, qualifications et emploi : une étude empirique sur l'industrie manufacturière</td></tr><tr><td>G 9505</td><td>D. GOUX - E. MAURIN<br>Persistance des hiérarchies sectorielles de salaires : un réexamen sur données françaises</td></tr><tr><td>G 9505<br>Bis</td><td>D. GOUX - E. MAURIN<br>Persistance de inter-industry wages differentials: a reexamination on matched worker-firm panel data</td></tr><tr><td>G 9506</td><td>S. JACOBZONE<br>Les liens entre RMI et chômage, une mise en perspective<br>NON PARU - article (sorti dans Economie et Prévision n°122 (1996) - pages 95 à 113</td></tr><tr><td>G 9507</td><td>G. CETTE - S. MAHFOUZ<br>Le partage primaire du revenu<br>Constat descriptif sur longue période</td></tr><tr><td>G 9601</td><td>Banque de France - CEPREMAP - Direction de la Prévision - Erasme - INSEE - OFCE<br>Structures et propriétés de cinq modèles macro-économiques français</td></tr><tr><td>G 9602</td><td>Rapport d'activité de la DESE de l'année 1995</td></tr><tr><td>G 9603</td><td>J. BOURDIEU - A. DRAZNIEKS<br>L'octroi de crédit aux PME : une analyse à partir d'informations bancaires</td></tr><tr><td>G 9604</td><td>A. TOPIOL-BENSAÎD<br>Les implantations japonaises en France</td></tr><tr><td>G 9605</td><td>P. GENIER - S. JACOBZONE<br>Comportements de prévention, consommation d'alcool et tabagie : peut-on parler d'une gestion globale du capital santé ?<br>Une modélisation microéconométrique empirique</td></tr><tr><td>G 9606</td><td>C. DOZ - F. LENGLART<br>Factor analysis and unobserved component models: an application to the study of French business surveys</td></tr><tr><td>G 9607</td><td>N. GREENAN - D. GUELLEC<br>La théorie coopérative de la firme</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>G 9608</td>
      <td>N. GREENAN - D. GUELLEC<br>Technological innovation and employment<br>reallocation</td>
      <td>G 9714</td>
      <td>F. LEQUILLER<br>Does the French Consumer Price Index Over-<br>state Inflation?</td>
      <td>G 9808</td>
      <td>A. Mourougane<br>Can a Conservative Governor Conduct an Ac-<br>comodative Monetary Policy ?</td>
      <td>G 9913</td>
      <td>Division « Redistribution et Politiques Sociales »<br>Le modèle de microsimulation dynamique<br>DESTINIE</td>
    </tr>
    <tr>
      <td>G 9609</td>
      <td>Ph. COUR - F. RUPPRECHT<br>L'intégration asymétrique au sein du continent<br>américain : un essai de modélisation</td>
      <td>G 9715</td>
      <td>X. BONNET<br>Peut-on mettre en évidence les rigidités à la<br>baisse des salaires nominaux ?<br>Une étude sur quelques grands pays de l'OCDE</td>
      <td>G 9809</td>
      <td>X. BONNET - E. DUBOIS - L. FAUVET<br>Asymétrie des inflations relatives et menus costs<br>: tests sur l'inflation française</td>
      <td>G 9914</td>
      <td>E. DUGUET<br>Macro-commandes SAS pour l'économétrie des<br>panels et des variables qualitatives</td>
    </tr>
    <tr>
      <td>G 9610</td>
      <td>S. DUCHENE - G. FORGEOT - A. JACQUOT<br>Analyse des évolutions récentes de la producti-<br>vité apparente du travail</td>
      <td>G 9716</td>
      <td>N. IUNG - F. RUPPRECHT<br>Productivité de la recherche et rendements<br>d'échelle dans le secteur pharmaceutique<br>français</td>
      <td>G 9810</td>
      <td>E. DUGUET - N. IUNG<br>Sales and Advertising with Spillovers at the firm<br>level: Estimation of a Dynamic Structural Model<br>on Panel Data</td>
      <td>G 9915</td>
      <td>R. DUHAUTOIS<br>Evolution des flux d'emplois en France entre<br>1990 et 1996 : une étude empirique à partir du<br>fichier des bénéfices réels normaux (BRN)</td>
    </tr>
    <tr>
      <td>G 9611</td>
      <td>X. BONNET - S. MAHFOUZ<br>The influence of different specifications of<br>wages-prices spirals on the measure of the<br>NAIRU : the case of France</td>
      <td>G 9717</td>
      <td>E. DUGUET - I. KABLA<br>Appropriation strategy and the motivations to use<br>the patent system in France - An econometric<br>analysis at the firm level</td>
      <td>G 9811</td>
      <td>J.P. BERTHIER<br>Congestion urbaine : un modèle de trafic de<br>pointe à courbe débit-vitesse et demande<br>élastique</td>
      <td>G 9916</td>
      <td>J.Y. FOURNIER<br>Extraction du cycle des affaires : la méthode de<br>Baxter et King</td>
    </tr>
    <tr>
      <td>G 9612</td>
      <td>PH. COUR - E. DUBOIS, S. MAHFOUZ,<br>J. PISANI-FERRY<br>The cost of fiscal retrenchment revisited: how<br>strong is the evidence ?</td>
      <td>G 9718</td>
      <td>L.P. PELÉ - P. RALLE<br>Âge de la retraite : les aspects incitatifs du ré-<br>gime général</td>
      <td>G 9812</td>
      <td>C. PRIGENT<br>La part des salaires dans la valeur ajoutée : une<br>approche macroéconomique</td>
      <td>G 9917</td>
      <td>B. CRÉPON - R. DESPLATZ - J. MAIRESSE<br>Estimating price cost margins, scale economies<br>and workers' bargaining power at the firm level</td>
    </tr>
    <tr>
      <td>G 9613</td>
      <td>A. JACQUOT<br>Les flexions des taux d'activité sont-elles seule-<br>ment conjoncturelles ?</td>
      <td>G 9719</td>
      <td>ZHANG Yingxiang - SONG Xueqing<br>Lexique macroéconomique français-chinois,<br>chinois-français</td>
      <td>G 9813</td>
      <td>A.Th. AERTS<br>L'évolution de la part des salaires dans la valeur<br>ajoutée en France reflète-t-elle les évolutions<br>individuelles sur la période 1979-1994 ?</td>
      <td>G 9918</td>
      <td>Ch. GIANELLA - Ph. LAGARDE<br>Productivity of hours in the aggregate production<br>function: an evaluation on a panel of French<br>firms from the manufacturing sector</td>
    </tr>
    <tr>
      <td>G 9614</td>
      <td>ZHANG Yingxiang - SONG Xueqing<br>Lexique macroéconomique Français-Chinois</td>
      <td>G 9720</td>
      <td>M. HOUBEBINE - J.L. SCHNEIDER<br>Mesurer l'influence de la fiscalité sur la locali-<br>sation des entreprises</td>
      <td>G 9814</td>
      <td>B. SALANIÉ<br>Guide pratique des séries non-stationnaires</td>
      <td>G 9919</td>
      <td>S. AUDRIC - P. GIVORD - C. PROST<br>Evolution de l'emploi et des coûts par quali-<br>fication entre 1982 et 1996</td>
    </tr>
    <tr>
      <td>G 9701</td>
      <td>J.L. SCHNEIDER<br>La taxe professionnelle : éléments de cadrage<br>économique</td>
      <td>G 9721</td>
      <td>A. Mourougane<br>Crédibilité, indépendance et politique monétaire<br>Une revue de la littérature</td>
      <td>G 9901</td>
      <td>S. DUCHÈNE - A. JACQUOT<br>Une croissance plus riche en emplois depuis le<br>début de la décennie ? Une analyse en compa-<br>raison internationale</td>
      <td>G 2000/1</td>
      <td>R. MAHIEU<br>Les déterminants des dépenses de santé : une<br>approche macroéconomique</td>
    </tr>
    <tr>
      <td>G 9702</td>
      <td>J.L. SCHNEIDER<br>Transition et stabilité politique d'un système<br>redistributif</td>
      <td>G 9722</td>
      <td>P. AUGERAUD - L. BRIOT<br>Les données comptables d'entreprises<br>Le système intermédiaire d'entreprises<br>Passage des données individuelles aux données<br>sectorielles</td>
      <td>G 9902</td>
      <td>Ch. COLIN<br>Modélisation des carrières dans Destinie</td>
      <td>G 2000/2</td>
      <td>C. ALLARD-PRIGENT - H. GUILMEAU -<br>A. QUINET<br>The real exchange rate as the relative price of<br>nontrables in terms of tradables: theoretical<br>investigation and empirical study on French data</td>
    </tr>
    <tr>
      <td>G 9703</td>
      <td>D. GOUX - E. MAURIN<br>Train or Pay: Does it Reduce Inequalities to En-<br>courage Firms to Train their Workers?</td>
      <td>G 9723</td>
      <td>P. AUGERAUD - J.E. CHAPRON<br>Using Business Accounts for Compiling National<br>Accounts: the French Experience</td>
      <td>G 9904</td>
      <td>Ch. COLIN<br>Evolution de la dispersion des salaires : un essai<br>de prospective par microsimulation</td>
      <td>G 2000/3</td>
      <td>J.-Y. FOURNIER<br>L'approximation du filtre passe-bande proposée<br>par Christiano et Fitzgerald</td>
    </tr>
    <tr>
      <td>G 9704</td>
      <td>P. GENIER<br>Deux contributions sur dépendance et équité</td>
      <td>G 9724</td>
      <td>P. AUGERAUD<br>Les comptes d'entreprise par activités - Le pas-<br>sage aux comptes - De la comptabilité<br>d'entreprise à la comptabilité nationale - A<br>paraitre</td>
      <td>G 9905</td>
      <td>B. CREPON - N. IUNG<br>Innovation, emploi et performances</td>
      <td>G 2000/4</td>
      <td>Bilan des activités de la DESE - 1999</td>
    </tr>
    <tr>
      <td>G 9705</td>
      <td>E. DUGUET - N. IUNG<br>R & D Investment, Patent Life and Patent Value<br>An Econometric Analysis at the Firm Level</td>
      <td>G 9801</td>
      <td>H. MICHAUDON - C. PRIGENT<br>Présentation du modèle AMADEUS</td>
      <td>G 9907</td>
      <td>B. CREPON - Ch. GIANELLA<br>Wages inequalities in France 1969-1992<br>An application of quantile regression techniques</td>
      <td>G 2000/5</td>
      <td>B. CREPON - F. ROSENWALD<br>Investissement et contraintes de financement : le<br>poids du cycle<br>Une estimation sur données françaises</td>
    </tr>
    <tr>
      <td>G 9706</td>
      <td>M. HOUBEBINE - A. TOPIOL-BENSAÏD<br>Les entreprises internationales en France : une<br>analyse à partir de données individuelles</td>
      <td>G 9802</td>
      <td>J. ACCARDO<br>Une étude de comptabilité générationnelle<br>pour la France en 1996</td>
      <td>G 9908</td>
      <td>C. BONNET - R. MAHIEU<br>Microsimulation techniques applied to inter-<br>generational transfers - Pensions in a dynamic<br>framework: the case of France</td>
      <td>G 2000/6</td>
      <td>A. FLIPO<br>Les comportements matrimoniaux de fait</td>
    </tr>
    <tr>
      <td>G 9707</td>
      <td>M. HOUBEBINE<br>Polarisation des activités et spécialisation des<br>départements en France</td>
      <td>G 9803</td>
      <td>X. BONNET - S. DUCHÈNE<br>Apports et limites de la modélisation<br>« Real Business Cycles »</td>
      <td>G 9909</td>
      <td>F. ROSENWALD<br>L'impact des contraintes financières dans la dé-<br>cision d'investissement</td>
      <td>G 2000/7</td>
      <td>R. MAHIEU - B. SÉDILLOT<br>Microsimulations of the retirement decision: a<br>supply side approach</td>
    </tr>
    <tr>
      <td>G 9708</td>
      <td>E. DUGUET - N. GREENAN<br>Le biais technologique : une analyse sur don-<br>nées individuelles</td>
      <td>G 9804</td>
      <td>C. BARLET - C. DUGUET -<br>D. ENCAOUA - J. PRADEL<br>The Commercial Success of Innovations<br>An econometric analysis at the firm level in<br>French manufacturing</td>
      <td>G 9910</td>
      <td>Bilan des activités de la DESE - 1998<br>Contrat d'insertion et sortie du RMI<br>Evaluation des effets d'une politique sociale</td>
      <td>G 2000/8</td>
      <td>C. AUDENIS - C. PROST<br>Déficit conjoncturel : une prise en compte des<br>conjonctures passées</td>
    </tr>
    <tr>
      <td>G 9709</td>
      <td>J.L. BRILLET<br>Analyzing a small French ECM Model</td>
      <td>G 9805</td>
      <td>P. CAHUC - Ch. GIANELLA -<br>D. GOUX - A. ZILBERBERG<br>Equalizing Wage Differences and Bargaining<br>Power - Evidence form a Panel of French Firms</td>
      <td>G 9911</td>
      <td>Ch. COLIN - FI. LEGROS - R. MAHIEU<br>Bilans contributifs comparés des régimes de<br>retraite du secteur privé et de la fonction<br>publique</td>
      <td>G 2000/9</td>
      <td>R. MAHIEU - B. SÉDILLOT<br>Equivalent patrimonial de la rente et souscription<br>de retraite complémentaire</td>
    </tr>
    <tr>
      <td>G 9710</td>
      <td>J.L. BRILLET<br>Formalizing the transition process : scenarios for<br>capital accumulation</td>
      <td>G 9806</td>
      <td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975<br>et 1996</td>
      <td>G 9912</td>
      <td>G. LAROQUE - B. SALANIÉ<br>Une décomposition du non-emploi en France</td>
      <td>G 2000/10</td>
      <td>R. DUHAUTOIS<br>Ralentissement de l'investissement : petites ou<br>grandes entreprises ? industrie ou tertiaire ?</td>
    </tr>
    <tr>
      <td>G 9711</td>
      <td>G. FORGEOT - J. GAUTIÉ<br>Insertion professionnelle des jeunes et proces-<br>sus de déclassement</td>
      <td>G 9807</td>
      <td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975<br>et 1996</td>
      <td>G 9912</td>
      <td>B. SALANIÉ<br>Une maquette analytique de long terme du<br>marché du travail</td>
      <td>G 2000/11</td>
      <td>G. LAROQUE - B. SALANIÉ<br>Temps partiel féminin et incitations financières à<br>l'emploi</td>
    </tr>
    <tr>
      <td>G 9712</td>
      <td>E. DUBOIS<br>High Real Interest Rates: the Consequence of a<br>Saving Investment Disequilibrium or of an in-<br>sufficient Credibility of Monetary Authorities?</td>
      <td>G 9808</td>
      <td>J. ACCARDO - M. JLASSI<br>La productivité globale des facteurs entre 1975<br>et 1996</td>
      <td>G 9912</td>
      <td>Ch. GIANELLA<br>Une estimation de l'élasticité de l'emploi peu<br>qualifié à son coût</td>
      <td>G 2000/12</td>
      <td>Ch. GIANELLA<br>Local unemployment and wages</td>
    </tr>
    <tr>
      <td>G 9713</td>
      <td>Bilan des activités de la Direction des Etudes<br>et Synthèses Economiques - 1996</td>
      <td>G 9809</td>
      <td>Bilan des activités de la Direction des Etudes et<br>Synthèses Economiques - 1997</td>
      <td>Bis</td>
      <td></td>
      <td>G 2000/13</td>
      <td>B. CREPON - Th. HECKEL<br>- Informatisation en France : une évaluation à<br>partir de données individuelles</td>
    </tr>
  </tbody>
</table>
- Computerization in France: an evaluation based on individual company data

G2001/01 F. LEQUILLER
- La nouvelle économie et la mesure de la croissance du PIB

- The new economy and the measurement of GDP growth

G2001/02 S. AUDRIC
La reprise de la croissance de l'emploi profonde-t-elle aussi aux non-diplômés ?

G2001/03 I. BRAUN-LEMAIRE
Evolution et répartition du surplus de productivité

G2001/04 A. BEAUDU - Th. HECKEL
Le canal du crédit fonctionne-t-il en Europe ? Une étude de l'hétérogénéité des comportements d'investissement à partir de données de bilan agrégées

G2001/05 C. AUDENIS - P. BISCOURP - N. FOURCADE - O. LOISEL
Testing the augmented Solow growth model : An empirical reassessment using panel data

G2001/06 R. MAHIEU - B. SÉDILLOT
Départ à la retraite, irréversibilité et incertitude

G2001/07 Bilan des activités de la DESE - 2000

G2001/08 J. Ph. GAUDEMET
Les dispositifs d'acquisition à titre facultatif d'annuités viagères de retraite

G2001/09 B. CRÉPON - Ch. GIANELLA
Fiscalité, coût d'usage du capital et demande de facteurs : une analyse sur données individuelles

G2001/10 B. CRÉPON - R. DESPLATZ
Evaluation des effets des dispositifs d'allégements de charges sociales sur les bas salaires

G2001/11 J.-Y. FOURNIER
Comparaison des salaires des secteurs public et privé

G2001/12 J.-P. BERTHIER - C. JAULENT
R. CONVENEVOLE - S. PISANI
Une méthodologie de comparaison entre consommations intermédiaires de source fiscale et de comptabilité nationale

G2001/13 P. BISCOURP - Ch. GIANELLA
Substitution and complementarity between capital, skilled and less skilled workers: an analysis at the firm level in the French manufacturing industry

G2001/14 I. ROBERT-BOBEE
Modelling demographic behaviours in the French microsimulation model Destinie: An analysis of future change in completed fertility

G2001/15 J.-P. ZOYEM
Diagnostic sur la pauvreté et calendrier de revenus : le cas du "Panel européen des ménages"

G2001/16 J.-Y. FOURNIER - P. GIVORD
La réduction des taux d'activité aux âges extrêmes, une spécificité française ?

G2001/17 C. AUDENIS - P. BISCOURP - N. RIEDINGER
Existe-t-il une asymétrie dans la transmission du prix du brut aux prix des carburants ?

G2002/01 F. MAGNIEN - J.-L. TAVERNIER - D. THESMAR
Les statistiques internationales de PIB par habitant en standard de pouvoir d'achat : une analyse des résultats

G2002/02 Bilan des activités de la DESE - 2001

G2002/03 B. SÉDILLOT - E. WALRAET
La cessation d'activité au sein des couples : y a-t-il interdépendance des choix ?

G2002/04 G. BRILHAULT
- Rétroposition des séries de FBCF et calcul du capital fixe en SEC-95 dans les comptes nationaux français

- Rétroposition of the investment series (GFCF) and estimation of fixed capital stocks on the ESA-95 basis for the French balance sheets

G2002/05 P. BISCOURP - B. CRÉPON - T. HECKEL - N. RIEDINGER
How do firms respond to cheaper computers? Microeconomic evidence for France based on a production function approach

G2002/06 C. AUDENIS - J. DEROYON - N. FOURCADE
L'impact des nouvelles technologies de l'information et de la communication sur l'économie française - un bouclage macro-économique

G2002/07 J. BARDAJI - B. SÉDILLOT - E. WALRAET
Évaluation de trois réformes du Régime Général d'assurance vieillesse à l'aide du modèle de microsimulation DESTINIE

G2002/08 J.-P. BERTHIER
Réflexions sur les différentes notions de volume dans les comptes nationaux : comptes aux prix d'une année fixe ou aux prix de l'année précédente, séries chaînées

G2002/09 F. HILD
Les soldes d'opinion résument-ils au mieux les réponses des entreprises aux enquêtes de conjoncture ?

G2002/10 I. ROBERT-BOBÉE
Les comportements démographiques dans le modèle de microsimulation Destinie - Une comparaison des estimations issues des enquêtes Jeunes et Carrières 1997 et Histoire Familiale 1999

G2002/11 J.-P. ZOYEM
La dynamique des bas revenus : une analyse des entrées-sorties de pauvreté

G2002/12 F. HILD
Prévisions d'inflation pour la France

G2002/13 M. LECLAIR
Réduction du temps de travail et tensions sur les facteurs de production

G2002/14 E. WALRAET - A. VINCENT
- Analyse de la redistribution intragénérationnelle dans le système de retraite des salariés du privé - Une approche par microsimulation

- Intragenerational distributional analysis in the french private sector pension scheme - A microsimulation approach

G2002/15 P. CHONE - D. LE BLANC - I. ROBERT-BOBEE
Offre de travail féminine et garde des jeunes enfants

G2002/16 F. MAUREL - S. GREGOIR
Les indices de compétitivité des pays : interprétation et limites

G2003/01 N. RIEDINGER - E. HAUVY
Le coût de dépollution atmosphérique pour les entreprises françaises : Une estimation à partir de données individuelles

G2003/02 P. BISCOURP et F. KRAMARZ
Création d'emplois, destruction d'emplois et internationalisation des entreprises industrielles françaises : une analyse sur la période 1986-1992

G2003/03 Bilan des activités de la DESE - 2002

G2003/04 P.-O. BEFFY - J. DEROYON - N. FOURCADE - S. GREGOIR - N. LAÎB - B. MONFORT
Évolutions démographiques et croissance : une projection macro-économique à l'horizon 2020

G2003/05 P. AUBERT
La situation des salariés de plus de cinquante ans dans le secteur privé

G2003/06 P. AUBERT - B. CRÉPON
Âge, salaire et productivité
La productivité des salariés décline-t-elle en fin de carrière ?

G2003/07 H. BARON - P.O. BEFFY - N. FOURCADE - R. MAHIEU
Le ralentissement de la productivité du travail au cours des années 1990

G2003/08 P.-O. BEFFY - B. MONFORT
Patrimoine des ménages, dynamique d'allocation et comportement de consommation

G2003/09 P. BISCOURP - N. FOURCADE
Peut-on mettre en évidence l'existence de rigidités à la baisse des salaires à partir de données individuelles ? Le cas de la France à la fin des années 90

G2003/10 M. LECLAIR - P. PETIT
Présence syndicale dans les firmes : quel impact sur les inégalités salariales entre les hommes et les femmes ?

G2003/11 P.-O. BEFFY - X. BONNET - M. DARRACQ-PARIES - B. MONFORT
MZE: a small macro-model for the euro area

G2004/01 P. AUBERT - M. LECLAIR
La compétitivité exprimée dans les enquêtes trimestrielles sur la situation et les perspectives dans l'industrie

G2004/02 M. DUÉE - C. REBILLARD
La dépendance des personnes âgées : une projection à long terme

G2004/03 S. RASPILLER - N. RIEDINGER
Régulation environnementale et choix de localisation des groupes français

G2004/04 A. NABOULET - S. RASPILLER
Les déterminants de la décision d'investir : une approche par les perceptions subjectives des firmes

G2004/05 N. RAGACHE
La déclaration des enfants par les couples non mariés est-elle fiscalement optimale ?

G2004/06 M. DUÉE
L'impact du chômage des parents sur le devenir scolaire des enfants

G2004/07 P. AUBERT - E. CAROLI - M. ROGER
New Techologies, Workplace Organisation and the Age Structure of the Workforce: Firm-Level Evidence

G2004/08 E. DUGUET - C. LELARGE
Les brevets accroissent-ils les incitations privées à innover ? Un examen microéconomique

G2004/09 S. RASPILLER - P. SILLARD
Affiliating versus Subcontracting: the Case of Multinationals

G2004/10 J. BOISSINOT - C. L'ANGEVIN - B. MONFORT
Public Debt Sustainability: Some Results on the French Case

G2004/11 S. ANANIAN - P. AUBERT
Travailleurs âgés, nouvelles technologies et changements organisationnels : un réexamen à partir de l'enquête « REPONSE »

G2004/12 X. BONNET - H. PONCET
Structures de revenus et propensions différentes à consommer - Vers une équation de consommation des ménages plus robuste en prévision pour la France

G2004/13 C. PICART
Évaluer la rentabilité des sociétés non financières

G2004/14 J. BARDAJI - B. SÉDILLOT - E. WALRAET
Les retraites du secteur public : projections à l'horizon 2040 à l'aide du modèle de microsimulation DESTINIE

G2005/01 S. BUFFETEAU - P. GODEFROY
Conditions de départ en retraite selon l'âge de fin d'études : analyse prospective pour les générations 1945 a1974

G2005/02 C. AFSA - S. BUFFETEAU
L'évolution de l'activité féminine en France : une approche par pseudo-panel

G2005/03 P. AUBERT - P. SILLARD
Délocalisations et réductions d'effectifs dans l'industrie française

G2005/04 M. LECLAIR - S. ROUX
Mesure et utilisation des emplois instables dans les entreprises

G2005/05 C. L'ANGEVIN - S. SERRAVALLE
Performances à l'exportation de la France et de l'Allemagne - Une analyse par secteur et destination géographique

G2005/06 Bilan des activités de la Direction des Études et Synthèses Economiques - 2004

G2005/07 S. RASPILLER
La concurrence fiscale : principaux enseignements de l'analyse économique

G2005/08 C. L'ANGEVIN - N. LAÎB
Éducation et croissance en France et dans un panel de 21 pays de l'OCDE

G2005/09 N. FERRARI
Prévoir l'investissement des entreprises
Un indicateur des révisions dans l'enquête de conjoncture sur les investissements dans l'industrie.
G2005/10 P.-O. BEFFY - C. L'ANGEVIN
Chômage et boucle prix-salaires : apport d'un modèle « qualifés/peu qualifiés »

G2005/11 B. HEITZ
A two-states Markov-switching model of inflation in France and the USA: credible target VS inflation spiral

G2005/12 O. BIAU - H. ERKEL-ROUSSE - N. FERRARI
Réponses individuelles aux enquêtes de conjoncture et prévision macroéconomiques : Exemple de la prévision de la production manufacturière

G2005/13 P. AUBERT - D. BLANCHET - D. BLAU
The labour market after age 50: some elements of a Franco-American comparison

G2005/14 D. BLANCHET - T. DEBRAND - P. DOURGNON - P. POLLET
L'enquête SHARE : présentation et premiers résultats de l'édition française

G2005/15 M. DUÉE
La modélisation des comportements démographiques dans le modèle de microsimulation DESTINIE

G2005/16 H. RAOUI - S. ROUX
Étude de simulation sur la participation versée aux salariés par les entreprises

G2006/01 C. BONNET - S. BUFFETEAU - P. GODEFROY
Disparités de retraite de droit direct entre hommes et femmes : quelles évolutions ?

G2006/02 C. PICART
Les gazelles en France

G2006/03 P. AUBERT - B. CRÉPON - P. ZAMORA
Le rendement apparent de la formation continue dans les entreprises : effets sur la productivité et les salaires

G2006/04 J.-F. OUVRARD - R. RATHELOT
Demographic change and unemployment: what do macroeconometric models predict?

G2006/05 D. BLANCHET - J.-F. OUVRARD
Indicateurs d'engagements implicites des systèmes de retraite : chiffrages, propriétés analytiques et réactions à des chocs démographiques types

G2006/06 G. BIAU - O. BIAU - L. ROUVIERE
Nonparametric Forecasting of the Manufacturing Output Growth with Firm-level Survey Data

G2006/07 C. AFSA - P. GIVORD
Le rôle des conditions de travail dans les absences pour maladie

G2006/08 P. SILLARD - C. L'ANGEVIN - S. SERRAVALLE
Performances comparées à l'exportation de la France et de ses principaux partenaires
Une analyse structurelle sur 12 ans

G2006/09 X. BOUTIN - S. QUANTIN
Une méthodologie d'évaluation comptable du coût du capital des entreprises françaises : 1984-2002

G2006/10 C. AFSA
L'estimation d'un coût implicite de la pénibilité du travail chez les travailleurs âgés

G2006/11 C. LELARGE
Les entreprises (industrielles) françaises sont-elles à la frontière technologique ?

G2006/12 O. BIAU - N. FERRARI
Théorie de l'opinion
Faut-il pondérer les réponses individuelles ?

G2006/13 A. KOUBI - S. ROUX
Une réinterprétation de la relation entre productivité et inégalités salariales dans les entreprises

G2006/14 R. RATHELOT - P. SILLARD
The impact of local taxes on plants location decision

G2006/15 L. GONZALEZ - C. PICART
Diversification, recentrage et poids des activités de support dans les groupes (1993-2000)

G2007/01 D. SRAER
Allègements de cotisations patronales et dynamique salariale

G2007/02 V. ALBOUY - L. LEQUIEN
Les rendements non monétaires de l'éducation : le cas de la santé

G2007/03 D. BLANCHET - T. DEBRAND
Aspiration à la retraite, santé et satisfaction au travail : une comparaison européenne

G2007/04 M. BARLET - L. CRUSSON
Quel impact des variations du prix du pétrole sur la croissance française ?

G2007/05 C. PICART
Flux d'emploi et de main-d'œuvre en France : un réexamen

G2007/06 V. ALBOUY - C. TAVAN
Massification et démocratisation de l'enseignement supérieur en France

G2007/07 T. LE BARBANCHON
The Changing response to oil price shocks in France : a DSGE type approach

G2007/08 T. CHANEY - D. SRAER - D. THESMAR
Collateral Value and Corporate Investment Evidence from the French Real Estate Market

G2007/09 J. BOISSINOT
Consumption over the Life Cycle: Facts for France

G2007/10 C. AFSA
Interpréter les variables de satisfaction : l'exemple de la durée du travail

G2007/11 R. RATHELOT - P. SILLARD
Zones Franches Urbaines : quels effets sur l'emploi salarié et les créations d'établissements ?

G2007/12 V. ALBOUY - B. CRÉPON
Aléa moral en santé : une évaluation dans le cadre du modèle causal de Rubin

G2008/01 C. PICART
Les PME françaises : rentables mais peu dynamiques

G2008/02 P. BISCOURP - X. BOUTIN - T. VERGÉ
The Effects of Retail Regulations on Prices Evidence form the Loi Galland

G2008/03 Y. BARBESOL - A. BRIANT
Économies d'agglomération et productivité des entreprises : estimation sur données individuelles françaises

G2008/04 D. BLANCHET - F. LE GALLO
Les projections démographiques : principaux mécanismes et retour sur l'expérience française

G2008/05 D. BLANCHET - F. TOUTLEMONDE
Évolutions démographiques et déformation du cycle de vie active : quelles relations ?

G2008/06 M. BARLET - D. BLANCHET - L. CRUSSON
Internationalisation et flux d'emplois : que dit une approche comptable ?

G2008/07 C. LELARGE - D. SRAER - D. THESMAR
Entrepreneurship and Credit Constraints - Evidence from a French Loan Guarantee Program

G2008/08 X. BOUTIN - L. JANIN
Are Prices Really Affected by Mergers?

G2008/09 M. BARLET - A. BRIANT - L. CRUSSON
Concentration géographique dans l'industrie manufacturière et dans les services en France : une approche par un indicateur en continu

G2008/10 M. BEFFY - É. COUDIN - R. RATHELOT
Who is confronted to insecure labor market histories? Some evidence based on the French labor market transition

G2008/11 M. ROGER - E. WALRAET
Social Security and Well-Being of the Elderly: the Case of France

G2008/12 C. AFSA
Analyser les composantes du bien-être et de son évolution
Une approche empirique sur données individuelles

G2008/13 M. BARLET - D. BLANCHET - T. LE BARBANCHON
Microsimuler le marché du travail : un prototype

G2009/01 P.-A. PIONNIER
Le partage de la valeur ajoutée en France, 1949-2007

G2009/02 Laurent CLAVEL - Christelle MINODIER
A Monthly Indicator of the French Business Climate

G2009/03 H. ERKEL-ROUSSE - C. MINODIER
Do Business Tendency Surveys in Industry and Services Help in Forecasting GDP Growth?
A Real-Time Analysis on French Data

G2009/04 P. GIVORD - L. WILNER
Les contrats temporaires : trappe ou marchepied vers l'emploi stable ?

G2009/05 G. LALANNE - P.-A. PIONNIER - O. SIMON
Le partage des fruits de la croissance de 1950 à 2008 : une approche par les comptes de surplus

G2009/06 L. DAVEZIES - X. D'HAULTFOEUILLE
Faut-il pondérer ?... Ou l'éternelle question de l'économètre confronté à des données d'enquête

G2009/07 S. QUANTIN - S. RASPILLER - S. SERRAVALLE
Commerce intragroupe, fiscalité et prix de transferts : une analyse sur données françaises

G2009/08 M. CLERC - V. MARCUS
Élasticités-prix des consommations énergétiques des ménages

G2009/09 G. LALANNE - E. POULIQUEN - O. SIMON
Prix du pétrole et croisssance potentielle à long terme

G2009/10 D. BLANCHET - J. LE CACHEUX - V. MARCUS
Adjusted net savings and other approaches to sustainability: some theroretical background

G2009/11 V. BELLAMY - G. CONSALES - M. FESSEAU - S. LE LAIDIER - É. RAYNAUD
Une décomposition du compte des ménages de la comptabilité nationale par catégorie de ménage en 2003

G2009/12 J. BARDAJI - F. TALLET
Detecting Economic Regimes in France: a Qualitative Markov-Switching Indicator Using Mixed Frequency Data

G2009/13 R. AEBERHARDT - D. FOUGÈRE - R. RATHELOT

Discrimination à l'embauche : comment exploiter les procédures de testing ?

G2009/14 Y. BARBESOL - P. GIVORD - S. QUANTIN
Partage de la valeur ajoutée, approche par données microéconomiques

G2009/15 I. BUONO - G. LALANNE
The Effect of the Uruguay round on the Intensive and Extensive Margins of Trade

G2010/01 C. MINODIER
Avantages comparés des séries des premières valeurs publiées et des séries des valeurs révisées - Un exercice de prévision en temps réel de la croissance trimestrielle du PIB en France

G2010/02 V. ALBOUY - L. DAVEZIES - T. DEBRAND
Health Expenditure Models: a Comparison of Five Specifications using Panel Data

G2010/03 C. KLEIN - O. SIMON
Le modèle MÉSANGE réestimé en base 2000
Tome 1 – Version avec volumes à prix constants

G2010/04 M.-É. CLERC - É. COUDIN
L'IPC, miroir de l'évolution du coût de la vie en France ? Ce qu'apporte l'analyse des courbes d'Engel

G2010/05 N. CECI-RENAUD - P.-A. CHEVALIER
Les seuils de 10, 20 et 50 salariés : impact sur la taille des entreprises françaises

G2010/06 R. AEBERHARDT - J. POUGET
National Origin Differences in Wages and Hierarchical Positions - Evidence on French Full-Time Male Workers from a matched Employer-Employee Dataset

G2010/07 S. BLASCO - P. GIVORD
Les trajectoires professionnelles en début de vie active : quel impact des contrats temporaires ?

G2010/08 P. GIVORD
Méthodes économétriques pour l'évaluation de politiques publiques

G2010/09 P.-Y. CABANNES - V. LAPÈGUE - E. POULIQUEN - M. BEFFY - M. GAINI
Quelle croissance de moyen terme après la crise ?

G2010/10 I. BUONO - G. LALANNE
La réaction des entreprises françaises à la baisse des tarifs douaniers étrangers
G2010/11 R. RATHELOT - P. SILLARD
L'apport des méthodes à noyaux pour mesurer la concentration géographique - Application à la concentration des immigrés en France de 1968 à 1999

G2010/12 M. BARATON - M. BEFFY - D. FOUGÈRE
Une évaluation de l'effet de la réforme de 2003 sur les départs en retraite - Le cas des enseignants du second degré public

G2010/13 D. BLANCHET - S. BUFFETEAU - E. CRENNER
S. LE MINEZ
Le modèle de microsimulation Destinie 2 : principales caractéristiques et premiers résultats

G2010/14 D. BLANCHET - E. CRENNER
Le bloc retraites du modèle Destinie 2 : guide de l'utilisateur

G2010/15 M. BARLET - L. CRUSSON - S. DUPUCH - F. PUECH
Des services échangés aux services échangeables : une application sur données françaises

G2010/16 M. BEFFY - T. KAMIONKA
Public-private wage gaps: is civil-servant human capital sector-specific?

G2010/17 P.-Y. CABANNES - H. ERKEL-ROUSSE - G. LALANNE - O. MONSO - E. POULIQUEN
Le modèle Mésange réestimé en base 2000
Tome 2 - Version avec volumes à prix chaînés

G2010/18 R. AEBERHARDT - L. DAVEZIES
Conditional Logit with one Binary Covariate: Link between the Static and Dynamic Cases

G2011/01 T. LE BARBANCHON - B. OURLIAC - O. SIMON
Les marchés du travail français et américain face aux chocs conjoncturels des années 1986 à 2007 : une modélisation DSGE

G2011/02 C. MARBOT
Une évaluation de la réduction d'impôt pour l'emploi de salariés à domicile

G2011/03 L. DAVEZIES
Modèles à effets fixes, à effets aléatoires, modèles mixtes ou multi-niveaux : propriétés et mises en œuvre des modélisations de l'hétérogénéité dans le cas de données groupées

G2011/04 M. ROGER - M. WASMER
Heterogeneity matters: labour productivity differentiated by age and skills