INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES

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G 2000 / 12

Local unemployment and wages

Christian GIANELLA *

NOVEMBRE 2000

I would like to thank David Blanchflower, Françoise Maurel, Eric Maurin, Guy Laroque and Andrew Oswald for helpful comments on previous versions of this paper.

I am especially grateful to Laurence Allain, who gave the impulsion of this study, and to Francis Kramarz and Sébastien Roux who provided the original data set.

All remaining errors are of course mine.

<footnote>* Faisait partie du Département des Etudes Economiques d'Ensemble - Division « Marchés et Stratégies d'Entreprise » au moment de la rédaction de ce document.</footnote>
# Local unemployment and wages

## Abstract

The purpose of this paper is to examine how the state of the local labour market influences pay, by estimating a Wage Curve for France. First it appears that individual wages are negatively correlated with regional unemployment rates, when taking into account individual characteristics. This feature is true for all categories of workers, for different measures of the local unemployment rate, and also for aggregate data. We find an elasticity of wages with respect to unemployment varying between 0.05 and 0.1, and show that permanent effects of the local unemployment on wages rate are stronger than transitory effects. Second we run estimations on cross section and find that the response of wages to unemployment has decreased over time. We try more flexible functional forms for the unemployment rate and it appears that the negative relationship between wages and unemployment is convex rather than linear. Finally, we do not find much autoregression in our wage equation (like Blanchflower and Oswald, 1994). It would mean that the levels and not the variations of wages are related to unemployment, contrary to a Phillips Curve specification.

**Theme:** Microeconomics of unemployment, Regional Labour Markets.

**Keywords:** Wage Curve, Wage setting, Unemployment Rate.

# Salaires et taux de chômage local

## Résumé

L'objet de cet article est d'examiner comment la situation du marché du travail local influence la formation des salaires, en estimant une courbe de salaires («Wage Curve») à la suite des travaux de Blanchflower et Oswald. Tout d'abord nos estimations confirment l'existence d'une relation négative entre le salaire réel et le taux de chômage au niveau local, une fois prises en compte les caractéristiques individuelles des individus. Cette corrélation est observée pour toutes les catégories de salariés, pour différentes mesures du taux de chômage, ainsi que sur des données agrégées. L'élasticité des salaires au taux de chômage local fluctue entre 0,05 et 0,1 selon les spécifications retenues, et il apparaît que les effets du taux de chômage local sur les salaires ont un caractère essentiellement permanent et que les effets de court terme sont faibles. Deuxièmement nous procédons à des estimations en coupe transversale année par année et il apparaît que la réponse des salaires au taux de chômage a décrû au cours du temps. L'estimation de formes plus flexibles de la courbe de salaires suggère que la relation entre salaires et taux de chômage est plutôt convexe que linéaire. Enfin, le degré de persistance des salaires dans l'équation est relativement faible, ce qui est conforme à ce qu'obtiennent Blanchflower et Oswald (1994) sur des données d'autres pays. Cela signifierait que ce sont plutôt les niveaux des salaires et non leurs variations qui sont liées au taux de chômage.

**Thème:** Microéconomie du chômage, marchés du travail locaux.

**Mots-Clés:** Wage Curve, formation des salaires, taux de chômage régional.

**Classification JEL:** J31, R23
# I. Introduction

The purpose of this paper is to examine how the state of the local labour market influences pay. Unlike the Phillips curve, which postulates a negative relationship between the rate of change of wages and the contemporaneous level of unemployment, we will focus on the link between the *level* of wages at the microeconomic level and the level of local unemployment rate. Blanchflower and Oswald (1994) have done considerable empirical works related to this issue for a broad set of countries. The conclusion of their studies is that wages are lower in labour markets with higher unemployment. They argue that this negative relationship, the so-called « Wage Curve », is remarkably stable over time and countries: an increase of the unemployment rate of 1 percent would lead approximately to a decrease of individual wages of 0.1 percent, when controlling for personal characteristics such as age, gender, education, and regional and temporal fixed effects.

This kind of study hence uses microeconomic methods to try to shed light on macroeconomic issues such as the responsiveness of wages to changes in unemployment rate. This negative relationship between the level of wages and unemployment raises many questions. Is there a link between the wage curve and the Phillips curve? Is it a quasi labour supply function? Blanchflower and Oswald argue that the wage curve is on the contrary « something new », which has different possible theoretical interpretations, all related to the microeconomic foundations of wage setting. In fact regionally based implicit contracts models, efficiency wage models, or union bargaining models give all three a consistent interpretation of the negative elasticity of wages with respect to unemployment. Card (1995) and Blanchard and Katz (1997) have however shown that it is not obvious to reject either the Phillips Curve or the labour supply explanation in favour of one of the models listed above.

For France few studies have been done at the microeconomic level, essentially because panel data on wages and education are hardly available. Glaude and L'Héritier (1993) used a cross section data set and also found an elasticity of wages with respect to the local unemployment rate close to 0.1. In our study we use an original data set, obtained by the merging of two data sources, which allow us to construct a panel with wages and both employees and employers characteristics. The results we obtained using the same methodology as Blanchflower and Oswald (1994) are more contrasted than those obtained by Glaude and L'Héritier (1993). First, we also find a negative slope for the wage curve, and the elasticity is close to 0.1 when we run the estimation without taking account of regional fixed effects or for cross sectional estimates. However once we control for local labour markets effects the elasticity is much lower and sometimes non significant. This feature is true for all categories of workers and for different measures of the local unemployment rate. We can then suspect a problem of identification for the coefficient of the wage curve. Local unemployment rates in France have in fact changed over time in the same pattern as the national unemployment and it is not always possible to make the distinction between permanent regional effects and effects due to the average level of unemployment in one region. Hence the specification of the wage curve can lead in this case to potential biases in the estimates of the elasticity of wages with respect to unemployment. Making estimations with and without regional dummies should however provide a lower and an upper bound of the elasticity of wages with respect to unemployment.

Second we run estimations on cross section and find that the response of wages to unemployment has decreased over time: we can suspect the decrease in inflation rate to be linked to this trend. We try more flexible functional forms for the unemployment rate (we add in particular higher order polynomials of the local unemployment rate) and it appears that the negative relationship between wages and unemployment is convex rather than linear. The « Wage Curve » is decreasing until the unemployment rate reaches 10% and flat above this level. Third, wages are more responsive for men than for women. Fourth, when we aggregate data by regions, we obtain an estimated value of the wage elasticity with respect to unemployment close to 0.05.
Finally when we introduce lagged wages in our set of explanatory variables, we do not find much autoregression in our wage equation, like Blanchflower and Oswald. It would mean that the level of wages are related to unemployment, but not the variation in wages contrary to a Phillips Curve specification.
## II. The Data<fnref n="1" />

The data are derived from merging two different surveys by the Institut National de la Statistique et des Etudes Economiques. Our main data source is the « Déclarations annuelles des salaires » (DAS), a large collection of matched employer-employee information in the private sector. The data are based upon mandatory reports of the gross earnings of each employee subject to French payroll taxes. This initial DAS file does not contain any information on education. We used complementary information available for 10% of the DAS, from the EDP (Echantillon Démographique Permanent), to have the level of education for all individuals in our sample.

The initial DAS file applies to all « declared » employees and self-employed persons. The Division des Revenus at INSEE prepares an extract of the DAS, covering all individuals employed in French enterprises who were born in October of even-numbered years, civil servants excluded. Our extract runs from 1984 to 1995, with 1990 excluded. After merging with the EDP, our initial dataset contains 973 763 observations. Each observation corresponds to a unique individual-year-enterprise combination and includes an identifier (called ID) that corresponds to the employee, and an identifier (SIREN) that corresponds to the enterprise or the plant. We have information on the number of days worked during the calendar year, which enables us to recover both the total nominal net wages and a daily net wage for each individual. In addition, we have basic information on the individual's sex, date and place of birth, occupation, status of work (full-time or part-time) as well as the location and industry of the employing plant. The DAS file enables us to evaluate the job seniority of each individual. Individuals fall in fact into two categories with respect to the calculation of the employer specific experience: those for whom the first year of observation was 1976 and those who first appeared in the sample after 1976. For the first category the expected length of the in-progress employment spell is estimated by regression analysis using a supplementary survey, the 1978 Salary Structure Survey (Enquête sur la Structure des Salaires), where establishments provide information on seniority (in 1978), occupation, date of birth, industry and work location for a sub-sample of the employees.

Some workers in the sample have multiple jobs at the same time. Individuals with more than 3 different employers within a year or who have occupied more than one job at the same period of time are eliminated from the sample. For individuals with more than one employer within a year we keep each job-worker pair as an observation. The EDP contains additional information on education for people born in the beginning of October (between the first and the fourth). It includes information on the highest degree obtained. Theses responses were grouped into eight degree-level categories: No terminal Degree, Elementary School, Junior High School, High School, Vocational-Technical School (Basic), Vocational-Technical School (Advanced), Technical College and Undergraduate University and finally Graduate School and other Post-Secondary Education.

For each year, we eliminate observations for which the difference between the logarithm of the net wage and the median value of the log wage exceeds in absolute value three interquartile spread of the log wage in the sample. We only keep workers belonging to the non agricultural market sector and who are not self employed.

The local unemployment rate is given by the INSEE macroeconomic time series data (Banque de Données Macroéconomiques). We used in fact two different definitions of this regional unemployment rate, but we usually considered the sub-division in 95 « départements ». We run also some estimates with a rougher division, with only 22 « régions ».

<footnote n="1">¹ We would like to thank Francis Kramarz and Sébastien Roux for providing us with their original dataset. See Abowd *et alii* (1999) for a complete description of the dataset.</footnote>
### III. Theoretical framework

Different models of wage setting predict a negative effect of unemployment on the wage level. We will briefly describe the mechanism by which unemployment affects wages in a simple bargaining model and in an efficiency wage model.

#### III.1 The bargaining model

We consider a static model of union bargaining. For simplicity we assume firms have the « right-to-manage » and they bargain with unions only over the level of wages. There is imperfect competition on the market for goods. Unions are risk neutral and wish to maximise the expected utility of insiders. We assume lay-offs are by random assignment and concern a proportion $(1-\mu_i)$ of workers in firm (i). Thus the objective function of the union can be written:

$$U_i = \mu_i w_i + (1-\mu_i) A \quad (1)$$

where $w_i = W_i / P$ is the real wage in firm (i), (A) the expected income outside the firm and $(\mu_i)$ the probability of being employed in the firm next period ($\mu_i$ depends negatively on the wage).

The expected alternative wage (A) depends on the probability to be employed elsewhere in the local labour market which is equal to (1-u) where u is the level of the local unemployment rate. Thus this alternative revenue is $A = (1-u)\bar{w} + uz$ where $\bar{w}$ is the average wage in the local labour market and (z) the real unemployment benefit (z=$Z/P$).

Turning to the firm, its objective is to maximize its current profit $\Pi_i = R(L_i) - w_i L_i$, which is simply the difference between its revenue R and the total cost of labour $w_i L_i$, where L denotes the level of employment. Wages are negotiated within each firm between employers and unions and the outcome of the bargaining process is given by the maximisation of a Nash bargaining program. The fall-back position of unions is the alternative revenue A, whereas the fall-back utility of firm is simply $\bar{\Pi} = 0$ (there is no production when negotiations break down). The contribution of each agent to the Nash criterium is the difference between the objective and the fall-back utility. We assume the bargaining power of unions is constant and equal to $\gamma$. The wage in firm (i) is then set as:

$$w_i = \arg\max[\Pi_i - \bar{\Pi}]^{1-\gamma} [\mu_i(w_i)(w_i - A)]^{\gamma} \quad (2)$$

The first order condition gives:

$$\frac{w_i - A}{w_i} = \frac{1}{-\varepsilon_{\mu w} + \frac{1-\gamma w_i L_i}{\gamma \Pi_i}} \quad (3)$$

where $\varepsilon_{\mu w}$ is the elasticity of $\mu_i$ with respect to the wage.

Assume for simplicity that the production function is a Cobb-Douglas, with capital pre-determined: $Y = K^{1-\alpha}L^{\alpha}$. The demand addressed to the firm is a function of its price:

$$\frac{Y_i}{Y} = \left(\frac{P_i}{P}\right)^{-\eta}$$
The maximisation of profit after wages are set gives the following first order condition:

$$w_i = \alpha \kappa \frac{P_i Y_i}{L_i} \qquad (4)$$

where $κ=(η-1)/η$ is an indicator of product market competitiveness.

Thus equation (3) becomes:

$$\frac{w_i - A}{w_i} = \frac{1}{-\varepsilon_{\mu w} + \frac{1-\gamma \alpha \kappa}{\gamma (1-\alpha \kappa)}} = \chi \qquad (5)$$

As (A) is a decreasing function of the regional rate of unemployment (u) in equation (5), it follows that the wage in firm (i) is a decreasing function of the local unemployment rate.

At the symmetric equilibrium, where all firms in the same labour market pay the same wages, equation (5) can be written

$$u\left(1-\frac{z}{w}\right) = \chi \qquad (6)$$

### III.2 The efficiency wage model

Let us consider a model close to Shapiro and Stiglitz (1984) efficiency wage model. The work force is assumed constant in each local labour market and each worker supply one unit of work. We assume no mobility of the labour force between local labour markets. The utility function of workers depend positively on the net wage (w) offered by the firm and negatively on the effort (e) they contribute to production. For simplicity we assume workers have the choice between a high level of effort E and no effort at all (e=0). We choose a linear form of the utility function

$$U = w - e \qquad (7)$$

Firms decide unilaterally on the level of wages, but employees have the choice between shirking (e=0) and not shirking (e=E). If they shirk and give the low level of effort they can be detected with probability (d) and are then fired immediately. Independently of their behaviour we also assume that workers loose their job with an exogenous probability q. Thus the instantaneous levels of the expected utility when sharking $V_s$ and not sharking $V_e$ verify respectively the following equations

$$rV_s = w + (d+q)(V_u - V_s) \qquad (8)$$

and

$$rV_e = w - E + q(V_u - V_e) \qquad (9)$$

where r is the real interest rate and $V_u$ the expected utility of being unemployed.

If firms want to give their workers the incentive to provide the high level of effort E (for example because sharking workers have a null productivity), they have to adjust the level of the wage they offer. In fact, the higher the wages, the higher the cost of being fired. The incentive constraint (no-sharking condition) is simply
$$V_e = V_s \tag{10}$$

The value of being unemployed $V_u$ depends on the level of unemployment benefits (z) and the instantaneous probability of finding a job when unemployed (a) so that

$$rV_u = z + a(V_e - V_u) \tag{11}$$

As firms maximise their profit, the wage set in one firm is the lowest wage that satisfy the no shirking condition. After having eliminated the value function in equations (8), (9) and (11) we obtain

$$w = z + E + E \frac{a+q+r}{d} \tag{12}$$

At the equilibrium local unemployment rate we have the following relationship between employment flows $au = q(1-u)$. The wage can be written

$$w = z + E + \frac{E}{d} \left( r + \frac{q}{u} \right) \tag{13}$$

Once again wages in the local labour markets are negatively correlated with the level of unemployment.
## IV. Empirical results

The wage equation we estimate is an extension of a classical human capital equation à la Mincer, where wages essentially depend on the level of investment in human capital accumulated by workers (i.e. education, experience, seniority within firms). We add the local unemployment rate as an explanatory variable, according to the models described in the previous section, and consider the following equation

$$ \ln w_{i,r}^{t} = a + x_{i}^{t}b + \lambda \ln u_{r}^{t} + \delta_{t} + \delta_{r} + \delta_{s} + \varepsilon_{irt} \quad (14) $$

where $w_{i,r}^t$ is the wage rate for person i observed in labour market r in period t, $u_r^t$ the unemployment rate in labour market r, $x_i^t$ a set of measured characteristics of individual i (gender, occupation, age, tenure and education), $\delta_t$, $\delta_r$ and $\delta_s$ are respectively temporal, regional and sector based dummies (t=1,...,T s=1,...S and r=1,...R.). $\varepsilon_{irt}$ is an error term assumed uncorrelated through time.

The results for the whole population, for males and females are summarized in table 1.

<table><caption>Table 1: Wage curve estimates with regional dummies</caption><thead><tr><th rowspan="2"></th><th colspan="2">All</th><th colspan="2">Males</th><th colspan="2">Females</th></tr><tr><th>Full-Time</th><th>Full-Time and Part-Time</th><th>Full-Time</th><th>Full-Time and Part-Time</th><th>Full-Time</th><th>Full-Time and Part-Time</th></tr></thead><tbody><tr><td>Age</td><td>0.04<br>(0.0004)</td><td>0.04</td><td>0.04<br>(0.0004)</td><td>0.04<br>(0.0004)</td><td>0.03<br>(0.0005)</td><td>0.03<br>(0.0005)</td></tr><tr><td>Age*Age</td><td>-0.0004<br>(0.0000)</td><td>-0.0004</td><td>-0.0005<br>(0.0000)</td><td>-0.0005<br>(0.0000)</td><td>-0.0003<br>(0.0000)</td><td>-0.0003<br>(0.0000)</td></tr><tr><td>Tenure</td><td>0.016<br>(0.0002)</td><td>0.013<br>(0.0002)</td><td>0.013<br>(0.0003)</td><td>0.012<br>(0.00001)</td><td>0.013<br>(0.0004)</td><td>0.014<br>(0.0003)</td></tr><tr><td>Tenure*Tenure</td><td>-0.0004<br>(0.0000)</td><td>-0.0002<br>(0.0000)</td><td>-0.0002<br>(0.0000)</td><td>-0.0002<br>(0.0001)</td><td>-0.0003<br>(0.00001)</td><td>-0.0003<br>(0.00001)</td></tr><tr><td>Male</td><td>0.183<br>(0.001)</td><td>0.17<br>(0.01)</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>360 days of work</td><td>-0.039<br>(0.001)</td><td>-0.03<br>(0.001)</td><td>-0.026<br>(0.001)</td><td>-0.03<br>(0.001)</td><td>-0.044<br>(0.002)</td><td>-0.04<br>(0.001)</td></tr><tr><td>Part time</td><td>-</td><td>-0.46<br>(0.001)</td><td>-</td><td>-0.42<br>(0.002)</td><td>-</td><td>-0.47<br>(0.001)</td></tr><tr><td>Unemployment rate</td><td><strong>-0.02</strong><br>(0.008)</td><td><strong>-0.03</strong><br>(0.007)</td><td><strong>-0.04</strong><br>(0.008)</td><td><strong>-0.06</strong><br>(0.009)</td><td><strong>0.01</strong><br>(0.01)</td><td><strong>0.01</strong><br>(0.01)</td></tr><tr><td>R<sup>2</sup></td><td>0.43</td><td>0.52</td><td>0.54</td><td>0.41</td><td>0.42</td><td>0.46</td></tr><tr><td>Number of observations</td><td>637755</td><td>733812</td><td>409504</td><td>436088</td><td>228251</td><td>297724</td></tr></tbody></table>

Source: Panel DADS-EDP, 1984-1995.

Notes: standard errors are presented in parentheses.

Independent variables include 4 Occupational Status (manual workers, clerical workers, professionals and managers), 8 Education groups, and also a set of regional (95 departements), temporal and industry dummies (according to the NAP 40 nomenclature).

When we include a full set of dummies (temporal, sector-based dummies and dummies for the « départements »), the effect of unemployment on wages is weak, particularly for females. As we include labour market dummies we do not take into account permanent effect of the local unemployment rate, but the transitory response of wages to unemployment. Table 2 shows the results obtained when we exclude the dummies, in other words when we estimate the elasticity of wages with respect to the permanent components of local unemployment. In that case the elasticity is much higher, significant and close to 0.1. It would suggest that the long term elasticity is higher than the short term
elasticity. This is the opposite of what is found in the United States where average levels of unemployment across states are weakly positively correlated with average wages, whereas « transitory » wages and unemployment are strongly negatively correlated. It could be related with the much stronger mobility of workers in the US.

<table><caption>Table 2: Wage Curve estimates without regional dummies</caption><thead><tr><th rowspan="2">Variables</th><th colspan="2">All</th><th colspan="2">Males</th><th colspan="2">Females</th></tr><tr><th>Full-Time</th><th>Full-Time and Part-Time</th><th>Full-Time</th><th>Full-Time and Part-Time</th><th>Full-Time</th><th>Full-Time and Part-Time</th></tr></thead><tbody><tr><td>Age</td><td>0.04<br>(0.0004)</td><td>0.04<br>(0.0003)</td><td>0.04<br>(0.0004)</td><td>0.04<br>(0.0004)</td><td>0.03<br>(0.0005)</td><td>0.03<br>(0.0005)</td></tr><tr><td>Age*Age</td><td>-0.0004<br>(0.0000)</td><td>0.0004<br>(0.0000)</td><td>-0.0004<br>(0.0000)</td><td>-0.0005<br>(0.0000)</td><td>-0.0003<br>(0.0000)</td><td>-0.0003<br>(0.0000)</td></tr><tr><td>Tenure</td><td>0.016<br>(0.0003)</td><td>0.013<br>(0.0002)</td><td>0.013<br>(0.0003)</td><td>0.012<br>(0.00001)</td><td>0.012<br>(0.0004)</td><td>0.014<br>(0.0003)</td></tr><tr><td>Tenure*Tenure</td><td>-0.0004<br>(0.0000)</td><td>-0.0003<br>(0.0000)</td><td>-0.0003<br>(0.0000)</td><td>-0.0002<br>(0.0001)</td><td>-0.0003<br>(0.00001)</td><td>-0.0003<br>(0.00001)</td></tr><tr><td>Male</td><td>0.18<br>(0.001)</td><td>0.17<br>(0.001)</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>360 days of work</td><td>-0.04<br>(0.001)</td><td>-0.03<br>(0.001)</td><td>-0.03<br>(0.001)</td><td>-0.03<br>(0.001)</td><td>-0.05<br>(0.02)</td><td>-0.04<br>(0.001)</td></tr><tr><td>Part time</td><td>-</td><td>-0.46<br>(0.001)</td><td>-</td><td>-0.43<br>(0.002)</td><td>-</td><td>-0.48<br>(0.002)</td></tr><tr><td><strong>Unemployment rate</strong></td><td><strong>-0.10<br>(0.002)</strong></td><td><strong>-0.09<br>(0.002)</strong></td><td><strong>-0.11<br>(0.02)</strong></td><td><strong>-0.11<br>(0.02)</strong></td><td><strong>-0.08<br>(0.003)</strong></td><td><strong>-0.07<br>(0.03)</strong></td></tr><tr><td>R<sup>2</sup></td><td>0.42</td><td>0.51</td><td>0.52</td><td>0.50</td><td>0.40</td><td>0.45</td></tr><tr><td>N</td><td>637755</td><td>733812</td><td>409504</td><td>436088</td><td>228250</td><td>297724</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995

Notes: standard errors are presented in parentheses.

Independent variables include 4 Occupational Status (manual workers, clerical workers, professionals and managers), 8 Education groups, and also a set of temporal and industry dummies (according to the NAP 40 nomenclature).

We also perform estimates by skill groups (see table 3), after having dropped part-time workers from our sample. We do not have in fact any information on the working time, and the wage rate of part-time workers is therefore subject to severe measurement errors. Hereafter we run estimates only for full-time workers.

For each class of skills we find the same kind of results as previously: when we exclude the dummies for the « départements » the elasticity jumps to 0.1, whereas it is low and not significant when they are included.

<table><caption>Table 3: Estimates by skill level for full-time workers</caption><thead><tr><th></th><th>Manual Workers</th><th>Clerical</th><th>Supervisors and technicians</th><th>Managers</th></tr></thead><tbody><tr><td>With regional dummies</td><td>-0.01<br>(0.01)</td><td>-0.02<br>(0.01)</td><td>-0.03<br>(0.04)</td><td>-0.01<br>(0.02)</td></tr><tr><td>Without regional dummies</td><td>-0.098<br>(0.003)</td><td>-0.088<br>(0.004)</td><td>-0.098<br>(0.004)</td><td>-0.12<br>(0.007)</td></tr><tr><td>N</td><td>268293</td><td>162631</td><td>140379</td><td>56994</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995, Full-Time Workers.

Notes: standard errors are presented in parentheses.

Independent variables include Age, age squared, Tenure, Tenure squared, Gender, Length of pay, 4 Occupational Status (manual workers, clerical workers, professionals and managers), 8 Education groups, and also a set of regional (95 « départements »), temporal and industry dummies (according to the NAP 40 nomenclature).

This feature is quite puzzling, and is not observed for other countries (see Blanchflower and Oswald (1994)), especially the United States. We may wonder if this result depends on the size of the local area considered. We tried estimates for a larger definition, i.e. the « régional » level (see table 4), with the same kind of results.
<table><caption>Table 4: Estimates for alternative definitions of the local unemployment rate</caption><thead><tr><th rowspan="2"></th><th colspan="2">Departemental unemployment rate</th><th colspan="2">Regional Unemployment Rate</th></tr><tr><th>With Dummies<br>for local area</th><th>Without dummies</th><th>With Dummies<br>for local area</th><th>Without dummies</th></tr></thead><tbody><tr><th scope="row">ln(u)</th><td>-0.02<br>(0.008)</td><td>-0.10<br>(0.002)</td><td>-0.02<br>(0.009)</td><td>-0.17<br>(0.002)</td></tr><tr><th scope="row">R<sup>2</sup></th><td>0.42</td><td>0.43</td><td>0.51</td><td>0.50</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995, Full-Time Workers (N=637755)

Notes: Standard errors are presented in parentheses.

One explanation could be the weak variability of the unemployment series across time and regions. When we look carefully at local unemployment rates in France over this period, it appears in fact that they changed in the same pattern. There are in fact differences in the average level of unemployment, but unemployment rates exhibit roughly the same kind of temporal evolution. In other words it seems that the local unemployment rates are well explained by regional and temporal dummies. Hence the addition of temporal and regional dummies in the regressions could lead to a lack of identification of the role of unemployment. In the case of France it is therefore difficult to identify separately short term and long term effects of the local unemployment rate on wages.

The fact that we find a low value of the elasticity could also be due to non linearities in the response of wages to the unemployment rate. Blanchflower and Oswald found in fact a convex rather than linear form of the wage curve. The level of unemployment in France is quite high during our period of observation and the elasticity of wages could then be lower at high levels of unemployment. We add higher order polynomials of the local unemployment rate in our estimates (table 5). The coefficient of order 2 or 3 is positive and significant, so that the negative relationship between wages and unemployment is effectively convex.

<table><caption>Table 5: Wage curve with higher polynomial order.</caption><thead><tr><th></th><th>With<br>regional dummies</th><th>Without<br>regional dummies</th><th>With<br>regional dummies</th><th>Without<br>regional dummies</th></tr></thead><tbody><tr><th scope="row">lnu</th><td>-0.09<br>(0.019)</td><td>-0.17<br>(0.01)</td><td>-0.17<br>(0.04)</td><td>-0.24<br>(0.02)</td></tr><tr><th scope="row">(lnu)<sup>2</sup></th><td>-</td><td>-</td><td>0.03<br>(0.01)</td><td>0.03<br>(0.01)</td></tr><tr><th scope="row">(lnu)<sup>3</sup></th><td>0.005<br>(0.001)</td><td>0.0004<br>(0.0008)</td><td>-</td><td>-</td></tr><tr><th scope="row">R<sup>2</sup></th><td>0.51</td><td>0.50</td><td>0.51</td><td>0.49</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995, Full-Time Workers.

Notes: Standard errors are presented in parentheses.

This result is confirmed by the estimation of a very flexible functional form for the unemployment rate, where we regress wages on the same explanatory variables and on dummies for several intervals of unemployment rate (see Table 6).
<table><caption>Table 6: Wage Curve with a flexible functional form</caption><thead><tr><th></th><th>Without regional dummies</th><th>With regional dummies</th></tr></thead><tbody><tr><td>u&lt;6</td><td>0.095<br>(0.003)</td><td>0.021<br>(0.007)</td></tr><tr><td>6&lt;=u&lt;7%</td><td>0.084<br>(0.003)</td><td>0.016<br>(0.006)</td></tr><tr><td>7%&lt;=u&lt;8%</td><td>0.067<br>(0.002)</td><td>0.011<br>(0.005)</td></tr><tr><td>8%&lt;=u&lt;9%</td><td>0.051<br>(0.002)</td><td>0.008<br>(0.005)</td></tr><tr><td>9%&lt;=u&lt;10%</td><td>0.027<br>(0.002)</td><td>0.006<br>(0.004)</td></tr><tr><td>10%&lt;=u&lt;10,5%</td><td>0.045<br>(0.002)</td><td>0.002<br>(0.004)</td></tr><tr><td>10,5%&lt;=u&lt;11%</td><td>0.016<br>(0.002)</td><td>0.001<br>(0.004)</td></tr><tr><td>11%&lt;=u&lt;11,5%</td><td>-0.001<br>(0.002)</td><td>0.001<br>(0.004)</td></tr><tr><td>11,5%&lt;=u&lt;12%</td><td>0.03<br>(0.002)</td><td>0.005<br>(0.003)</td></tr><tr><td>12%&lt;=u&lt;13%</td><td>0.024<br>(0.002)</td><td>-0.002<br>(0.003)</td></tr><tr><td>13%&lt;=u&lt;14%</td><td>0.004<br>(0.002)</td><td>-0.001<br>(0.002)</td></tr><tr><td>u&gt;14%</td><td>Ref</td><td>Ref</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995 (standard errors in parentheses).

The shape of the curve obtained in table 6 is plotted on figure 2 of Appendix C. The reference is a level of the unemployment rate greater than 14%. So, only the differences between coefficients can be interpreted. Above a certain level, approximately 10%<fnref n="2" />, we have no significant effect of unemployment on wages. The wage curve seems then to be decreasing at the beginning and having a flat profile for high values of unemployment. It is therefore less surprising to find in our previous estimates a low value of the elasticity over the period 1984-1995 where the unemployment rate was rather high in many regions. These results hold when we include or exclude regional dummies. They are consistent with the findings of Blanchflower and Oswald and Glaude and L'Héritier for France, who even obtain a positive elasticity for high level of unemployment. It could mean that long term unemployed people, whose proportion is usually higher when the unemployment rate is high, are no more able to compete with insiders. The latter could therefore bargain on their wages without taking into account long term unemployed people, who are excluded from the labour market.

In order to study the stability of this elasticity and also to compare our results with those obtained by Glaude and L'Héritier on cross section data, we run estimations year by year, from 1984 to 1995 (Table 7). It is worth notice that the elasticity of wages with respect to unemployment is decreasing over the period, while the aggregate level of unemployment rate slightly increased from 9.8 in 1984 to 11.6 in 1995. This decreasing trend could hardly be related to non linearity in the response of wages to unemployment (see Figure 1), since the situation of the French labour market improved significantly between 1987 and 1990.

<footnote n="2">² For the flexible form as well as the quadratic or cubic estimates.</footnote>
<table><caption>Table 7: Estimation year by year for full-time workers</caption><thead><tr><th></th><th>In u</th><th>N</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>1984</td><td>-0.16<br>(0.006)</td><td>52400</td><td>0.51</td></tr><tr><td>1985</td><td>-0.16<br>(0.007)</td><td>54538</td><td>0.48</td></tr><tr><td>1986</td><td>-0.13<br>(0.007)</td><td>55283</td><td>0.48</td></tr><tr><td>1987</td><td>-0.12<br>(0.007)</td><td>55546</td><td>0.47</td></tr><tr><td>1988</td><td>-0.094<br>(0.006)</td><td>55745</td><td>0.50</td></tr><tr><td>1989</td><td>-0.095<br>(0.006)</td><td>57350</td><td>0.51</td></tr><tr><td>1991</td><td>-0.081<br>(0.005)</td><td>56961</td><td>0.51</td></tr><tr><td>1992</td><td>-0.084<br>(0.003)</td><td>58814</td><td>0.52</td></tr><tr><td>1993</td><td>-0.068<br>(0.007)</td><td>61173</td><td>0.47</td></tr><tr><td>1994</td><td>-0.06<br>(0.007)</td><td>59062</td><td>0.52</td></tr><tr><td>1995</td><td>-0.046<br>(0.006)</td><td>61425</td><td>0.54</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995, Full-Time Workers (standard errors in parentheses).

This feature could be linked to the evolution of inflation in France over the same period. The latter decreases from a fast two digit level to less than 2% in 1995 (see Figure 1). Downward rigidities in nominal wages could then explain the difficulty for real wages to decrease when inflation is low, even if the unemployment rate is high. Of course such an explanation should be confirmed by other evidence. A change in the mobility of workers could also affect the value of the elasticity, but when we look precisely at the evolution of unemployment across regions, it appears that differences are quite persistent. Hence an increase in the mobility would have lowered the dispersion of the unemployment rate, which is not what is observed.

<figure><img src="image_1.png" /><figcaption>Figure 2: Comparison of the wage elasticity to unemployment and inflation year by year.</figcaption></figure>

There is another issue concerning the specification of equation (14). In fact, if individuals of the same labour market share a common component of variance that is not attributable to their observed characteristics or to the local unemployment rate, the error component $\epsilon_{irt}$ will be positively correlated across people from the same labour market. As a result, standard errors are potentially downward biased (see for example Moulton, 1986, 1990). To control for this difficulty, a simple idea consists in running two regressions
(Card, 1995). First estimating equation (14) including unrestricted region cross year dummies and then, in a second stage, regressing these dummies on year and regional effects and the local unemployment rate (equation 12).

$$ \ln w_{i,r}^t = a + x_i^t b + \delta_s + \sum_{r,t} \alpha_r^t \cdot 1_{\text{Region}=r} \cdot 1_{\text{time}=t} + \varepsilon_{irt} \quad (15) $$

and

$$ \alpha_r^t = a + \lambda \ln u_r^t + \delta_t + \delta_r + \varepsilon_{rt} \quad (16) $$

Table 8 shows slightly different values of the elasticity from those obtained previously - more precisely we obtain results that are between those reported in tables 1 and 2³. In fact estimations are in this case less dependent on the inclusion of regional dummies. With or without regional dummies the elasticity of wages with respect to unemployment fluctuates around 0.05 for males, the same value as the one found for the US.

<table><caption>Table 8: Aggregate Wage Curve</caption><thead><tr><th rowspan="2"></th><th colspan="2">All</th><th colspan="2">Males</th><th colspan="2">Females</th></tr><tr><th>With regional dummies in the second stage</th><th>Without regional dummies in the second stage</th><th>With regional dummies in the second stage</th><th>Without regional dummies in the second stage</th><th>With regional dummies in the second stage</th><th>Without regional dummies in the second stage</th></tr></thead><tbody><tr><th>ln u<sub>rt</sub></th><td>-0.04<br>(0.016)</td><td>-0.05<br>(0.015)</td><td>-0.07<br>(0.019)</td><td>-0.05<br>(0.017)</td><td>0.03<br>(0.02)</td><td>-0.05<br>(0.014)</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995, Full-Time Workers (N=637755)

N.B. For these estimates we consider the 22 « régions » as our local areas.

Even if not always stable, all the estimates presented in this paper provide convincing evidence that there exists a negative relationship between wages and unemployment -at least in the long term. The elasticity fluctuates from 0.05 to 0.1 for males and seems to be lower for females. The natural question is then: what is exactly this relationship, is it really the new so-called « wage curve » or does it represent something else, like a quasi-labour supply function or a misspecified Phillips Curve? In order to give a beginning of answer the last step of this study consists in examining the degree of auto-correlation in such a wage equation.

We start by estimating equation (15) as previously and in the second stage we add the lag of the region\*time dummy variable, except for the year 1991, as expressed in equation (17).

$$ \alpha_r^t = \rho \alpha_r^{t-1} + \lambda \ln u_r^t + \delta_t + \delta_r + \varepsilon_{rt} \quad (17) $$

<footnote n="3">³ We used here the “régions” as the definition of our local area because of computation problems.</footnote>
<table><caption>Table 9: Auto-regressive form of the Wage Curve (with regional dummies)</caption><thead><tr><th rowspan="2"></th><th colspan="2">OLS</th><th colspan="2">IV</th></tr><tr><th>All</th><th>Males</th><th>All</th><th>Males</th></tr></thead><tbody><tr><th>ρ</th><td>0.19<br>(0.07)</td><td>0.07<br>(0.07)</td><td>0.35<br>(0.14)</td><td>0.08<br>(0.09)</td></tr><tr><th>In u</th><td>-0.04<br>(0.019)</td><td>-0.07<br>(0.02)</td><td>-0.05<br>(0.019)</td><td>-0.06<br>(0.02)</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995.

Results in table 9 proves that the current wage is not strongly correlated to the past wage, a result similar to Blanchflower and Oswald (1994) and very different from Blanchard and Katz (1997). When we run instrumental variables estimates –taking lagged average wages as instruments– it appears that the coefficient of the unemployment rate is very similar (-0.06 for males and -0.05 for the whole population). The value of the autoregressive coefficient seems to be slightly larger but is very imprecise (we can not reject the equality of the coefficients for both regressions). However when we consider male workers only, the autocorrelation is still very weak. At this stage of the analysis, the Phillips Curve specification seems to be rejected. Blanchard and Katz argued that the latter result could be linked to the use of annual data, and may be very different when weekly or hourly wages are used, since measurement errors in the wage rate lead to a downward bias of the coefficient of the lagged log wage. However the DADS source gives declarative wage from the employers and are therefore very reliable. Second we run estimations on the average wage, for which measurement errors are probably negligible. And finally the instrumentation procedure gives the same kind of results than those with OLS estimations.
Conclusion

When we control for observable characteristics of workers such as sex, education level, tenure, age, it appears empirically that the level of wages and the local unemployment rate are negatively correlated. This negative relationship is stronger when we do not include regional dummies in the estimation of our wage equations. It would mean that permanent differences in unemployment rate would play a larger role on wage setting, with an elasticity of around 0.1, than transitory variation of the local unemployment rate (for which we obtain a weak and non significant negative effect). Second it seems that wages of men react more to the state of the labour market than women. Third both results hold whatever the definition of the region we use, either the « départements », or the « régions ».

Like Blanchflower and Oswald, we observe that the negative relationship between wages and unemployment is rather convex than linear. When we run estimations year by year it appears that the elasticity of wages with respect to unemployment has decreased over the period 1984-1995. The decrease of the rate of inflation over the same period would hence indicate that downward nominal rigidities might have limited the adjustment of real wage over the last decade.

Finally, we try to evaluate the degree of autocorrelation in the wage equation in order to check whether the « wage curve » is a misspecified Phillips Curve or not. We find only little auto-correlation in the wage equation, like Blanchflower and Oswald. This last result could however be linked to the use of annual data, and it would be interesting to compare with the results we could obtain from the Labour Survey.
References

Abowd J., Kramarz F., and Margolis D. (1999), « High Wage Workers and High Wage Firms », Econometrica, Vol. 67 N°2, pp.251-333.

Blanchard O.J., and Katz L. F. (1997), « What we know and do not know about the natural rate of unemployment », Journal of Economic Perpective, Vol.11, N°1, pp.51-72.

Blanchflower D. and Oswald A. (1994), « The Wage Curve », MIT Press.

Blanchflower and Oswald (1995), « An Introduction to the Wage Curve », Journal of Economic Perspectives, Vol.9 N°3, pp.153-167.

Card D. (1995) The Wage Curve: A Review », Journal of Economic Literature, Vol. XXXIII, pp.785-799.

Glaude and L'Héritier (1993), « Salaire et taux de chômage local, salaires et carrière incomplète, salaire et niveau de vie, trois études statistiques sur données individuelles », mimeo.

Harris J., and Todaro M.P., (1970), « Migration, Unemployment, and Development: A two-sector Analysis », American Economic Review, vol. 60(1) pp.126-142.

Layard Nickell and Jackman (1991), « Unemployment », Oxford University Press.

Moulton Brent R. (1990) « Random Group Effects and the Precision of Regression Estimates », Journal of Econometrics, n° 32 (3), pp. 385-97

Moulton Brent R. (1990), « An illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units », Review of Economics and Statistics, Vol 72 (2), pp. 334-338

Phelps E. (1992) « A Review of Unemployment », Journal of Economic Literature, September, Vol. 30(2), pp.1476-1490.

Phillips A. (1958) « The relation between Unemployment and the rate of Change of Money Wage Rates in the United Kingdom », Economica, Vol. 25 (100) pp.283-299.

Shapiro C., Stiglitz J. E., (1984) « Equilibrium Unemployment as a Worker Discipline Device », American Economic Review, Vol. 74(3), pp.433-444.
# Appendix A

## Summary Statistics

<table><thead><tr><th></th><th>Average<br>logarithm of net<br>Annual Wage*</th><th>Average<br>logarithm of net<br>Wage<br>for Full-Time<br>workers</th><th>Average<br>unemployment<br>rate</th><th>Percentage of<br>Male</th><th>Number of<br>observations</th></tr></thead><tbody><tr><td>1984</td><td>10.56</td><td>10.76</td><td>9.9</td><td>59.3</td><td>73473</td></tr><tr><td>1985</td><td>10.56</td><td>10.77</td><td>10.2</td><td>58.9</td><td>74708</td></tr><tr><td>1986</td><td>10.57</td><td>10.78</td><td>10.4</td><td>58.8</td><td>76199</td></tr><tr><td>1987</td><td>10.56</td><td>10.77</td><td>10.5</td><td>58.5</td><td>77058</td></tr><tr><td>1988</td><td>10.52</td><td>10.75</td><td>10.0</td><td>57.3</td><td>86179</td></tr><tr><td>1989</td><td>10.51</td><td>10.76</td><td>9.3</td><td>56.9</td><td>90694</td></tr><tr><td>1991</td><td>10.51</td><td>10.79</td><td>9.6</td><td>56.2</td><td>94868</td></tr><tr><td>1992</td><td>10.50</td><td>10.78</td><td>10.5</td><td>55.7</td><td>97509</td></tr><tr><td>1993</td><td>10.47</td><td>10.75</td><td>11.9</td><td>55.0</td><td>98200</td></tr><tr><td>1994</td><td>10.41</td><td>10.83</td><td>12.2</td><td>54.5</td><td>100318</td></tr><tr><td>1995</td><td>10.41</td><td>10.82</td><td>11.6</td><td>54.6</td><td>104557</td></tr></tbody></table>

Source: Panel DADS-EDP 1984-1995.

* Wages are expressed at constant price of year 1980.
Appendix B1

Unemployment rate by area

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

Lecture: The map gives the average unemployment rate by "départements" over the period 1984-1995.
Appendix B2

Average wage component by “départements” for males

<figure><img src="image_3.png" /></figure>

Lecture: The map represents the average value of $\alpha_r^t$ for males over the period 1984-1995 where $\alpha_r^t$ is given by the following regression (equation (15) in the text)

$$ \ln w_{i,r}^t = a + x_i^t b + \delta_s + \sum_{r,t} \alpha_r^t \cdot 1_{Region=r} 1_{time=t} + \varepsilon_{irt} $$
Appendix C

<figure><img src="image_4.png" /><figcaption>Figure 2: Flexible functional form of the Wage Curve
(with its polynomial tendency curve).</figcaption></figure>