Nicolas Delaunay

Nathalie Deltimple

Eric Kerhervé

Didier Belot

A RF Transmitter Linearized Using Cartesian Feedback in CMOS 65nm for UMTS Standard

Keywords: Linearization techniques, Power Amplifier, CMOS technology, Wireless communication

A fully CMOS transmitter including a power amplifier (PA) using a Cartesian Feedback (CFB) technique is presented. This system aims at improving the linearity of the transmitter, designed in 65nm CMOS technology from STMicroelectronics, essentially the power amplifier linearity. This transmitter delivers a maximum output power of 23dBm. Thanks to this linearization technique, the ACPR has been improved by 22dB at 5MHz from the carrier.

I. INTRODUCTION

Nowadays, abundant research focuses on the improvement of power amplifier's linearity performances [START_REF] Katz | Sspa linearization[END_REF]; [START_REF] Tee | A cartesian-feedback linearized cmos rf transmitter for edge modulation[END_REF][START_REF] Dawson | Feedback linearization of rf power amplifier[END_REF][START_REF] Abed | Linearization techniques in power amplifiers for 1.9 ghz wireless transmitters[END_REF][START_REF] Kim | A new wideband adaptive digital predistortion technique employing feedback linearization[END_REF][START_REF] Chung | Open-loop digital predistortion using cartesian feedback for adaptive rf power amplifier linearization[END_REF]. Linearization techniques remain an important and hot domain of research with UMTS (Universal Mobile Telecommunications System) standards [START_REF]Utra repeater radio transmission and reception[END_REF] and the future 4G standards called LTE (Long Term Evolution). These standards have been created for high data rate wireless communications and use a non-constant envelope modulation like HSPK (Hybrid Phase Shift Keying) for UMTS. As a consequence, both linearity and efficiency in the design of a cellular PA are becoming harder to maintain. A useful parameter to observe the complexity of a modulation is the PAPR (Power Average to Peak Ratio) -also called PAR (Peak Average Ratio). The PAPR of GSM, UMTS, and LTE are 3dB, 3.5-7dB, and 5-8.5dB respectively. Hence, designing a linear and efficient PA is a difficult task regarding to the PAPR value.

In the past years, a lot of solutions have been proposed to improve PA performances. These solutions can be divided into two purposes: the first ones, such as Envelope Elimination and Restoration (EER) [START_REF] Kahn | Single-sideband transmission by envelope elimination and restoration[END_REF], Envelope Tracking (ET) [START_REF] Kimball | High-efficiency envelopetracking w-cdma base-station amplifier using gan hfets[END_REF], improve the PA efficiency; while the others improves its linearity: Indeed, the power amplifier is one of the most critical component and a major source of distortion for a transmitter. These techniques mainly work on the signal and not on the power amplifier, as pre-distortion (analog, digital or both) [START_REF] Tee | A cartesian-feedback linearized cmos rf transmitter for edge modulation[END_REF], feedforward, Cartesian Feedback [START_REF] Dawson | Feedback linearization of rf power amplifier[END_REF] etc. Despite the excellent results of these techniques on the linearity, studies to integrate such methods on Silicon remain very recent [START_REF] Abed | Linearization techniques in power amplifiers for 1.9 ghz wireless transmitters[END_REF].

We propose to apply Cartesian feedback technique on an integrated transmitter in a 65nm CMOS technology from STMicroelectronics. This linearization technique has already been realized with discrete components or III-V technology for base-station [START_REF] Kim | A new wideband adaptive digital predistortion technique employing feedback linearization[END_REF], [START_REF] Chung | Open-loop digital predistortion using cartesian feedback for adaptive rf power amplifier linearization[END_REF], but for the best of our knowledge, a CMOS transmitter using CFB has not been reported in the literature for mobile handset. Thus, main challenges are to realize a single chip on 65nm CMOS technology and to increase performances of the transmitter for UMTS standard communication.

Section 2 describes the Cartesian Feedback architecture with its advantages and precautions to take into account. Each building block has been designed in a CMOS 65nm technology and measurement results are given. Section 3 presents the system level behavior of the overall architecture.

II. TRANSMITTER ARCHITECTURE

The trend of these last years is to reduce the transmitter area and so its cost. To achieve this goal, CMOS integrated transmitter with thick gate transistors are developed, making harder the design of power amplifiers with a high output power. This has a direct consequence on the linearity of a transmitter, which is actually a major preoccupation for the research domain. This non-linearity affects transmission results and adds distortion on the adjacent channels. With new wireless communication standards, the power amplifier has to deliver always more output power with a widen bandwidth. For example, the bandwidth of the channel for GSM, UMTS and LTE communications is 200 KHz, 5 MHz, and 20 MHz respectively. The Fig. 1 shows the spectral mask defined by the standards UMTS and a signal WCDMA associated.

Solutions must be developped to match this mask and fight against the difficulty of designing both linear and efficient transmitters. The proposed solution is to integrate a Cartesian Feedback loop on Silicon 65nm CMOS.

A. Improvement of the Linearity using a Cartesian Feedback Loop A RF transmitter is typically composed by several components such as filters, IQ modulators, mixers, local oscillators, power amplifier and an antenna. As we can see on the Fig. 2, analog baseband signals fed the IQ modulator, and then up-converted to a RF frequency by mixers associated with a local oscillator. Finally, the resulting RF signal is strengthened by the power amplifier before driving the antenna. In a context of non-constant envelope modulation as HPSK for UMTS, precautions to design and not degrade the signal have to be taken in account. Indeed when the transmitter works close to the compression point (non linear area), distortions appear on the signal and can be spectrally observed on adjacent channels. It is therefore advisable to use components most linear as possible to avoid these distortions, and consequently a degradation of the transmitted information. Those are called Adjacent Channel Power Ratio (ACPR, also called, ACLR -Adjacent Channel Leakage Ratio). As it is shown on Fig. 1, ACPR enables to characterize distortions of the transmitter by determining the ratio between the power level of the main and the adjacent channel.

In order to decrease these phenomena we adopt the Cartesian Feedback loop which is a linearization techniques applied to correct the linearity of a transmitter. This choice has important advantages. The most important is the portability; indeed the Cartesian feedback corrects nonlinearities of any type of power amplifier. This system, thantks to the feedback path, works directly on the signal, according to the behavioural changes of the power amplifier (bias, temperature, aging etc.), and the changes related to the PA upstream components of the direct path.

Another major advantage is the possibility to implement the system on a single chip. In order to make the integration easier, and thus reduce the cost of production, some parts of the system can be implemented on Fig. 3.

Architecture of a Cartesian Feedback linearization technique the digital domain (e.g phase correction). Last but not least, the Cartesian feedback is able to correct not only the amplitude distortions (AM/AM) but also the phase distortions (AM/PM). The main drawback is the stability of the system, a fact that demands the achievement of a carefully study to avoid this problem.

The architecture of the Cartesian feedback is depicted in Figure 3. Like the Zero-IF architecture, the direct path has the same functioning: to send a signal through the antenna. Therefore a feedback path has been added to correct the information from the output of the PA. In fact, this output signal is attenuated and down-converted to baseband domain. The intermodulation products, related to IQ demodulation, are thereupon removed by a low pass filter.

An operation of phase adjustment is applied to I F B and Q F B baseband signals. The aim is to eliminate any rotation of the IQ constellation caused by the nonlinearities from the direct path of the transmitter. Feedback signals are then subtracted from the original signal in order to obtain I Error and Q Error . These signals represent the nonlinearities of the forward path of the system. This means that I Error and Q Error are predistorded signals in amplitude and phase. They will be compensated through distortions added by the direct path, and more accurately, the power amplifier. All delays are corrected by the phase alignment and subtraction opertations. The linearity of the entire system will be improved and transmitted datas as well.

B. Building Blocks Description

The linearized transmitter depicted in Fig. 3 is made up of both analog and digital building blocks. Indeed, as decreasing the cost of production remains an important objective for industry, operations of subtraction and phase alignment were moved in the digital domain. All of the others components (converters, mixers, attenuator, filters, and power amplifier) have been designed in 65nm CMOS technology from STMicroelectronics. All the active circuits have been measured and the results are given in Tab. I.

The power amplifier is the main contributor of nonlinearities. Its design is based on Stacked Folded Differential Structure (SFDS) [START_REF] Luque | A 65 nm cmos -stacked folded fully differential (sffd) pa structure for w-cdma application[END_REF], which is inspired by the push-pull structure. At 1.95 GHz, the power gain of the PA is equal to 15dB. It offers a saturation power of 23dBm with an output compression point (OCP1) of 21dBm. These large signal characteristics fulfil the W-CDMA standard (21dBm at 1.95GHz -Class 4) in terms of output power and operating frequency. General information of this last is resumed on the Tab. I, as other components. Thanks to this table, a 3mm² analog core area can be targeted, consuming 1.51W with 80% coming from the PA.

III. SYSTEM LEVEL BEHAVIOR All building blocks making the linearized transmitter have been designed in CMOS 65nm technology with cadence spectre RF framework and have been characterized stand-alone. Now, we are able to realize system level simulations in order to validate the overall architecture. The long time expended and the convergence problem made simulations on the transistor level harder, whyfor ADS Software has been used. A. Output Spectrum

The complete system exhibits a gain of 45dB and -20dB, respectively, for the forward and the feedback path. Fig. 4 depicts the output spectrum of the PA with and without Cartesian Feedback technique for a same output power. The PA output clearly shows a decrease of the distortions on the adjacent channel due to the forward path. In fact comparing with the mask presented in section II, the output spectrum for a Zero-IF architecture is out of specifications defined for UMTS communications, in opposition with the output spectrum of the Cartesian Feedback.

B. ACPR

The ACPR at 5MHz from the carrier for UMTS standards must to be less than -33dBc, as explained in Section II. To illustrate it, the Fig. 5 shows the evolution of the ACPR according to the output power of the power amplifier. In open loop mode only the behavior of the forward path is observed, while in closed loop mode linearity correction is applied. As we can notice on this figure, with the open loop for an output power of 12dBm, the ACPR does not respect the UMTS specifications. On the other hand, for the same output power using the Cartesian Feedback, we notice that ACPR respects the specifications and is improved by 22dB at 5MHz from the carrier.

C. Constellations

Another interesting result is the constellation before and after the PA, as shown in Fig. 6. We observe that the EVM (Error Vector Magnitude) at the output of the power amplifier is better than the other one at the input. This confirms our hypothesis explained in Section II-A about the predistortion of the I Error and Q Error baseband signals.

D. Comparison with literature

To finish, the Table II presents a comparison of our system with a recent state of the art. As we can see, references [START_REF] Kim | A new wideband adaptive digital predistortion technique employing feedback linearization[END_REF] and [START_REF] Chung | Open-loop digital predistortion using cartesian feedback for adaptive rf power amplifier linearization[END_REF] are also using Cartesian feedback correction, whereas the last one [START_REF] Chan | New linearization method using interstage second harmonic enhancement[END_REF] uses another technique of correction called Harmonic Injection. For a same PA class operation and a same standard, the improvement of our system is 7dB better than reference [START_REF] Kim | A new wideband adaptive digital predistortion technique employing feedback linearization[END_REF]. Moreover, this work is a single circuit that offers a compact and cheaper system than the others.

IV. CONCLUSION

This paper presents the linearization of a RF transmitter by Cartesian feedback technique. It is important to note that all active components of this transmitter have been designed and realized in 65nm CMOS technology from STMicroelectronics. Measurement results gave a maximum output power of 23dBm at 1.95GHz. Their integration on a single chip with this technology remains the main challenge, and we can estimate the size of the core area about 3mm² for a power consumption of 1.5W. The whole single chip transmitter is in foundry. Once each building characterized block , system level simulations have been done to observe the ACPR. The ACPR improvement is equal to 22dB at 5MHz from the carrier. System level simulation results demonstrate the feasibility of designing a complete transceiver with CFB technique in a low cost CMOS technology.

With the emergence of multi-standard communication systems, future work is to adapt our system to an all CMOS multi-mode linearized transmitter.

Fig. 1 .

 1 Fig. 1. Mask of UMTS standard

Fig. 2 .

 2 Fig. 2. Zero-IF Architecture

Fig. 4 .

 4 Fig. 4. Output Spectrum with and without CFB

  22dB

Fig. 5 .

 5 Fig. 5. ACPR at 5 MHz offset for W-CDMA signal in open and closed loop

Fig. 6 .

 6 Fig. 6. Constellations for the input and output signal from the PA


Chi-Chur Chao

Bharat R Hazari

Jean-Pierre Laffargue
email: jean-pierre.laffargue@wanadoo.fr.

A simple theory of the optimal number of immigrants

Keywords: F22, H41, O41 congestion, immigration, public good, segregation Congestion, Immigration, Public good, Segregation JEL Classification: F22, H41, O41

This paper develops a simple model to explain two stylised facts about immigration. First, some countries have a low ratio of migrants in their population, while other wealthy countries have a high number of migrants. In fact such migrants are of the same order of magnitude as their domestic workforce. Secondly, migrants are often segregated in jobs. The domestic residents do not wish to be employed in these jobs due to their unattractive working conditions and payments.

The model assumes that domestic residents are all identical in terms of their skills and wealth and furthermore that native and foreign workers have the same skills. However, foreign migrants cannot be excluded from the use of public services, the quality of which decreases due to congestion created or enhanced by migrants. On the basis of our model we show that the stylised facts are consistent with an optimal immigration policy, defined by domestic residents who have neither altruistic feelings nor ethnic prejudice toward foreign migrants.

Introduction

Immigration is a very important issue in many countries, both developed and developing. Legislation to grant amnesty to migrants was submitted and failed before the US Congress. Fences have also been erected in the USA to stop the flow of migrants from Mexico. Even a country like India with an enormously large population and high unemployment receives a large number of illegal migrants from neighbouring countries. Given the importance of migration in many countries, it is important to ask: what are the effects of foreign migration on the economy of the host country, and in particular the effects on the welfare of the domestic residents. Several economists dealing with this question have focused on the income distribution effects of migration. For instance, do wages decrease, or do the cost and the sustainability of the income transfer policy of the government worsen? One reason for discussing this aspect of the migration issue is that the anti-immigration feelings are especially strong in specific social groups 1 . Find more recent illustrative facts.

The motivation of this paper comes from the following stylised facts. First, some countries have a moderate ratio of migrants in the population. OECD countries are a typical example of this moderate percentage, about 13% of the US population is foreign born. Second, other countries have a very large body of migrants. The International Migration Outlook of the OECD (2006) notes that most foreign migrants in OECD countries are allowed to settle in OECD countries for non-economic reasons: asylum seekers, family reunification, the regularisation of illegal migrants and so on. People who migrate for economic reasons, in general are hired in specific jobs, often but not always with low or no skills, which domestic workers do not want to take because of their unattractive working conditions 1 Benhabib(1996) examines how immigration policies would be determined under majority voting when native agents differ in their wealth holding and vote to maximise their income. [START_REF] Razin | Tax burden and migration: A political economy theory and evidence[END_REF] complement this approach and investigate the link between migration and tax transfer policy when domestic residents differ in ability and hold different skills. These papers are based on one-sector models. Other papers use a Heckscher-Ohlin framework, for instance [START_REF] Wellisch | Why do rich countries prefer trade over free immigration? The role of the modern Welfare State[END_REF]. [START_REF] Scheve | Labor market competition and individual preferences over immigration policy[END_REF] analyse opinion surveys and show that people with less skill (who directly compete with foreign migrants) are more hostile to immigration. [START_REF] Facchini | Individual attitudes toward immigrants: Welfare-State determinants across countries[END_REF] confirm this result, and complete it by showing that people with high income (who pay the taxes, which finance the welfare transfers to migrants) are also more hostile to immigration. and payments. The number of migrants who are given these working permits is low, especially in Western Europe. However, a few countries admit a much higher number of migrants. In its report for 2005, the International Organisation for Migration writes: "It is estimated that by 2000 international migrants constituted 38 per cent of the population in Bahrain, 49 per cent in Kuwait, 26 per cent in Oman, 70 per cent in Qatar, 24 per cent in Saudi Arabia and 68 per cent in the United Arab Emirates."

Other evaluations given in the report are higher, and the share of migrants in labour force is still higher: it is equal to 55.8 per cent in Saudi Arabia and represents 70 per cent in all Gulf Cooperation Council (GCC) countries.

The model we suggest has its roots in the literature on migration theory starting with [START_REF] Berry | Some welfare aspects of international migration[END_REF]. They proved the important result that the income of domestic residents is an increasing and unbounded function of the number of migrants. However, the marginal effect of immigration on this income is zero when in the initial equilibrium the number of migrants is zero. [START_REF] Borjas | The Economic Analysis of Immigration[END_REF] confirmed that this result rema ins approximately valid when the number of migrants is of the order of magnitude observed in OECD countries. He concludes that the presence of migrants, who represented about 10 per cent of the labour force of the U.S. economy, increased at most by 0.4 per cent the income of American citizens 2 . This result is the second reason for the lack of interest of economists for the effect of immigration on the income of the natives. This paper will suggest an explanation of the stylised facts and provides reasons as to why, in spite of the theoretical result that the income of domestic residents is an increasing and unbounded function of the number of migrants, migrants are unwelcome in OECD countries, the exception being those who are segregated in unattractive and poorly paid jobs. It will also explain why in other wealthy countries the number of legal migrants is very high. The analysis and the explanation given in this paper eliminate all considerations related to income distribution: domestic residents are identical and there is no place for income redistribution policy. We will also assume that there is no difference in skills between domestic and foreign workers. Thus, our paper differs from most previous approaches. We will use a simple neo-classical model and compute the optimal number of migrants. Our domestic residents are selfish and bear no altruistic feeling for migrant workers. They also are not prejudiced against them. Thus, our analysis excludes motivations based on a taste for discrimination or racism3 .

The optimal number of migrants in the model is not infinite because domestic residents consume a public service, which is a complement of a private good in consumption. Migrants cannot be excluded from the use of the public service. Then, for a given level of this service, the benefits obtained by its users decrease with the number of migrants because its quality decreases due to congestion. The supply of the public service can be increased at a cost. However, as the output of the public service also depends on fixed inputs such as land and space, its marginal cost is increasing. In this scenario although migrants make a positive contribution to national income, they will reduce the welfare of the domestic residents when too many of these migrants are present in the economy.

Public service has a very wide meaning in this paper. It includes health and education. As the costs of providing them are approximately constant, migrants do not create congestion if they pay a fair amount of taxes. However, the supply of other services can be raised only at increasing cost, because their input includes land, air, water and other natural resources with inelastic supply. OECD countries, with no lack of space such as Australia and Canada, are also those with the highest proportion of foreign born in total population. In this paper, the only externalities created by migrants work through the congestion effect. We will not consider other externalities, positive or negative, such as the taste for for cultural diversity, or the desire to keep the society homogenous, of domestic residents4 .

We begin by assuming that the domestic residents and migrants are perfect substitutes. When the number of migrants in the country is zero, we know that a small inflow of migrants has no effect on the income of domestic residents. However, the quality of the public service declines, and the welfare of domestic residents decreases. As the number of immigrants approaches infinity, the quality of the public service converges to zero, and the welfare of domestic residents converges to its minimum value.

The first result of the paper is that if the preference of domestic residents for the consumption of the public service relative to the consumption of the private good is low enough, the welfare of domestic residents will start by decreasing with the number of migrants, then increases, reaches a maximum and finally decreases. A corollary of this result is that when the preference for the public service decreases, the optimum number of migrants will start from zero and remain at this value. Then it will jump to a positive value, and will increase indefinitely. However, the jump is very large, which means that the optimum number of migrants is either zero or very large. Moreover, we obtain a positive optimal number of migrants only for very low preferences for the public service, and so for an unreasonable small share of the population working in the government sector. Thus, under the assumption that migrants and domestic workers are perfect substitute, the model cannot explain the immigration policies of OECD and even GCC countries.

If the Government can segregate migrants in specific jobs, where jobs are imperfect substitute for each other (but, which requires the same skill), then results tur n out to be different. A typical example of this is the refusal of medical practitioners to practice in rural areas in Australia. Immigrant doctors are happy to go to rural areas. Their visas are issued on the understanding that they practice for a few years in the rural areas. Then, migrants displace the domestic residents who held these jobs, and considerably expand the number of these jobs. Thus, the wages they pay become much lower. Under these circumstances, the optimal number of migrants will take reasonably small positive values, provided the size of the sectors of the labour market where they are allowed to work is small. The higher proportion of immigrants in the population of GCC countries can be explained by the access of these immigrants to a wider range of jobs (so by less segregation) than in industrialised countries.

The paper assumes that for the government, domestic residents and immigrants are different and the last group is used only for extracting rent. Migrants do not invest in their host country. So, either they will consume their whole income or they will remit part of it to their country of origin. However, many migrants become permanent residents and later citizens. They may have planned that when they decided to immigrate, or they could have made the decision of permanently settling in the country several years after their arrival. The assumptions of this paper do not apply to these cases. The definition of an optimal policy of immigration in this situation is also very different from the definition we give in this paper. It is an open and important question as to what stage of his "integration" a migrant would be considered as a fellow domestic resident by the nationals of the host country.

The model used in this paper is presented in section 1, under the assumption of perfect substitutability between the two kinds of labour. The effects of immigration on the welfare of domestic residents are investigated in section 2 at the theoretical level and in section 3 by running a series of simulations.

Section 4 extends the previous results to the case of the imperfect substitutability of labour. The last section concludes.

The model

The model assumes an economy, which produces a private consumption good and a public good. The production technology of each good uses labour and a specific factor, which is supplied in a fixed quantity and normalised to 1. Domestic and foreign workers are perfect substitutes. The economy is closed to the rest of the world, except for international immigration and the remittance that immigrants may send home. The current output of private and public goods are respectively given by

β Y AL Y = , with 1 0 < < β and 0 > A (1) γ G BL G = , with 1 0 < < γ and 0 > B (2)
where Y L and G L are the labour inputs used by each sector. There is no technical progress.

The quantity of domestic labour is fixed and normalised to 1. M denotes the number of migrants working in the country. The equilibrium of the labour market gives

M L L G Y + = + 1 (3)
The private good is produced by the private sector, which sets the wage rate w to the marginal productivity of labour. We have

β β - = 1 / Y L A w (4)
The public good is produced by the government, which owns (or can use freely) the specific factor and pays his workers the same wage w as the private sector. National workers and migrants are paid the same wage. Setting lower wages for migrants would require the introduction of mechanisms that justify this difference and would bring little insight to the problems we are investigating.

The public good is made available freely to all by the government and migrants cannot be excluded from its consumption. This non exclusion has humanitarian and other reasons. The production cost of the public good is equal to the wages paid by the government, G wL . This cost is financed by a lump sum tax, which is equally shared between domestic residents and migrants.

The specific factor used by the private sector is entirely owned by domestic residents. Their net income is equal to the rent they earn on this factor plus their wages, minus their taxes,

( ) ( ) M wL w wL Y G Y + - + - 1 /
. This income is entirely spent on their consumption of private good

C . We have Y wL M M Y C + - = 1 (5)
The net income of migrants is equal to their wages minus their taxes

Y G wL M M wL M M wM + = + - 1 1 .
It is spent on the purchase of private good, which they consume or transfer to their families at home5 .

We assume that the public good is subject to congestion, and that its quantity available to an individual declines as the number of users increases. The simplest way to model the congestion effect is to assume that the public good creates a public service S , equally enjoyed by each individual, which is equal to the total quantity of the public good divided by a function of the number of users:

( ) ϕ M G + 1 / , with 0 > ϕ
. So public services are rival and non-excludable.

We can deduce from the previous equations the following expression of the supply set of the economy

( ) ( ) [ ] ( ) ( ) ( ) 1 / 1 / 1 1 1 / 1 / ) ( / 1 / 1 / ) 1 ( = + + - + + - - γ γ γ ϕ β β β β β B S M A C M M (6)
This expression shows how the trade off between the consumption of private good and of public service by the domestic residents, C and S , depends on the number of migrants M . Domestic residents can obtain a zero amount of public service and a consumption of private good

[ ] ( ) β β - + - + = 1 1 / ) 1 ( 1 M M A C
. This consumption increases with the number of migrants. On the other hand domestic residents can obtain a zero amount of private consumption good and a consumption of public service (

)

) ( 1 γ ϕ - - + = M B S
. This consumption decreases with the number of migrants if the congestion effect is high enough: γ ϕ > . Finally, when we move along the supply set,

from 0 = C to [ ] ( ) β β - + - + = 1 1 / ) 1 ( 1 M M A C
, the slope of the tangent to this set decreases from 0 to minus infinity. Figure 1 represents the supply set of the economy for two values of the number of migrants. This figure was computed for the calibrated version of the model presented in section 3 (and under the assumption γ ϕ > ) . We can see how an increase in the number of immigrants expands the supply set in the direction of the consumption of private good and contracts it in the direction of the consumption of public service.

The utility of domestic residents, u , is a CES function of their consumption of private good and of public service.

( ) [ ] σ σ σ σ σ σ / ) 1 ( ) 1 /( ) 1 /( / + + + + = b S C u , with 0 > b if 0 1 < < -σ ( ) [ ] σ σ σ σ σ σ / ) 1 ( ) 1 /( ) 1 /( + + + + = bS C u , with 0 ≥ b if 0 > σ b CS u = , if 0 = σ and ( ) b S C Min u / , = if 1 - = σ (7)
Along an indifference curve, the substitution rate , dC dS / -, decreases with the value of parameter b . Thus, this parameter can be interpreted as a measure of the relative taste of the public service by domestic residents.

The government sets the number of migrants and the production of public good, by maximising the utility of domestic residents (7) under the resource constraint (6). Thus, we implicitly assume that the number of foreign workers who want to enter the country is always greater than the number the government wishes to allow in the country. Even when the optimal number of migrants is very high, the decrease in wages will be insufficient to discourage workers from foreign countries. Moreover, we give the government strong empowerment and the ability to control the legal situation of any worker without cost.

The effects of immigration on the welfare of domestic residents

The computation of the effects of immigration is especially easy and revealing when the private consumption good and the public service are complementary in the preferences of domestic residents . We also assume in this section that the elasticity of output to employment is the same in both sectors: β γ = . Then, we deduce from the equation of the supply set of the economy the expression of the welfare of domestic residents

( ) β - = M f u , with ( ) ( ) ( ) [ ] ( ) ( ) β β β ϕ β β β β β / 1 / ) ( / 1 / 1 / ) 1 ( / 1 ) / 1 ( 1 1 1 B b M A M M M f - - - + + - + + = (8)
Migrants have two opposite effects on the welfare of domestic residents. We will have a better understanding of the first effect by considering the extreme case where the taste for the public service b is zero. Then the government sets the production of public good and taxes to zero. The utility of domestic residents is equal to their consumption of private good, itself equal to their income

[ ] ( ) β β - + - + = = 1 1 / ) 1 ( 1 M M A C u
. It is an increasing function in the number of migrants and tends to infinity with this number. More precisely we have:

( )M M w M C ' / - = ∂ ∂
. Thus a small increase in the number of migrants decreases the wage of all migrants and increases the income and the consumption of domestic residents by the same amount. The effect of a small increase in the number of migrants on the utility of domestic residents is zero when there are no migrants present in the country; it is maximum when the number of migrants already in the country is

) 1 /( 1 β - (the utility function is convex in the number of migrants when ) 1 /( 1 β - < M
and concave otherwise).

When the taste for the public service b is positive, a second effect appears which is that migrants create congestion, which reduces the welfare of domestic residents. The following proposition describes how under these two effects the optimal number of migrants is determined. It shows how the second effect leads to a finite optimal number of migrants, which becomes zero when the taste for the public service is high enough Proposition 1. If the congestion effect is weak that is if β ϕ ≤ then the optimal number of migrants is infinity. If β ϕ > , there exist two thresholds for b :

2 1 0 b b < <
, such that when the number of migrants increases from zero to infinity, then: a) if the taste for the public service b is larger than 2 b , the utility of domestic residents decreases; b) if the taste for the public service b is between 1 b and 2 b , the utility of domestic residents first decreases, then increases and then decreases. More importantly, the optimal number of migrants, which is the number of migrants that maximises the utility of domestic residents, is still zero; c) if the taste for the public service b is smaller than 1 b , the utility of domestic residents still first decreases, then increases and then decreases. However, the optimal number of migrants is positive and equal to the largest of the two roots of the equation in M

( ) ( )( ) ( ) [ ] 1 / 1 / ) 1 ( / 1 1 1 1 1 / / ) 1 ( + - - + + - = - β β ϕ β β β ϕ β M M M bA B (9)
This number is a decreasing function of b and increases indefinitely when b tends to 0.

Proof. See the appendix.¦ When the congestion effect is weak, the increase in congestion created by a higher number of migrants can be cancelled by affecting a part of these migrants to the production of more public good. The other migrants work in the private sector and increase the net income and the consumption of private good of domestic residents. Thus, the supply set expands in both directions when the number of migrants increases.

When the congestion effect is stronger we are in the configuration of Figure 1 that we commented on earlier. We saw that, when there are no migrants in the country, a small inflow of immigrants has no effect on the welfare of domestic residents, according to the first effect of immigration. However, the second effect, which is the increase of the congestion of the public good, leads to a decrease of this welfare. This explains why an inflow of migrants always reduces the welfare of domestic residents when the number of migrants already present in the country is low. When there are more migrants in the country, the first effect turns positive, which compensates the higher congestion of the public service if the taste for this service is low enough. This could explain why, as [START_REF] Boeri | Why are Europeans so tough on migrants?[END_REF] notice, immigration policy has become less restrictive from 1994 to 2004 in Spain and in Greece (these countries had very few migrants in 1994, then the number increased substantially).

If the taste for the public service is low enough, 1 b b < , then a decrease in this taste leads to a higher optimal number of migrants. The change in the production of public good will result from two opposite effects. On one hand, the labour force in the economy is higher, which should imply a higher production of both goods. On the other hand the composition of this production changes in favour of more private consumption good and less public good. We cannot establish which effect is the strongest. The amount of public service delivered to domestic residents, will suffer of a third effect, which is that a higher number of immigrants increases the congestion of the public good.

Proposition 1 implies that when the taste for the public service decreases from infinity to zero, then the optimal number of migrants will start from zero and remain at this value, then it will jump to a positive value and increase indefinitely. The following corollary gives a lower bound for the size of this jump.

Corollary. When the utility function of domestic residents has a local maximum associated to a positive number of migrants, the minimum value of this number of migrants, is the positive root of the equation of variable

M ( ) ( ) [ ] M M M β β ϕ - + + = 1 1 2 1 (10)
This root is a decreasing function of the strength of the congestion effect, ϕ , and tends to zero when ϕ increases indefinitely.

Proof. We have

( ) ( ) ( )( ) ( ) β β - - = = 1 / 1 1 2 2 / 1 / ' A b B M M f M f
. So, M is the solution of the equation

M M M 1 ) 1 ( 1 1 1 1 1 1 1 = - + -         + + + - β β β β ϕ
. The right side of equation ( 10) decreases from infinity to zero when M increases from zero to infinity. The expression of the associated value of the preference for public services, 2 b , can be deduced from equation ( 9). ¦ Of course the smallest positive optimal number of immigrants, associated to a taste for the public service equal to 1 b , is largest than this bound.

The results of this section are based on the assumption that the two kinds of consumption are perfect complement in the preferences of domestic residents. If we assume instead a Cobb Douglas utility function that is a unitary elasticity of substitution between both kinds of consumption, we get the following expressions of their optimal values, for a given number of migrants

( ) [ ] ( ) [ ]( ) β β β + - + - + + = 1 1 1 1 1 / 1 M M b A C and ( ) [ ] ( ) β ϕ β + - + + = M b b B S 1 1 / . So, the utility of domestic residents is ( ) ( ) ( ) ( ) β ϕ β β β β - + - + - +       + + = b b b M M b b b AB u 1 1 1 1 1 1 (11) If ( ) β ϕ β - < / b
, u first decreases, then increases and tends to infinity when M increases from zero to infinity then. In the opposite case, u decreases and tends to zero. Thus, the optimal number of migrants is either infinity (if the preference for the public service is low enough) or zero.

If, instead of the two assumptions made in the beginning of this section we assume that the elasticity of substitution between the two kinds of consumption is larger than one ( 0 > σ ), then, for a given level of the number of migrants, a feasible choice by the government is to produce a zero output of public good 0 = = G S . Then the welfare of domestic residents and their consumption of private good

is [ ] ( ) β β - + - + = = 1 1 / ) 1 ( 1 M M A C u
. Both increase indefinitely with the number of migrants, which establishes that its optimal value is infinity.

We will continue the analysis by simulation methods.

Simulations

We set the share of labour in private production 3 / 2 = β and we assume that β γ = . We also set . For these values of parameters we can draw Figure 1, which represents the supply set of the economy, given by equation ( 6), when there are no migrants and when the number of migrants is equal to 30% of the population of domestic residents. This figure was commented in section 1.

The results of last section suggest that the most favourable case to obtain a reasonable positive value for the optimal number of migrants is when both kinds of consumption are perfect complement in the preferences of domestic residents. We will make this assumption in the rest of the section. Simulations not presented here, run for elasticities of substitution higher than -1, confirm this intuition. However, even in this favourable case, we will see that when the optimal number of migrants is positive and finite, its value is unreasonable high. Moreover, to obtain nonzero optimal numbers of migrants, we must assume a preference for public services extremely low, which implies a extremely small size of the government sector in the absence of immigration.

We set the value of the congestion parameter 3 = ϕ . Equation (10) shows that this value implies that the positive optimal levels of immigration will be more than 0.33. Smaller values for this parameter would increase the value of this lower bound, and to obtain a smaller lower bound we would have to set this parameter to a still higher value. , then the utility function has the same shape as before, but the optimal number of migrants is positive (equal to 0.60 times the population of domestic residents). Other simulations show that if the preference for the public good is above 0.0274 , then the optimal number of migrants is zero. If this preference is less than 0.0273 the optimal number of migrants is more than 58% of the population of domestic residents. A preference for the public service as low as 0.0273 implies that, without migrants, less than 1% of the population would work in the production of public good.

If we set the congestion effect at the more reasonable value 1 = ϕ , equation (10) shows that the optimal number of migrants will be either zero or more than . This value of parameter b is consistent with reasonable values for the allocation of the labour force between the two sectors when there are no migrants (77% in the private sector and 23% in the public good sector). But the optimal number of migrants is unreasonably high.

We ran a series of simulations for a smaller elasticity of the production of public good to its labour input, 3 / 1 = γ . We adjusted the value of parameter B to 4.275, so that without migrants the economy was still able to produce the respective amounts 10 = Y and 5 . 2 = G of goods, with the allocation of labour 0.8 and 0.2 between the two sectors. We keep the last value of the congestion effect 1 = ϕ . Then, we get less dramatic results than in last paragraph. The smaller positive value for the number of migrants is equal to 1.14 times the population of domestic residents, and the associated value of the preference for the public good is 111 . 0 = b . However, with this new parameterization, the allocation of labour between the two sectors becomes 97.4 and 2.6%, which gives an unreasonably low value to the size of the government sector.

These results suggest that the optimal number of migrants in industrialised countries is zero or is extremely large. The observed numbers of migrants in GCC countries are of an order of magnitude more consistent with the results of the simulations of the model. However, we should assume for these countries a strong congestion effect, a strong complementarity between both kinds of consumption in the preferences of domestic residents and a low value for the preference for the public service. The validity of these conditions is debatable.

We cannot accept the validity of the conclusion that all migrants who enter OECD countries cause a decline in the welfare of their domestic residents. In the next section we will assume that foreign and national workers are imperfect substitute, and we will reach less extreme conclusions.

Imperfect substitutability between national and foreign labour

Extension of the model

In this section we will assume that there are two kinds of jobs in the economy, denoted 1 and 2. These two jobs differ by their nature, but they ask for the same skill. A domestic resident can take any of the two jobs, but the government can freely allocate immigrants between these jobs. We start by considering the private sector, which produces the consumption good. We assume that this sector

≥ Y Y Y Y M M N N , Y Y Y N N N = + 2 1 and Y Y Y M M M = + 2 1
. The production function of the private sector becomes

( ) ( ) δ β 2 2 1 1 Y Y Y Y M N M N A Y + + = (12)
with the following conditions on the parameters:

1 0 < < < β δ , 1 < + β δ
. We assume that there are relatively few of the second kinds of jobs, which means that the value of β δ / is small. To simplify the exposition we will only consider the case where the number of migrants satisfies the condition

( ) Y Y N M δ β / ≤ (13)
The two jobs pay the respective wages

( ) ( ) δ β β 2 2 1 1 1 1 Y Y Y Y M N M N A w + + = - (14) ( ) ( ) 1 2 2 1 1 2 - + + = δ β δ Y Y Y Y M N M N A w (15)
We can easily see that the wage rate of domestic residents (and of migrants) working on jobs 1 increases with the number of immigrants working on jobs 2.

The government allocates migrants between the two jobs so as to maximise the gross income that domestic residents obtain from the private sector:

2 2 1 1 Y Y M w M w Y R - - =
. The economy is i n one of the three following regimes

• 2 1 w w = , ( )( ) ( ) 1 / / 1 1 2 2 = + + Y Y Y Y M N M N δ β and 0 , 2 1 ≥ Y Y N N 6 . • 2 1 w w > , ( )( ) ( ) 1 / / 1 1 2 2 > + + Y Y Y Y M N M N δ β , Y Y N N = 1 and 0 2 = Y N . • 2 1 w w < , ( )( ) ( ) 1 / / 1 1 2 2 < + + Y Y Y Y M N M N δ β , 0 1 = Y N and Y Y N N = 2 .
In the first regime, the two kinds of jobs pay the same wages, and domestic residents are indifferent between them. In the second regime, the second kind of jobs pays lower wages than the first kind, no domestic residents take the former jobs, but migrants may be authoritatively allocated to them by the government. In the third regime the first kind of jobs pays lower wages and no domestic residents take them. We can establish the following proposition.

Y Y Y N M N ψ β δ ≤ < / with ( )( )( ) β δ β β δ β δ β δ ψ - - - + + = 1 1 / 1 / / 2
, then it will be optimal for the government to segregate all the immigrants in the second kind of jobs. No domestic residents will take these jobs, which pay a lower wage than the jobs of the first kind. If Proof. See the appendix.¦ [START_REF] Ottaviano | Rethinking the gains from immigration: Theory and evidence from the US[END_REF] note that, for given education and experience attainment the choice of occupation of foreign-born residents is quite different from that of natives. They conclude that overall 6 We can easily how that under this regime the production function ( 12) can be rewritten as

( ) ( ) δ β β δ δ β β δ δ β + + + + = Y Y M N A Y
. Formally, we are in the same situation as in the model of section 1. immigration over the 1980-2000 period significantly increased the average wages of U.S. born workers (by around 2%). Now, we will complete the model. The production function for the public good is

( ) ( ) δ β 2 2 1 1 G G G G M N M N B G + + = (
≥ G G G G M M N N , G G G N N N = + 2 1 and G G G M M M = + 2 1
. In order to better focus on the problem of the segregation of migrants we limit the analysis of the section to the case where the elasticities of production to its two inputs of labour are the same in both sectors. We assume that the Government pays the same wages as the private sector for both kinds of jobs, 1 w and 2 w . It allocates its manpower between these jobs such as to minimise its production cost that is its wage bill. We have

) ( / ) ( / 2 2 1 1 2 1 G G G G M N G M N G w w + ∂ ∂ + ∂ ∂ = (17)
The production cost of the public good is covered by a lump sum tax. We make the simplifying assumption that the taxes paid by migrants cover the wages cost of migrants working for the government. The specific factor used by the private sector is entirely owned by domestic residents.

Their net income is equal to the rent they earn on this factor plus their wages, minus their taxes (which are equal to the wages cost of domestic workers for the government). This income is entirely spent on their consumption of private good C . We have

C M w M w Y Y Y = - - 2 2 1 1 (18)
Finally, the equilibrium of the two job markets gives the two last equations

1 = + G Y N N (19) M M M G Y = + (20)
We will solve the model under the assumption that ( )

Y Y Y N M N ψ β δ ≤ < / (21)
Under this condition, the second kind of jobs pays lower wages and migrants are segregated in these jobs and forbidden to take the first kind of jobs. Of course, domestic residents do not accept to work on the second kind of jobs. We deduce from equations ( 14), ( 15) and ( 17) the ratios between the two kinds of labour inputs in the two sectors

M N M N M G G Y Y = = / / (22)
Thus, condition (21) can expressed in the terms of the total number of migrants who have entered the economy

ψ β δ ≤ < M / (23)
After a succession of eliminations we can express the outputs of the private consumption good and of the public good in the terms of the employment of domestic residents by the private sector ( )

δ δ β δ M AN C Y + - = 1 (22) δ δ β M N B G Y + - = ) 1 ( (23) with 1 0 ≤ ≤ Y N
If we eliminate Y N between these two equations, and if we remember that

( ) ϕ M G S + = 1 / ,
we get the following expression of the supply set of the economy

( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] 1 / 1 ) 1 ( / / 1 / / 1 = + + - + + + + - δ β δ β ϕ δ β δ β δ δ B S M A C M (24)
This expression, as equation ( 6) in section 1, shows how the trade off between the consumption of private good and of public service by domestic residents, C and S , depends on the number of migrants M . Domestic residents can obtain a zero amount of public service and a consumption of private good

( ) δ δ AM C - = 1
. This consumption increases with the number of migrants. On the other hand domestic residents can obtain a zero amount of private consumption good and a consumption of public service

( ) ϕ δ - + = M BM S 1
. This consumption decreases with the number of migrants if we introduce the assumption that the congestion effect is high enough:

δ β ϕ + >
. Finally, when we move along this set from 0

= C to ( ) δ δ AM C - = 1
, the slope of the tangent to this set decreases from 0 to minus infinity.

Extension of the results

The computation of the effects of immigration is still especially easy and revealing when the private consumption good and the public service are complementary in the preferences of domestic residents that is when 1 -= σ

. Then, the Government sets the production of public good G such that b S C u / = = . We deduce from the equation of the supply set of the economy the expression of the welfare of domestic residents ( ) ( )

δ β + - = M g u , with ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] δ β δ β ϕ δ β δ β δ δ + + + + - + + - = / 1 / / 1 / / 1 ) 1 ( / 1 B b M A M M g (25)
Migrants have two opposite effects on the welfare of domestic residents. In the extreme case where the taste for the public service b is zero, the government sets the production of public good and taxes to zero. The utility of domestic residents is equal to their consumption of private good, itself equal to their income

( ) δ δ M A C u - = = 1
. It is an increasing function in the number of migrants and tends to infinity with this number. The reason is that a higher number of migrants drive the wages and the rent of domestic residents up. When the taste for the public service b is positive, a second effect appears decreases from ( ) min M f to zero. We noticed before that ( ) ( )

0 min f M f > . 1
b is the value of parameter b such that ( ) ( )

0 2 f M f = .¦
Proof of Proposition 2. a) In the third regime we have the condition ( )( ) , so as to maximise function R . The derivative of this function is

1 / / 1 2 < + Y Y Y M M N δ β
( ) ( ) [ ] 2 2 2 2 1 / 1 1 1 1 Y Y Y Y Y Y Y Y M M N M M M N dM dR R - + - - - - + - + - = β δ δ δ β
. It has the same sign as ( )

      + - - - + +       + + - + Y Y Y Y Y Y Y Y Y M N M N M M M N M β δ δ δ β δ β δ 1 1 2 / 2

  the production of public good G such that b

Figure 2

 2 Figure 2 represents the utility of domestic residents in function of the number of immigrants, for three values of the preferences for the public good, b . If 030 . 0 = b , then the utility of domestic residents

Proposition 2 .

 2 If the number of migrants working in the private sector Y M belongs to the interval ( )

  on the second kind of jobs, which pay lower wages, but some migrants might be allocated to the first kind of jobs. If is in the first regime and the allocation of migrants and domestic residents between the two kinds of jobs, which pay the same wages, is a matter of indifference.

M

  represent the number of domestic residents and immigrants having taken the second kind of jobs,

.

  This condition is not satisfied. b) In the second regime the wages paid by the two jobs are

  bound of regime 2. So, we can see that this regime dominates regime 1

Figure 1 Figure 2 Figure 3

 123 Figure 1

However, the distribution effect can be very high; the income of capital may increase by until 12 per cent and the income of domestic workers may decrease by 6 per cent.

There exists an empirical literature, using opinion surveys, which tries to disentangle economic reasons from racist and xenophobic sentiments in the reluctance of public opinion against a softening of immigration controls. See for instanceDustman and Preston (2004) andMalchow-Moller and alii (2006).

The approach used in this paper is connected to but different from the important literature evaluating the impact of immigration on the costs of the welfare systems.Nannestad (2007) gives an excellent review of this literature.

Migrants have lower income per head than domestic residents because they do not get a share of the rent earned by the specific factor used by the private sector. However, they pay the same taxes as domestic residents. We made this assumption to simplify the analysis. In a previous version of this paper we explored the case when migrants pay no taxes. The results we obtained were qualitatively the same, although the optimal number of migrants was lower under this assumption.

2

The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK4603/05H).

which is that migrants create congestion, which reduces the welfare of domestic residents. Proposition 1 has to be revised in the following way.

. The derivative of function g has the same sign as

. When M incrases from 0 to infinity, ( ) M g 1 increases from 0 to infinity and ( )

. So, the derivative of function g has at least one positive root. The derivatives of functions ( )

. Then, we have , we are in a situation where all migrants are segregated in jobs 2, which pay lower wages. We can see that the optimal number of immigrants is 12.7%, which is quite a reasonable value.

We obtain a local maximum of utility in the case of total segregation of the immigrants on jobs 2, for , the optimal number of migrants is equal to 6.2% of the population of domestic residents. However, this high value of b implies that without migrants, the economy would allocate 34.3% of its manpower to the production of public good. If 409 . 0 > b , the optimal number of immigrants is zero.

We²also simulated the model for a positive elasticity of substitution between the two goods in the preferences of domestic residents (that is for 0 1 < < -σ

. We set the value of parameter b such that, without migrants, the optimal allocation of production between the two goods was still 10 = Y and 5 . 2 = G (of course the value of b has to be changed with the value of σ ). We found that when σ increases from -1 to 0, the optimal number of migrants only increases from 12.7% to 14.1% of the population of domestic residents.

Thus, we see that this new version of the model can explain optimal numbers of migrants of the same order of magnitude as what we can see in reality.

Conclusion

This paper offers a simple explanation of important features of the immigration policies of host countries, which are observed in many countries these days. Many countries admit few foreign migrants for economic reasons and segregate them in jobs, which domestic workers do not wish to undertake. Some other countries admit a much larger number of immigrants and segregate them to a wider range of jobs. The paper assumes that domestic residents are all identical. Thus, it eliminates considerations based on the specific interest of a class of natives and on economic and political conflicts arising in a heterogeneous society. Moreover, it assumes that although domestic residents have no altruistic feelings toward immigrants, they do not bear xenophobic or racist sentiments against them.

There exist episodes in the past when such an explanation would have been insufficient. For instance, if a large number of foreign migrants were allowed to settle in Western Europe in the fifties and the sixties, this was probably to prevent a rise in industrial wages and to allow firms to make enough profits to modernise and expand their equipment. This policy strengthened the depressing effects on wages induced by domestic migration from the countryside to urban areas. Both movements stopped with the wage explosions, which took place in Europe at the end of the sixties. The current debate on immigration in the U.S. widely reflects a contradiction between the economic interests of different social classes. However, we are convinced that much can be explained on the policy of immigration controls by focusing the investigation on the defence of national interest.

Appendix

Proof of Proposition 1. We have ( ) ( ) ( )

is negative or zero. Then, the optimal number of migrants is infinity.

is an increasing function of M with ( )


Andrew Clark
email: andrew.clark@ens.fr

Nathalie Colombier
email: nathalie.colombier@univ-rennes1.fr

David Masclet
email: david.masclet@univ-rennes1.fr

Never the Same After the First Time: The Satisfaction of the Second-Generation Self-Employed

Keywords: Satisfaction, Self-employment, Parents, Intergenerational comparisons JEL CLASSIFICATION: J20, J21, J23, J24

Previous empirical work has shown that the self-employed are generally more satisfied than salaried workers. This paper contributes to the existing literature in two ways. First, using French data from the ECHP and British data from the BHPS, we investigate the domains over which this differential operates. We show that, after controlling for occupation, self-employed workers are generally more satisfied with working conditions and pay, but less satisfied than employees with respect to job security. We then consider the differences between the firstand second-generation self-employed. The first-generation self-employed (those whose parents were not self-employed) are more satisfied overall than are the second-generation self-employed. We argue that this finding is consistent with the self-employed partly comparing their labor market outcomes with those of their parents, as well as parental transfers which loosen the self-employment participation constraint. This result is found in both pooled and panel analysis.

Introduction

One of the most consistent findings in the literature on self-employment is that the selfemployed earn less than comparable salaried workers [START_REF] Lazear | Incentives, productivity, and labor contracts[END_REF][START_REF] Carrington | The role of employer/employee interactions in labor market cycles: Evidence from the self-employed[END_REF][START_REF] Hamilton | Does entrepreneurship pay? An empirical analysis of the return to selfemployment[END_REF]. For example, using 1984 data from the Survey of Income and Program Participation (SIPP) panel, [START_REF] Hamilton | Does entrepreneurship pay? An empirical analysis of the return to selfemployment[END_REF] estimates that, at a given level of work experience, the self-employed earn 19% less than employees. [START_REF] Carrington | The role of employer/employee interactions in labor market cycles: Evidence from the self-employed[END_REF] report similar results. However, whilst the financial aspects of work likely constitute an important part of the decision to become self-employed, non-pecuniary aspects of the job, such as being one's own boss and the degree of autonomy, may well make up for lower earnings [START_REF] Hamilton | Does entrepreneurship pay? An empirical analysis of the return to selfemployment[END_REF].

To bring the varied aspects of the job together, some authors have proposed the use of self-reported job satisfaction as a subjective summary measure of the utility from labormarket choices. 1 Perhaps the second most consistent finding in the literature is that, despite any income differences, the self-employed are more satisfied with their jobs than are employees (Clark and Senik, 2006; Kawaguchi, 2006; Bradley and Roberts, 2004; Falter, 1 The analysis of subjective measures such as life or job satisfaction has recently become a part of mainstream micro-economic analysis (e.g. Freeman, 1978). Economists sometimes hesitate to use subjective job satisfaction measures, due to doubts about their relationship to underlying utility. However, labour economists have made significant efforts to incorporate such satisfaction measures into economic analyses of labor market outcomes (see the surveys in [START_REF] Frey | What Can Economists Learn from Happiness Research?[END_REF][START_REF] Frey | What Can Economists Learn from Happiness Research?[END_REF][START_REF] Clark | Relative Income, Happiness and Utility: An Explanation for the Easterlin Paradox and Other Puzzles[END_REF]. might be thought to slacken the participation constraint. Loosely speaking, such transfers allow some individuals who are not particularly cut-out for self-employment to become selfemployed. This mixture of increased resources, potential constraint, and participation produces an overall effect of indeterminate sign.

A separate argument revolves around the idea that individuals do not only consider their own situation in an absolute sense, but compare their situation with that of their reference group, where this latter may include their relatives, and in particular their parents. If this is so, and under the typical finding that the self-employed are more satisfied than are employees, the first-generation self-employed may be more satisfied than the secondgeneration self-employed, since the former compare their situation to their salaried (or at least non self-employed) parents while the latter compare themselves to self-employed parents.

Only relatively little work in the nascent well-being literature in Economics has considered how individual well-being relates to the income of other family members, and in particular whether there is any role for household comparisons. [START_REF] Clark | L'utilité est-elle relative? Analyse à l'aide de données sur les ménages[END_REF] uses BHPS data to relate individual job satisfaction, conditional on own wage, to the wages of their partners and the average wage of other household members. The results show that individuals do indeed report lower job satisfaction scores the higher are the wages of other workers in the household.

McBride (2001) also introduces a family benchmark, appealing to the following question in the 1994 GSS: "compared to your parents when they were the age you are now, do you think your own standard of living now is: much better, somewhat better, about the same, somewhat worse, or much worse?". Regression analysis showed that the respondent's happiness was significantly positively correlated with doing better than one's parents, conditional on the level of the respondent's actual income. [START_REF] Boes | Hedonic Adaptation to Living Standards and the Hidden Cost of Parental Income[END_REF] are able to directly measure parents' income in recent waves of the German Socio-Economic Panel, by matching younger respondents who have moved away from home (and thus constitute new panel households) to their parents (who continue as panel members). They show that respondents' financial satisfaction increases with own income, as expected, but is negatively correlated with parents' income, consistent with the existence of an intergenerational externality.

We do not expressly consider these kind of income comparisons, but rather the broad effects of parents' labor force status in the context of self-employment. Our results on British and French panel data show first that the self-employed are indeed more satisfied than salaried workers. A more detailed analysis of the different job satisfaction domains shows that the self-employed report greater satisfaction with pay and working conditions, but are less satisfied with job security.

However, the self-employed are not all the same: the second-generation self-employed are less satisfied with their jobs overall than are the first-generation self-employed. This applies also to satisfaction with pay and satisfaction with the work itself. This is consistent with transfers from parents allowing less apt children to become self-employed, and with constrained choice by the children. It is also consistent with children comparing themselves to their parents, so that job satisfaction is partly relative.

The remainder of the paper is organized as follows. Section 2 presents the data and establishes that the self-employed are more satisfied with their jobs than are the employed.

Section 3 then splits up the self-employed according to their parents' labor-force status, showing that the least satisfied are those with at least one parent who was also self-employed. Section 4 concludes.

Self-employment and Job Satisfaction

Descriptive Analysis

The analysis of job satisfaction is based on panel data from the British Household Panel Survey (BHPS) and the French component of the European Community Household Panel (ECHP). In both surveys, all adults in the household are interviewed separately with respect to their socio-demographic characteristics, income, employment, and health. The British Household Panel Survey is an annual panel which initially consisted of around 10 000 individuals in around 5 000 different households in Great Britain; increased geographical coverage has pushed these figures to around 16 000 and 9 000 in more recent waves. We here make use of data from the first fifteen waves (1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005). Further details of this survey are available at the following address: http://www.iser.essex.ac.uk/ulsc/bhps. The French data come from the eight waves of the French component of the ECHP, which was run annually from 1994 to 2001, this has broadly similar numbers of individuals and households per year as the latter waves of the BHPS. Details of the ECHP are available at http://forum.europa.eu.int/irc/dsis/echpanel/info/data/information.html.

Our key variable is job satisfaction, which we take here to be a proxy measure of the utility from work. In the BHPS, all employees are asked about their satisfaction with seven aspects of the job (Promotion Prospects, Total Pay, Relations with Boss, Security, Use of Initiative, Work Itself, and Hours Worked). All of these are measured on a scale of one to seven, where 1 means completely dissatisfied and 7 means completely satisfied. These are followed by the question "All things considered, how satisfied or dissatisfied are you with your present job overall using the same 1-7 scale"? The self-employed are asked about five aspects of the job (the same list as above, less Promotion Prospects and Relations with Boss, which are largely inapplicable here), followed by the same summary question.

In the ECHP, job satisfaction is measured on a six-step ladder, going from not satisfied at all to very satisfied. Job satisfaction is part of a general series of satisfaction questions formulated as follows: "Could you indicate, on a scale going from 1 -"not satisfied at all"-to 6 -"very satisfied"-your degree of satisfaction concerning each of the following items: your job or main occupation; your financial situation; your housing; your health; your time available for leisure; your social contacts; and your past education"? In the job part of the questionnaire, another set of questions related to satisfaction with various aspects of the job are asked in a similar way: "Could you indicate, on a scale going from 1 -"not satisfied at all"-to 6 -"very satisfied"-your degree of satisfaction concerning each of the following items: labor income; job security; number of working hours; work schedule; type of activity; working conditions; and commuting distance"? These labor-related questions are asked of all those active in the labor market, independent of their status.

We restrict our sample in both datasets to those who are self-employed or employees, and only consider those who are aged between 16 and 65. In both datasets, workers are counted as self-employed if they answered "Yes" to a direct question on self-employment.

These restrictions reduce the ECHP sample over eight waves to 50579 observations, with 5871 observations (11.6% of the sample) on the self-employed. In the fifteen waves of the BHPS, we retain 103 504 observations, with 11 996 on the self-employed, again representing 11.6% of those who are in employment.

[Table 1 about here] Table 1 presents summary statistics for our key variables in both datasets. The first three columns show figures for respectively all of those who work, employees, and then the self-employed in the eight waves of the ECHP data; columns 4-6 repeat the procedure for the fifteen waves of the BHPS. Table 1 reveals that the self-employed are older, and more likely to be men. They are also generally less-educated than employees: in the ECHP, 72% of the self-employed have less than a high-school degree, against 58% of employees. However, the self-employed are a little more likely to have a Masters degree. The same broad pattern is found in the BHPS. Table 1 also shows that the self-employed are more likely to be property owners, especially in France. The self-employed have higher incomes than employees in France, but not in Great Britain. 3 This is due to the presence of what are known as the "professions libérales" amongst the French self-employed (for example, Doctors and Lawyers). In fact, ten per cent of the self-employed in the French data earn more than 6 800 Euros per month.

Our key right-hand side variable here is the labor force status of the individual's parents. In the BHPS, this is measured by a series of two questions. All individuals are asked "Thinking back to when you were 14, what job was your father doing at that time"? Those who reported that their father was working are then asked "Was he (your father) an employee or self employed"? An analogous question is asked with respect to the respondent's mother.

We create a dummy variable for the individual having at least one parent self-employed. The situation in the ECHP is a little different. Here individuals are asked to report the most recent occupation of their father and mother. This can potentially change from wave to wave for younger respondents whose parents are still active in the labor market.

The figures towards the bottom of Table 1 show that, perhaps unsurprisingly, the selfemployed are more likely than employees to have a self-employed parent: in France, 60% of the self-employed have at least one self-employed parent, as opposed to only 26% of employees. In Great Britain, the analogous figures are 28% and 15%. 4Finally, the bottom panel of Table 1 presents the mean scores of the four different satisfaction measures that we consider. In the raw data, the self-employed report higher satisfaction scores with respect to the work itself, but lower satisfaction regarding security.

The situation with respect to pay satisfaction is mixed. In France, the self-employed are less satisfied with their pay, whereas the reverse holds in Great Britain. However, in both countries the self-employed report higher overall job satisfaction on average than do employees.

Estimates of Job satisfaction

The first stage of our investigation relates the various job satisfaction measures in Table 1 to a standard set of demographic characteristics (including education, gender, age and marital status). We also control for the individual's occupation. The variable we are most interested in is a dummy variable indicating whether the individual is self-employed. The equations are estimated by ordered probit techniques, with standard errors that are clustered at the individual level.

[Table 2 about here] Columns 1 and 5 in Table 2 show the estimates for overall satisfaction in France and Britain respectively. In both countries the self-employed are more satisfied with their jobs overall, conditional on the other control variables. As noted in Section 1, this is consistent with the results in a number of existing pieces of work. The remaining columns of Table 2 add detail by showing the correlation between self-employment and various types of domain satisfaction. In both countries the self-employed are more satisfied with the work itself, but less satisfied with job security. In Great Britain, the self-employed are more satisfied with their pay, but no significant effect is found for this domain in France.

The estimated coefficients on the other control variables are fairly standard. Men mostly report lower levels of job satisfaction than do women in both countries (Clark, 1997, Sousa-Poza and[START_REF] Sousa-Poza | Taking Another Look at the Gender/Job-Satisfaction Paradox[END_REF], and there is a U-shaped relationship between age and all measures of job satisfaction [START_REF] Clark | Is Job Satisfaction U-shaped in Age?[END_REF]. While the marriage and children satisfaction "premia" are seemingly well-defined in Great Britain, there are no robust effects in France.

The estimated coefficient on log income is mostly positive and significant in France, but less so in Great Britain. In neither country is higher income associated with greater satisfaction with the work itself, perhaps suggesting some kind of compensating differential. In both countries, homeowners are more satisfied with their total pay, but less satisfied with their job security.

Overall, the regression results in Table 2 mostly confirm a number of existing results in the satisfaction literature, although the estimates on domain satisfaction are more novel.

Our main interest in this paper is to underline that the broad results that appear in this Table might actually obscure sharp differences between different groups of the self-employed. We concentrate in particular on the first-and second-generation self-employed. As discussed above, the net effect of the transfers received by the second-generation self-employed and the potential constraint of following their parents is ambiguous. The next section brings regression analysis to bear on the question, and shows that the second-generation self-employed are in fact systematically less satisfied at work than are their first-generation counterparts.

The First-and Second-Generation Self-Employed

This section investigates whether, ceteris paribus, second-generation entrepreneurs are happier than those of the first generation. There are a number of potential differences between the two groups of self-employed. A by now fairly substantial body of previous work has emphasized that the observed intergenerational correlation in type of work may reflect transfers from parents (Colombier andMasclet 2007, 2008;[START_REF] Hundley | Family Background and the Propensity for Self-Employment[END_REF][START_REF] Parker | The Economics of Self-employment and Entrepreneurship[END_REF][START_REF] Dunn | Financial Capital, Human Capital, and the Transition to Self-Employment: Evidence from Intergenerational Links[END_REF][START_REF] Blanchflower | What makes an entrepreneur[END_REF]Laferrère and McEntee, 1996;[START_REF] Taylor | Earnings, Independence or Unemployment: Why become Self-employed?[END_REF][START_REF] Lentz | Entrepreneurial Success and Occupational Inheritance Among Proprietors[END_REF][START_REF] De Wit | An Empirical Analysis of Self-Employment in the Netherlands[END_REF][START_REF] Carrol | The career dynamics of self-employment[END_REF][START_REF] Cooper | Entrepreneurship and Paths to Business Ownership[END_REF]Lindh and Ohlsson, 1986). 5 These parental transfers may be financial or of informal human capital reflecting some kind of know-how.

The broad consequence of these transfers will likely be to relax capital-market constraints and increase the probability of children's success in self-employment. We may therefore expect the second generation, who are perhaps then more successful, to be more satisfied than the first generation self-employed. However, it can also be argued that parents' transfers will reduce self-employment rents analogously to the role played by inheritances in the National Child Development Survey data analyzed by [START_REF] Blanchflower | What makes an entrepreneur[END_REF].

On a somewhat different note, it can be argued that the second generation may be less satisfied than the first generation self-employed if the former are to an extent obliged to follow in the footsteps of the latter. 6 Finally, we can appeal to the broad idea of comparisons, and consider that individuals compare their labor market situation (not only in terms of income, but also status and job) to the types of jobs occupied by others in the family, and in particular to their parents. Climbing up the social ladder (from the rung that the parents occupied) can therefore lead to higher job satisfaction, while in contrast a fall in social status relative to one's parents may reduce job satisfaction. For all of these reasons we expect the first-and second-generation self-employed to report different satisfaction levels.

Differences between the First-and Second-generation Self-employed

Table 3 provides some preliminary information about the distribution of satisfaction between the employed and the first-and second-generation self-employed. Due to the relatively few individuals who report very low satisfaction levels, we have grouped the first three cells together in both datasets, producing satisfaction scales that run from 3-6 for the ECHP, and 3-7 for the BHPS.

[Table 3 about here] The distribution of satisfaction in Table 3 first broadly confirms that employees are less satisfied than are the self-employed. In addition, it highlights that, for most of the satisfaction measures, the second-generation self-employed seem to do less well than the firstgeneration self-employed. For example, while only 9% of French employees are very satisfied (the highest category), the corresponding figures are 18% for the first-generation and 13% for the second-generation self-employed. The same broad data shape also applies to overall job satisfaction in Great Britain.

With respect to domain satisfaction, the self-employed are more satisfied than employees with both pay and working conditions, but again with the first-generation selfemployed reporting the highest numbers. In contrast, the self-employed are less satisfied than employees with respect to job security, and here the first-generation self-employed report the lowest satisfaction scores.

Table 3 thus suggests higher job satisfaction for the newly self-employed, with respect to both overall job satisfaction and to pay and working conditions, and lower satisfaction with job security for the newly self-employed. These preliminary results are consistent with the idea that individuals compare their current situation with that of their parents. Since the selfemployed are overall more satisfied than employees, it makes sense that those whose parents are employees report greater satisfaction compared to second generation self-employed workers: the former are doing better relative to their parents. In contrast, second generation workers report higher relative satisfaction with respect to job security since they are less likely to compare their situation with that of employees and are used to lower levels of job security.

It is of course possible that some of the observed differences between the first-and second-generation self-employed reflect different income, hours, occupations, and so on.

Table 4 shows the results of regression estimation of the various satisfaction measures, distinguishing between the first-and second-generation self-employed. The explanatory variables include all of the variables from Table 3, as well as a dummy variable for having at least one self-employed parent ("Mother or Father Self-Employed"), and the interaction between own and parents' self-employment status ("Self-Employed and Mother or Father Self-Employed"). The estimated coefficient on this latter shows how the first-and secondgeneration self-employed differ.

[Table 4 about here]

The results are quite remarkably similar across the two datasets. In both France and Great Britain, the first-generation self-employed are significantly more satisfied than are employees (as shown by the estimates on the "Self-Employed" variable) both overall and with respect to the work itself; they are less satisfied with respect to job security. In the BHPS data, the first-generation self-employed are more satisfied with their pay than are employees; in the French ECHP data, the relevant estimated coefficient is also positive, but is not significant.

The difference between the first and second-generation self-employed is revealed by the coefficient on the interaction variable, the third in Table 4. This is significant in six out of the eight regressions. Perhaps more importantly, it is systematically of the opposite sign to the main self-employed effect. Whatever the first-generation self-employed like about their job, the second generation like less; whatever the first-generation self-employed dislike about their job, the second generation dislike less. Greater success, or looser participation constraints, would imply coefficients on the interaction variable of one sign only. The symmetric mean reversion in Table 4 is consistent with parents acting as a reference group.

Panel Results

Both of our datasets are panel. As such, they allow us to control for individual fixed effects.

Heuristically, we consider the change in job satisfaction when the individual moves from employment to self-employment, or vice versa.

While this is a useful exercise, it does have some limitations. The ordered probit estimates in Table 4 described the distribution of well-being for all those who we observed to be self-employed. Panel analysis will drop those who do not change labor force status. The coefficient on self-employment is identified by "movers", so in some sense we are considering only the more ephemeral self-employed here. In particular, those who have always worked in their parents' business will not appear in panel estimation. This restriction probably applies particularly to the ECHP data, which only covers eight years.

Table 5 presents the panel results, from conditional fixed effect logit estimation. The dependent binary variable equals 1 if satisfaction is over 4 in the ECHP, and over 5 in the BHPS. The results with respect to the first-generation self-employed (the estimates on the first variable, "Self-Employed") are very similar to those in the pooled cross-section analysis of Table 4. The variable showing whether at least one parent was self-employed attracts a coefficient in the French data, as it varies over time (although none of the estimates are significant). As in Table 4, the variable that interests us the most is the third, which shows any differences between the first-and the second-generation self-employed. This is negative for three out of the four satisfaction measures in the French ECHP data, showing the secondgeneration self-employed to be less satisfied than the first-generation self-employed, but is only significant for satisfaction with pay. It is possible that these weaker panel results in France result from the relatively short time span of the ECHP data, with the associated reduction in the number of individuals who transit between employment and selfemployment.

The situation in the BHPS is different. Here three out of the four estimates on the interaction variable are negative and significant. This shows that those who move from employment to self-employment with a self-employed parent will experience less of a satisfaction boost than will those with non self-employed parents. 7 These results are consistent with comparison to parents, and with a loosening of participation constraints for the children of the self-employed, with an associated reduction in rents.

Conclusion

This paper has used British and French panel data to bring together two separate topics in the growing literature in the Economics of Happiness. The first concerns relative utility and comparisons to others, and the second the ubiquitous finding that the self-employed report higher levels of job satisfaction than do employees.

We introduce relative utility into self-employment by suggesting that individuals might compare their own labor market experience with that of their parents. Both the British BHPS and the French part of the ECHP contain information on parents' labor force status (measured when the respondent was aged 14 for the former, and the most recent for the latter). If utility is relative, then self-employment should seem better if my parents were not self-employed themselves.

Both the British and the French data suggest that this is indeed the case: the firstgeneration self-employed are significantly more satisfied than are the second-generation selfemployed. This is consistent with comparisons to parents, but also with transfers from parents relaxing the self-employment participation constraint, so that some of the associated rent dissipates, reminiscent of Blanchflower and Oswald's finding that the self-employed who had received inheritances were no more satisfied than were employees.

Considering some of the separate domain satisfactions provides one small piece of evidence in favor of the comparisons, rather than rent dissipation, interpretation. With respect to both pay and the work itself, the same pattern is found as for overall job satisfaction: the first-generation self-employed are more satisfied, but the second-generation less so. The difference occurs with respect to job security, where the second-generation self-employed are actually more satisfied than the first-generation (although only significantly so in the French data). While a number of different explanations are possible, this is at least consistent with individuals evaluating their own labor force status relative to that of their parents.

Whichever of the interpretations turns out to be the best, it seems undeniable that the self-employed are not a homogeneous group. In particular, the second-generation selfemployed are not the same as the first-generation self-employed. Specifically, even with the same income, hours and occupation, they are less satisfied with their jobs. One implication is that having successful parents may be something of a poisoned chalice, either because they allow children to enter occupations in which their relative advantage is less evident, or due to an intra-generational externality where the parents' success serves to up their offspring's satisfaction benchmark. Note: The numbers in parentheses are Standard Deviations.

a In France, the category "less than high school" refers to individuals with the baccalaureat; "Associate degree" to those with two years of education post-baccalaureat; "Bachelor's degree" to three years of education postbaccalaureat; and "Masters degree or more" to four or more years of education post-baccalaureat. The first five education categories add up to 100%. In addition, we know whether individuals hold a technical qualification or not.

b In Great Britain, the category "A/O/Nursing" refers to individuals with GCE A or O-Levels or their equivalent, or a Nursing qualification;; "High" to those with a First or Higher Degree, or a Teaching or Other Higher Qualification; and "Other" to those with other (lower) qualifications.

Table 1 .

 1 Summary Statistics of individual characteristics

			France (ECHP)			Great Britain (BHPS)
	Variable	Whole sample Employees (E) Self-employed	Whole sample Employees (E) Self-employed
				(SE)			(SE)
	Individual characteristics
	Gender (Male)	.552 (.497)	.536 (.499)	.676 (.468)	.514 (.499)	.486 (.499)	.727 (.445)
	Age	39.4 (1.75)	38.5 (1.44)	46.3 (1.58)	38.6 (11.74)	38.0 (11.72)	43.2 (10.88)
	Marital Status
	Married	.755 (.430)	.755 (.430)	.761 (.426)	.589 (.492)	.576 (.494)	.686 (.464)
	Have Children	.598 (.490)	.608 (.488)	.525 (.499)	.373 (.483)	.369 (.482)	.405 (.491)
	Human Capital a, b
	Less than high school	.597 (.490)	.581 (.493)	.720 (.450)
	Associate's degree	.113 (.317)	.117 (.321)	.084 (.277)
	Bachelor's degree	.036 (.186)	.037 (.189)	.026 (.159)
	Master's degree or more	.065 (.247)	.063 (.244)	.078 (.268)
	Other	.189 (.385)	.202 (.396)	.092 (.273)
	Technical Qualification	.350 (.477)	.348 (.476)	.368 (.482)
	Education: Other				.218 (.413)	.214 (.410)	.249 (.432)
	Education: A/O/Nursing				.351 (.477)	.354 (.478)	.326 (.468)
	Education: High				.431 (.495)	.431 (.495)	.425 (.494)
	Financial capital
	Monthly Labour Income (Euros)	1653 (1064)	1603 (1096)	2230 (5550)
	Monthly Labour Income (£)				1113 (994)	1120 (878)	1065 (1624)
	Home Owner	.537 (.499)	.512 (.499)	.723 (.447)	.695 (.460)	.692 (.461)	.725 (.446)
	Social environment
	At least one parent SE	.284 (.450)	.256 (.436)	.601 (.489)	.164 ( .370)	.149 (.356)	.279 (.449)
	Satisfaction
	Overall	4.317 (1.255) 4.422 (1.044) 4.496 (1.154) 5.405 (1.309) 5.383 (1.315) 5.573 (1.248)
	Total pay	3.560 (1.265) 3.587 (1.248) 3.319 (1.394) 4.845 (1.596) 4.830 (1.590) 4.971 (1.630)
	Work itself	4.265 ( 1.138) 4.249 (1.144) 4.406 (1.074) 5.519 (1.329) 5.477 (1.343) 5.842 (1.161)
	Security	4.202 (1.379) 4.239 (1.367) 3.887 (1.435) 5.359 (1.561) 5.380 (1.546) 5.188 (1.673)

Table 2 .

 2 Job Satisfaction and Self-Employment

		Overall	Total Pay	Work Itself	Security	Overall	Total Pay	Work Itself	Security
	Self-Employed	0.149***	-0.018	0.223***	-0.526***	0.209***	0.245***	0.326***	-0.048**
		(0.044)	(0.046)	(0.040)	(0.043)	(0.023)	(0.023)	(0.023)	(0.024)
	Male	-0.005	-0.143***	-0.035*	-0.099***	-0.251***	-0.223***	-0.141***	-0.214***
		(0.020)	(0.021)	(0.020)	(0.022)	(0.013)	(0.014)	(0.013)	(0.014)
	Age	-0.045***	-0.073***	-0.028***	-0.021***	-0.045***	-0.026***	-0.024***	-0.058***
		(0.006)	(0.007)	(0.006)	(0.007)	(0.004)	(0.004)	(0.004)	(0.004)
	Age-squared/1000	0.486***	0.806***	0.293***	0.318***	0.605***	0.366***	0.391***	0.699***
		(0.078)	(0.084)	(0.075)	(0.082)	(0.046)	(0.047)	(0.046)	(0.047)
	Married	0.017	0.071***	-0.020	0.024	0.074***	0.104***	0.047***	0.070***
		(0.021)	(0.022)	(0.021)	(0.022)	(0.014)	(0.015)	(0.014)	(0.015)
	Has Children	0.002	-0.054***	0.015	-0.075***	0.105***	0.071***	0.091***	0.050***
		(0.019)	(0.020)	(0.019)	(0.020)	(0.013)	(0.014)	(0.013)	(0.014)
	Log Monthly Labour Income	0.166***	0.351***	-0.002	0.348***	-0.020***	0.100***	-0.019***	0.002
		(0.014)	(0.019)	(0.013)	(0.019)	(0.005)	(0.006)	(0.005)	(0.005)
	House Owner	0.013	0.061***	0.008	-0.028	-0.045***	0.030**	-0.060***	-0.031**
		(0.019)	(0.020)	(0.019)	(0.020)	(0.014)	(0.015)	(0.014)	(0.014)

TABLE 3 .

 3 Job Satisfaction by Labor Force Status

	Overall Job
	satisfaction

Table 4 .

 4 Overall and Domain Job Satisfaction of the First-and Second-Generation Self-Employed: Pooled.

	Overall	Total Pay	Work Itself	Security	Overall	Total Pay	Work Itself	Security

Table 5 .

 5 Overall and Domain Job Satisfaction of theFirst-and Second-Generation Self-Employed: Panel

	All	Total Pay	Work Itself	Security	All	Total Pay	Work Itself	Security

There are two sources of income information in the French ECHP data. First, individuals are asked in October of each year between 1994 and 2001 about their personal income at the interview date. Second, individuals were also asked every year to retrospectively state their annual income over the past year (e.g. in 2000 for the survey conducted in 2001). As the second measure prevents us from using 2001 data, we use the first measure, expressed as monthly income. In the BHPS, the derived income variable refers to labor income last month, expressed in real 1991 terms. Those who reported non-positive self-employment earnings were excluded from the analysis[START_REF] Evans | An Estimated Model of Entrepreneurial Choice under Liquidity Constraints[END_REF].

The fact that 28% of respondents have at least one self-employed parent, whereas the current self-employment rate is under 12%, reveals that the rate of self-employment must have fallen in France.[START_REF] Marchand | Salariat et non salariat dans une perspective historique[END_REF] describes the post-War growth in French salaried employment, due to the shift away from Agriculture and increased female labor-force participation.

A number of these papers have focused on the influence of the parents' activity, showing that individuals whose parents are self-employed were more likely to become themselves self-employed.[START_REF] Dunn | Financial Capital, Human Capital, and the Transition to Self-Employment: Evidence from Intergenerational Links[END_REF] note that parents' financial capital has a positive effect on children's transition into self-employment;[START_REF] Hundley | Family Background and the Propensity for Self-Employment[END_REF] explores how family background influences the type of employment, revealing effects of both entrepreneurial and economic inheritance.

For example, farmers may well transfer the farm to their children.

There is no estimate on the variable "Mother or Father Self-Employed" in the BHPS panel regressions, as this does not vary over time, being measured only at the point when the respondent was 14 years old.

grateful to Andrew Oswald for suggestions. Thanks to Billy Bragg for part of the title

The BHPS data were made available through the ESRC Data Archive. The data were originally collected by the ESRC Research