Sylvie Démurger
email: demurger@gate.cnrs.fr

Marc Gurgand
email: gurgand@pse.ens.fr

Li Shi
email: lishi@bnu.edu.cn

Yue Ximing
email: yueximing@yahoo.com

Migrants as second-class workers in urban China? A decomposition analysis

Keywords: Chinese labor market, earnings differentials, migration, discrimination JEL classification: J71, J31, O15, P23 Chinese labor market, earnings differentials, migration, discrimination

In urban China, urban resident annual earnings are 1.3 times larger than long term rural migrant earnings as observed in a nationally representative sample in 2002. Using microsimulation, we decompose this difference into four sources, with particular attention to path dependence and statistical distribution of the estimated effects: (1) different allocation to sectors that pay different wages (sectoral effect); (2) hourly wage disparities across the two populations within sectors (wage effect); (3) different working times within sectors (hours effect); (4) different population structures (population effect). Although sector allocation is extremely contrasted, with very few migrants in the public sector and very few urban residents working as self-employed, this has no clear impact on differential earnings. Indeed, the sectoral effect is not robust to the path followed for the decomposition. We show that the migrant population has a comparative advantage in the private sector: increasing its participation into the public sector would not necessarily improve its average earnings. The second main finding is that the population effect is robust and significantly more important than wage or hours effects. This implies that the main source of disparity between the two populations is pre-market (education opportunities) rather than on-market.

Introduction

The urban labor market in China has gone through tremendous changes over the last three decades of economic reforms. One of the most dramatic over the recent years is related to rural-urban migration that has soared with the loosening of administrative controls over population movements between rural and urban areas. Although it is difficult to evaluate precisely the actual number of rural migrants in Chinese cities, estimations reported by the National Bureau of Statistics amount to 132 million rural workers in cities in 2006 (National Bureau of Statistics, 2007) 1 .

For decades since the late 1950s, the overall distribution of the Chinese population had been shaped by the strict policy of the household registration (hukou) system, which aimed at restricting migrations both between rural and urban areas and across regions. The main institutional barrier to mobility was then the exclusion of rural residents from the urban welfare system, which provided food ration, housing, medical care, education, childcare, and pension to urban residents. This system made it practically very difficult, if not impossible for rural hukou holders to survive in cities.

Economic reforms implemented from the late 1970s onwards have increased both the supply of and the demand for rural migrants in urban areas. As a consequence, population movements have risen sharply although not smoothly especially during the 1990s. Labor surplus in agriculture combined with reduced employment opportunities in township and village enterprises, increasing demand for labor by the booming urban private sector as well as a central government's policy of laisser-faire towards rural migration first fostered rural population movements to urban areas in the early 1990s. As a consequence, the number of rural migrants jumped from about 30 million in 1989 to 62 million in 1993 [START_REF] Li | Rural Migrant Workers in China: Scenario, Challenges and Public Policy[END_REF].

However, the reform of State-owned enterprises (SOEs) dramatically changed the situation faced by rural migrants because millions of urban laid-off workers entered the urban labor market after 1997. The harder competition on the urban labor market between urban unemployed and rural migrants was further reinforced by administrative regulations against rural migrants. By the end of the 1990s, several city governments had implemented local regulations to restrict rural migrants' employment and even forced enterprises to lay off migrant workers in favor of urban local workers. Other administrative regulations included a restricted access to certain job positions to urban residents only, or the imposition of fees to migrant workers and their employers [START_REF] Knight | Chinese Rural Migrants in Urban Enterprises: Three Perspectives[END_REF][START_REF] Appleton | Contrasting Paradigms: Segmentation and Competitiveness in the Formation of the Chinese Labor Market[END_REF], Knight and Yueh 2004a[START_REF] Knight | Urban insiders versus rural outsiders: Complementarity or competition in China's urban labor market?[END_REF][START_REF] Zhao | Migration, Labor Market Flexibility, and Wage Determination in China: A Review[END_REF]. This official administrative discrimination against rural migrants prevailed until recently when the central government issued a series of documents explicitly requiring local governments to enforce equal opportunities in employment and rights for rural migrants [START_REF] Li | Rural Migrant Workers in China: Scenario, Challenges and Public Policy[END_REF]. This change in policy towards rural labor mobility made the flow of rural migrants jumping again from about 80 million in 2001 to 132 million in 2006.

As it is often the case when two distinct labor force groups are competing in a labor market, the growing participation of rural migrants in the Chinese urban labor market raises the issue of potential discrimination behaviors against migrants. And indeed, various difficulties faced by rural migrants in terms of income and working conditions have been highlighted in the literature. Besides low income, the delayed payment of wages is a common feature for rural migrants. Their job mobility is much higher than local urban workers (Knight and Yueh 2004a) and they seldom have a contract signed with their employers. Their working conditions are tough, and they usually work much longer than the legal working time in lowend jobs that local urban workers do not want to take2 [START_REF] Yao | Social Exclusion and Economic Discrimination: The Status of Migrants in China's Coastal Rural Areas[END_REF][START_REF] Li | Rural Migrant Workers in China: Scenario, Challenges and Public Policy[END_REF]. As emphasized by [START_REF] Zhao | Migration, Labor Market Flexibility, and Wage Determination in China: A Review[END_REF], the hukou system still makes it very difficult for rural migrants to enter the formal sector. Measures of perceived discrimination by rural migrants themselves illustrate these points by showing that in many aspects rural migrants consider that they do not enjoy the same treatment as urban workers. As an example, the Chinese Household Income Project (CHIP) 2002 survey data used in this paper indicate that 70% of rural migrants perceive discrimination in terms of wage paid for equal work, 71% in terms of type of work and 61% in terms of working hours. The disadvantaged position of rural migrants is not limited to earnings differentials and working conditions. Again, according to CHIP data, 81% of rural migrants consider being discriminated against in their chance to be promoted, 82% in housing provision, and 85% in social security.

This paper intends to contribute to the understanding of the discriminatory behaviors against rural migrants by specifically focusing on the explanation of earnings differentials between rural migrants and urban residents. To that purpose, we use a nationally representative sample of urban residents and rural migrants for the year 2002 and we propose an extended form of Oaxaca-Blinder decompositions to explain the observed earnings differentials between the two populations. One important issue raised in the literature concerns the respective contribution of different allocations into sectors versus different wages earned within each sector, what [START_REF] Liu | Occupational segregation and wage differentials between natives and immigrants: evidence from Hong Kong[END_REF] refer to as between-and withinoccupation wage effect. We explore this question by focusing on two possible sources of segregation: (1) a differentiated access to sectors (we distinguish here the public sector, the private sector and self-employment); and (2) differentiated earnings within each sector.

Although the evolution of the labor market in urban China has received a large attention, evaluations of the earnings gap between rural migrants and urban residents in China remain limited, mainly because of the paucity of relevant data. Even when adequate data is available, their scope tends to be limited to a few regions or cities [START_REF] Knight | Chinese Rural Migrants in Urban Enterprises: Three Perspectives[END_REF][START_REF] Meng | The Informal Sector and Rual-Urban Migration -A Chinese Case Study[END_REF][START_REF] Meng | The Two-Tier Labor Market in Urban China -Occupational Segregation and Wage Differentials between Urban Residents and Rural Migrants in Shanghai[END_REF]. Given the huge regional differences across China, this limitation makes cross-study comparisons difficult and any generalization irrelevant. The most in-depth analysis of earnings differentials between rural migrants and local urban workers in China to date is certainly that of [START_REF] Meng | The Two-Tier Labor Market in Urban China -Occupational Segregation and Wage Differentials between Urban Residents and Rural Migrants in Shanghai[END_REF]. Using two comparable household survey data sets for Shanghai in 1995, they find evidence of discrimination against rural migrants in terms of both occupational attainment and earnings. Following the methodology of [START_REF] Brown | Incorporating occupational attainment in studies of male-female differentials[END_REF], they analyze the extent to which earnings differentials between rural migrants and urban residents are due to inter-or intra-occupational gaps and find that 82 percent of the hourly wage differential is due to unequal payment within occupation.

This paper tries to provide a general overview of earnings differentials between rural migrants and urban residents in China, using data from a nationally representative sample for 2002 made of comparable surveys for urban residents and rural migrants. The data set was collected under the China Household Income Project (CHIP), and contains about 8,000 observations for working individuals. It not only provides a wider scope than previous analyses, but also enables the comparison of two sub-populations that may be in strong competition for jobs in urban China. Indeed, rural migrants surveyed in the CHIP data were selected from resident communities [START_REF] Khan | China's household income and its distribution, 1995 and 2002[END_REF]. Although not capturing the wide spectrum of rural migrants (those living in construction sites and factories were excluded from the sampling process), these data are relevant for the purpose of our study since the surveyed migrants, already settled in cities, can be expected to have characteristics closer to urban residents against whom they are competing in the labor market.

Furthermore, we adopt a decomposition analysis based on microsimulation that substantially departs from the traditional approach based on the [START_REF] Brown | Incorporating occupational attainment in studies of male-female differentials[END_REF] extension of Oaxaca-Blinder decompositions. Our approach, formally based on sector allocation models allows for the evaluation of direct as well as indirect effects of changes in sector allocation on earnings differentials. In particular, it shows differences in comparative advantages between sectors for rural migrants and urban residents in the urban labor market.

The paper is structured as follows. The next section presents the decomposition methodology and section 3 describes the data used. Occupational distribution and wages and hours structures are discussed respectively in section 4 and 5. Section 6 presents the results of the decomposition analysis and discusses the various effects at stake. Concluding remarks are given in section 7.

Decomposition methodology

On average, our dataset shows that urban residents earn 1.3 times as much as rural migrants in 2002. We decompose this gap into 4 complementary effects: (1) the effect of different allocations between self-employment, public jobs and private jobs; (2) the effect of different hourly earnings structures; (3) the effect of different working times; and (4) the effect of the distribution of observed individual characteristics in the two populations. The decomposition is implemented by first estimating job allocation, earnings and hours equations, and then simulating counterfactual job status, earnings and hours.

The traditional approach to decomposition in this context follows the [START_REF] Brown | Incorporating occupational attainment in studies of male-female differentials[END_REF] extension to Oaxaca-Blinder decompositions, which explicitly treats differences in occupational distributions between the two groups under investigation. This method has been applied in particular by [START_REF] Liu | Occupational segregation and wage differentials between natives and immigrants: evidence from Hong Kong[END_REF] for Hong Kong and [START_REF] Meng | The Two-Tier Labor Market in Urban China -Occupational Segregation and Wage Differentials between Urban Residents and Rural Migrants in Shanghai[END_REF] for China. Our approach, however, is substantially different from the Brown et al. model in that it takes into account the fact that participation changes have indirect effects on within sector average earnings, as they affect population composition in the sectors. As will be illustrated, taking this dimension into account may greatly affect the results.

Model

To decompose the difference in average earnings between urban residents and rural migrants, we start with the following model. We consider two groups of workers, urban residents (u) and rural migrants (m), who can work into 3 different sectors indexed by k = 1, 2, 3 (self-employment, public sector and private sector). If Z is a vector of individual characteristics, the individual latent propensity to work in sector k for a person i belonging to group g = {u, m} is assumed to be of the form:

k i gk i k i Z P η δ + =
where the parameters δ gk are group and sector specific. A person is observed working in sector

k if { } j i j k i P P max = .
Within each sector k, hourly earnings are given by:

k i gk i k i u X w + = β log
where X is a subset of Z that contains human capital variables. Working time is given by:

k i gk i k i v Z h + = γ
These parameters can have various interpretations. As a general setting, the propensities to be found working in a sector, as well as the working time in that sector, may depend on: (i) the expected income in sector k, (ii) individual preferences for sector k, and (iii) a restricted access to some sectors for some groups. Since the above specifications are reduced forms, the parameters δ gk and γ gk can capture both preferences and constraints. In particular, a difference between δ uk and δ mk can be explained by occupational segregation (demand driven) between urban residents and rural migrants as well as by different preferences (supply driven) across the two populations. Differences in earnings parameters β gk are more readily interpretable in terms of segmentation, although they could also reflect compensating differentials.

The sector allocation model is estimated by maximum likelihood using a multinomial logit model. Residuals k i η are thus assumed to be i.i.d, with a Gumbell distribution [START_REF] Mcfadden | Conditional logit analysis of qualitative choice behavior[END_REF]. In this model, the probability to work in sector k is:

∑ = j gj i gk i i Z Z Z k ) exp( ) exp( ) Pr( δ δ
if i belongs to group g. The sectoral choice model can also be used to correct for selectivity in earnings equations [START_REF] Bourguignon | Selection bias corrections based on the multinominal logit model: Monte-Carlo comparisons[END_REF]. Yet, achieving identification in the selectivity model is problematic since no available variable can be considered as a fully exogenous instrument. However, in an attempt to control for possible selectivity bias, we estimated selectivity-corrected earnings functions but found no quantitative difference for the general results (see Appendix 3). We therefore present results based on models estimated without selectivity correction (earnings and hours equations are estimated by ordinary least squares) to keep the presentation and discussion simple.

Decomposition

To present the decomposition methodology, the above model is embedded into a more general notation. If we note δ g the full vector of sector choice parameters specific to any group g, and β g and γ g accordingly, the observed differential in average income between the two populations can be decomposed into four parts as follows:

1. The part due to different activity generating processes (δ u versus δ m ), through the simulation of the sector in which urban residents would be working if they had the same activity allocation rule as migrants, and inversely. Dropping hours for clarity, a typical decomposition in the [START_REF] Brown | Incorporating occupational attainment in studies of male-female differentials[END_REF] approach would be: This algebraic decomposition works well when the activity dimension is absent, as in the original Blinder-Oaxaca approach. However, including activity in the decomposition generates composition effects across sectors: by changing the sector allocation rule (e.g. from

∑ ∑ ∑ = = = - + - + - = - 3 1 3 1 3 1 )] , ( ) , ( ) , ( ) , ( [ )] , ( ) , ( )[ , ( )] , ( ) , ( )[ , ( k m k m k m k m k k m k u k m k k m k u k u k m u m w m s u w u s u w u w u s u s u s u w y y β δ β δ β β δ δ δ β
δ u to δ m
) while keeping the rest constant (notably the earnings generating process), the average earnings in each sector is modified accordingly because the individuals allocated to each sector are not the same any more. This is part of the activity effect. In contrast, the above decomposition uses observed average earnings ( ) , ( u k u w β ) to evaluate the effect of activity changes. Such earnings level has no counterfactual meanings. This is an important issue if some variables do affect the sectoral allocation differently in the urban and the migrant models. This problem is specific to the introduction of activity choice and does not appear in the original Oaxaca-Blinder approach.

As a result, we propose the following decomposition:

∑∑ ∑∑ ∑∑ ∑∑ ∑∑ ∈ = ∈ = ∈ = ∈ = ∈ = = - = + - = + = - = = - m i k m i m i k u i k m i m i k u i k m i k u i k m i u i k m i u i k u i k u i u i k m u k Z s Z w M k Z s Z w U Z w Z w k Z s U k Z s Z w U k Z s Z w U y y 3 1 3 1 3 1 3 1 3 1 ] ) , ( [ 1 ) , ( 1
] ) , ( [ 1 ) , ( 1
)] , ( ) , ( ][ ) , ( [ 1 1 ] ) , ( [ 1 ) , ( 1
] ) , ( [ 1 ) , ( 1
δ β δ β β β δ δ β δ β (1)
where 1[.] is an indicator variable, u i ∈ means all individuals i belonging to the urban resident population and U is the total size of this population (resp. m and M for migrants). Implementing this decomposition requires simulating individual counterfactual occupations. To that aim, we initially draw values of η for each individual, conditional on Z and his/her observed activity. We then use these drawn values to determine the allocation into counterfactual sectors. For instance, if individual i is a migrant and has received (

K i i η η ... ˆ1 )
compatible with her observed sector, her urban resident sector allocation counterfactual will be

] ) , ( [ k Z s u i = δ if { } j i uj i j k i uk i Z Z η δ η δ max ) ( + = +
. Earnings and hours counterfactuals also plug in residuals u ˆ and v ˆ based on observed status4 .

A last issue, often overlooked in the literature, is path-dependence. The sector allocation effect in equation ( 1) is computed on the urban resident population and using the urban resident earnings determination rule β u . But it could also be based on the rural migrant population, or with β m , or both. There is no reason to expect that the effect will be identical for all combinations. The same holds for each term of the above decomposition, so that the contribution of the various terms can be sensitive to the chosen path. It is thus necessary to compute every variant and check the robustness of the results.

An interesting situation where path-dependence can be important occurs when the optimal sector allocation rules are very different for the two populations. In that case, no allocation is generally superior. Consider for example the case where urban residents are better paid than migrants in every sector, but migrants receive higher wages in the private sector, whereas urban residents receive higher wages in the public sector. Since urban residents are far more concentrated in the public sector than migrants, the result of moving from δ u to δ m (sector allocation effect) will be to decrease the share of the public sector.

Depending on the model chosen for generating earnings, this shift would either decrease (urban residents earnings model) or increase (rural migrants earnings model) overall income.

This is a situation that will appear in the data.

Data

The data used in this paper has been collected during spring 2003 under the China household income project (CHIP), coordinated by the Institute of Economics, Chinese Academy of Social Sciences, with assistance from the National Bureau of Statistics (NBS).

The urban section of the household income survey contains two distinct sub-samples, one on urban hukou households and the other on households living in urban areas without urban hukou. These rural-urban migrant households are selected from the same twelve provinces5 as urban households, but not from all of the cities included in the urban survey. Since rural-urban migrants are mostly concentrated in large cities, the provincial capital cities plus one or two medium-sized cities in each province have been selected for the migrant survey. We restrict our analysis to cities common to the two sub-samples and to individuals aged 16 to 60 who declared working at least part of the year and earning wages or income from self-employment.

The sample contains 4,978 observations for urban hukou working individuals and 3,035 observations for rural migrants.

The sample scheme for the rural migrant survey was to allocate 200 households to each province in the coastal and interior regions and 150 households to each province in the western region. Within each province, 100 households were drawn from the capital city and 50 households from other cities. Within cities, only rural-urban migrant households living in residential neighborhoods were sampled. This implies that migrant workers living on construction sites or in factory dormitories are not accounted for [START_REF] Khan | China's household income and its distribution, 1995 and 2002[END_REF] 6 .

With little outside knowledge about the distribution of the migrant population by age, gender and location, it is difficult to make a judgment on how representative the migrant data is. This judgment also depends on how migrant households are defined. As indicated in some statistics from rural-urban individual migrants, the majority of migrants are single workers living in dormitories or construction sites. However, these single migrant workers are not our analysis unit since they experience temporary and short-term migration, with lower expectation to settle down with their families in cities. The migrant households covered in our sample are rather representative of long-term migrants living with their family and, as such, more directly comparable to local urban households. The average length of stay in cities for rural migrants is 7.34 years at survey year and 50% have been living in cities for more than 6 years; more than 75% had been staying in cities for the whole year.

Although the information collected in the two sub-surveys is meant to be consistent (with similar questions asked in the two surveys), earnings deserve particular attention. For urban hukou holders, questions concerning earnings are rather comprehensive. As discussed in the literature, the CHIP data is particularly careful with earnings measures: although it does not fully account for all fringe benefits provided by the public sector (such as implicit contribution to pensions, health insurance, or preferential housing rents), it includes some important non-monetary benefits (e.g. housing, medical care, child care and regional subsidies).

For urban hukou holders, the earnings variable is thus defined as the individual income of active workers earned from their own private business or work units 7 . For wage-earners, it is the sum of cash labor compensations (basic salary, bonuses, allowances, subsidies and other wages or income) and income in kind. For rural migrants, earnings are computed from the reported average monthly income in 2002 from their current job and the total (net) income from other sources. Available data do not allow us to take income in kind into account for rural migrants, which may slightly bias upward the observed income gap between migrants and urban residents. However, given that rural migrants have restricted access to subsidized services, this should not be a serious issue.

An important component of earnings differentials in China may arise from differences in living standards between different cities. To account for this issue, earnings are adjusted for provincial purchasing power differences, using [START_REF] Brandt | Spatial Price Differences in China: Estimates and Implications[END_REF] urban provincial-level spatial price deflators. This adjustment makes cross-provinces data much more comparable than the non-deflated data usually used in the literature.

Table 1 shows statistics on sector allocation, average earnings and working time by sector (self-employment, public sector and private sector). Urban residents' annual earnings are 1.3 times larger than rural migrant earnings: 11,881 yuan vs. 9,335 yuan. This results from a large difference in hourly wage between the two populations that is compensated by longer migrant working hours. The hourly wage of urban residents is on average twice that of rural migrants, the ratio being much higher in the public sector (2.3) than in both self-employment

(1.3) and the private sector (1.5). However, rural migrants work on average 69 hours per week, whereas urban residents work on average 44 hours a week. The fact that rural migrants, who receive lower hourly earnings, also tend to work longer may imply a strong income effect in labor supply behavior, but may also result from working constraints imposed by employers to workers with limited negotiating power.

Table 1 also shows that occupational distributions are extremely contrasted across the two groups and, as such, this is a potentially important source of income differences, as sectors have different wage-setting structures [START_REF] Chen | Earnings differentials and ownership structure in Chinese enterprises[END_REF]. Indeed, there is a very strong concentration of rural migrants in self-employment and, to a lower extent, in the private wage-earning sector (respectively 57% and 36%), whereas urban residents are overwhelmingly employed in the public sector (71%) and only slightly in self-employment (4%).

The comparison between the public and the private sector hourly wage structure also reveals an interesting difference between urban residents and rural migrants. Indeed, while urban residents working in the public sector get a much higher hourly wage than those working in the private sector (1.4 times higher), rural migrants earn slightly less in the public sector than in the private sector.

Occupational distribution

As described in section 2, we can evaluate the extent to which the occupational distribution is "biased" against rural migrants by simulating the occupational distribution of each group using the other group's sector allocation model. We first run a multinomial logit model over the choice of activity (self-employment, public sector, private sector), whose results are reported in Table 3. Explanatory variables include individual characteristics (education, age, gender, communist membership, geographical residence) as well as household characteristics (household size, number of children less than 6 years old).

Education influences the choice of both urban residents and rural migrants towards the public sector, the estimated effect being significantly stronger for urban residents8 . This implies that the urban resident model selects educated workers into the public sector much more strongly than does the rural migrant model. Moreover, although education increases the probability for rural migrants to work in the private sector as compared to self-employment, it does not significantly increase their chances to work in the public sector as compared to the private sector (which is not the case for urban residents).

The impact of age on activity choice only appears significant for rural migrants.

Estimations show an inverted U-shape relationship between age and the probability of entering self-employment: rural migrants in their early 40s have the highest probability to work as self-employed. A potential explanation is that young migrants entering the urban labor market mostly start working in the wage-earning sector and only switch to a more risky position when they have acquired enough economic, human and social capital9 .

From the multinomial logit model, we can simulate the sector allocation of each individual in the sample, under the rules that prevail in the other population. In other words, the simulation answers the question: "in which sector would urban residents (rural migrants) work if they were allocated to activities according to the rural migrants (urban residents) model?". Table 4 compares the observed and the simulated marginal distributions.

Shifting from the migrant model to the urban model decreases the share of selfemployment from 57% to 11% if applied to the migrant population and from 50% to 4% if applied to the urban population. Inversely, the same model change increases public sector share from 7% to 52% in the migrant population and from 14% to 72% in the urban population. The fact that the amplitude of these effects is sensitive to the population indicates that contrasted occupational distributions are only partly explained by a segregation (or model) effect and that population characteristics do play a role. However, it is interesting to note that the distribution of occupations based on the rural migrant model is much less sensitive to population changes than the distribution based on the urban model. This suggests that observed individual characteristics play a stronger role in the urban resident model than in the rural migrant model, as was already apparent from Table 3 10 .

Earnings and hours structures

Six earnings and hours equations have been estimated, for self-employment, the public and the private sectors, and for the two populations (see Appendix A1 and A2). Table 5 provides a synthetic view of the corresponding structures11 . In order to neutralize withinpopulation composition effects, simulated hourly earnings (and working hours) are computed separately for the whole urban and migrant populations, and for each of the six selfemployment/public/private urban/migrant model combinations. For instance in panel A, the first row shows in the first column, the average hourly earnings for the whole urban resident population under the 'urban/self-employment' earnings model (i.e. based on β u,self ), and in the second column, the average hourly earnings for the whole urban resident population under the 'migrant/self-employment' earnings model (i.e. based on β m,self ). It indicates that, if paid according to the urban rules, the urban population would earn 3.90 yuan per hour on average in self-employment, whereas, according to the migrant rules, the same population would earn only 3.11 yuan per hour in the same sector.

Unsurprisingly, whatever the earnings model, the simulated wage for the urban population (left table) is always higher than the corresponding simulated wage for the migrant population (right table). Hence, for any wage structure, rural migrants earn less than urban residents, which is clearly a composition effect.

Table 5 also shows that the urban resident's earnings structure is always more favorable than the migrant's earnings structure when applied to the urban population, but not when applied to the migrant population. Indeed, according to the urban resident earnings model, the average hourly earnings for the urban population would be 3.90 yuan in selfemployment, 5.92 yuan in the public sector and 4.93 yuan in the private sector, whereas according to the rural migrant earnings model, the corresponding average hourly wage for the same population would respectively be only 3.11 yuan, 5 yuan and 3.52 yuan. Results for the migrant population highlight a different pattern since, in the private sector, the migrant model is actually more favorable to migrants than is the urban resident model: the simulated hourly wage under the migrant earnings model (2.83 yuan) is higher than the simulated wage under the urban resident earnings model (2.61 yuan).

Another interesting result is that the public sector always pays better than selfemployment and the private sector, except for migrants under the migrant model. Indeed, in the migrant model, both self-employment and the private sector are more favorable to migrants (with a simulated hourly wage of respectively 2.90 yuan and 2.83 yuan) than is the public sector (2.59 yuan per hour).

These results suggest that migrants may have a comparative advantage with respect to self-employment and the private sector. Since this feature does not apply to the urban resident population, it is certainly related to some specific combinations of productive characteristics.

One explanation lies in the nature of public jobs offered to migrants and in returns to human capital. Indeed, rural migrants generally hold low-end non-tenured jobs in the public sector, which are very poorly paid on average, but with some returns to education. On the other hand, self-employment and the private sector provide better paid jobs to migrants, but with smaller returns to education12 . As a result, in a population with a low education level, higher returns to education in the public sector do not make up for low baseline wages: public wages are lower on average. Hence, rural migrants are relatively better off in self-employment and the private sector where the returns to human capital are lower for them. In the more educated urban population, a higher return to schooling ensures that public wages are higher on average. As mentioned in section 2, this feature is likely to generate strong path-dependence in the sectoral decomposition because shifting migrants away from self-employment would not necessarily make them better off.

Decomposition analysis

Putting all these elements together, we can decompose the earnings differential between urban residents and rural migrants into activity, earnings, hours and population effects. As mentioned in section 2, there are several paths to the decomposition. For instance, the effect of changing the sector choice model can be computed either on the urban or on the migrant population, and in each case, using either urban or migrant earnings and hours models.

This results in 8 different possibilities. To start with an overview, Table 6 presents the average effects over all paths, both in absolute value and as a percentage of the observed gap.

The average observed difference in annual earnings is 2,546 yuan. If the two populations differed only by their allocation into sectors, this difference would be only -32 yuan on average, or 2% of the total difference. Unsurprisingly, moving from the migrants' hourly earnings model to the urban residents' hourly earnings model would increase the earnings gap to 1,162 yuan (46% of the total). Inversely, everything else equal, migrants would earn 2,068 yuan more than urban residents as a result of their much longer working time (82% of the total). Finally, the strongest effect is related to differences in observed characteristics between the two populations: by itself, it generates a 3,487 yuan earnings difference. In a nutshell, this means that given the significant working time effect, urban residents would not earn much more on average if they did not have much better endowments, such as education and city work experience. This is reinforced by the fact that part of the hourly earnings effect may also capture unobserved productive characteristics that are not evenly distributed in the two populations (and should belong to the population effect)13 .

There are, however, several sources of uncertainty over the meaning of these averages.

One is path dependence. Another comes from the fact that all counterfactual earnings are based on estimated parameters: if these parameters are not precisely estimated, we may well shift on one side or the other by mere chance. Therefore, it is important to take into account the variances of the estimators. Finally, some residuals follow from random draws, which brings additional randomness.

In order to assess the robustness of our results, we have bootstrapped (200 times) the data so as to generate a distribution of occupation, earnings and hours equation parameters.

For each of the 200 iterations, we have drawn new residuals and computed the effects along all possible paths. Figures 1 to 4 draw the resulting distribution of each of the four decompositions presented in Table 6, expressed as a percentage of the observed earnings gap.

Each figure shows the full distribution for the different paths. For example, Figure 1 4) is robust, although the population effect is rather sensitive to the model of reference, as anticipated in section 4 14 .

Both the activity effect and the hourly earnings effect deserve specific attention.

Figure 1 and Table 7 indicate that the small average activity effect actually hides strong path dependence. They both show the effect on total earnings of moving from the migrant to the urban occupation model, when applied alternatively to the urban and the migrant population and using the urban or the migrant earnings and hours structures. The effect is clearly positive when applied to the urban population using the urban earnings structure. In contrast, it is clearly negative when applied to the migrant population using the migrant earnings structure.

Indeed, the effect of shifting from migrant activity (e.g. self-employment) to urban resident activity (e.g. public sector) increases total earnings with the urban wage model, whereas the effect of being more into the public sector decreases income under the migrant wage model.

The main reason for this latter (negative) effect has been anticipated in section 5: migrants differences in wage and participation structure (δ, γ, and β) across the two populations, what may in fact belong to an unobserved composition effect. As there is usually no natural experiment able to create exogenous variations in group identity, this is a general identification problem in the segmentation/discrimination literature. 14 There are only two paths for the population decomposition because we have only computed exact decompositions for the sake of internal consistency: population change is computed once changes in all other parameters have been introduced, so that they rely either on all urban parameters or on all migrant parameters.

have a comparative advantage in the private sector or self-employment given their earnings generating structure. Since the urban occupation rules imply fewer people in self-employment and the private sector and more in the public sector, these rules are suboptimal for migrants under the migrant wage structure, and would imply lower incomes on average. Our results corroborate [START_REF] Meng | The Two-Tier Labor Market in Urban China -Occupational Segregation and Wage Differentials between Urban Residents and Rural Migrants in Shanghai[END_REF] findings of a small impact of occupational segregation on the earnings gap between migrants and urban workers in Shanghai, but they also highlight the possibility of a strong path dependence that reveals interesting patterns.

From Table 7, it seems that using the urban population and the migrant wage model generates a strong positive effect. However, Figure 1 clearly shows that this is an average over a very imprecise simulation, driven by a large right tail. As a result, the activity decomposition lacks robustness mainly because it is extremely path dependent and, to some extent, because of statistical imprecision.

Regarding hourly wage, Figure 2 shows generally positive effects, although small and quite imprecise when applied to the migrant population using the migrant activity structure.

Indeed, the urban resident earnings structure is most of the time more favorable, but the private sector pays better under the migrant model for the migrant population (Table 5). The impact of this on hourly earnings structures is small when the private sector has a limited weight (i.e. under the urban activity model) but it is strong under the migrant activity model. Finally, it should be noted that employment in the public sector encompasses a variety of statuses. For urban residents, 95% are tenured jobs, most of the time as civil servants.

However, rural migrants employed in the public sector are mostly under short-term contracts.

As such, some of the differences in the public wage structures between urban and migrant employees may result from contrasted employment status and could arguably be interpreted as sectoral effects rather than wage segmentation. Therefore, we have reproduced the whole estimation and simulation procedure with all non-tenured public jobs allocated to the private sector category15 . As shown in Table A4, the decomposition is not affected by this definition change: average effects are similar in magnitude and the small activity effect is again the result of contrasted paths.

Conclusion

This paper assesses the sources of the strong income differences between urban residents and long term rural migrants in contemporary urban China, using nationally representative data. In particular, we disentangle the effect of different earnings structures within self-employment, the private and the public sectors from the effect of a different allocation into sectors with different payments. This is important because migrants' access to the public sector is very restricted, so that this could be expected to be an important source of income differences.

A decomposition analysis based on microsimulations indicates that despite a much contrasted sectoral allocation, the impact of sector allocation on earnings differences is neither strong nor robust. We find a stronger, but only partly robust within sector earnings discrimination effect between urban residents and rural migrants. Explanations of these results can be found in the fact that the sector allocation and, to a lesser extent, the earnings effects, are path dependent in the decomposition because rural migrants have a comparative advantage into self-employment and the private sector: shifting into the public sector is not always advantageous to them, whereas it is for urban residents or using the urban resident earnings structure. This result may cast doubt on the literature that concludes to limited sectoral effects on wage contrasts without checking path dependence.

Our findings on a segmented labor market between urban residents and rural migrants that reflects different comparative advantages are consistent with previous studies based on smaller datasets. Using data on 2,900 migrants surveyed in 1995 in 118 enterprises located in four cities, [START_REF] Knight | Chinese Rural Migrants in Urban Enterprises: Three Perspectives[END_REF] find that urban residents and rural migrants are highly imperfect substitutes in urban firms' production function. Rural migrants are both able to bear hardships and easily manageable, two "assets" that make them accept jobs that non-migrants would not. Using data on 1,500 migrants in Jinan city in 1995, [START_REF] Meng | The Informal Sector and Rual-Urban Migration -A Chinese Case Study[END_REF] finds that among rural migrants, those who possess higher human capital are more likely to be self-employed in the informal sector and are better off than those who work in the formal sector, which is consistent with our findings.

Are rural migrants second-class workers in urban China? Our analysis suggests that segregation in terms of both access to jobs and on-the-job earnings is not the major explanation for a large share of earnings differences between urban residents and rural migrants in 2002 as compared to differences in endowments. The strongest source of earnings differences is indeed found to be related to differences in population structures. The two populations are substantially different: rural migrants are younger, much less experienced and much less educated than urban residents. Pre-market discrimination, resulting mainly from lower education opportunity in rural areas, is thus more important in explaining earnings differences than any form of on-market discrimination resulting from sector allocation or earnings generating processes. The key policy implication of this result is to emphasize the importance of public policies towards rural education in order to reduce the endowment gap between rural migrants and urban residents in the urban labor market. Notes: Mean differences between urban residents and migrants are all significant at 1% level, except for the "male" variable. "City work experience" is measured as actual number of years of work in urban areas.

Source: CHIP data, authors' calculation.

2.

  The part due to different hourly earnings generating processes (β u versus β m ), through the simulation of how much urban residents would be paid if they were paid according to the migrants' earnings generating model in a given activity, and inversely. 3. The part due to different hours generating processes (γ u versus γ m ), through the simulation of how long urban residents would be working if their working time model was that of migrants, and inversely. 4. The part due to a different distribution of observed characteristics Z in the two populations.

δβ

  is the proportion of urban residents (u) in sector k when the sector allocation rule is δ is the average hourly earnings of urban residents actually observed in activity k when the hourly earnings generating process is β u .

  Line 1 minus line 2 gives the sector allocation effect (δ u vs. δ m ), the third line gives the earnings effect (β u versus β m ) and line 4 minus lines 5 gives the population effect 3 .

  shows the distribution of the activity effect for the four possible paths: the urban population under the urban earnings/hour model (urbpop/urbwage), the urban population under the migrant earnings/hour model (urbpop/migwage), the migrant population under the urban earnings/hour model (migpop/urbwage), the migrant population under the migrant earnings/hour model (migpop/migwage). The sign of the hours and population decompositions (Figures 3 and

Figures

  Figures A1 to A4 in Appendix 3 show the robustness of these results to the inclusion of selectivity correction in the earnings equations, with the activity decomposition being again very path dependent. The main difference lies in the fact that the distributions have much larger variances within each path, which comes from the fact that the selectivity model is less precisely estimated.

FigureFigure 4 :

 4 Figure 1: Distribution of activity decompositions

Table 2

 2 older (34.31 versus 27.07) and most are married (90% versus 55%), which is consistent with the fact that we are focusing on less temporary migrants. Urban residents are also far more often members of the Communist Party and have much more experience than rural migrants, experience being measured by the actual number of years of work in urban areas. Last, in terms of job status, the lower average qualification of rural migrants is illustrated by their very low share in white collar jobs: only 4.5% of rural migrants hold professional or technician positions (to be compared with 32.7% of urban residents) and 2.2% are office workers (against 19.6% for urban residents).

provides a description of individual characteristics, which highlights very important endowment differences between the two groups. Hence, urban residents are on average older and much more educated (almost 4 years difference) than rural migrants. As compared to the Shanghai sample used by

[START_REF] Meng | The Two-Tier Labor Market in Urban China -Occupational Segregation and Wage Differentials between Urban Residents and Rural Migrants in Shanghai[END_REF]

, migrants in our sample are slightly

Table 1 -Earnings, working time and activity of urban residents and rural migrants in 2002

 1

		Urban residents	Rural migrants	Mean test
	Rural migrants	Mean or %	Std. Dev.	Mean or %	Std. Dev.
	Annual earnings	11,881	7,713	9,335	13,387	**
	Self-employed	10,223	12,015	10,077	11,536	NS
	Public sector	12,742	7,435	6,967	5,139	**
	Private sector	9,639	7,061	8,625	11,929	*
	Hourly wage	5.60	4.34	2.83	4.03	**
	Self-employed	3.64	4.23	2.86	3.89	**
	Public sector	6.14	4.51	2.64	2.16	**
	Private sector	4.33	3.38	2.82	4.50	**
	Weekly working time	44	11	69	19	**
	Self-employed	61	20	74	17	**
	Public sector	42	8	57	18	**
	Private sector	46	12	64	18	**
	Activity
	Self-employed	4.16%		56.97%
	Public sector	71.47%		7.08%
	Private sector	24.37%		35.95%
	# of obs.	4,978		3,035

Notes:

The mean test column indicates the significance level of mean differences between urban residents and migrants. NS non significant, * significant at 5%; ** significant at 1%. Source: CHIP data, authors' calculation.

Table 2 -Individual characteristics of urban residents and rural migrants in 2002 Urban residents Rural migrants

 2

		Mean or %	Std. Dev.	Mean or %	Std. Dev.
	Years of schooling	11.72	2.88	7.97	2.71
	City work experience	20.71	9.73	7.15	5.01
	Age	40.71	9.07	34.31	8.09
	Male	56.33%		56.51%
	Ethnic minority	3.42%		8.27%
	Communist membership	29.07%		3.13%
	Married	87.06%		89.95%
	Household size	3.12	0.68	2.77	0.91
	Long-term tenure	74.16%		5.09%
	Professional or	32.74%		4.48%
	technicians
	Office workers	19.62%		2.17%
	Workers	42.01%		32.52%
	Self-employed	4.16%		56.97%
	# of obs.	4,978		3,035

Table 3 -Estimation of the Multinomial Logit Model for occupational choice Public sector versus Self-employment Private sector versus Self-employment Private sector Versus Public sector

 3

		Coef.	Std. Err.	Coef.	Std. Err.	Coef. Std. Err.
	Urban residents
	Years of schooling	0.255**	0.027	0.112**	0.028	-0.143** 0.014
	Age	-0.072	0.092	-0.064	0.095	0.008	0.037
	Age 2	0.002	0.001	0.001	0.001	-0.001	0.000
	Coast	0.423**	0.197	0.692**	0.203	0.268** 0.082
	West	0.039	0.171	0.086	0.179	0.047	0.088
	Spouse of the household head -0.480**	0.165	-0.347**	0.172	0.133*	0.079
	Married	-0.357	0.395	-0.794**	0.403	-0.437** 0.150
	# of children below 6	-0.107	0.258	-0.182	0.270	-0.075	0.132
	Household size	-0.133	0.108	-0.008	0.112	0.125** 0.052
	Communist membership	0.931**	0.230	0.234	0.241	-0.697** 0.095
	Male	-0.559**	0.164	-0.578**	0.170	-0.019	0.073
	Constant	1.303	1.727	2.448	1.766	1.145	0.719
	Rural migrants
	Years of schooling	0.072**	0.030	0.035**	0.016	-0.037	0.031
	Age	-0.256**	0.065	-0.274**	0.039	-0.019	0.065
	Age 2	0.004**	0.001	0.003**	0.001	0.000	0.001
	Coast	1.655**	0.202	0.326**	0.099	-1.329** 0.204
	West	1.251**	0.203	-0.303**	0.098	-1.554** 0.209
	Spouse of the household head	-0.201	0.191	0.165	0.102	0.366*	0.197
	Married	-0.404	0.309	-0.408**	0.176	-0.004	0.306
	# of children below 6	0.009	0.217	-0.082	0.109	-0.090	0.223
	Household size	-0.223**	0.088	-0.055	0.048	0.168** 0.090
	Communist membership	1.020**	0.307	0.123	0.247	-0.897** 0.323
	Male	0.168	0.181	0.108	0.099	-0.060	0.186
	Constant	1.505	1.144	4.885**	0.659	3.380** 1.134
	# of observations	Urban residents: 4,978	Rural migrants: 3,035
	Log likelihood	Urban residents: -3,309	Rural migrants: -2,495
	Notes: * significant at 10%; ** significant at 5%.

Source: CHIP data, authors' calculation.

Table 4 -Observed and simulated occupational distribution of urban residents and rural migrants in 2002 Urban residents Rural migrants

 4

		Frequency	%	Frequency	%
	# of obs.	4,978		3,035
	Occupation
	Observed
	Self-employed	207	4.2	1,729	57
	Public sector	3,558	71.5	215	7.1
	Private sector	1,213	24.4	1,091	36
	Simulated with the other group model
	Self-employed	2,499	50.2	328	10.8
	Public sector	712	14.3	1,582	52.1
	Private sector	1,767	35.5	1,125	37.1

Table 6 -Decomposition of observed earnings gaps between urban residents and rural migrants, 2002 Means over all observed paths

 6 : means over 200 bootstrapped replications -see Figures1-4for the full distributions.

	(Yuan)	(%)

Note

Source: CHIP data, authors' calculation.

Table 7 -Path dependence for the activity effect Means by path

 7 : means over 200 bootstrapped replications -see Figures1-4for the full distributions.

	Population	Wage/hours model		Activity effect
			(Yuan)	(% of observed)
	Urban residents	Urban residents	451	18%
	Urban residents	Rural migrants	1,376	53%
	Rural migrants	Rural migrants	-1,270	-51%
	Rural migrants	Urban residents	-689	-27%
	Source: CHIP data, authors' calculation.

Note

Table A2 -Working hours equations Self-employment Public sector Private sector Urban residents Rural migrants Urban residents Rural migrants Urban residents

 A2 Notes: 1. The dependent variable is the number of hours worked in a year.2. The reference category for regional location is the central region.3. Numbers in italics are t-statistics. * Significant at 5 percent level ** Significant at 1 percent level Source: CHIP data, authors' calculation.

					Appendix 2
		Figure A3: Hours decompositions (w/ selectivity correction)
	Years of schooling City work experience City work experience 2 .005 .01 .015 .02 .025	20.72 0.68 -10.38 -0.31 0.06		-1.17 -0.14 -2.66 -0.20 -0.03	-5.69* -2.29 -18.96** -5.09 0.37**		-23.87 -1.09 -22.21 -0.55 0.39	-23.96** -3.29 -14.59 -1.59 0.19	Rural migrants -48.24** -4.31 1.39 0.10 -0.12
			0.06		-0.04	4.45		0.20		0.84	-0.20
	Coast	0	245.74		65.21	-57.80**		23.94	-209.18** -207.54**
		-500	1.28 -400		1.15 -300	-3.64 -200		0.14	-100	-4.91	0	-3.13
	West		687.07**	363.46** Share of earnings gap -25.05	488.37*	-124.04*	93.50
			4.29	7.39 urb pop/mig act	-1.51	2.73 urb pop/urb act	-2.69	1.31
	Communist	-184.32	-242.90 mig pop/urb act	0.17	-75.73 mig pop/mig act	-141.00*	-250.93
			-0.80		-1.80	0.01		-0.34		-2.59	-1.49
	# of children below 6	74.83		-180.73**	-3.71		-255.09	-70.85	16.53
	0.34 -101.32 -0.81 Figure A4: Population decompositions (w/ selectivity correction) -3.45 -0.14 -1.52 -1.00 # of children at school -35.46 18.42 34.91 13.76 123.88* 0.23 -1.14 1.25 0.31 0.33 2.68 .015
	Married		-314.62		329.35**	66.25**		-97.82	68.87	-95.88
			-1.18		3.49	2.18		-0.46		0.99	-1.18
	Male	.01	-43.50 -0.30		-4.83 -0.11	64.55** 4.67		3.78 0.03		182.09* 4.94	-61.26 -1.08
	Constant	3274.73** 3514.66** 2362.30** 3185.18** 2817.03** 3841.76**
			6.58		28.63	53.06		10.32	25.65	29.03
	Observations .005	207		1,729	3,558		215		1,213	1,091
	R 2		0.11		0.05	0.02		0.10		0.06	0.05
		0
		50		100		150		200	250
					Share of earnings gap
			mig wage/mig act			urb wage/urb act

Source: CHIP data, authors' calculation.

Given that

20% of rural migrant workers are estimated to live with their family in urban areas, the total number of rural-urban migrant population is estimated at around 160 million in 2006.

The construction sector is a typical example here. According to the Project Team of ResearchCouncil, State Council (2006), data from the 2000 Census indicate that 80% of all the jobs in the construction sector are taken by rural migrants. These jobs are typically low-skilled, hard and dangerous, and as such are not valued by urban residents.

If hours had not been dropped for legibility, there would be an additional term showing the working hours effect.

Whenever the individual is not simulated in her original sector, she is given a residual value from the destination sector observed distribution, so that her rank in her initial distribution is preserved.

The twelve provinces are: Anhui, Beijing, Chongqing, Gansu, Guangdong, Henan, Hubei, Jiangsu, Liaoning, Shanxi, Sichuan and Yunnan.

A full description of the sampling method and the data can be found in[START_REF] Li | 1995 and 2002 Household Surveys: Sampling and Data description[END_REF].

Measuring income for self-employed is a highly debated issue. A recent paper by[START_REF] De | Measuring Microenterprise Profits: Must we ask how the sausage is made?[END_REF] compares the relative quality of direct reports of profits with details of revenues and expenses, and concludes that the former are likely to be more accurate in measuring firms' profits. In this vein, our earnings variable is based on reported net income of private businesses.

Although coefficients absolute values are not directly comparable in Table3, the significance of the difference between urban residents and rural migrants equations has been checked by pooling the data and adding interaction terms for all variables with a "migrant" dummy.

This result is consistent with[START_REF] Meng | The Informal Sector and Rual-Urban Migration -A Chinese Case Study[END_REF] who finds that, in 1995, rural migrants in Jinan city are more likely to be self-employed in the informal sector as their city work experience increases.

In this respect, the population effect in the decomposition should be stronger whenever based on the urban occupation model (see section 6).

The simple structure of weekly hours given in panel B does not deserve much explanation and will not be discussed here. The main result is that working hours are longer in self-employment and the private sector, as well as in the migrant model, with no exception. As urban residents are more concentrated in the public sector, this provides two reasons for the lower average working hours observed in this population.

Table A1 illustrates these differences in returns to schooling across sectors for migrants.

A common limitation of the earnings differentials literature is that the constants incorporate differences in means of unobserved characteristics across populations. In this respect, we arbitrarily incorporate into

We are left with only 2% of the migrant population in tenured public jobs (instead of 7% in all public jobs).

Source: CHIP data, authors' calculation.

The reference category for regional location is the central region.

Numbers in italics are t-statistics. * Significant at 5 percent level ** Significant at 1 percent level Source: CHIP data, authors' calculation.


Mohamed Abid

Nicolas Delaunay

Bertrand Le Gal

Dominique Dallet

Chiheb Rebai

Nathalie Deltimple

Eric Kerherve

Didier Belot

Mixed Cartesian Feedback for Zero-IF WCDMA Transmitter

Keywords: Cartesian feedback loop, WCDMA transmitter, Architecture matching algorithm I

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Third generation wireless communication standard WCDMA uses non-constant envelope modulation techniques to increase spectral efficiency for high data rates [START_REF] Gpp | User Equipment (UE) radio transmission and reception[END_REF]. Those modulations require high linear radio-frequency (RF) power amplifier (PA), whereas, power efficiency is maximized when the PA operates at its non-linear region. The current state of the art is to design a moderately linear PA and to employ some linearization technique. The amplifier operates as close as possible to saturation, maximizing its power efficiency, and the linearization system maximizes the spectral efficiency in this near-saturated region. Many methods (analog or digital) are proposed to reduce the effects of nonlinearities like Predistortion [START_REF] Cripps | Advanced Techniques in RF Power Amplifier Design[END_REF], Post-distortion [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF], Feedback [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF] and Feedforward [START_REF] Cripps | Advanced Techniques in RF Power Amplifier Design[END_REF] techniques. Among these, Cartesian feedback (CFB), which forms an alternative feedback technique, is an attractive option for two reasons: first it automatically compensates all process variations and secondly its linearization process is applied to all components in the loop. Nevertheless, historically the technique has suffered from practical shortcoming; it needs a phase corrector to compensate delay around the loop. In addition, the analog implementation of phase corrector is difficult to realize and highly area expensive. In this paper, authors propose a new solution to overcome this problem with a digital phase rotator approach. Due to the increasing demand of cost reduction, a Zero-Intermediate Frequency (Zero-IF) architecture avoiding the use of external filter has been chosen. Moreover, CFB with a Zero-IF architecture brings few additional components for an efficient linearity improvement. Full-analog CFB architecture has been studied and realized [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF]. There are some drawbacks associated with this solution such as high area occupation and high power consumption. Delegating the phase rotation adjustment processing to a digital stage provide flexibility, higher integration and less area size than in full-analog architecture.

The paper is organized as follow. Section II presents Zero-IF transmitter with the CFB linearization loop and design consideration. Section III deals with implementation study of the digital stage where two solutions are presented and discussed. Section IV shows synthesis results such as occupied area and power consumption for ASIC target.

II. CARTESIAN FEEDBACK TRANSMITTER

A. Linearization Technique

Proposed linearization technique architecture based on a digital CFB implementation is shown in "Fig. 1". Quadrature baseband signals are directly up-converted to 1.95 GHz [START_REF] Gpp | User Equipment (UE) radio transmission and reception[END_REF]. The RF signal is then amplified thanks to PA. In the feedback path, the PA output is attenuated, downconverted to the baseband quadrature signals and filtered out. After the analog to digital convertor (ADC), a phase adjustment is applied to I FB and Q FB in order to cancel phase rotation around the loop. Feedback signals are subtracted from the input to provide return signals I return and Q return . These signals include the forward path non linearity. By loop effect, forward path non linearity is subtracted from input signals. Thus, input I/Q signals are pre-distorted to provide a linearized PA output. CFB transmitter is commonly implemented as a fully analog circuit [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF]. In such topology, subtraction operator and phase corrector have to be highly linear with low noise components. A digital implementation of subtraction and phase corrector relax linearity and in-band noise constraints than a full analog circuit. By having an optimized and high integrated digital stage, lower power consumption can be reached than analog configuration.

B. CFB Digital Stage and Design Consideration

Delay in the loop can lead to Error Vector Magnitude (EVM) degradation and instability [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF]. The baseband loop filters in the feedback path lead to delay and symbol rotation when feedbacks signal and input signal are subtracted. Phase variations are cancelled by using the circular transformation given in [START_REF] Gpp | User Equipment (UE) radio transmission and reception[END_REF], where θ is the phase correction value "Fig. 2".

(1) θ is calculated by comparing forward and feedback paths phases. Two architectures are evaluated for the circular transform implementation. The first architecture uses lookup table (LUT) and complex multiplier which is an expensive solution in terms of area occupation. The main advantage of this solution is to not introduce a large delay into the loop. The second architecture uses a Coordinate Rotation Digital Computer (CORDIC) algorithm [START_REF] Volder | The CORDIC Trigonometric Computing Technique[END_REF] which requires less area than a complex multiplier when the data path exceeds 10 bits. Pipelined CORDIC introduce latency in the loop, a tradeoff between area occupation, latency and throughput is revealed, a fine tuning of the implementation variables will lead to optimal solution. Delay in the loop is limited by period of WCDMA data (T chip ) for stability consideration [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF]. Digital stage operating frequency threshold is set to 242 MHz due to DAC and ADC characteristics "Fig. 1".

III. DIGITAL CFB IMPLEMENTATION

As already presented, the main task of the digital stage is to perform the vector rotation. Previously, the angle of rotation has to be estimated. This angle is the difference between the phase of the direct channel I/Q and the return channel I FB /Q FB . Therefore, the digital CFB architecture is organized using three blocks as shown in Fig. 2.

x phase estimation, x vector rotation, x subtraction.

A. Phase Estimation

Regarding phase estimation, it is very important to notice that phase subtraction must be done "modulo 2π" to keep the same range of variation of the angle applied to the next block (vector rotation). It implies that the phase estimation block is divided into two sub functional units: direct, feedback phase estimations (atan function) and modulo function.

1) "atan" function implementation

Different implementations of the digital atan function are proposed in the literature [START_REF] Altmeyer | Design Implementation, and Testing of a High Performance ASIC for Extracting the Phase of a Complex Signal[END_REF] and one of them, which is the most trivial, uses a look up table (LUT) [START_REF] Th | Optimisation and implementation of the arctan function for the power domain[END_REF]. This solution seems to be over-sized and very tasty in Silicon consumption in comparison with other alternatives such as the CORDIC algorithm. A comparative study regarding implementation of these two solutions is presented, as well as output performances.

a) LUT based architecture LUT based solution, illustrated in Fig. 3, consists first making the division of "Q" to "I" and then going through an interpolation table (LUT) where all the values of the atan function are stored. LUT length is function of the phase estimation precision so "1" deg precision lead to 1440 bits ROM. Thanks to symmetry properties of atan function, size of the LUT can be limited to the half [START_REF] Chung | Open-Loop Digital Predistortion Using Cartesian Feedback for Adaptive RF Power Amplifier Linearization[END_REF]. To implement the division, multitude algorithm solutions can be considered. An algorithm called "Restoring Division Algorithm" [START_REF] Oberman | Division algorithms and implementations[END_REF] is used since it allows a very adequate operating frequency. This algorithm requires that the operands are positive and the numerator is greater than or equal to the denominator. Additional developments can process negative operands. Division by "0" results in saturation at the maximum value.

b) CORDIC based architecture

Another alternative for atan function implementation is to use an iterative algorithm called "CORDIC algorithm" [START_REF] Volder | The CORDIC Trigonometric Computing Technique[END_REF]. CORDIC based solution doesn't require division as shown in Fig. 4. It takes as input the two coordinates of the vector and provides its phase [START_REF] Volder | The CORDIC Trigonometric Computing Technique[END_REF]. This algorithm was designed to use adder and subtractor resources only as presented in Fig. 5. It was subsequently improved in order to calculate trigonometric functions (exp. cos, sin, atan ...) and this is done by configuring wisely its inputs variables. Implementation of CORDIC algorithm can be done with several ways [START_REF] Chang | Digital Systems Design with VHDL and Synthesis: An Integrated Approach[END_REF]. A tradeoff between throughput and design area is required by application as specified in section 2. The small computation complexity of the algorithm and its modularity gives considerable flexibility in the implementation phases and a full-pipelined architecture was adopted.

2) "Modulo" function implementation

Due to the extensive range of phase variation, the subtraction can overflow and so, it should be standardized to be adequate for the input of the next stage. It consists in calculating modulo 2π function. The idea is to calculate the remainder of the Euclidean division of the wanted angle by K*2π. A smart implementation of this function can be described by an algorithm organized as follows. First, a sign test is effectuated to benefit from the symmetry property of this function. Then the angle value is tested if it has exceeded a full circle turn. If so, 2π is subtracted from it and the test continues, else this value is retained as the output result.

B. Vector Rotation 1) LUT and multipliers solution

This first solution consists in following precisely the mathematical function of the rotation vector as it is described in equation (1). Fig. 3 shows an implementation example. Thanks to the phase cosine and sinus values, the complex multiplication can be done. To compute those coefficient; LUTs that contains the values of sine and cosine function can be used. An optimization step uses a single LUT (e.g. cosine) and trigonometric relationships to move from one function to another. A second optimization step exploits quarter wave symmetry.

2) CORDIC based solution

As shown in Fig. 4, the CORDIC algorithm can perform a vector rotation without multiplier resources allocation. A simple initialization on his entries, with the vector on which we rotate: namely I FB /Q FB and the angle to perform, is enough.

C. Subtraction

Subtraction is simple enough to be implemented in digital. Indeed, it is necessary to calculate the two's complement of the second operand and then use an adder.

IV. SYSTEM VALIDATION AND SYNTHESIS RESULTS

A. Linearization Technique Validation

All building blocks making the digital stage have been designed in hardware descriptive language (HDL) with ModelSim® and have been characterized stand-alone. Now, we are able to realize system level simulations in order to validate the overall architecture, whyfor ADS Software have been used. Fig. 6 and Fig. 7 depicts the output spectrum of the PA with and without CFB technique for a same output power [START_REF] Delaunay | A RF Transmitter Linearized Using Cartesian Feedback in CMOS 65nm for UMTS Standard[END_REF]. This last exhibits clearly a decrease of the distortions on the adjacent channel due to CFB loop (Adjacent channel power ratio (ACPR) receives an improvement of 22dB at 5MHz from the carrier). In fact comparing with the mask define by the standards UMTS [START_REF] Gpp | User Equipment (UE) radio transmission and reception[END_REF], the output spectrum for a Zero-IF architecture is out of specifications, in opposite with the output spectrum of the CFB loop.

B. Implementation Results

To validate this digital stage, we compared results obtained by floating simulation on Matlab® with those provided by HDL on ModelSim®. Fig. 8 shows results of the phase alignment stage simulation. Note that the impact of the resolution (number of bits chosen) ensures convergence. The algorithm begins to track the desired value with acceptable accuracy after certain latency fixed by the number of internal registers. We also note that the algorithm oscillates around the solution when the values are close to "0". To respect the real-time constraint, the point on which we will act is none other than the throughput of the synthesized circuit, so it is imposed as 242 MHz.

Table 1 summarizes ASIC synthesis results on 65nm technology (CORE65LPLVT1.00V) in terms of area occupation and energy consumption for our two considered solutions (CORDIC and LUT). Two power types are presented: the dynamic power which depends on throughput and the leakage power whose consumption is constant. LUT based solution consumes less energy in comparison with the CORDIC one with almost likely surface occupation; therefore it is more adequate for our application. Nevertheless, hybrid architecture could be considered by combining the LUT solution for the phase estimation bloc and the CORDIC one for the vector rotation bloc. It is important to notify that the proposed solution tree time less energy than the full-analog one; 2.94 mW for our solution compared to 8.8 mW in the case of full-analog architecture [START_REF] Dawson | Automatic Phase Alignment for a Fully Integrated Cartesian Feedback Power Amplifier System[END_REF].

V. CONCLUSION

The problem of phase alignment has stood as the primary barrier to the widespread use of the Cartesian feedback technique. In this paper a Cartesian feedback direct conversion transmitter with digital processing has been presented and evaluated for a Zero-IF WCDMA transmitter. This mixedsignal architecture allows the linearity constraints on the subtractor, on the phase corrector and also on the DACs to be relaxed.

Figure 1 .

 1 Figure 1. Zero-IF WCDMA transmitter with digital CFB loop

Figure 2 .

 2 Figure 2. Digital stage architecture

Figure 3 .

 3 Figure 3. LUT based solution

Figure 4 .

 4 Figure 4. CORDIC based solution

Figure 5 .

 5 Figure 5. CORDIC example implementation

Figure 6 .Figure 7 .

 67 Figure 6. Output spectrum without CFB

Figure 8 .

 8 Figure 8. Outputs stage simulation

TABLE I

 I

		.	ASIC SYNTHESIS RESULTS
				CORDIC	LUT
	Phase estimation	Occupation Dynamic Power Leakage power	6656 µm 2 1.01 mW 2.95 µW	4480 µm 2 0.46 mW 2.09 µW
		Occupation	9477 µm 2	14935 µm 2
	Rotation	Dynamic Power	1.4 mW	1.19 mW
		Leakage power	4.17 µW	5.72 µW
		Occupation	613.6 µm 2
	Subtraction	Dynamic Power	0.098 mW
		Leakage power	0.277 µW
		Occupation	23402 µm 2	24461 µm 2
	Whole solution	Dynamic Power	3.77 mW	2.94 mW
		Leakage power	10.35 µW	10.24 µW


Paul Sharp
email: paul.sharp@econ.ku.dk.

Jacob Weisdorf
email: ja-cob.weisdorf@econ.ku.dk.

A Malthusian Model for all Seasons *

Keywords: JEL classification codes: J22, N13, O10 Agricultural Intensification, Boserup, Labour Surplus, Malthus, Seasonality

 and others, which suggests that harvest seasons in traditional agriculture are characterized by severe labour shortage.

Introduction

The so-called 'Malthusian' model is frequently used by development economists, growth economists and economic historians to capture development in a traditional agricultural society. An issue often discussed in relation to agricultural development-but about which the Malthusian model is silent-is the effect on agricultural labour productivity of more intensive land-use. According to [START_REF] Hunt | Labor Productivity and Agricultural Development: Boserup Revisited[END_REF], scholars divide into two camps. On the one hand, [START_REF] Boserup | The Conditions of Agricultural Growth[END_REF] makes a strong case that agricultural intensification raises labour costs per unit of food produced. In her view, therefore, agricultural labour productivity is negatively correlated with land productivity, a notion referred to by Hunt as the 'decline thesis'. Other scholars, however, have pointed to the nearly fourfold increase of England's population level between 1500 and 1800 and compared it to the halving of the share of England's population employed in agriculture over the same period as convincing evidence that agricultural labour productivity is positively correlated with land productivity. Following Hunt, this position has become known as the 'rise thesis'.

In this paper, we demonstrate that the 'rise thesis' and the 'decline thesis' can both be understood within the context of a single framework through an acceptance of the importance of seasonality in agriculture. This we demonstrate by adding two salient features about traditional agriculture to a stylized Malthusian model. The first feature involves making a distinction between two types of seasonal activities in agriculture: cultivation and harvesting.

The second feature builds on evidence reported by [START_REF] Boserup | The Conditions of Agricultural Growth[END_REF] and others, which suggests that land productivity in traditional agriculture is limited, not by how much food can be grown, but by how much labour is available in the harvest season. In our seasonalityaugmented version of the Malthusian model, the sign of the correlation between land and labour productivity depends simply on the relative rate of growth of technological progress in cultivation and harvesting activities.

The model

Following [START_REF] Clark | A Farewell to Alms: A Brief Economic History of the World[END_REF], a defining characteristic of a traditional agricultural society is that technological progress over the long run permits a larger population but does not affect income per capita which remains at the level of subsistence. The stylized Malthusian model captures this through the use of two components: (i) a positive relationship between income and population growth, and (ii) diminishing returns to labour in production. Our modified version of the Malthusian model builds on both components. The former is described in detail in the following; the latter is described further below.

Consider a one-sector, one-good agricultural economy. Economic activities extend over infinite (discrete) time. Unless explicitly noted, all variables are considered in period t. In period t, the population consists of N t identical individuals. Consistent with the stylized Malthusian model, the reproductive success of an individual is 'checked' by the size of its income. Symbolically, the number of surviving children of an individual is given by the functional relationship n = n(w), where w is income per individual and where n(•) is continuous and monotonic, with n(0) = 0 and n(∞) > 1. This implies that a 'subsistence' income level exists, defined as the income level at which an individual is able to raise exactly one surviving offspring. Since all individuals are identical, change in the size of the labour force between any two periods is given by N t+1 = n t N t .

To introduce aspects of seasonality, suppose that goods are generated according to a two-step procedure. This involves first the production of intermediate goods (think: crops cultivated for the purpose of harvesting), then the production of final goods (think: harvested crops). Thus, there are two types of seasonal activities in the model: cultivation (seeding, weeding, harrowing, hoeing etc) and harvesting.

Suppose that the production of output is subject to constant returns to land and labour.

Each individual is endowed with one unit of labour, which, as will be explained below, is divided endogenously (but, for the individual, parametrically) between output-generating activities and unemployment. Consistent with the stylized Malthusian model, land, measured by X, is in fixed supply, and is normalized to one (X ≡ 1). For simplicity, there is no property rights over land, and each period the land mass is divided equally between the indi-viduals. In symbolic terms, the land mass per individual is thus given by x = X/N ≡ 1/N . Let subscript C and H denote Cultivation (intermediate goods) and Harvesting (final goods) activities, respectively. Output per individual in season i ∈ {C, H} can thus be written as

y i = A i (γ i e i ) α (x) 1-α ≡ A i (γ i e i ) α µ 1 N ¶ 1-α , α ∈ (0, 1) , i ∈ {C, H} , (1)
where γ i ∈ (0, 1) is the fraction of the year for season i ∈ {C, H} (implicitly, therefore, With reference to seminal work by [START_REF] Lewis | Economic development with unlimited supplies of labour[END_REF], the labour resources not used for outputgenerating activities, i.e. γ c (1e c ), can be thought of as surplus labour or disguised unemployment.

γ C + γ H ≤ 1); e i ∈ (

Stability and Comparative Statics

We want to analyze the correlation between land and labour productivity in a steady state.

In a steady state, all variables grow at a constant rate (possibly zero). Specifically, this means that the steady state population growth rate is constant. A constant rate of growth of population implies that income per individual must be constant over time. For tractability of the analysis, we parameterize the Malthusian relationship between income and population growth, so that n(w) = w. Then, using [START_REF] Boserup | The Conditions of Agricultural Growth[END_REF], it follows that the gross rate of growth in income per individual is given by

w t+1 w t = A H (γ H ) α ³ 1 n t N t ´1-α A H (γ H ) α ³ 1 N t ´1-α = µ 1 w t ¶ 1-α .
Hence, in steady state (marked with an asterisk), income per individual is w * = 1. Notice that stability of the steady state requires that ∂w t+1 /∂w t | wt=w * < |1|, a condition that is fulfilled when α ∈ (0, 1), which is equivalent to having diminishing returns to labour in production.

By use of the parameterization above, having w * = 1 means that each individual is able to raise exactly one surviving offspring, i.e. n * = 1. In steady state, therefore, there is no population growth, so the population level is constant (N t+1 = N t ). Thus, by construction, w * = 1 is the subsistence income. Such a steady state is normally referred to as a 'Malthusian' equilibrium.

In the following, we calculate land and labour productivity in steady state. Using (1), it follows that land productivity-defined as final output per unit of land-in steady state is

D * ≡ y H x = ((γ H ) α A H ) 1 1-α . (2)
Labour productivity-defined as final output per unit of land divided by labour input per unit of land-in steady state is

E * ≡ y H /x (1/x) • P i={C,H} γ i e i = 1 γ H (1 + ( A H A L ) 1/α ) (3)

Conclusion

This paper introduces aspects of seasonality in agriculture to a stylized Malthusian model.

The analysis shows that labour productivity in agriculture may go up or down with agricultural intensification, depending on the relative rate of growth of technological progress in harvesting and cultivation activities, respectively. The theory should be testable through an analysis of changes in relative seasonal wage rates following season-specific technological progress in traditional agriculture.

  0, 1) is the labour input of an individual in season i ∈ {C, H}; and A i is the level of technology (total factor productivity) in season i ∈ {C, H}. It follows that income per individual is equal to the individual's final output, i.e. w = y H .

	e C =	γ C γ H	µ	A C A H	¶ 1

Time-budget studies done in traditional agricultural societies suggest that harvest seasons are normally characterized by severe labour shortage (hence the term peak season), and that the harvest season labour supply, therefore, sets the upper limit to agricultural output (see e.g.

[START_REF] Boserup | The Conditions of Agricultural Growth[END_REF][START_REF] Jones | Seasons and Prices: The Role of the Weather in English Agricultural History[END_REF]

. Following this approach, individuals in the model employ their entire labour resources in the harvesting season (i.e. e H = 1). Assuming absence of uncertainty, the number of intermediate goods produced equals the number of final goods that can be harvested, i.e. y C = y H . It then follows that the labour input per individual needed in the cultivation season (for intermediate goods production) is given by α . Notice the season-specific effects of technological progress on the demand for labour in cultivation activities. Technological progress that occurs in relation to harvesting activities is labour-demanding (when more final output can be generated in the harvest season, it takes more labour input in the cultivation season to produce more intermediate goods). Technological progress that occurs in relation to cultivation activities, by contrast, is laboursaving (it needs less labour input to generate the number of intermediate goods needed in the harvest season).

  Notice once again the season-specific effects of technological progress. Starting in a steady state, a positive shock to harvesting technology means that individuals can produce more final output, and, therefore, need to cultivate more intermediate goods. In the absence of technological progress in cultivation activities, individuals thus have to put in more labour in the cultivation season. Altogether, therefore, the annual labour input of an individual goes up in response to technological progress in harvesting activities.At the same time, though, because each individual also generates more final output, at least to begin with, income per individual increases. This leads to growth in the size of the population. However, more people means less land per individual, which ultimately drives down income per individual until population growth is brought to a halt. Eventually, therefore, the economy returns to a steady state with a higher population level, but where income per individual is back at the level of subsistence, a result identical to that of the stylized Malthusian model (see[START_REF] Clark | A Farewell to Alms: A Brief Economic History of the World[END_REF].However, the introduction of seasonal aspects allows us to take the analysis one step further. Since output per individual over the long run is unaffected whereas individual labour input has gone up, a positive shock to harvesting technology in the current model increases land productivity but reduces labour productivity. According to the present framework, The latter result helps shed light on how land and labour productivity can be positively correlated. To see this, let g i = 0 denote the net rate of growth of technology in season i ∈ {C, H}. It then follows from (2) and (3) that, if g H > g C ≥ 0, then the 'decline thesis' applies. By contrast, if g C > g H > 0, then the 'rise thesis' applies. In words: if the labourdemanding effect of technological progress in harvesting is dominated by the labour-saving effect of technological progress in cultivation, then land and labour productivity are positively correlated, and the 'rise thesis' is valid. If, by contrast, the labour-saving effect is dominated by the labour-demanding effect, then land and labour productivity are negatively correlated, and the 'decline thesis' is valid.

therefore, if technological progress occurs only in relation to harvesting activities, then the 'decline thesis' holds true.

Meanwhile, we still need to analyze the effects on land and labour productivity of technological progress in relation to cultivation activities. It follows from (2) that a positive shock to cultivation technology has no effect on land productivity. However, technological progress in cultivation means that the amount of intermediate goods needed for the harvesting season can now be generated using less labour. Obtaining the same output using less labour input, labour productivity, therefore, has gone up as a result of technological progress in cultivation.