Claire Naiditch
email: claire.naiditch@univ-lille1.fr.

Radu Vranceanu
email: vranceanu@essec.fr.

A TWO-COUNTRY MODEL OF HIGH SKILL MIGRATION WITH PUBLIC EDUCATION

Keywords: High-skill migration, Brain-gain, Public education, Human capital, Government. JEL Classi…cation: F22, I25, H11

This paper proposes a two-country model of migration in a transferable skill sector, where workers' education is provided free of charge by governments. We study …rstly the non-cooperative equilibrium where the poor country decides on the education level and the rich country decides on the quota of skilled migrants. Additional migration raises earnings prospects in the source country and attracts more talented people to that profession, what we refer to as the sector-speci…c brain gain e¤ect. This game presents a single stable equilibrium with positive migration. Compared to the cooperative equilibrium, in the noncooperative equilibrium the poor country systematically under-invests in education. Whether migration is too strong or too weak depends on the size of the brain gain e¤ect. Furthermore, the size of the welfare gain to be reaped by moving from non-cooperative to the cooperative organization of migration also depends on the strength of the sector-speci…c brain gain.

Introduction

Slovenia is one of the smallest Eastern European countries, but also one of the wealthiest. There were 6.346 doctors and dentists working in the public health system in 2010. According to o¢ cial estimates, additional 2.284 doctors would be needed to "secure the professional development of the system". Facing a shortage of capacity of the two faculties of medicine (Ljubljana and Maribor), the Slovenian government decided to "import doctors", mainly from the Eastern neighbor countries. In January 2011, the Parliament passed a law that reduced the procedure time for recognition of professional quali…cations of foreign doctors from around one to two years to only a month. 1 This anecdotal evidence is representative for an important trend in skilled migration. There are now between 192 and 216 million people living outside their place of birth (IOM, 2011;[START_REF] Ratha | Migration and Remittances Factbook 2011[END_REF], which represents between 3 and 3.2 per cent of the world population. This means that roughly one of every thirty-…ve persons in the world is a migrant. Among these migrants, highly skilled workers represent an ever-growing share: looking at those living in OECD countries, their number increased by 70% during the 1990s; at the same time the number of low skilled immigrants increased by only 30%. Massive migration of high-skill workers is often referred to as the "brain drain" e¤ect, a concept that emphasizes the migration-driven erosion of human capital in countries that need it mostly. Several researchers have emphasized that migration of high-skill workers in "strategic occupations" such as health care and teaching could be extremely harmful for emerging countries, and this negative e¤ect is enhanced when skilled migrants are trained in the source countries [START_REF] Beine | A panel data analysis of the brain gain[END_REF].

The dataset compiled by [START_REF] Docquier | A gendered assessment of highly skilled emigration[END_REF] provides emigration stocks and ‡ows towards OECD countries from all the countries of the world at three educational levels.

It shows that, over the last decades, the brain drain has increased in terms of stocks but not necessarily in terms of emigration rates. High income countries may provide more high-skill workers in magnitude, but higher emigration rates are found in middle-income countries. Data 1 Based on information provided by Slovenian Government at www.ukom.gov.si. provided by [START_REF] Docquier | A gendered assessment of highly skilled emigration[END_REF] do not di¤erentiate between various professions and occupations. In their review of the economic literature on skilled migration, [START_REF] Docquier | Globalization, brain drain, and development[END_REF] provide some case studies on notorious examples of brain drain: African medical doctors, European scientists and researchers and Indian IT specialists, showing that these highskill migrants di¤er in many respects but also have many things in common.

The economic literature on the brain drain mainly focuses on issues such as the determinants of skilled workers migration (see [START_REF] Docquier | Brain drain in developing countries[END_REF][START_REF] Ortega | The causes and e¤ects of international migrations: Evidence from OECD countries 1980-2005[END_REF]Beine, Docquier and Ozden, 2011;[START_REF] Grogger | Income maximization and the selection and sorting of international migrants[END_REF][START_REF] Belot | Immigrant selection in the OECD[END_REF] and the impact of skilled emigration on origin countries (see [START_REF] Docquier | Globalization, brain drain, and development[END_REF] for an extensive literature review on this topic). In the late nineties, economists became more sensible to the argument according to which a country's pre-migration human capital stock could be endogenous to the prospect and realization of migration. A "New Economics of the Brain Gain" [START_REF] Stark | The new economics of the brain gain[END_REF] emerged around the idea according to which, in presence of migration opportunities, individuals will invest more in education, thus raising the average human capital of educated individuals in the domestic country (see for instance [START_REF] Stark | A brain gain with a brain drain[END_REF][START_REF] Stark | Human capital depletion, human capital formation, and migration: A blessing or a "curse"?[END_REF][START_REF] Mountford | Can a brain drain be good for growth in the source economy?[END_REF][START_REF] Beine | Brain drain and economic growth: Theory and evidence[END_REF]Ozden, 2011;[START_REF] Stark | International migration, human capital formation, and savings[END_REF]. Several empirical studies tend to corroborate these theoretical models [START_REF] Beine | Brain drain and economic growth: Theory and evidence[END_REF][START_REF] Beine | Brain drain and human capital formation in developing countries: Winners and losers[END_REF]Beine, Docquier et Ozden, 2011, Chand and[START_REF] Chand | Skilled emigration and skill creation: A Quasiexperiment[END_REF][START_REF] Batista | Testing the 'brain gain' hypothesis: Micro evidence from Cape Verde[END_REF][START_REF] Gibson | The microeconomic determinants of emigration and return migration of the best and brightest: Evidence from the Paci…c[END_REF][START_REF] Cortes | Relative quality of foreign nurses in the United States[END_REF]; they show that this brain gain e¤ect exists, and that it is not negligible.

While the above mentioned theoretical literature has brought substantial insights to the process of human capital accumulation through private education, it is nevertheless important to notice that in many countries tertiary education is mostly …nanced through public funds. Individuals only have to …nance a small part of the cost of their higher education; the main burden for students is thus their opportunity cost of postponing entering the job market. For instance, in 2009, OECD countries spend on average 6.2% of their GDP on educational institutions and tertiary education accounts for nearly one-quarter of this expenditure, or 1.6% of OECD countries'GDP. This represents on average US$ 13 728 per tertiary student. 2 Expenditure per student by tertiary institutions increased by 5 percentage points from 2000 to 2005 and by 9 percentage points over the 2005-09 period. In 2009, public funding accounts for 73% of all funds for tertiary educational institutions on average in OECD countries (it accounted for 78% in 1995, 77% in 2000 and 73% in 2005) (OECD, 2012; Figure 1). Among OECD countries, public funding accounts for more than 85% of all funding of higher education in European countries [START_REF] Eurydice | Modernisayion of Higher Education in Europe: Funding and the Social Dimension[END_REF]; Figure 2). Looking at developing countries and in particular at African countries, the picture is not so di¤erent. African countries steadily spent on average 0.78% of their GDP on tertiary institutions between 1995 and 2010. This represents approximately 20% of Africa's current public expenditure on education; this rate is comparable to the world average and higher than the corresponding rate of non-African developing countries (18%). The public resources per student in tertiary education as welfare services to students, OECD countries annually spend on average US$ 8 944 per student at the tertiary level. funds represent approximately 75% of national expenditure on higher education (this …gure is based on a sample of 18 countries only). The share contributed by households varies widely, from less than 10 percent in Mali, Chad, and the Republic of Congo to about 60 percent in Uganda and Guinea-Bissau. External assistance to higher education represents another important source of funds for tertiary education in Africa. Between 2002 and 2006, external assistance to higher education in Sub-Saharan Africa amounted to about US$ 600 million annually. Note however that more than 70% of this amount was spent in donors'universities to compensate them for the cost of educating African students (World Bank, 2010).

This paper aims at analyzing skilled migration in a setup where (1) higher education is supplied by governments free of charge for individuals and (2) the opportunity to migrate attracts more talented persons to a given profession. The model is most relevant when applied to civil service sectors with high worker cross-border mobility (transferable skills), such as health care, higher education or fundamental research. In these sectors governments would commit to deliver a given volume of activity, and most often will sponsor the education of the civil servants.

Our sector-speci…c de…nition of the "brain gain" is close to that used by the above-mentioned literature: the prospect of migration raises the human capital of workers in the profession under scrutiny. Unlike other papers, we do not focus on individual decisions concerning the investment in education, but merely assume that Borjas'(1987) conditions for positive self-selection are ful…lled; thus, better earnings prospects in the profession open to migration (transferable skills) attracts better people from the rest of the economy (including the non-transferable skills sectors). In this respect, there is no overall brain gain, since the best people just move from the non-transferable to the transferable skills sector.

The problem is cast as a non-cooperative game between the source ("poor") country which chooses the education level per worker, taking as given the number of high-skill emigrants, and the host ("rich") country which decides on the number of highly skilled immigrants, taking as given their human capital. It will be shown that this game presents a single, stable Nash equilibrium with a positive number of migrants and a positive investment in education in the poor country. Changes in parameter values will be related to documented trends such as the development of emerging economies, or a higher price for capital in the wake of the Great Recession. The outcome of the non-cooperative equilibrium will then be compared to the cooperative solution. As it will be shown, the nature of the cooperative equilibrium depends to a large extent on the strength of the sector-speci…c brain gain e¤ect.

To our knowledge, only a few migration studies have considered the case of public …nancing of education. [START_REF] Stark | Inducing human capital formation: migration as a substitute for subsidies[END_REF] as well as [START_REF] Docquier | Is migration a good substitute for education subsidies?[END_REF] analyze the appropriate policy mix between public subsidy for education and migration opportunities, when individuals …nance part of their education cost and decide on their level of human capital, and origin countries' governments maximize a social welfare function. In a theoretical model, [START_REF] Poutvaara | Public and private education in an integrated Europe: Studying to migrate and teaching to stay?[END_REF] emphasizes the in ‡uence of the brain drain on the type of education publicly …nanced (internationally applicable or country-speci…c), when individuals choose their study e¤ort.

Our model is closer to the two-country model presented by [START_REF] Djajić | Migration of skilled workers: Policy interaction between host and source countries[END_REF]. In their paper, the rich country decides on the duration of migrants'work permits and the poor country decides on the amount of public education per individual. Comparing the non-cooperative with the cooperative equilibrium where a social planner maximizes total welfare, they show that in the non-cooperative setting the poor country tends to under-invest in education; whether the duration of the work permit is too short or too long compared to the cooperative equilibrim level depends on the parameters. Besides a di¤erent policy transmission mechanism, what could be seen as an original contribution of our paper is the emphasis set on how migration is shifting the distribution of talents in the transferable skills sector.

The paper is organized as follows. The next section introduces the main assumptions of the model and studies the behavior of each country in the non-cooperative setup; in particular, we study the existence and stability properties of the equilibrium, as well as the local e¤ects of the parameters on equilibrium variables. Section 3 analyzes the cooperative equilibrium in a bargaining framework. The last section presents the conclusion and some policy implications.

The non-cooperative game

There are two countries, referred to as the "Rich" and the "Poor" country, as we assume that there is a substantial gap between their development levels. Both need to produce a predetermined ‡ow of a speci…c public service (for instance health care, fundamental research or higher education).

Production of the public service requires e¤ective labor services provided by quali…ed civil servants (respectively doctors, nurses, researchers or professors) and a constant amount of physical capital per civil servant. E¤ective labor services are proxied by the product between the number of workers and their average human capital. In turn, human capital depends on workers'education and on workers'talent, heterogeneously distributed in the population of workers attracted to that profession. Education of civil servants is provided for by the government, free of charge for the individuals. We focus on professions where skills are transferable from one country to another.

For instance, a researcher in nuclear physics trained in India can …nd an equivalent job in the US.

On the opposite, an Indian judge, trained in speci…c Indian law, cannot easily work as a judge in the US.

Civil servants trained in the poor country migrate to the rich country provided that they get a work permit. Implicitly, we make the standard assumption according to which, for civil servants in the poor country, utility from working in the rich country is higher than the cost of migrating, and the net utility when migrating is higher than the utility when staying. The rich country decides on the number of work permits.

Both countries aim at minimizing the investment cost of delivering the required amount of public services.

In a …rst step, the problem is studied as a non-cooperative game between the two countries.

More precisely, the rich country decides on the number of migrants it is willing to accept (work permits delivered), taking as given their human capital. The poor country will choose the education level per worker, taking as given the number of migrants. In the Cournot-Nash equilibrium, each country adopts its best strategy, given that the other country follows its best strategy.

The "poor" country

The poor country must provide a predetermined amount of a speci…c public service (health care for instance), denoted by Y P . Following an approach introduced by the e¢ ciency wage theory [START_REF] Solow | Another possible source of wage stickiness[END_REF], we assume that the production function can be written:

Y = F P (N q); (1)
where F P () has the standard neoclassical properties, and N q is the volume of e¤ective labor services, delivered by N civil servants (e.g. doctors) having an average human capital q: Production also requires a …xed amount of physical capital per employed worker (such as real estate, various equipment, computers, etc.).

We denote human capital of individual i by q i = q(e; t i ), where e is the education received by an individual and t i is the individual's talent or ability to transform education in valuable skills for "real work". We admit that q i = et i .

The total number of young people who graduate in the required profession is N + M; where N are those who will get a job at home and M are those who will migrate. The public education budget thus is E e(N + M ). Following [START_REF] Beine | Brain drain and economic growth: Theory and evidence[END_REF], we consider that the ability to migrate depends on some characteristic that is independent of acquired human capital (family wealth, the network of friends, etc.). Thus migrants are drawn at random from the population of graduates; the average human capital of the migrants will thus be identical to the average human capital of the left-home persons. 3We admit that individuals attracted by the perspective of getting a job as a civil servant in the profession with migration opportunities are heterogenous with respect to talent t. To keep the analysis as simple as possible, we assume that t is uniformly distributed on the interval [0; t sup ];

where t sup denotes the upper bound of the talent distribution.

Better prospects of migration raise the expected wage of workers that would train for that profession. 4We make the somehow trivial assumption according to which a higher expected wage attracts to that profession "the more able" persons from the rest of the economy (including from the non-transferable skills sector). The precise conditions for such positive self-selection to occur were stated by [START_REF] Borjas | Self-selection and the earnings of immigrants[END_REF] building on the classical paper by [START_REF] Roy | Some thought on the distribution of earnings[END_REF]. In particular, the wage distribution in the transferable skills sector should be larger than in the rest of the economy, which is consistent with the higher wage abroad hypothesis, and the correlation of talents in the two sectors should be large enough. Taking a macroeconomic perspective that simpli…es the underlying process, we further consider that the upper bound of the talent distribution in the transferable skills sector is positively related to the number of migrants M . To keep the analysis as simple as possible, we assume that t sup is a linear function in M; t sup = t 0 + M , where > 0 is the sensitivity of talent to M; and t 0 > 0:

In this paper we will refer to "the sector-speci…c brain gain e¤ect" as the positive impact of migration prospect on the talent of workers attracted to the transferable skills sector (the parameter captures the "strength" of the e¤ect). As mentioned in the introduction, there is no scope for "global" brain gain, since good people attracted to the transferable skills sector actually leave from the other sectors of the economy.

The average talent is: t av = 0:5 (t 0 + M ). In turn, the average human capital of individuals trained in the poor country can be written:

q = 0:5 (t 0 + M ) e: (2)
Since we assumed that migrants self-select on a di¤erent criterion than talent, it turns out that the average human capital of migrants and of the left-home persons is identical.

Given the production function (1), the amount of labor services required to achieve the production target Y P is:

N q = F 1 P (Y P ): (3)
Replacing q by expression (2), we get:

0:5N (t 0 + M ) e = F 1 P (Y P ): (4)
The former equation indicates the pairs (N; e) the poor country can choose in order to reach his service target, given M decided by the rich country. For instance, we can write:

N = 2 e (t 0 + M ) with = q 2F 1 P (Y P ) (5)
or, alternatively, e as a function of N .

We assume that the poor country aims at achieving the service target Y P with the lowest investment cost in human and physical capital. The investment cost of obtaining any service target is:

C P = cN + e(M + N ); ( 6
)
where c is the (constant) per-capita cost of the physical capital required to equip domestic workers, and e is the per-capita education cost, that applies to both future migrants and left-home persons.

So the decision problem of the poor country government is:

8 > > < > > : min N;e fC P = cN + e(M + N )g with: N = 2 e (t 0 + M ) (7)
In order to solve it, we introduce the constraint in the objective:

C P = (c + e) e 2 (t 0 + M ) + eM (8)
and we look for the minimum of C P : The FOC dC P =de = 0 leads to the optimal education level (denoted by e P ):

e P = p c p M (t 0 + M ) : (9)
The relationship between e P and M is the best response function of the poor country, indicating the optimal education level given the quota of migrants chosen by the rich country. We have

lim M !0 e P = +1, lim M !+1
e P = 0, de P dM < 0 and d 2 e P dM 2 > 0. We will alternatively refer to the e P = e P (M ) function as the P P 0 curve, as represented in Figure 3. We can further check that d 2 C P =de 2 > 0; the optimal solution corresponds to a minimum of the cost function.

Expression (9) indicates that e P is decreasing in M . Indeed, if the rich country raises the quota of migrants (dM > 0), all things equal, the cost of producing the service Y P increases. The rest of the story depends on the strength of the sector-speci…c brain gain e¤ect. If the brain gain e¤ect is weak enough, then the productivity gain is modest; facing a higher total investment in education, the poor country might want to reduce the education level per worker and hire more locals. If the brain gain e¤ect is strong, then, for a given dM > 0; there is a powerful productivity gain. The poor country can achieve the same level of service while reducing its investment in education, even if this will o¤set to some extent the …rst e¤ect. 5

Notice that changes in parameters shift the P P 0 curve as indicated by the arrows in Figure 3. Indeed, from expression (9), it can be seen that: @e P @ > 0; @e P @t0 < 0; @e P @c > 0 and @e P @ < 0:

In line with intuitive reasoning, the required (optimal) education level increases if the production target is raised, or if talent is "scarcer". The required education level also increases if the cost of equipping a worker increases; in this case, it is better to employ less sta¤, but each of them must be more productive thanks to a better training.

Introducing equation (9) in equation ( 5), we can also determine the optimal number of sta¤ needed at home for the production of the public service, N P :

N P = p c r M t 0 + M : (10)
where N P is an increasing function in M:

5 In section 3 we move beyond this intuitive analysis and study more in depth the cost response to changes in e and M (depending on ):

The "rich" country

As in the poor country, the rich country government must provide a given amount of public services Y R , at the lowest investment cost. At di¤erence with the poor country, the rich country can use either locals trained locally, or migrants trained in the poor country. While the rich country can decide on the number of work permits M; it takes the education level of migrants as given.

Production of the public service also requires a …xed amount of physical capital per worker.

We have denoted by M the migrants, and by q their average human capital. Denoting by Z the number of locals and by their average human capital (exogenously given), the production function is:

Y = F R (Z ; M q): (11)
The production function must allow for partial complementarity and partial substitution between the two types of e¤ective labor services, mostly because of coordination problems. For instance, when the group is dominated by a category of persons (be them locals or foreigners), it is bene…cial to integrate a di¤erent one, since it comes with complementary skills, but this will a¤ect the internal cohesion of the group. It is also reasonable to assume that the production function features constant returns to scale. A convenient form that has these properties and also allows to reach analytical solutions is the Cobb-Douglas function:

Y = (Z ) 0:5 (M q) 0:5 : (12)
For the rich country, the education cost of a migrant is assumed to be nil. Let w be the cost of training a domestic worker, and c be the cost of physical capital per worker (for simplicity, it is assumed to be the same as in the poor country). We denote the relative cost of employing a worker trained in the rich country compared to a worker trained in the poor country by =

w + c c = w c + 1 > 1.
The investment cost C R , whatever the production target, can be written as:

C R = (w + c) Z + cM: (13)
The rich country decision problem is:

8 > > > > > > < > > > > > > : min Z;M fC R = (w + c) Z + cM g with: (Z ) 0:5 (M q) 0:5 = Y R with: q = 0:5(t 0 + M )e (14)
Note that the rich country has no impact on the education level e; but can have an impact on the human capital of the migrants, anticipating that higher migration opportunities should attract better people to that profession in the poor country.

Given the production function ( 12) and the expression of q (eq. 2), the amount of native labor services required to achieve the production target Y R is:

Z = 2 (Y R ) 2 eM (t 0 + M ) : (15)
The former equation indicates the pairs (Z; M ) the rich country can choose in order to reach his service target, given the education level e decided by the poor country. For instance, we can write:

Z = 2 (Y R ) 2 e M (t 0 + M ) (16)
or, alternatively, M as a function of Z.

So the decision problem of the rich country government can be re-written as:

min M ( C R (M ) = 2 (w + c) (Y R ) 2 e M (t 0 + M ) + cM ) : (17)
The FOC dC R (M )=dM = 0 leads to the implicit de…nition of the optimal migration level (denoted by M R ), given e and the various parameters:

[M R (t 0 + M R )] 2 (0:5t 0 + M R ) = 1 e (2Y R ) 2 : (18)
We de…ne:

G(M ) = [M (t 0 + M )] 2 0:5t 0 + M (19) b = (2Y R ) 2 (20)
and we get the implicit de…nition of M R :

G(M R ) = b e : (21)
We can state:

Proposition 1 There is a single M R ; such that G(M R ) = b e .
Proof. It can be seen that G(0) = 0 and lim

M !+1 G(M ) = +1. Furthermore, G(M ) is a monotonously increasing function in M : G 0 (M ) = M (t 0 + M ) (0:5t 0 + M ) 2 h 3 2 M 2 + 3t 0 M + (t 0 ) 2 i > 0; 8M > 0 (22) Since b e > 0; 9! M R > 0 such that G(M R ) = b e :
Proposition 2 M R is a decreasing function in e.

Proof. By di¤erentiating equation ( 21) we get:

G 0 (M R )dM R = b e 2 de ( 23
) dM R de = b e 2 G 0 (M R ) < 0 (24)
The optimal quota of migrants M R is a decreasing function in the education level e such as decided by the poor country.

Indeed, if e decreases, all things equal the rich country should bring in more migrants to provide the required service level. Allowing for additional migration would raise the average quality of these migrants, which would partially o¤set the …rst direct e¤ect, without canceling it.

The relationship between M R and e can be interpreted as the best response function of the rich country, when the poor country decides on the level of e.

Since M R (e) is monotonous on the interval ]0; +1[, it admits a reciprocal e R (M ) that we will refer to as the RR 0 curve (represented in Figure 3):

e R (M ) = b G(M ) = b 0:5t 0 + M M 2 (t 0 + M ) 2 : (25)
The function e R (M ) is decreasing in M and convex, with lim

M !0 e R = +1, lim M !+1 e R = 0, de R dM < 0 and d 2 e R dM 2 > 0.
Changes in parameters shift the RR 0 relationship as indicated by the arrows in Figure 3. Since b = (2Y R ) 2 1 + w c ; it turns out that @e R @Y R > 0; @e R @w > 0; @e R @c < 0 and @e R @ < 0: We also can show that @e R @t0 = bM (0:5t0+1

;5 M ) [M (t0+ M )] 3 < 0 and @e R @ = b (t0+ M ) 3 < 0:
Eventually, the optimal number of locals Z R can be determined by introducing M R in equation ( 16).

The Nash Equilibrium

A Cournot-Nash equilibrium of this game is a pair (e ; M ) satisfying simultaneously Equation ( 9)

and Equation ( 25). If such a pair exists, the poor country decides on the optimal education level taking as given the quota of migrants decided by the rich country, and the rich country optimally decides on the number of migrants taking as given their education level such as chosen by the poor country. The total numbers of workers trained by the poor country and of local workers employed by the rich country are also obtained as equilibrium values (Equations 10 and 16).

The equilibrium condition is:

e P (M ) = e R (M ) (26) p c p M (t 0 + M ) = b (0:5t 0 + M ) [M (t 0 + M )] 2 : (27)
We de…ne:

J(M ) = [M (t 0 + M )] 3 (0:5t 0 + M ) 2 : (28)
After some calculations, the equilibrium condition (26) can be written as:

J(M ) = 1 c b 2 (29)
where we recall that b = (2Y R ) 2 1 + w c and = q 2F 1 P (Y P ): This condition implicitly de…nes the equilibrium number of migrants, denoted by M :

Proposition 3 There is a single, positive, …nite number of migrants satisfying the Cournot-Nash equilibrium condition (29).

Proof. It can be seen that J(0) = 0 and lim

M !+1 J(M ) = +1: The function J(M ) is monotonously increasing in M : J 0 (M ) = [M (t 0 + M )] 2 h (t 0 + 2 M ) 2 + 0:5 (t 0 ) 2 i (0:5t 0 + M ) 3 > 0; 8M > 0: (30) Since 1 c b 2 > 0; thus 9! M > 0 such that J(M ) = 1 c b 2
.

The fact that the solution to Equation ( 29) is single tells us that the P P 0 curve and the RR 0 curves cross only once in the interval ]0; +1[:

The equilibrium education level is then determined by: e = e P (M ): (31)

Figure 3 shows the best response functions of the poor country (P P 0 curve) and of the rich country (RR 0 curve). Point A is the Cournot-Nash equilibrium.

Figure 3: The Cournot-Nash equilibrium

We can also show that:

Proposition 4 The Cournot-Nash equilibrium of this game is dynamically stable.

Proof. We consider the sequence of adjustments where the poor country chooses e t given M t 1 , and the rich country chooses M t given e t , and so on. 6 The equilibrium is dynamically stable if starting from any outside point (e; M ), the system converges toward the equilibrium solution (e ; M ): The stability condition is e R (M ) > e P (M ) 8 M < M , and e R (M ) < e P (M ) 8 M > M :

We know that e R (M )

e P (M ) 2 = 1 c b 2 (0:5t0+ M ) 2 [M (t0+ M )] 3 = J(M ) J(M ) : Since J(M ) is increasing in M , the
stability condition is met.

Comparative statics

We recall the compact notations of the parameters: = q 2F 1 P (Y P ) and b = (2Y R )

2 w+c c

:

Table 1 summarizes the equilibrium values for the main endogenous variables.

Rich country

8 > > > > > > < > > > > > > : M = J 1 1 c b 2 Z = 2(Y R ) 2 p c p M (t0+ M ) C R = 2(w+c)(Y R ) 2 p c p M (t0+ M ) + cM Poor country 8 > > > > > > > > > > < > > > > > > > > > > : e = p c p M (t0+ M ) N = p c q M t0+ M C P = 2 p c p M (t0+ M )+ t0+ M E = e (M + N ) = t0+ M h + p c p M (t 0 + M ) i
Table 1: Equilibrium values for both countries.

From Figure 3 or total di¤erentiation of the equilibrium conditions, we can determine the impact of parameter changes on the following key variables: the number of migrants, the education level in the poor country, the number of skilled locals hired to produce the public service in the poor country, and the number of skilled locals hired in the rich country (see Appendix). Table 2 summarizes the main …ndings.

w c t 0 Y P Y R M + =+ + e + + + N + ? + Z ? ? ? ?
Table 2: Comparative statics.

Note that the local e¤ect of the sensitivity of talent to migration opportunities ( ) on the equilibrium number of migrants (M ) is :

dM d = (0:5t0 M )(M ) 2 4( M ) 2 +4t0 M +1:5(t0) 2 (see Appendix).
Thus the equilibrium number of migrants M increases with if and only if M < 0:5t 0 , i.e. when the incentive e¤ect of migration is not "too high"; in the opposite case, M decreases with .

Some variations in parameters can be related to global trends and policy changes.

For instance, if a poor country is developing, it is very probable that the need for public services will increase, that is dY P > 0: As expected, the education level per civil servant would then increase. However, in equilibrium, the number of migrants would decrease, which, to some extent, would reduce workers'human capital, and would require a stronger education per worker.

After a …nancial crisis such as the 2007-2009 Great Recession, a higher cost of physical capital per worker (c) would raise the education level in the poor country, because the poor country would like to hire less people but better trained. Yet, since in the rich country the relative price of people trained at home compared to migrants ( ) declines, the rich country would host less migrants. The human capital of migrants would further decline, and reinforce the need to raise the education level in the poor country.

As is often the case with non-cooperative equilibria, when decision makers play "one against the other", the outcome is Pareto-ine¢ cient. In other words, should they negotiate on the key decision variables (in our case, e and M ), the resulting cooperative equilibrium would bring about an improvement in welfare for both parties.

The next section investigates this cooperative equilibrium. In particular, we would like to know in what direction endogenous variable move when we go from the non-cooperative to the cooperative equilibrium. The analysis will emphasize the key role of the sector-speci…c brain gain e¤ect: the type of the cooperative equilibrium depends to a large extent on the sensitivity of talent to migration (as captured by our parameter ):

3 The cooperative equilibrium

Starting from the Cournot-Nash equilibrium, the two countries might strive to work out a Pareto-e¢ cient allocation of resources by bargaining about migration to the rich country and education in the poor country. Let us denote by C P and C R the investment costs in the poor (respectively rich) country as evaluated at the Nash equilibrium values e and M (see Table 2), and let us assume that should the negotiations fail, the non-cooperative solution prevails. In this case, the Nash solution to the negotiation problem would be obtained by maximizing the product of each country's net gain of cooperating raised respectively to the power and (1 ), with 2 [0; 1] being representative of the relative bargaining power:

7 8 > > > > > > > > > > < > > > > > > > > > > : max e;M f[cN + e(M + N )] C P g 1 f[(w + c)Z + cM ] C R g with: Y P = F P (N q) with: Y R = F R (Z ; M q) with: q = 0:5(t 0 + M )e (32)
The solution will be denoted by (ê; M ): It is di¢ cult to solve this non-linear problem and …nd an explicit solution. One way to circumvent the analytical complexity of this problem is to focus on the isocost curves; this approach will allow us to provide a graphic solution.

Poor country isocost curves

According to Equation ( 8) which takes into account the production target constraint in the poor country, the total investment cost in physical and human capital can be written as a function in e and M :

C P (e; M ) = (c+e) e 2 (t0+ M ) + eM .
An isocost curve is made of all pairs (e; M ) verifying condition: C P (e; M ) = ct: The shape of such isocost curves can be inferred from analyzing the derivative dM de C P =ct : Total di¤erentiation of the isocost condition leads to: if the isocost curve is represented in the referential (Oe; OM ); we know that the curve will have a zero slope right on the best response function of the poor country. In the opposite referential (OM; Oe), the slope of the isocost curve is in…nite, i.e., the curve is tangent to a vertical line at the crossing point with the best response function.

dM de C P =ct = M c e 2 2 (t0+ M ) (c+e) e 2 (t0+ M ) 2 e : (33)
We are interested in the sign of the denominator of expression (33) in the neighborhood of e P (M ). Replacing e by e P (M ); we can show (after some calculations) that the sign depends in a critical manner on the strength of the brain gain e¤ect:

(c + e P (M )) e P (M ) 2 (t 0 + M ) 2 e P (M ) ? 0 , ? c e P (M ) t 0 M : (34)
In particular, these inequalities hold for the Cournot-Nash equilibrium values (e ; M ) which also depend on .8 So, equation:

= c e ( ) t 0 M ( ) (35)
implicitly de…nes a …xed point 0 > 0 such that:

For a weak (or inexistent) sector-speci…c brain gain e¤ect (0 < 0 ), in the neighborhood of (e ; M ) we have dM de C P =ct > 0 for e < e ; and dM de C P =ct < 0 for e > e :

For a strong sector-speci…c brain gain e¤ect ( > 0 ); in the neighborhood of (e ; M ) we have dM de C P =ct > 0 for e > e ; and dM de C P =ct < 0 for e < e .

In order to draw correct families of isocost curves, we use a numerical simulation. 9 We use the same (OM; Oe) referential as for the non-cooperative equilibrium. Figure 4 In case of a small brain gain e¤ect, isocost curves located toward the NW correspond to lower investment costs for the poor country.

In case of a strong brain gain e¤ect, isocost curves located toward the SE correspond to lower investment costs for the poor country.

Rich country isocost curves

In the same way, the total investment cost in physical and human capital in the rich country can be written as a function of e and M .

First, according to Equation ( 16) which takes into account the target production condition and the de…nition of q, we can write Z as a function of M and e: Z =

(Y R ) 2 0:5 M (t0+ M )e .
The investment cost of producing Y R can thus be written:

C R (e; M ) = 2 (Y R ) 2 (w + c) eM (t 0 + M ) + cM (36)
de dM C R =ct = c 2(Y R ) 2 (w+c) e (t0+2 M ) M 2 (t0+ M ) 2 2(Y R ) 2 (w+c) e 2 1 M (t0+ M ) (37)
The isocost curve has a zero slope right for M = M R (e) = G 1 ( b e ) as de…ned in the previous section. Furthermore, since G(M ) is increasing in M , we can show that de dM C R =ct > 0 for

G(M ) > b e , M > M R (e); and de dM C R =ct < 0 for G(M ) < b e , M < M R (e):
In other words, rich country isocost curves have a U-shape in the referential (OM; Oe), with the troughs on the best-response function of the rich country. In Figure 6 we represent the RR 0 best response curve of the rich country and a family of isocost curves.

Isocost curves located toward the North of the (OM; Oe) plane correspond to lower investment costs.

Two types of cooperative equilibria

As shown before, the form of the isocost curves of the poor country depends on the strength of the sector-speci…c brain gain e¤ect (as captured by ). As a consequence, we have two types of cooperative equilibria, depending on this key parameter.

As it will be shown, in our model, there is no structural di¤erence between the extreme zero impact assumption and the positive but moderate brain gain assumption. A structural di¤erence can be revealed in the case of a strong brain gain e¤ect. Whatever the cooperative equilibrium (ê; M ); we know that it will be located in the region between the two isocost curves, thus would require higher education for (all) locals in the poor Proposition 5 In the case of a relatively small (or inexistent) brain gain e¤ ect, without coordination the poor country tends to under-invest in education, and the rich country tends to hire too many migrants.

Proof. Cf. graphic analysis of the cooperative solution.

The region of Pareto-e¢ cent contracts is made up of the locus where the isocost curves of the two countries are tangent (i.e., have the same slope) : de dM C R =ct = de dM C P =ct .

How the gain of moving from the non-cooperative to the cooperative equilibrium is split between the two countries depends on their relative negotiation power. If the rich country has the whole negotiation power, the equilibrium solution will be the point where the highest isocost curve of the rich country is tangent to the isocost curve C P (e; M ) = C P of the poor country; this requires very high education per capita. If we move toward the center of the cooperative region and the equal split of the gains from cooperation, the required education level is smaller. The number of migrants is less sensitive to the negotiation power.

Cooperative equilibrium: the case of a strong brain gain e¤ect

In the opposite case of a strong brain gain e¤ect, the isocost curves of the poor country have the opposite shape. Figure 8 shows non-cooperative equilibrium (e ; M ) at point A and the two isocost curves that correspond to this equilibrium education and migration levels. This time the Pareto ameliorating region has a narrow, closed shape (it was quite large in the "small brain gain" case). In other words, gains from cooperation can only be modest. We can however notice that:

Proposition 6 In the case of a relatively large brain gain e¤ ect, without coordination the poor country tends to under-invest in education, and the rich country tends to impose too much restrictions on migration.

Proof. Cf. graphic analysis of the cooperative solution.

From the analysis of the two cases, we can infer without ambiguity that in a non-cooperative setting, poor countries tend to under-invest in education of their civil servants (doctors, teachers, researchers, etc.) -whatever the strength of the brain gain e¤ect. Thus, we reach the same conclusion as [START_REF] Djajić | Migration of skilled workers: Policy interaction between host and source countries[END_REF], using a model that builds on a di¤erent transmission mechanism.

Conclusion

This paper has developed an original model of skilled migration, where migrants education is supplied for free by the government of the migrants'origin country. Such a framework is most relevant to analyze the migration of civil servants with high cross-border mobility and transferable skills such as doctors, nurses, teachers, researchers, etc. As the migration literature has pointed out, brain drain in such "strategic occupations" could be extremely harmful for developing countries.

This provides substantial motivation for researchers to analyze the various policy transmission mechanisms and welfare implications.

In our model, governments in both source and host countries aim at delivering a predetermined amount of civil services, at the lowest investment cost. The problem is analyzed as a game between the poor country that decides on the education level of the civil servants and the rich country that decides how many such migrants it wants to host. The model takes into account the potentially favorable impact of migration on attracting highly talented people towards that profession, what we have de…ned as the sector-speci…c brain gain e¤ect. Despite the relatively high analytical complexity of the problem, the paper presents a neat solution with positive migration and positive investment in education. It can be shown that the equilibrium is unique and stable, and comparative statics allow to comment on possible trends in migration; in particular, in this model, economic growth in poor countries would bring about less migration and additional education per worker.

We then analyze the cooperative equilibrium, where the two countries can negotiate on the Pareto-e¢ cient education-migration bundle. We show that the nature of the cooperative equilibrium depends to a large extent on the strength of the sector-speci…c brain gain e¤ect. When the sensitivity of talent to migration opportunities is relatively small (not di¤erent from the case where the e¤ect does not exist at all), in the non-cooperative equilibrium the poor country tends to invest too little in education, and the rich country tends to attract too many migrants. In the opposite case of a strong brain gain e¤ect, the poor country still neglects education, while the rich country does not host enough migrants.

The welfare gains to be reaped when moving from a non-cooperative to a cooperative organization of international relationships on migration also depend to a large extent on the strength of the brain gain e¤ect. These gains can be quite large if the brain gain e¤ect is small or zero, they might be quite modest in the case of a large brain gain e¤ect. In a pragmatic approach to policy making, as long as empirical studies on this speci…c form of brain gain did not reach a de…nitive conclusion, common sense would favour the cooperative solution; there is nothing to lose in one case, but a large expected gain in the other case.

In this paper we focused on the case where each country uses its own national resources to fund the public provision of tertiary education. However, as mentioned before, developed countries tend to …nance part of the tertiary education provided by developing countries through the o¢ cial development aid (and part of that aid is used by developed countries to educate students from developing countries in their own universities). This is one important limitation of our analysis.

Future research might study the optimal education transfer policy from richer to poorer countries. , we get:

dZ = Y R [ ] 2 p c p M (t 0 + M ) 4 dY R Y R 2 d + 2 d + c dc (Y R ) 2 p c [M (t 0 + M )] 3=2 h M dt 0 + (M ) 2 d + (t 0 + 2 M )dM i (A.43)
A.2 Partial derivatives of equilibrium values (Table 2)

of: with respect to: with respect to: w

M 2 J 0 (M ) (2Y R ) 4 (w+c) 2 2 ( c) 3 < 0 2 J 0 (M ) (2Y R ) 4 ( ) 2

Figure 1 :

 1 Figure 1: Distribution of expenditure in tertiary education in OECD countries, 2009. Source: OECD; Argentina: UNESCO Institute for Statistics (www.oecd.org/edu/eag2012).

Figure 2 :

 2 Figure 2: Total public expenditure on tertiary education in European countries.(as a percent of GDP). Source: Eurostat, in Eurydice (2011).

2 M

 2 Notice that dM de CP =ct = 0 implies M = c e 2 2 (t0+ M ) or e = q c (t0+ M ) = e P (M ): In other words,

  represents a family of isocost curves obtained for a small ( = 0:005), Figure5represents a family of isocost curves obtained in the case of a larger ( = 0:05): On both graphs we also represent the curve P P 0 ; i.e. the best response function of the poor country in the non-cooperative equilibrium. As it can be seen, isocost curves present an in…nite slope (they are tangent to a vertical line) at points where they cross the best response function. But they have a "D form" in the …rst case, and a "reverse D form" in the second case.

Figure 4 :

 4 Figure 4: Poor country isocost curves -small brain gain e¤ect

Figure 5 :

 5 Figure 5: Poor country isocost curves -strong brain gain e¤ect

Figure 6 :

 6 Figure 6: Rich country isocost curves

3. 3 . 1

 31 Figure7displays the non-cooperative equilibrium A (e ; M ) at the crossing point between the two best response functions, and the two isocost curves, one for the poor country and another for the rich country, that correspond to the constant investment cost C P and respectively C R .

Figure 7 :

 7 Figure 7: The region of the cooperative equilibrium -Small brain gain e¤ect

Figure 8 :

 8 Figure 8: The region of the cooperative equilibrium -Large brain gain e¤ect

  ) 2 t0M p c[M (t0+ M )] 3=2 h M +t0 4( M ) 2 +4t0 M +1:5(t0) 2 i < 0

Excluding activities peripheral to instruction such as research and development and ancillary services such

Other papers[START_REF] Chiquiar | International migration, self-selection, and the distribution of wages: Evidence from Mexico and the United States[END_REF][START_REF] Mckenzie | How important is selection? Experimental vs. non-experimental measures of the income gains from migration[END_REF][START_REF] Cortes | Relative quality of foreign nurses in the United States[END_REF] consider the issue of the self-selection of migrants, which implies that migrants are necessarily those individuals at the higher end of the human capital distribution. Probably, in real life, human capital has an impact on the realization of migration, but whether this impact is strong as compared to other factors is a question still open to debate.

The expected wage of a candidate to education in that sector being (N w P + M w R ) =(N + M ), where w P (w R ) is the wage in the poor (rich) country, with w R > w P .

The rationale would not change if we allow for a delay in adjusting migration quotas as well.

In an extreme but plausible case, the rich country has all the power, = 1:

By de…nition of the non-cooperative equilibrium, e = e P (M ).

Parameter values are: F 1 (Y P ) =

105; Y R = 120; t = 2; c = 1; = 4; w = 3:

A Appendix. Comparative statics calculations

A.1 The main equilibrium equations By totally di¤erentiating the equilibrium condition

we get:

Di¤erentiating condition e = p c [M (t 0 + M )] 1=2 , we get:

of:

with respect to:

of: with respect to: with d dY P =


Alice Vittrant
email: vittrant@vjf.cnrs.fr

How typology allows for a new analysis of the verb phrase in Burmese

Description, classification, diversity and universality of languages are the key terms of linguistic typology, which first aims at answering the following question: what do languages have in common and in what ways do they differ? 1

In other words, typology is concerned with finding properties that are shared by languages (invariants in Lazard terms) 2 , and has to do with cross-linguistic comparison. Its first task is therefore to describe languages in terms of pre-established features, leading to a classification of languages into different structural types according to the affinities that emerge from the descriptions. Typologists are also concern with the areal [or geographical] distribution of structural features among the world's languages 3 .

In this article, I would like to emphasize the usefulness of typology and the notions developed within typological frameworks, for describing and analyzing little-known or undescribed languages. My claim will be illustrated by a new description of the Burmese verb phrase as a serial verb construction, a morpho-syntactic notion developed along with typological studies.

About Burmese verbal phrase or the origin of the new analysis proposed

Burmese has been studied by Western scholars since the 18 th century and recent works contain good descriptions of the language. However reviewing previous descriptions, such as those of Allott, Okell, Bernot, Bernot & al. and Wheatley, leads me to the following double observation.

First, as I examined previous analyses of the Burmese verb phrase, I noticed great variation in the definition of grammatical verbal morphemes, in particular the optional ones. The number and the functions of these optional verbal morphemes vary depending on the criteria used by the author for his analysis. For instance, the classification given by [START_REF] Okell John | Burmese / Myanmar: a dictionary of grammaticals forms[END_REF] based on semantic criteria, leads to a list of 60 verbal morphemes, whereas the classifications of [START_REF] Bernot | Le prédicat en birman parlé[END_REF] and [START_REF] Wheatley | Burmese : A grammatical sketch[END_REF], which are based on phonological, syntactic and semantic criteria, distinguish between auxiliaries and verbal particles, although they do not list exactly the same morphemes.

The second point concerns verb phrases in other languages of the area. As noticed by, Matisoff 1986, 1991[START_REF] Hansson Inga-Lill | Verb concatenation in Akha[END_REF][START_REF] Clark | Hmong and Areal South-East Asian[END_REF][START_REF]Serialisation in Mainland Southeast Asia[END_REF][START_REF] Scott | The origins of verb serialization in Modern Tibetan[END_REF]and Bisang 1996, sequences of verbs without any connector between them are found in many other Asian languages, such as Lahu, Mandarin Chinese, Hmong, Thai and Tibetan. As expected, given the many features common to the languages of the area [START_REF] Enfield | Areal linguistics and Mainland Southeast Asia[END_REF], these strings of verbs also exist in Burmese [START_REF] Vittrant | Les constructions verbales en série, une nouvelle approche du syntagme verbal birman[END_REF], as illustrated by sentences (1) to (3), each of which contains a sequence of several verb roots that are not linked by any marker. However, the underlying structure of each string differs from the others, as suggested by the translation given, whereas the surface forms are identical. 1 See Croft (1990: 1), [START_REF] Gilbert | What are typologists doing?[END_REF], [START_REF] Van Der | Cognitive linguistics and typology[END_REF] for a more detailed definition of typology. Two verbs (in bold) within the string of four verbs (underlined) that appears in (1), form a compound verb, an idiomatic form that is listed in bilingual dictionaries such as Bernot 1978-88 (VOL.7 p. 157) and the Burmese-English Dictionary published by the Burmese Ministry of Education in Yangon 4 .

(1) tc= én^mH , Cx= :rè p® I : Tu . Ti u x= :anpu . rtè ; lU xÚtc= éy,k= h,... t ne 1 = Ma 2 shiN 3 y 3 =Pi 3 thoN 2 -ThaiN 3 a 1 na 1

one day = LOC be poor = SUB be silly -be idiot be stupid be ignorant poN 2 ya 1 = T 1 lu 2 -2 t-y = ha 2 ...

SUB

get =REL:R man-be young one-CLF(hum) =TOP

One day, a young man, who was really poor and moreover who seemed really idiotic [... arrived at the wealthy man's place.] 5

In (2), however, the string of verbs constitutes a single predicate, i.e. the complex verb 6 of a single clause, and refers to a unique event; in other words, the string of verbs should be analyzed as a prototypical Serial Verb Construction (henceforth SVC).

Whereas in example (3), some of the verb roots have undergone semantic and structural changes: they have either been grammaticalized (and become auxiliaries such as [ne 2 ], 'to stay > inaccomplished aspect in (a)), or else lexicalized (becoming a compound verb as [iN 3 .liN 3 ] in (b)).

(2) îP® %cx= h, Kp= éw:éw:tc= énr,ki u ép® ,x= :ér‹ ^énTi u x= Kè ; tÚ < u 3 phyu 2 siN 2 =ha 2 kha-we 3 -we 3 t ne 2 ya 2 =Ko 2

U Phyu Sin = TOP rather-be far (x 2) one place = OBJ pyN 3 -hwe 1 ne 2 -ThaiN 2 =Kh 1 =T 2 to move out to live = SPT = REAL.ASS U Phyu Sin moved out to live in a far-off place.

(3) a. ... ép® ,Ci u énkR tè ; ck,:ki u (...) pu n= :éntè ; îP® %cx= k kR ,:sW ,:tÚ < ... py 3 sho 2 ne 2 Ca 1 = T 1 zKa 3 = Ko 2 (...) Notice however that the compound does not appear as such in unilingual Burmese dictionary.

5

About examples: Our phonemic transcription roughly follows [START_REF] Bernot | Le prédicat en birman parlé[END_REF]'s proposal, with minor changes for tones and diphthongs. Thus tones are indicated by superscript numbers at the end of the syllable. [ 1 ] stands for brief, high and creaky tone ; [ 2 ] stands for long, low (and breathy) tone; [ 3 ] stands for long, clear, highfalling tone. The fourth tone corresponds to a glottal stop. Atonal (and unmarked) syllables may appear in bisyllabic words with [] as vowel. Capital letters stands for stops that can be realized as voiced or unvoiced depending on the phonological (and syntactical) context. Most of the grammatical morphemes start with a capital letter, given that they are usually (but not always) syntactically closely related to the preceding morpheme.

6

The term complex verb ('complexe verbal' in French) refers to a combination of bare verbs (with or without verbal morphemes) into a morpho-syntactical unit and does not comprise any nominal phrase such as the object's constituent. In that sense, it has to be distinguished from verb phrase ( ' s y n t a g m e v e r b a l ' o r 'constellation verbale'), of which it could be seen as the core. It also has to be distinguished from 'complex predicate' ('prédicat complexe' in French), that contains verbs with different status, i.e. head verb plus dependant verbs. The complex verb notion is first found in Hagège (1975) and his study of Chinese prepositions that originate from verbs.

Given the identical surface forms of these verb phrases that differ structurally and semantically, I looked for a framework that could reveal the relationship between these phenomena, which are traditionally analyzed separately in Burmese linguistics. In other words, I looked for a cross-linguistically valid model that would allow me to deal simultaneously with compound verbs, pre-verbs or "versatile verbs" 7 , and auxiliaries.

The notion of Serial Verb Construction (SVC) have been used first to describe morphosyntactic phenomenon in African languages [START_REF] Bamgbose Ayo | On serial Verbs and Verbal Status[END_REF], Givon 1975). Then extended to other languages [START_REF] Sebba | The syntax of serial verbs. An investigation into serialisation in Sranan and other languages[END_REF], it was generalized more recently by authors such as Lord (1993), Déchaine (1993[START_REF] Durie Mark | Grammatical structures in verb serialization[END_REF] and Aikhenvald & Dixon (2006) among others. The notion proved to be useful for building an adequate framework for a more global approach to the verb phrase in Burmese.

Serial Verb Constructions (SVC): a theoretical reminder

Definition

The term "Serial Verb Construction", or verb serialization, has been applied to different types of construction. However, most of the definitions reviewed characterize the SVC as a string of verbs or verb phrases (i) that are not separated by a connector, (ii) that share the same grammatical information and sometimes the same arguments, and (iii) that describe a single event (cf. [START_REF] Vittrant | Les constructions verbales en série, une nouvelle approche du syntagme verbal birman[END_REF]. For instance, Dechaine (1993:799) writes that: "A serial verb construction is a succession of verbs and their complements (if any) in a single clause with one subject and one tense or aspect value.", Bisang (1995:138) defined verb serialization as "the unmarked juxtaposition of two or more verbs or verb phrases (with or without subject and/or object) each of which would also be able to form a sentence on its own.", and Durie (1997: 290) insists on the 'uniqueness' of the event: "The archetypal serial verb construction consists of a sequence of two or more verbs which in various (rather than strong) senses, together act like a single verb." See also Bril & Ozanne-Rivierre (2004:2), Aikhenvald & Dixon (2006:1) 8 and Vittrant (2006:309) 9 .

Moreover, in languages that possess SVCs, these constructions generally exist along with other structures of dependency, i.e. such as coordination, complementation and subordination. Most studies of SVCs distinguish between serialization, clause-chaining 10 (complex predicates) and sequence of clauses. These distinctions are mainly based on the criterion of monoclausality, a syntactic criterion that needs to be formally defined for every single language (Foley 2010).

In Burmese, the difference between subordinate or coordinate clauses, clause chains, and verb serialization is illustrated by examples (4) to (6).

In (4), the two clauses are linked by the temporal subordinator [pi 3 ] that indicates the end of the dependent clause. The end of the head clause, on the other hand, is marked by a final verbal particle conveying realis modality, considered as evidence of finiteness in Burmese.

The sentence in (5) contains two verbs that are separated by the object of the second one, i.e. 'hand ' [l]. As suggested by the translation, we have here two clauses that are chained and not subordinated as in the previous example, while example (6) illustrated a SVC. The term Versatile verb has been coined by Matisoff (1969: 70) to refer to dependent verbs, that have undergone a semantic bleaching, that could precede or follow the head verb. In our usage, versatile verbs differ from auxiliaries as for their syntactic position: the former precede the head verb whereas the later follow it. Aikhenvald & Dixon (2006:1): "A serial verb construction is a sequence of verbs which act together as a single predicate, without any overt marker of coordination, subordination or syntactic dependency of any sort." 9 Vittrant (2006:309): "Une construction de verbes en série (CVS) est une séquence de verbes qui ne sont syntaxiquement ni coordonnés ni subordonnés. Elle a d'autre part, la forme de surface d'un syntagme verbal unique." 10 Clause-chaining may be defined as a sequence of one fully finite verb and one (or more) less finite medial verb(s). Clause-chaining, which has been described for Papuan languages, is similar to Japanese Complex predicates, as described for Japanese or Korean [START_REF] Shibatani | On the form of complex predicates: toward demystifying serial verbs[END_REF].

Actually, in this sentence, the object of the second verb, i.e. 'words' [zKa 3 ], precedes the string of verbs, which suggests that syntactically the two verbs are closely associated.

(4) pu lx= :k gU Tè ki u émY,p® I : wx= sW ,:tÚ < (5) ... pn= :kn= :Tè érTv= ^lk= éC:p® I :...

Main Features and subtypes of SVC

As pointed out by Senft 2004, the little agreement about how the phenomenon of serial verbs should be defined is partly due to the lack of a common framework for describing and comparing language systems. However, various studies (and authors) agree on a set of common features or key characteristics [START_REF] Durie Mark | Grammatical structures in verb serialization[END_REF](Durie, : 2019-91)-91), (Bril, 2004: 2-3).

-Usually, an SVC describes what corresponds conceptually to a unique event.

-The verbs of an SVC share tense, aspect, modality and polarity information.

-The verbs of an SVC share at least one argument, and can have one subject only.

-None of the SVC verbs is a subordinated verb, that is to say none of the verbs in the SVC is the syntactic argument of another verb in the SVC. -The SVC constitutes a single prosodic unit (without any pause), i.e. it has the intonation of a single clause. To summarize, SVCs are monoclausal but multi-predicational (Jarkey 2010:5) 11 .

Moreover, diachronic studies show the strong tendency of SVCs to move towards grammaticalization or lexicalization -see Clark (1989:190), [START_REF] Scott | The origins of verb serialization in Modern Tibetan[END_REF]:3), Lord (1993:3, 215, 236), Bisang (1996:533, 563) 12 .

Notice however that for most of the authors, an SVC may possess all or only some of these features. In other words, none of these properties is defining per se.

Therefore, verbal serialization or the SVC is far from being a uniform phenomenon, and most of the authors, after agreeing on this core set of properties, propose sub-types of SVC. Generally, two main classes of SVC can be distinguished, even if from one author to the other, the two classes may contain different sub-types of SCV. These two classes of SVC will be labeled 'Symmetrical SVC class' (co-ranking predicates) and 'Asymmetrical SVC class' (implying a head-modifier hierarchy), according to [START_REF] Bril | Complex nuclei in Oceanic languages: Contribution to an areal typology[END_REF] and Aikhenvald and Dixon 11 Jarkey (2010:110) :" SVCs are monoclausal but multi-predicational. That is, they involve two or more distinct predicating morphemes, linked together in a single clause by virtue of the fact that they share one or more argument positions through coindexation."

12 Bisang (1996 : 533) : "Because the unmarked juxtaposition of verbs in the languages of East and mainland South East Asia is particulary easy and widespread, all the products of grammaticalization derived from verbs are the result of grammaticalization combined with the influence of attractor positions on constructions of verb serialization." (p. 563): "As pointed out above, grammaticalization is tightly linked to verb serialization." (2006).

The symmetrical SVC may be first characterized by the absence of syntactically or semantically dependent verbs. Verbs belong to open classes without grammatical or semantic constraints. Then, the order of the actions (or sub-events) described by the SVC is generally iconic: it reflects the temporal order of the actions. Lastly, the event described by the SVC is conceived as a unique and single event 13 . According to Durie (1997), there are two explanations for this 'unitary-event' characteristic: a cognitive one and a cultural one.

The cognitive one is based on the observation that the processes meaning "take (away)" or "bring (back)" are currently expressed through SVC in languages that possess this construction. The verbs used mean roughly 'take' and 'go' (or 'come'), as exemplified in Vietnamese, Yoruba and Burmese 14 . Similarities in human environment and experience seem a good explanation for the high frequency of this string of verbs (Durie 1997: 321), (Vittrant 2006:311) 15 .

YORUBA (Niger-congo, West-Africa) from Stahlke 1970 quoted by [START_REF] Kroeger | Analyzing syntax[END_REF] However, this cognitive explanation fails to explain why some verbal serializations are presented by speakers as unique and consistent events. In many cases it seems relevant to take into account the socio-cultural context. As shown by Jarkey 1991, writing about dancing while blowing bamboo pipes in Hmong culture 16 (cited by Durie (1997: 321)), each speech community decides what events should be conventionalized verbally within the frame of a SVC. This cultural explanation allows me to give an account of SVCs such as (10), which presents a process conceived in/by Burmese culture as a unitary event. The process [to 1 sa 3 ] ("dip-eat") refers to a way of eating a certain kind of food: actually a Burmese meal is generally served with little poached vegetables called [to 1 zya 3 ] ("dip-NMLZ"), that is to say 'dip-able things'. Used as pickles or side-dishes, they are eaten with the hands as we do with radish, dipping them in salt or in a sauce. 13 See also Baker & Harvey (2010)'s distinction of complex vs. simplex event, the latter being defined by formal constraints (single predicate, coverb construction or monomorphemic predicate).

14

In languages where SVC is absent or rare, other means are used to express this human experience. See for instance French 'ap-porter'/'em-porter', 'a-mener'/'em-mener', or 'a-lunir', 'a-terrir', 'en-voler', where the prefix a-is equivalent to 'come' in SVC, whereas en(m)-express a motion away from speaker.

15 See also Vittrant forthcoming on the cognitive and cultural explanations, and the different strategies to express semantic compositionality in languages.

16

Bamboo pipes are usually played by Hmong people during death ceremonies (or other types of ritual), to accompany the dead person up to his last 'home'. The pipes performers have to dance in a certain and codified way while playing the pipes. Therefore whenever the pipes are played, the performer dances along with the music, the two processes are inseparable from each other. So it is natural for Hmong to recognize 'dancingwhile-playing' as a single event, which is not the case for dancing and listening, considered as distinct events.

Therefore, the process of "eating-and-dipping" is conceived as a single event in Burmese culture and is expressed by an SVC.

(10) C,:nè ^ ti u c,:p? <

sha 2 =n 1 to 1 sa 3 = Pa 2 Ø salt =with dip eat = POL (IMP)
Dip-(it) in salt (and) eat-(it).

The second type of SVC, i.e. the asymmetrical SVC may be characterized by the following properties. First, one verb (at least) of the string belongs to a limited class and may be viewed as a modifier of a head verb. It often undergoes semantic change too. In other words, an asymmetrical SVC generally contains a fully-fledged verb (or plain verb) and one (or more) verb(s) that has/have undergone semantic depletion or semantic bleaching.

"The asymmetrical subtype is generally assigned modification (property, value) or specification of circumstances (manner, result, location, etc.), while the less frequent symmetrical subtype expresses sequential orpurposive actions". (Bril 2004 :24) Thus, numerous linguists have noticed the relationship between SVCs and lexicalization and grammaticalization processes 17 . See for instance DeLancey (1991) on grammaticalizations that originate from SVCs in different Tibeto-Burman languages.

"The Tibeto-Burman languages manifest a considerable range of grammaticalized verb constructions. Thus the individual and comparative study of such constructions in various Tibeto-Burman languages provides insight into diachronic processes of serialization, auxiliarization and morphologization of originally independent lexical verbs." (DeLancey, 1991: 3) Then, unlike symmetrical SVCs, asymmetrical SVCs are not necessarily iconic: sub-events need not to refer to sequential actions.

Finally, given its semantic heterogeneity, the asymmetrical SVC class is often divided into several sub-types. The distinction may be based on semantic criteria, leading to the following main sub-types of serialization: directional SVC, resultative SVC, causative SVC, and more generally aspecto-temporal or modal SVC -see Givón (1991: 83), Lord (1993:9), Bisang (1996: 149ff), Durie (1997: 335), Bril (2004:16ff), Bisang (1996: 150).

However, other classifications exist that rely on syntactic properties. For instance, Li & Thompson (1981: 607) 18 talk about the 'Pivotal construction' 19 , a construction where "a noun phrase is simultaneously the subject of the second verb and the direct object of the first verb", as opposed to serialization where "one verb phrase or clause is the subject or direct object of another verb " (1981: 598). But in Role and Reference Grammar, SVCs are described as Nuclear (or tight) vs. Core (or loose) serializations, the two terms referring to the layered structure of the clause (Bril, 2004: 4). 17 See Givòn (1991: 118), Lord (1993: 215ff, 233, 236), Bisang (1996: 533, 563), Durie (1997 : 291), Bril (2004: 13, 38ff) inter al.

18

Li & Thompson 1981 distinguished four types of SVC: (1) SVC that express events related in a way (consecutive, purposive, alternating, circumstance); (2) descriptive clause construction that "involves a transitive verb whose object is described by a following clause", and the two other types already discussed in this section.

Criteria used to analyze the Burmese verb phrase

Irrelevancy of criteria generally used in studies of SVCs

The usual criteria for distinguishing between sequences of clauses, clause-chains and SVCs, or to tell apart the different subtypes of SVC, may not be used in certain languages. For instance, Bril (2004: 9) notices that Oceanic languages generally lack morphological clues, and that "the sharing of TAM morphemes [is] often [an] elusive criteria". Similarly, criteria such as agreement, case marking, syntactic dependency, position of the arguments, are not relevant in Burmese. As shown by example (11), no agreement is morphologically expressed, nor is case marking, although syntactic functions may be marked in Burmesesee examples ( 3) and ( 4), with respectively [Ko 2 ] object marker of 'words' [zeKa 3 ], and [Ka 1 ] subject marker of 'bottle ' [pliN 3 ]. Moreover, constituent order fails to be discriminating, because the order of arguments, if and when they are expressed, is pragmatically (and not syntactically) constrained.

(11) hx= :KYk= tÚ <

hiN 3 ch =T 2 soup cook = REAL.ASS

{I, you, he} cook {cooked} {a, some} soup

Since we lack a cross-linguistic definition of the SVC, we need to build language-specific tests that help to clarify the status of strings of verbs in a language. Therefore, relying on the notion of SVC and its key features, I look for criteria that allow me to distinguish in Burmese among similar surface forms with different underlying structures, i.e. among:

-string of verbs that behave similarly to compound lexemes -string of verbs that represent semantically complex events but expressed in a single clause -strings of verbs that contain a modifying verb that specifies the process expressed by another (head) verb.

-strings of verbs containing a verb that has undergone semantic change, that is to say a verb on a grammaticalization path.

Criteria relevant to the analysis of Burmese SVCs

Four criteria seem relevant for analyzing Burmese strings of verbs. The first (phonological) criterion is the assimilation of initial consonants of verbs. The second is functional and deals with changes (either functional or semantic) in some elements of the string of verbs, while the last two criteria are syntactic: negation scope and the introduction of subordinators into the string of verbs.

Phonological criterion

In Burmese phonology, initial consonant realization is conditioned by (1) the nature of the previous phoneme and (2) the degree of morphosyntactic bondedness of the syllables. In other words, the initial consonant of a syllable is VOICED if the final segment of the previous syllable is a vowel or a nasal consonant AND if the two syllables are part of the same phrase; the initial consonant is UNVOICED if the final segment of the previous syllable is a glottal stop or if the two syllables are parts of two different phrases (Bernot, 1980: 19-41).

This criterion therefore seems relevant to show the tight juncture between the verbs of an SVC, i.e. to demonstrate that the SVC behaves as a single phrase with closely tied verbs. However, this criterion is limited; it cannot apply when a syllable ends with a glottal stop: in this case, the consonant of the following syllable will automatically be pronounced unvoiced, regardless of the bondedness of the syllables.

In example (12) (example (10) repeated here for convenience), both sentences contain two verbs. In (a), the verb [to 1 ] 'to dip' ends in a vowel, whereas in (b) the verb [siN 3 ] 'to mince' ends in a nasal consonant. Therefore, in both cases, the following verb (and syllable) [sa 3 ] 'to eat', could be voiced. Actually the [sa 3 ] verb is voiced only in (b) where the two verbs are tightly bound. We have here a lexicalized SVC, i.e. a compound lexeme. On the other side, [sa 3 ] is realized unvoiced in (a) as the two verbs are not in close juncture. The string of verbs in (a) behaves like a symmetrical SVC, typically iconic. Finally in (13), no sandhi can occur: [sa 3 ] is preceded by the verb [kai] 'bite' ending in a glottal stop, and the following consonant will be automatically uttered unvoiced, since the segmental features do not allow such a sandhi process to take place.

(12) a. C,:nè ^ ti u c,:p? < The lion devoured the lamb.

Despite this reservation, the 'phonological unit of the SVC criterion has a discriminating role in Burmese. It allows me to distinguish between:

(1) a true (symmetrical) SVC and an almost lexicalized SVC, on one hand.

(2) and a true (asymmetrical) SVC and a grammaticalized SVC on the other hand.

Semantic change

Semantic change, a defining criterion for asymmetrical SVC, also has a discriminating role and it generally implies a semantically subordinate relationship, although this subordination, i.e. this specialization of verbs, displays different stages between slightly different lexical meanings and grammatical functions. Thus some verbs may have a slightly different meaning according to their position as V1 or V2 in the string (example ( 14), whereas others may have undergone a categorial change and become grammaticalized.

For instance, [pyaN 2 ], used as the main verb, means 'to return, to go back' as in (14a). However, as a V1 or a V2 in a string of verbs, it has a slightly different meaning (14b & c).

Compare with [lai], meaning "to follow" as a main verb, but carrying a aspectual meaning (terminative) when used as a V2 as in example (13). See also [ne 2 ] meaning "to leave, to stay" as a main verb (cf. ( 2)), which conveys inaccomplished aspect as in (3) and (14c). Actually this criterion helps to distinguish in Burmese between asymmetrical SVCs expressing a modification or specification of circumstances (manner, result), and SVCs containing true auxiliaries, i.e. 'grammaticalized SVCs'.

It is also relevant to set apart 'lexicalized SVCs', as stated by Durie (1997: 323): "Related to lexicalization of particular verb combinations is the tendency for particular verbs to develop distinct meanings when used in serialization".

Inserting an item between the components of the SVC

Authors such as Matisoff (1991) and Aikhenvald & Dixon (2006) have noticed that inserting an item (subordinator or coordinator) between the different components of a SVC generally leads to a semantically non-equivalent sequence.

In Burmese too, insertion of a subordinator correlated with a semantic change discriminates between different types of SVC. Actually it separates out lexicalized SVCs and (true) symmetrical SVCs on one hand, and grammaticalized SVCs vs. asymmetrical, nongrammaticalized SVCs on the other.

For instance, inserting the temporal subordinating morpheme [Pi 3 ] between the two verbs of the SVC in example ( 15), is correlated with a semantic change. We have a lexicalized symmetrical SVC. On the other hand, when [Pi 3 ] is inserted between the two verbs of the SVC in example (16), it does not change the content meaning of the SVC. Example (16) shows a (true) symmetrical SVC as the insertion of [Pi 3 ] is not correlated with any semantic change here. However, although the clausal meanings of (16)a and ( 16)b are equivalent, some informants identify a pragmatic difference between these two sentences: the use of the subordinator brings out one stage of the process described by the SVC. For instance, in (17)b, the emphasis is put on the way of eating, that is to say dipping in salt that may prevent a sour taste.

(17) a. dI srk= sI :ki u C,:nè ^ ti u ^c,:p? > aè d? ar,s, pi u Qi tÚ < di 2 yi 3 =Ko 2 sha 3 =n 1 to 1 sa 3 = Pa 2 DEM mango = OBJ salt = with dip eat = POL -da 2 ya 2 a 2 po 2 i 1 =T 2 DEM:anaph. -this taste VV:be more have = REAL.ASS Dip this mango in the salt (and) eat it. It is tastier.

b. dI srk= sI :ki u C,:nè ^ ti u ^p® I :c,:p? < d?mH mhu t= rx= rm= :KYVtÚ <

di 2 yi 3 =Ko 2 sha 3 =n 1 to 1 =Pi 3 sa 3 =Pa 2 DEM mango = OBJ salt = with dip = SUB.TPS eat = POL da 2 -m a 1 -m-ho-yiN 2 yaN 3 chiN 2 =T 2
if not very be sour = REAL.ASS Dip this mango in the salt (and/ to) eat it. If not, it is very sour.

Scope and position of negation

The position of the negation marker in a SVC is known to be an important criterion for verb phrase analysis in South-East Asian languages. It is currently used to distinguish free verb morphemes from bound morphemes (Matisoff, 1991: 393), (Bjorverud, 1998: 86).

In Burmese, this criterion reveals either the lexicalized or grammaticalized nature of an SVC. In both kinds of SVC, only the preverbal position (before the string of verbs) of the morpheme [m] negates the whole process described by the SVC; the insertion of the negative morpheme 20 [m] between two verbs in the string, is either impossible or leads to a different meaning as shown in ( 18

About Burmese Serial Verb Constructions (SVC)

The aim of this paper was to provide a new and more global approach to the Burmese verb phrase given the range of constructions that shows up with identical forms and different underlying structures.

Despite the ongoing debates on the relevancy of the notion of verbal serialization [START_REF] Gunter | What do we really know about serial verb constructions in Austronesian and Papuan languages?[END_REF][START_REF] Shibatani | On the form of complex predicates: toward demystifying serial verbs[END_REF][START_REF] Foley William | Events and serial verb construction[END_REF], this notion turns out to be relevant for our analysis of the Burmese verb phrase, and useful for distinguishing among the different structures found.

In this last section, I will present our analysis of the verb phrase in terms of serialization, highlighting the subtypes of SVC relevant for Burmese and their properties.

Properties of the different SVCs

Four sub-types of SVC emerge from our analysis of verbal serialization in Burmese that is to say of string of verbs with different underlying structures. Based on the criteria presented in the previous section, I distinguished:

(1) Lexicalized (symmetrical) SVCs (2) 'True' symmetrical SVCs (3) 'True asymmetrical SVCs (4) Grammaticalized (asymmetrical) SVCs

Symmetrical SVCs and their properties

Three properties are important for distinguishing between lexicalized and true symmetrical SVCs: the phonological behavior of the initial consonant of the second (or inner) verb, the semantic change undergone by verb(s) and the boundness of the components of the SVC, which can prevent negation or other items being inserted.

-First, lexicalized SVCs show a phonological unity with voicing when allowed (see § 3.2), while in true symmetrical SVCs, unvoiced initial consonants remain unvoiced.

-Lexicalized SVCs become idiomatic expressions; their meaning cannot be deduced from the meaning of their verbal components. By contrast, true symmetrical SVCs are semantically transparent (see the verbs in bold in (20)a and b). -Moreover, the two kinds of symmetrical SVC behave differently regarding syntactic criteria (position of the negative marker, insertion of a subordinating marker): whereas no item neither negation nor subordinating markers may be inserted between the components of a lexicalized SVC, true symmetrical SVCs are inconsistent in their syntactic behavior, accepting various positions for these markers.

-Finally, symmetrical SVCs are known to be time-iconic, referring to sequential actions (or action-goal, action-result, cause-effect events), which constitute the various phases of a single event. Burmese 'true' symmetrical SVCs do not depart from the general rule. However, iconic principles may sometimes be irrelevant due to coincident actions, language-specific constraints (see Matisoff 1969:84 on the order of concrete and abstract verbs in Lahu), or idiomaticity. Thus, lexicalized (symmetrical) SVCs, which are highly idiomatic, do not conform to the iconic principle.

Asymmetrical SVCs and their properties

The main difference between symmetrical and asymmetrical SVCs is whether they belong to an open class or a closed class. In asymmetrical SVCs, one (at least) verb shows dependency 21 on another verb; thus the head verb belongs to an open class, while the modifier verb(s) usually come(s) from a closed class. This dependency comes with semantic change. This semantic change is defining per se of the asymmetrical SVC; it affects some but not all the verbal components of the SVC, and so differs from what happens in lexicalized SVCs. In this latter construction, the change in meaning affects the whole string, producing an idiomatic meaning.

The degree of change discriminates between 'true' asymmetrical SVCs and grammaticalized (asymmetrical) SVCs: some verbs may have undergone a slight specialization, with a modifying meaning easy to infer from the original meaning of the verb, while others may have become auxiliaries. Finally, the position of the subordinate verb is not consistent in asymmetrical SVCs, although a tendency becomes clear: when subordinate verbs are the first components of the SVC, i.e. V1 position, the SVC is a 'true' asymmetrical SVC. By contrast, most of the verbs that have undergone grammatical change, i.e. auxiliaries, appear after the head-verb, as V2.

The table summarizes the core properties of the four sub-types of SVC distinguished for Burmese.

Table ( Following Bril (2004:24), I subsume under 'dependency' the following relations: (a) relations of dominance within hierarchical structures and (b) relations of governance between constituents. Asymmetrical serialization generally displays the former (dominance), but excludes the latter (governance).

22

Example from Okell & Allott (2001:198) Grammaticalized (asymmetrical) SVC -dependency (head-modifier relationship) -restricted class of the modifying verb -semantic change > grammatical function modifying-verb as V2 (after Vhead) Generally no insertion between components of the SVC

A continuum with prototypical types of SVC

Although the different sub-types presented could be characterized with phonological, syntactic and semantic properties, what also emerges from these definitions is that our four sub-types are not clear-cut categories of SVC.

A better way to give an account of Burmese verb phrases is therefore to analyze the different sequences of verbs studied as belonging to a continuum marked out by four prototypical categories, as shown in figure 1. This approach is confirmed by diachronic studies of verb serialization that show a tendency for verbs to shift from isolation (serial verbs) to boundness (see footnote To put it in other words, serial verbs tend to lexicalize or to grammaticalize, with common crosslinguistic changes. See for instance Ozanne-Rivierre & Rivierre (2004) on the gradual development of contiguous verbs involving gesture and action into compounds in New Caledonian languages, or Matisoff (1991:414ff) on areal and universal patterns of 'verbleaching' and 'verpositions' 23 in East and Southeast Asian languages.

There is a very strong diachronic tendency to lexicalization and grammaticalization of the meaning of serial complexes: this can involve treating the whole serial complex as a single lexical(ized) item, or 'demotion' of the meaning and grammatical status of one of the verbs to that of a modifier or case-marker. (Durie, 1997: 291)

Conclusion

Given our aim to provide a more global description of the Burmese verb phrase, the notion of Serial Verb Construction helped to give a global account of those verb phrases that are identical on the surface but have different underlying structures.

Although no clear-cut categories of serial verb construction emerge, some tendencies can be highlighted: for instance post-head position of modifying verbs in grammaticalized SVCs vs. pre-head position of modifying verbs in asymmetrical position; transparency vs. semantic change to distinguish between symmetrical and asymmetrical SVCs.

Moreover, the criteria retained for our analysis -such as the phonological criterion-, clearly discriminate between SVCs at each end of the continuum, i.e. lexicalized and grammaticalized SVCs. Notice however the similar behavior of lexicalized SVCs on one side and grammaticalized SVC on the other end of the continuum, which differ only in their semantic properties.

Table (2) summarizes and illustrates properties of various SVCs in Burmese. Although I present our results according to our continuum, notice that this table could have 23 'Verbleaching' refers to "the semantic process by which a full verb undergoes abstractification, at the same time as it expands its co-occurrence possibilities. [...] When this process is far enough advanced, the bleached morpheme can become a satellite to an indefinite number of heads -an auxiliary, helping, or 'versatile' verb." (Matisoff, 1991: 402), while 'verpositions' is a label for "verb-derived morphemes that have come to function like preposition" (p. 433).

been presented with the split between symmetrical and asymmetrical SVC, which would have shown that the extremities of the table meet.

Abbreviations : ANAPH: anaphoric, ASS: assertive, AUX: auxiliary, BENEF: benefactive, CLF: classifier, CFUGE: motion away from deictic center; CPETE: motion toward deictic center; CRS: current relevant state, DEM: demonstrative, DIM: diminutive, DM: discourse marker, DIR: directional, IMP:imperative, INACC: inaccomplishment, INCHOAT: inchoative (aspect); IR: irrealis modality, ITER: iterative (aspect), LOC: locative, NMLZ: nominalizer, object, PERF: perfect, POL: politeness, PLUR: plural, QST: question marker, R. or REAL: realis modality, REL: relator, RESULT: resultative (aspect), S: source of the action (« ablative » or « nominative »), SUB: subordinator, SPT: spacio-temporal, TERM: terminative (aspect), TOP: topic; W.S.: woman speaking

2

  See Lazard 2005, Lazard 2008. 3 See Bickel & Nichols 2006, and Haspelmath & al 2005.

  7

  8

19

  On Pivotal and other types (Cotemporal, Disposal and Attainment) of SVCs based on syntactic properties, see Jarkey 1991, 2010.

  ) in salt(and) eat (it).b. x? rp= cV:c,:tÚ > si l,: > ...a 2 ya siN 3 . Sa 3 =T 2 i 1 =la 3 1SG stop mince. eat = REAL.ASS know = QSTYou know, I stop and think about it...(13) K® é°s; h, si u :kél: ki u ki u k= c,: li u k= tÚ <chiN 2 e 1 =ha 2 o 3 Kle 3 =Ko 2

(

  14) a. ai m= p® n= mÚ < iN pyaN 2 =m 2 house return = IRR.ASS I am going back home. b. cau p= p® n= ép:p? < sa 1 .o pyaN 2 pe 3 =Pa 2 book return give = POL Give (me) back (the) book.

(

  15) a. éQ:tu n= :k s,:tc= éy,k= émW :c,:PU :tÚ< e 3 .ToN 3 .Ka 1 a 3 t-y mwe 3 .Sa 3 Phu 3 =T 2 In the past son one-CLF(hum) adopt, raise EXPER.= REAL.ASS In the past, (he) adopted a son. b. kR k= émW :p® I :c,:tÚ< c mwe 3 = Pi 3 sa 3 =T 2 chicken give birth, raise = SUB eat = REAL.ASS (He) breeds some chicken and eat (them). or (He) breeds chicken to eat [to earn his living].

(

  16) a. ‡i k= st= li u k= p? < yai a lai = Pa hit, beat kill TERM. = POL Hit (him) and kill (him) up! b. ‡i k= p® I :st= li u k= p? < yai =Pi 3 a lai=Pa hit, beat = SUB.TPS kill TERM. = POL Hit (him) and kill (him) up!

  cannot eat (it) mincing (it). or (I) was not used to eating (it while) mincing (it).

(

  19) a. sU kYmki u mm® x= ôi u x= `BU : < u 2 cma 1 =Ko 2 m= myiN 2 naiN 2 =Phu 3 3SG 1SG (W.S.) =OBJ NEG = see to win/CAPAC.= NEG He cannot see me.

  b. *sU kYmki u m® x= môi u x= BU : < u 2 cma 1 =Ko 2 myiN 2 m=naiN 2 =Phu 3 3SG 1SG (W.S.) =OBJ see NEG= to win/CAPAC.= NEG 20 Negation is expressed in Colloquial Burmese with a discontinuous morpheme [m ... Phu 3 ]. However, the negative value is conveyed essentially by the first part [m], a form cognate to many negative morphemes in Tibeto-Burman languages (see Matisoff 2003:488). Another clue is the absence of the form [Phu 3 ] in negated clauses in archaic dialects such as Arakanese, where the use of the [m] form is enough to negate a process.

(

  20) a. célmH , Bu n= :kR I : Qx= :p® tè ; li p= > ... the turtle about which the monk, in Sale, explains [the story] lit. ... the turtle that the monk shows clearly [the story].... b. lm= :P® t= kU :tÚ < across cross = REAL.ASS (He) cut [and] crossed the road.

Figure ( 1

 1 Figure (1) : Continuum of Serial Verb Constructions (SVCs)< tendency towards tendency towards > LEXICALIZATION

  For instance, in (21)(compared with (6)), the motion verb [la 2 ] 'come' has a slightly different meaning when used as the last verb of the sequence; it has undergone a functional specialization (a kind of intermediate stage between lexical and grammatical function): it actually marks deixis, i.e. the direction of the process from the viewpoint of narrator (Grinevald 2011: 56). In (22) however, the change is more radical: it has become an aspectual marker, conveying a change of state with progression in time or an inchoative meaning.

	(21) ék,x= mél: ép® ,x= :Kx= :Tè kén p® n= TW k= l,tÚ
	kaN 2 ma 1 le 3 pyN 3 .KhiN 2 th 3 =Ka 1 ne 2 pyaN 2	thw la 2 =T 2
	woman come>CPETE = REAL.iN 2 .thaN 2 ca 1 = T 2 corn. field inside = FROM (go)back go out wa 1 la 2 =T 2
	to marry	be in certain state = SUB.TPS	fat	come>INCHOAT = REAL.ASS
	She got fat when she married. 22

ASS

The young woman come out back from (inside) the corn field [towards me].

(22) ai m= éT,x= kYét,; wl,tÚ <