Alan R Kay

Jacques Neyton

Pierre Paoletti

A startling role for synaptic zinc

published or not. The documents may come

A startling role for synaptic zinc.

Zinc is an indispensable element in the molecular economy of all cells. While most zinc ions are trapped within proteins, as structural or catalytic co-factors, in the brain there is a pool of zinc that is less tightly bound and that can be revealed by histochemical techniques, such as the Timm's stain. The distribution of this potentially mobilizable zinc is remarkable for two reasons: first, it is mainly restricted to higher brain regions (viz. neocortex, hippocampus, striatum and amygdala); second, at the ultrastructural level, histochemically reactive zinc is localised almost exclusively within synaptic vesicles of a subset of glutamatergic axon terminals, where it is accumulated by the vesicular zinc transporter ZnT3 (Frederickson et al., 2005). However, there are notable exceptions to these rules since recently some staining of "chelatable" zinc has also been found in certain inhibitory axon terminals of the cerebellum and spinal cord (Danscher and Stoltenberg, 2005).

Most of the key players in fast synaptic transmission are highly sensitive to extracellular zinc (Smart et al., 2004;Frederickson et al., 2005). This is the case for both the neurotransmitter receptors and transporters of excitatory and inhibitory transmission and, depending on the nature of the target, zinc may either boost or depress the synaptic response. Zinc is a potent inhibitor of NMDA and GABA A receptors as well as glutamate and GABA transporters. In contrast, at glycine receptors, zinc displays a biphasic effect, potentiating at submicromolar concentrations and inhibiting at submillimolar concentrations.

The abundance of potential synaptic targets and the location of zinc in synaptic vesicles all seem to point to a role for zinc as a modulator of synaptic transmission (Vogt et al., 2000). However, despite clear indications that endogenous zinc is involved in excitotoxicity under pathological conditions (Choi and Koh, 1998), there has been no clear demonstration of a role for zinc in synaptic transmission under physiological conditions. Moreover, two recent findings have cast some doubt upon the physiological relevance of zinc modulation. Knocking-out the ZnT3 gene leads to the total disappearance of histochemical reactive zinc, yet results in no marked phenotype other than a moderate increase in susceptibility to epileptic seizures (Cole et al., 2000). Furthermore, whether zinc is indeed elevated in the synaptic cleft during neuronal activity has been challenged by experiments using zinc-sensitive fluorescent indicators, which suggest that zinc may after exocytosis stick to the presynaptic membrane and not diffuse freely in the cleft (Kay, 2006).

In this context, the paper by Hirzel et al. in Exciting as these results are, there are of course many questions that remain, e.g.: how much zinc is seen by the receptors? Does zinc act in a tonic or phasic fashion? Where does it come from? Surprisingly, Hirzel et al. found that application of exogenous zinc at low µM concentrations to wt slices did not increase the amplitude of glycinergic IPSCs, suggesting that in slices the zinc potentiating site on GlyRs is persistently saturated. Consistent with this interpretation, the authors found that application of the chelator tricine depressed the IPSCs in wt but not KI animals.

However, the authors' conclusion that the levels of ambient zinc are in the µM range is more questionable. This relies on the estimated affinity of the zinc potentiating site on GlyRs. Using buffered zinc solutions with controlled free zinc concentrations, other groups have measured zinc affinities of native and cloned glycine receptors more than one order of magnitude higher than that reported by Hirzel et al. (Suwa et al., 2001;[START_REF] Miller | [END_REF]. Therefore, synaptic zinc levels in the 10-100 nM range may be sufficient to prevent potentiation by exogenously applied zinc.

There are two ways in which we can imagine zinc modulating synaptic transmission (see Figure 1). Firstly, phasically, where synaptic zinc diffuses freely into the synaptic cleft after exocytosis and then binds to post-or pre-synaptic receptors and transporters. Zinc modulation would then wane rapidly as the zinc diffuses away and is transported into cells. Secondly, tonically, where zinc is bound to proteins within the synaptic vesicle and is externalized on exocytosis but not much diffuses into the cleft. Under this scenario, a few zinc ions could be supplied to a extracellular layer of zinc, termed the 'veneer' (Kay, 2006), where the metal stays associated with proteins on the pre-and post-synaptic membranes, including the neurotransmitter receptors. The degree of tonic zinc modulation would be determined by the number of zinc ions in the veneer, which accumulate slowly and progressively with synaptic activity and declines as zinc is removed from the veneer. High enough tonic zinc would explain the absence of effect seen by Hirzel et al. upon application of exogenous zinc. However, these results are also compatible with a phasic mechanism assuming that during normal synaptic activity zinc transiently reaches concentrations high enough to saturate the GlyR zinc binding site. Thus, whether the modulation occurs via the phasic rise of zinc or through regulation of the tonic level of extracellular zinc remains wide open; clearly more experiments are needed. This question applies also to two other major neurotransmitter receptors involved in fast neurotransmission, NMDA and GABA A receptors, since both receptor families harbour zinc binding sites of high-sensitivity (nM affinity; Paoletti et al., 1997;Hosie et al., 2003).

What is the source of zinc at a glycinergic synapse? One possibility could be that glycinergic presynaptic vesicles accumulate zinc as do glutamatergic and some GABAergic terminals. Looking for ZnT3 expression in glycinergic neurons and analyzing zinc modulation of glycinergic transmission in ZnT3-/-animals should help clarifying this point, although the fact that ZnT3 KOs do not show hyperekplexia makes it unlikely that ZnT3 loads vesicles associated with GlyR modulation. There is certainly no shortage of potential zinc transporters that could do the job, as numerous genes have been identified that code for proteins transporting zinc into intracellular compartments (Palmiter and Huang, 2004). Spillover of zinc from neighbouring synapses, likely glutamatergic, may provide an alternative source of zinc [START_REF] Kodirov | Proc. Natl. Acad. Sci. USA[END_REF] and see Figure 1).

The work of Hirzel et al. puts a nice dent in the zinc armour, which held firm for more than 50 years, with their demonstration that this ion acts as a physiological neuromodulator of glycinergic transmission. Oddly enough, zinc makes its début as a synaptic neuromodulator not where one would have expected, at the zinc-enriched glutamatergic synapses of the forebrain, but rather at glycinergic synapses in the hindbrain. We have little doubt that this initial success by inhibitory "outsiders" will trigger excitement in the glutamatergic transmission field, where the paradox of the co-existence of an activator (glutamate) and an inhibitor (zinc) remains unsolved.

Selected Reading

Vogt, K., Mellor, J., Tong, G., and Nicoll, R. (2000). Neuron 26,[187][188][189][190][191][192][193][194][195][196].

  It has long been known that the synaptic vesicles of certain glutamatergic terminals, as well as some inhibitory terminals, are richly supplied with zinc ions, yet the functional role of this pool of zinc in synaptic transmission has remained elusive. In this issue of Neuron, Hirzel et al. provide the first in vivo evidence that endogenous zinc is required for proper functioning of neuronal circuitry in the brain stem and spinal cord. They show that knock-in mice carrying a point mutation which eliminates zinc potentiation of α

  this issue of Neuron, will certainly revive the flagging hopes of zincologists. This work provides the first demonstration that interfering with zinc modulation of a synaptic pathway leads to a significant alteration in the phenotype of the animal. The authors used an original approach that circumvents most of the bugaboos encountered in previous attempts to pin down the role of zinc. Rather than modifying zinc levels with zinc chelators or genetic manipulations, which necessarily produce pleiotropic effects, Hirzel et al. chose to modify a specific synaptic zinc target, the glycine receptor, which mediates synaptic inhibition in the brain stem and spinal cord. Given the strong association of zinc with glutamatergic terminals, picking this particular target was risky butHirzel et al. clearly show that it paid off. The authors produced a knock-in (KI) mouse by introducing in the gene coding for the murine α1 glycine receptor subunit a point mutation (D80A) known from previous studies on recombinant receptors to suppress high-affinity zinc potentiation. Around P12, when the adult α1 GlyR subunit replaces the neonatal α2 subunit, KI mice develop both motor and sensory deficits typical of impaired glycinergic transmission: inducible tremor, delayed righting reflex, abnormal gait, increase in electro-retinogram b-wave amplitude and an enhanced acoustic startle response. This behavior is similar to a genetic disorder in human infants termed hyperekplexia (startle disease), which is characterized by an exaggerated startle reflex, with ensuing stiffness and marked brain-stem reflexes.At the cellular level, the authors carefully verified that the mutation selectively eliminated the high-affinity zinc potentiation of glycine receptors without affecting their glycine sensitivity, expression level and synaptic targeting. They further compared inhibitory transmission in wild-type (wt) and KI animals by recording in brain stem slices spontaneous IPSCs from hypoglossal motoneurons. The striking observation was that at P14-P16, when α1 GlyR subunit dominates, both the IPSC amplitude and decay are reduced in KI compared to wt animals. These results clearly indicate that in wt animals, endogenous zinc effectively binds to and potentiates synaptic glycine receptors by increasing receptor sensitivity to the agonist. Undoubtedly this work is important, since it is the first demonstration that zinc acts as an endogenous modulator of synaptic transmission.

Figure 1 :

 1 Figure 1: Possible mechanisms for zinc modulation of glycinergic neurotransmission


Belal Ehsan Baaquie
email: belalbaaquie@gmail.com

Bertrand M Roehner
email: roehner@lpthe.jussieu.fr

Qing-Hai Wang
email: qhwang@nus.edu.sg

The wage transition in developed countries and its implications for China

Keywords: productivity, demographic transition, economic growth, wage, earnings, agriculture, industry, primary sector, secondary sector, tertiary sector

The expression "wage transition" refers to the fact that over the past three decades in almost all developed economies wage increases have leveled off. There has been a widening divergence and decoupling between wages on the one hand and GDP per capita on the other hand. Yet, in China wages and GDP per capita climbed in sync (at least up to now). In the first part of the paper we present comparative statistical evidence which measures the extent of the wage transition effect. In a second part we consider the reasons of this phenomenon, in particular we explain how the transfers of labor from low productivity sectors (such as agriculture) to high productivity sectors (such as manufacturing) are the driver of productivity growth, particularly through their synergetic effects. Although rural flight represents only one of these effects, it is certainly the most visible because of the geographical relocation that it implies; it is also the most well-defined statistically. Moreover, it will be seen that it is a good indicator of the overall productivity and attractiveness of the non-agricultural sector. Because this model accounts fairly well for the observed evolution in industrialized countries, we use it to predict the rate of Chinese economic growth in coming decades. Our forecast for the average annual growth of real wages ranges from 4% to 6% depending on how well China will control offshoring and the development of its healthcare sector.

Introduction

Among economic variables wages are somewhat neglected items 1 . In comparison gross domestic product (GDP) and stock market indexes draw much more attention both in the news and in the economic literature. One reason for that may be the fact that (as explained in Appendix A ) wages can be defined and measured in several different ways. Therefore it may be of interest to start by explaining briefly why wages captured our attention.

The stunning wage stagnation effect

In our societies the idea of a steady, uninterrupted economic development permeates our conception and thoughts. Some data may indeed support this view. As an illustration, let us consider the case of GDP in the United States. In the 40 years from 1976 to 2016 real GDP (that is to say adjusted for inflation) was multiplied by 3 (from 5,488 to 16,651 billion dollars) while in the same time interval the population was multiplied by 1.47 (from 217 to 320 millions). This corresponds to an average annual growth rate of 2.79% for the GDP and 0.96% for the population. Thus, the GDP per capita increased at an average rate of 1.83% resulting in a doubling during this 40-year period.

With this kind of evidence in mind, the discovery that during the same time interval in the United States the real wage at best stagnated (see Fig. 2) came as a great surprise 2 . While we noticed this fact some ten years ago, for may years we have been assuming that this effect was special to the United States. Then, little by little, evidence emerged which showed that it was in fact common to all developed countries (see Fig. 3).

In the meanwhile another observation (described below) provided a possible clue.

The emergence of low productivity jobs

In the period immediately following World War II many European countries had to be rebuilt and modernized. As labor was in short supply it was regarded as a rare and costly resource that had to be economized. At that time the dominant idea was that thanks to rationalization and modernization low productivity jobs would progressively disappear. Then, in the 1980s, something happened which showed that this was no longer the mainstream view. Following in the footsteps of New York and other American cities, 1 Let us mention that an extended version of the present paper is available on the "arXiv" data base of preprints. For instance, it comprises a discussion of a number of data sources which may be useful in the perspective of future work.

2 As a matter of fact, around 1975 there was a sudden change in the trend of many other economic (e.g. income inequality) and social indicators (e.g. proportion of inmate population). Such changes are documented more fully in Roehner (2009, chapters 9-11).

home-delivery of pizzas started to become popular in many west European cities. This was a low productivity business, however, which could be profitable only if done by poorly paid employees. It was the harbinger of the creation of a whole range of jobs similarly characterized by poor pay and low productivity. A common feature of most of these jobs was that they belonged to the service sector. As emphasized by economists such as Jean Fourastié, the fact that the price of hair cuts or opera tickets remained unchanged over a broad historical time span shows that tertiary sector jobs hold little promises for productivity improvement. At the end of the paper we will propose an explanation which relies on the fact that most service activities have little potential for synergetic interactions with other activities.

Inflow of cheap labor

As any economic factor, labor is subject to the rule of supply and demand. The widespread multiplication of low paid service jobs was only possible because of a major increase in the supply of labor. Indeed, bridges were established between developed countries and developing countries which had an excess supply of cheap labor. Taking again the case of the United States, the Mexican born population in the US increased by 190% between 1970 and 1980 to reach 2.2 millions and then 4.5 millions in 1990 (Pew Research Center).

At the same time production activities were sent offshore to take advantage of the same reservoirs of cheap labor. One of the first massive case was the establishment by US companies of the so-called maquiladora3 zone on the Mexican side of the border with the United States.

While undoubtedly increasing the short-term profit margin, in the long-run such a policy is a sure disincentive for investing in labor saving technology and organization. Why should a company invest in robots if manpower is so cheap?

In the mainstream view the establishment of so-called post-industrialized societies is seen as a desirable and almost ineluctable objective.

Post-industrial societies

In the dominant conception the post-industrial stage reached by most developed countries and in which at least 75% of employment is in the service sector is a superior stage. It seems to realize the dream of clean, energy efficient and highly productive economies. Clean and energy efficient they may be, but are post-industrial societies also highly productive? This is one of the main questions that we try to answer in the present paper.

Outline of the paper

The paper will proceed as follows.

(1) In the next section we describe the demographic transition because this parallel will help us to understand what difficulties it raises and what benefit can be expected from the present study.

(2) In the following section we formulate the wage transition rule and we explain briefly how it can be used for predictive purposes.

(3) Then, we describe the wage transition in the United States and its connection with the shift from an agriculture-based economy to a service-based economy.

(4) The following section gives comparative statistical evidence for the wage transition effect and discusses the cases of outliers.

(5) Then we examine whether a decomposition of economies into their various sectors can help to understand the wage transition.

(6) A formal model is presented which describes the decomposition of an economy into two sectors, e.g. agriculture versus all other sectors. Our objective is to estimate the change in global productivity which results from a transfer of manpower from one sector to the other. It will be seen that transfers from the agriculture sector to the manufacturing sector does not directly account for more than 20% of GDP growth.

(7) Then, in the last section before the conclusion, we give a closer look to the rural population in China in order to see for how long it can indeed fulfill its role of a reservoir of manpower.

(8) In the conclusion we summarize our results and enlarge the picture by including other Asian nations such as India and South Korea.

(9) Two appendices close the paper. The first is methodological; it compares different metrics for measuring wages. In the second we rank capital outlays in terms of enhanced productivity for the society as a whole; the purpose of this discussion is to define more precisely the synergy effect.

Parallel with the demographic transition

Before describing the wage transition it may be useful to present a transition of same kind, namely the well-known "demographic transition". The two transitions are of same kind in the sense that they occur over a similar time span and mostly in the same countries.

There are many factors which may affect women fertility, that is to say the average number of children that a woman will have during her life-time. Just as illustrations one can mention the following: the mean age at marriage, the infant mortality rate, the attitude of the prevailing religion with respect to birth control, the laws ruling inheritance, the place of residence (whether rural or urban4 ), whether or not the family needs a second salary, the extent to which girls have access to education. Many other factors could be added to this list. As a matter of fact, the list is boundless in the sense that for each "primary" factor one can cite many "secondary" factors. For instance, the mean age at marriage can be seen as a primary factor but it is affected by countless social and economic circumstances. The thin lines are centered moving averages (over intervals of 5 years) of the differences between birth and death rates for 4 countries: Germany (black), Denmark (blue), England and Wales (green). Sweden (red). The thick line is the average of the 4 cases. The demographic transition consisted in an almost simultaneous fall of death rates (mostly due to a decrease in infant mortality) and birth rates; however, because the second effect was predominant the net effect was a decrease in the rate of natural increase. The graph shows that this transition was marked by several ups and downs. In addition, for some countries (e.g. the Netherlands or France) this rule did not apply at all. Source: Flora et al. (1987, vol. 2, chapter 6) One may think that by focusing on a single country the question will become more clearly defined and hence easier to solve. This is an illusion, however. As an illustration, consider the case of France. Between 1850 and 1940, the average fertility rate of French women and the resulting rate of natural increase of the French population were much lower than in other Western European countries 5 . The explanation most commonly accepted by historians relies on the observation that according to French inheritance laws all children were entitled to an equal part of their father's landholding. Thus, it is said, to avoid splitting their land, farmers did not wish several children. However, can such an explanation be sufficient when one realizes that in 1906 only 43% of the labor force was working in agriculture and that only one half of this percentage, that is to say some 20% of the labor force, were landowners (Flora et al. 1987, p. 500)?

On the contrary, if, instead of focusing on a single case, the scope of the analysis is broadened to a whole range of similar countries, then a fairly well defined pattern emerges which is called the demographic transition.

It consists in the fact that between 1900 and 1940, in almost all west European countries the annual rate of natural increase (per 10,000 population) fell from about 120 to less than 50 6 .

In the second half of the 20th century there were two other demographic transitions.

• In most developed countries, the transition described by Fig. 1 was in fact followed by a second one that brought down fertility rates well below the replacement rate of 2.1.

• Between 1965 and 2015 a similar demographic transition unfolded in many developing countries, e.g. Brazil, India, Indonesia, Mexico, South Korea, Turkey, Vietnam. This transition was even of greater magnitude than the first in the sense that within 50 years fertility rates fell from a high level of about 5 to a level of 2 (or even less as in South Korea). There were also a few countries which did not follow the rule, e.g. the Philippines, Nigeria and other African countries.

The wage transition rule

Statement

In the present paper, we describe what can be called a wage transition. It may be summarized by the following statement:

Wage transition rule. In developed economies, after an initial phase during which real wages increased exponentially (with a doubling-time of about 30 years), a second phase set in around 1980 during which average wages leveled off or even fell slightly. Most often this second phase set in after the share of number of immigrants to the United States or to Latin America. There is a strong contrast between the massive flows of Germans and Italians and the very small numbers of French immigrants. 6 For instance, in Germany the fall was from 141 to 54, in Britain from 116 to 30, in Sweden from 111 to 25, in Switzerland from 100 to 46 (Bunle 1954, p. 16). There were exceptions however, the most conspicuous of which were Italy and the Netherlands. In both cases, the rate of natural increase remained around 100. France should not be considered as an exception because with its initial increase rate of only 11 per 1,000, no transition could happen.

agriculture in the labor force had fallen under 10%.

Before stating this rule we discussed briefly the demographic transition because the two transitions share several important aspects.

• Although (as will be shown below) the wage transition is confirmed by a large amount of statistical evidence, there are a few exceptions.

• The demographic transition could not be attributed to a single factor but was rather correlated with a whole bundle of variables; similarly the wage transition comes along with a whole range of changes.

• Despite these limitations, the wage transition rule provides a framework that gives a better understanding and allows testable predictions.

As an example of a better understanding one can mention the case of the United States. When this example is considered alone it might appear surprising that wages increased sharply until 1975 and slumped thereafter up to present day. The observation becomes less puzzling when seen in the light of the wage transition rule because then it just appears as an early instance of a transition that took place in most countries. This tells us that instead of trying to explain it by purely American causes we should rather consider factors that are common to most industrialized countries.

Implication for the growth of the Chinese economy

As an example of a testable prediction, one can mention the issue of the growth of the Chinese economy, a question much debated currently (November 2015). The wage transition rule and the observation that the share of Chinese agricultural employment will not fall under 10% until at least 2025 suggest the following prediction.

After increasing exponentially (with a doubling time of 8.4 years) from 1990 to 2015, the average wage in China should follow the same trend for at least another decade that is to say until 2025.

During the past three decades the increase of the average wage paralleled the growth of the Gross Domestic Product (GDP). From 1990 to 2015 the GDP per capita (at current prices) grew from 1,866 RMB to 49,300 RMB. With an increase of the GDP deflator from 12 to 42 this gives a multiplication by 7.5 for the real GDP per capita. The average annual growth rate was 8.2% which corresponds to a doubling time of 8.4 years. In a country as large as China, domestic consumption plays a crucial and increasing role which means that a rising average wage is both the effect and engine of economic growth.

The following qualifications may apply as second order effects.

• If productivity progress slows down because of a rapid development of the healthcare sector (there is a longer discussion of this point below) then one would expect a somewhat slower growth, say around 6%.

• In addition, in the coming decades it is likely that, as in western countries, the share of non-salary earnings will increase. As a result, salaries may grow slower than the GDP/capita. This would lead to an annual growth forecast for salaries in the range 4% -5%.

Actually, in the previous prediction the key-point is not the exact value of the rate but rather the statement that such a long-term trend will not be derailed by one or two short-lived recessions 7 . Nevertheless, it may not hold if there is an upheaval similar to what happened in the Soviet Union in the years following 1991.

Connected issues

Before starting the discussion of the wage transition, it may be helpful to keep in mind the following observation. In economics all phenomena are inter-connected. Therefore, it would be easy to list many effects which may possibly play a role in the leveling off of wages. For instance, the financialisation of the economy contributes to the divergence between GDP/capita and wages; growing inequality contributes to the divergence between high and low earnings; through expansion of the supply side, immigration contributes to eroding wages; the gradual disappearance of unions may have the same effect.

Although all these effects may play a role, thanks to our comparative perspective, we know that they do not play the main role. Indeed, the great advantage of this approach is that it allows us to filter out secondary factors. In Japan there is little immigration, in Sweden unions are still important forces, in Germany, financialisation of the economy is less developed than in the US. Nevertheless, in all these countries the wage transition effect can be observed. In short, even if the previous effects exist, they are only second-order effects in the sense given to this expression in physics.

The wage transition in the United States

Observation

There are two good reasons for starting this investigation with the case of the United States. The first is that, as already said, it was the first country where this transition 7 Just for the purpose of comparison, it can be of interest to consider the case of Mexico. Between 1980 and 2013 it experienced 3 major crises.

• In December 1982 the country was bailed out after defaulting on its sovereign debt. It was not until 1994 that the GDP/capita resumed its pre-crisis level.

• Then, in early 1995 a second bail out ($50 billion) was necessary to prevent a new default.

• Finally, the worldwide crisis of 2008 led to a 5% fall of GDP. As nowadays for Greece, there were a succession of debt restructuring plans: e.g. the Baker, Brady and Clinton plans. Because of these recurrent crises, the GDP/capita expressed in US dollars increased by only 31% in the 33 years from 1980 to 2013. Expressed in constant dollars the growth would be about zero. Thus, it can be said that the "North American Free Trade Agreement" (NAFTA) which started in 1994 has had but a dismal effect on the economic growth of Mexico.

occurred. Secondly, it is probably the country where the wage transition was the sharpest. This can be seen clearly by comparing Fig. 2 and Fig. 3. In phase 1 the mean wage, w, increased exponentially at an average rate of 2.0% per year whereas in phase 2 it stagnated. Simultaneously the proportion of the labor force employed in agriculture, f a , fell from 41% in 1900 to 4.4% in 1970. There is a high correlation, namely 0.987, between the two changes. The relationship between the logarithms of the two variables is: log w = -a log f a + b, a = 0.67 ± 0.09, b = 1.87 ± 0.06. Sources: Historical Statistics of the United States 1975, Liesner 1989, US Bureau of Labor Statistics, "Trading Economics" website) Whereas in the US the transition from exponential increase to stagnation occurred abruptly, elsewhere there was a smooth transition involving a progressive reduction of the growth rate.

Local versus global explanations

If we limit our attention to the US case, many possible "explanations" may come to mind. One can mention the following for instance.

• The decades after 1945 were marked by a progressive erosion of the fighting capability and bargaining power of American unions. This trend already started with the Taft-Hartley Act of 1947 but it really gained momentum only in the 1970s. One of its clearest manifestations was the dramatic fall in the frequency of strikes. More details can be found in [START_REF] Roehner | Hidden collective factors in speculative trading[END_REF]. For instance, in the private sector the unionization rate dropped from about 30% in the 1950s to 8% in 2007.

• The oil shock of 1974.

• The confidence crisis which affected the dollar in the late 1960s and which eventually led to President Nixon's action in 1971 ending its convertibility to gold.

• The slump of stock prices at the New York Stock Exchange in the 1970s.

• The aftershocks of the Vietnam War débâcle.

In order to narrow down the set of possible "explanations" we must consider a broader range of cases. This is what is done in the next section. The fact that the same wage transition can be observed in many countries will ipso facto eliminate all specifically American explanation. In the previous, apart from the first factor, all others were confined to the US.

Divergence between GDP per capita and wages

In contrast with Fig. 2a, the US GDP per capita increased steadily without showing any saturation effect (see Fig. A1). How can one explain the divergence observed in the past 40 years? There are two fairly standard explanations.

• The fact that an increasing number of house wives have a full time job. As an illustration in the form of a thought experiment consider two households A and B, each composed of a husband, a wife and a baby. In situation 1 the wives do not work to take care of their babies. In situation 2 , wife A has a full time job as baby sitter in family B, while wife B similarly works full time as a baby sitter in family A. Although in terms of service and income the two situations are completely identical, due to the two baby sitter jobs the GDP will be substantially higher 8 .

• The fact that an increasing share of the GDP comes from non-salary earnings (e.g. dividends or earnings from real estate transactions). Another factor which is less often mentioned is immigration. In the decades following 1975 there was a steady increase in the number of immigrants and, along with them, also of illegal immigrants. The later contribute to GDP growth but as they are not recorded in the official population, the GDP per capita will be artificially inflated. There is a similar effect with offshore manufacturing.

The wage transition in comparative perspective

Average wage increases

As seen in the previous section regarding the United States, and as will be seen in the present section for the European countries and Japan, wage stagnation is in fact a phenomenon which started over two decades ago. However, like the demographic transition, the wage transition did not occur simultaneously in all places but rather gradually with country-dependent time lags. This is illustrated in Fig. 3.

Explaining the cases of outliers

It should not come as a surprise that there are a few outliers. We have seen that this was also the case for the demographic transition. In what follows we will consider more closely two cases, namely Britain and Singapore. It will be seen that despite being apparent outliers these cases do not really contradict the wage transition rule.

The case of Britain

8 While dependent on the income of the husbands, the percentage increase should be at least 30%.

Average annual wage (1,000 euros of 2015)

Positions of turning points:

USA Japan Switzerland

UK Germany

USA Japan Switzerland UK Germany Fig. 3 Wage transition in several countries. In phase 1 the average wage increased exponentially whereas in phase 2 it stagnated or increased more slowly. The names of the countries at the bottom of the graph indicate the years when the transition occurred. For Germany and Japan the end of World War II was followed by a reconstruction period which lasted some 20 years; these so-called "economic miracles" produced two fairly artificial wage transitions around 1970 that we discarded. To the 5 countries shown one could add Singapore whose transition occurred in 2005 as discussed in the text. Sources: USA: see Fig. 2; Japan: Historical Statistics of Japan, average monthly contractual earnings; Switzerland: The website of the "Federal Office of Statistics" gives an annual series of real wages starting in 1939; UK: Until 1985: Liesner 1989Liesner , 1990Liesner -2015: : Office of National Statistics, average weekly earnings of manual workers; Germany: Until 1985: Liesner 1989, 1990-2015: Federal Statistical Office, gross hourly earnings for manual production workers.

Britain stands apart both in Fig. 3 and in Fig. 6. One may wonder why.

In 1846, that is to say very early compared with other European countries, through the repeal of the "Corn Laws" which had imposed heavy duties on grain imports, Britain decided that grain supplies could be obtained in a much cheaper way through overseas imports particularly from the British Empire (e.g. from Canada or India 9 ). This step was foreshadowed by recurrent land "Enclosure Acts" (e.g. those of 1801 and 1845) which transformed into private property the "common lands" that hitherto had allowed farming by landless farmers.

Through these steps poor people were compelled to move from the countryside to cities. Thus, the massive replacement of agricultural jobs by industrial jobs started in Britain in the early 19th century whereas in other European countries it started in the mid-or late 19th century. Because, it occurred earlier at a time when industrial productivity was lower than 50 or 100 years later, this process led to earlier and slower wage increases. In short, the process was so to say diluted over a longer time span. This is indeed what we observe in Fig. 3 and5.

The case of Singapore

At first sight, it may seem that the case of Singapore is irrelevant for our study because this city-state has no agricultural sector which means that there cannot be any labor force transfer from agriculture to manufacturing. In other words there can be no productivity increase through rural flight. However, this is precisely what makes this case interesting for indeed Singapore also exhibits a wage transition. Obviously, this requires an explanation. First of all, let us examine what was the evolution of wages in Singapore?

Between 1965 and 2005 real wages for the lowest paid workers have been multiplied by 5.5. However, in the last decade they have stagnated [START_REF] Shanmugaratnam | Budget speech given in Parliament[END_REF].

First of all, we must understand why productivity progress could allow such a high increase in wages prior to 2005. Did we not suggest that service economies do not generate much productivity growth?

The important point is that, despite being a city-state, Singapore is not a pure service economy. In 2000 its manufacturing sector represented 25% of its GDP. In addition, its semi-industrial port activity represented 33% of its GDP. Thus, altogether the industrial and semi-industrial activities represented 58% of GDP, i.e. much more than the share of 15% represented by manufacturing, transportation and warehousing in the United States 10 . Another factor is that Singapore benefits from massive investments by western companies. This brought its economy in line with the capital cities of developed countries. Not surprisingly, now that it has reached the same level it also experiences the 9 To the point that India exported grains to Britain even in years when there were famines in some parts of the country. 10 Manufacturing represented 11.5%, transportation and warehousing 3.5%. The data are for 2007 and the source is: Wikipedia: sectors of US economy as percent of GDP (1947GDP ( -2009)).

same slowing down11 . In short, Singapore is a very useful outlier for it shows that there is no need of an agriculture sector for a wage transition nonetheless to take place.

Insight provided by a decomposition by sectors

Any economy can be decomposed into sector-based components. In a sense this may seem similar to the spectral decomposition of light but, unfortunately, as explained in the next subsection the decomposition into sectors is fairly arbitrary in several respects.

Difficulties of the decomposition into sectors

Table 1 shows that with respect to productivity the only clear and long-term distinction is the one between agriculture and manufacturing. The tertiary service sector is a mixed bag involving activities of very different productivity levels. Moreover, the composition of this sector will be different from one country to another and in each country it will change in the course of time. For instance, the software industry which nowadays is an important component in the United States was non-nonexistent some 30 years ago and is still under-represented in European countries. Another example is the health care industry; according to table 1, in 2012 this sector represented 12% of the total employment and 7.1% of the total GDP12 ; some 30 years ago the weight of this sector was much smaller and nowadays it is still much lower in many other developed countries.

It is this changing shape of the tertiary sector which makes it difficult to set up a model which would have a permanent validity. The global productivity of the tertiary sector is a weighted average which in the case of the sectors listed in Table 1 (i.e. all 13 sectors except agriculture, manufacturing and mining) is equal to $122, 000 per employee, a figure which is mid-way between the productivity of agriculture and manufacturing.

In the next section we examine the implications for economic growth.

A two-sector model for the USA and China

For China in 2013 the weights and productivity of the agricultural sector on the one hand and of all non-agricultural sectors on the other hand are given in Table 2. With respect to rural flight, in the United States the major transformation took place between 1900 and 1950. In this time span the percentage of the labor force engaged in agriculture fell from 41% to 11%, that is to say at an annual rate of 0.6%. Based on the data of Table 1 and 2, Fig. 4 summarizes the respective situations of the United States and China. In the United States between 2000 and 2010 the percentage of the labor force employed in agriculture fell from 2.5% to 1.5%, that is to say at an annual rate of 0.1%. In China during the same time interval, this percentage fell from 50% to 36%, that is to say at an annual rate of 1.4%. Whereas nowadays in the United States this transfer of jobs from the agricultural sector to the non-agricultural sector represents a very marginal source of productivity progress, in the first half of the 20th century it had been a major source of productivity growth. However, the present transfer rate in China is twice as fast as it was at that time in the US. It was between 1940 and 1950 that the US transfer rate reached its maximum with an annual rate of 0.9%, still lower than seen in China in the past decades. Notes: p = G/E denotes the GDP per employee for the whole economy. The GDP per employee in sector i is:

g i = G i /G e i = E i /E f i = g i /e i k = p i /p 1 [% of GDP] [% of employment] 1990 Agriculture g 1 = 25 e 1 =
p i = G i /E i = (g i /e i )(G/E) = (g i /e i )p = f i p.
Between 1990 and 2013 the percentage of the total labor force engaged in the agricultural sector fell from 60% to 34%. In 2013 the productivity gap between agriculture and the rest of the economy was 4.6; this was three times the ratio of 1.47 found in Fig. 4 Transfer of rural population to the non-agricultural sector. In China the transfer rate was over 10 times faster than in the United States.The figure respects the order of magnitude of the productivity gap within each country and also the magnitude of the respective rates of transfer. The scales of the two vertical productivity axes are not the same; this allowed us to draw two identical rectangles to represent the nonagricultural sectors. Sources: Tables 1 and2.

Model description of the transfer effect

In order to test to what extent the mechanism described in Fig. 4 can explain longterm wage increases we need to set up a model along these lines. It will be a purely descriptive model for we do not yet have a clear understanding of the mechanism that is at work. The investigation of other cases of wage transitions should help to separate circumstancial and essential factors. As an example of another case, one can mention the wage transition (in this case an increase) which followed the "Black Death" and the disappearance of one third of the European population 13 .

Definition of the productivity multiplier

In order to make the model as simple as possible, we will introduce only two sectors: agriculture (sector 1) on the one hand and the rest of the economy (sector 2) on the other hand. At first sight this may seem a very rough approximation; for instance, mining and health care will be together in sector 2; however, mining is a fairly small sector (it is 21 times smaller than health care). The purpose of our two-sector model is to provide a broad picture and to explain (and predict) long-term trends.

With the notations defined in Table 2, the productivity factor f i = g i /e i = p i /p expresses how the productivity p i of sector i stands with respect to the productivity p of the whole economy. For instance, f i < 1 is observed for the agricultural or health care sectors whereas f i > 1 is observed for manufacturing or financial activities.

In order to discuss the implications of rural flight we introduced a variable k that we call the productivity multiplier with respect to agriculture which expresses how much the productivity of sector 2 is higher than the one of sector 1.

Productivity multiplier 2/1:

k = p 2 p 1 = (g 2 /e 2 )p (g 1 /e 1 )p = (1 -g 1 )/(1 -e 1 ) g 1 /e 1
The interesting point is that k can be computed as soon as one knows the two numbers g 1 , e 1 .

Order of magnitude and changes of key-variables in the US and China

In order to give some substance to these definitions, let us give some numerical values for the United States and China. The data for p are expressed in dollars of 1982 and renminbi of 2013 respectively.

• USA:

1900 : p = $9, 593, e 1 = 41%, g 1 = 23%, g 1 /e 1 = 0.56, k = 2.32

1950 : p = $20, 424, e 1 = 11%, g 1 = 6.9%, g 1 /e 1 = 0.62, k = 1.66 1980 : p = $32, 095, e 1 = 3.4%, g 1 = 3.0%, g 1 /e 1 = 0.88, k = 1.14

• China:

1983 : p = RMB 5, 114, e 1 = 67%, g 1 = 33%, g 1 /e 1 = 0.49, k = 4.12 2000 : p = RMB 24, 184, e 1 = 50%, g 1 = 50%, g 1 /e 1 = 0.30, k = 5.67

2013 : p = RMB 73, 513, e 1 = 34%, g 1 = 10%, g 1 /e 1 = 0.32, k = 4.63

13 Needless to say, in this case it will be more difficult to find accurate data.

A noteworthy point is the stability of g 1 /e 1 ; it changes much less than e 1 and g 1 separately and also much less than p. How should this be interpreted? The fact that g 1 /e 1 = p 1 /p is quasi-constant in spite of the fact that p doubles, triples or quadruples means that agricultural productivity increases approximately at the same pace as global productivity. Moreover, it can be observed that k changes fairly slowly which for a structural variable is of course a welcome characteristic.

Other data will be found in During these 25 years the GDP per employee has been increasing exponentially both in the agricultural sector and in the rest of the economy. The coefficients of correlation (t, log p i ) are 0.97 and 0.99 respectively. The exponents are given in the notes of Table 3. Notes: From the last column it can be observed that the rates of change of the labor force are an order of magnitude smaller than the rates of change of the GDP. When intermediate values are introduced one finds that both p 1 and p 2 increase as exponentials with exponents α 1 = 0.062 ± 0.016 (doubling time of 11.1 years) and α 2 = 0.075 ± 0.011 (doubling time of 9.2 years). As a result, in the long-term the productivity gap increases as p 2p 1 ∼ exp(α 2 t) Sources: World Bank, Trading Economics, http://www.investopedia.com.

The exponential increase of p 1 and p 2 has two interesting implications.

• As is well known, in a limited world an exponential growth cannot last for ever which means that a saturation effect will set in sooner or later. The data shown in Fig. 6 suggest that it should not occur before 2025.

• Over past decades the productivity gap between the agriculture sector and the rest of the economy has increased exponentially:

p 2 -p 1 = p 2 (1 -p 1 /p 2 ) = p 2 [1 -(A 1 /A 2 ) exp(-dt)] , d = α 2 -α 1 = 0.013
For large t the gap becomes equal to p 2 itself. Thus, any labor transfer from sector 1 to sector 2 will trigger a productivity jump whose magnitude increases exponentially in the course of time. This effect may compensate for diminishing transfers as e 1 becomes smaller. In other words, the productivity effect of rural flight will remain significant even when e 1 will fall under 10% as may happen around 2030 according to Fig. 6.

Direct GDP change due to a transfer of labor force

Now, in order to describe the mechanism of Fig. 4 we must assume that e 1 decreases by a quantity ∆e 1 . In fact, in what follows it will be more convenient to follow the variable e 2 because its variations ∆e 2 = -∆e 1 are positive in the course of time. The change in G resulting from a transfer of population from sector 1 to sector 2 will be:

G = G 1 + G 2 = p 1 e 1 E + p 2 e 2 E → ∆G = (p 1 ∆e 1 + p 2 ∆e 2 ) E = (p 2 -p 1 )E∆e 2
(1) In the above expression of ∆G the productivities p 1 , p 2 have been kept constant because we wish to focus on the sole effect of a labor force transfer14 . By introducing the factor k, expression (1) becomes:

∆G = (k -1)p 1 E∆e 2 = (k -1) g 1 e 1 G∆e 2 → 1 ∆e 2 ∆G G = (k -1) g 1 e 1 (2)
We can take advantage of our previous observation regarding the stability of g 1 /e 1 to simplify expression (2) into:

1 ∆e 2 ∆G G = (k -1) < g 1 e 1 > (3)
where < g 1 /e 1 > represents the average value of g 1 /e 1 over a period of several decades. For the United states, one would have < g 1 /e 1 >= 0.69 whereas for China: < g 1 /e 1 >= 0.35.

The left-hand side represents the percentage variation ∆G/G for a 1% variation of e 2 .

Note that equation (3) applies to any transfer of labor force. In particular, it can also describe the decline in GDP that results from the transfer of labor force from manufacturing to healthcare, a key-feature in industrialized countries over the past three decades15 . This point may be developed in a subsequent paper.

Labor force transfers as an engine of productivity growth

Rural flight seen in the perspective of overall labor force transfers So far in this paper the focus was on the effect of rural flight on economic growth. There are two main reasons for that.

• This labor force transfer has a clear statistical definition because of the fact that agriculture is a well defined economic sector. In contrast, a sector such as healthcare has a fairly fuzzy statistical definition. For instance, do nursing homes belong to healthcare or to the hospitality industry?

• Historically rural flight has been of great importance in all developed countries and nowadays it is still a major factor in countries such as China and India.

However, this focus should not hide the fact that rural flight is only one case (albeit the most significant) of a broad variety of labor force transfers which take place continuously. For instance in developed countries two sectors have had a rapid growth over the past 50 years: (i) healthcare and (ii) the information technology sector. According to Table 1, around 2012 in the United States healthcare employed about 15% of the total work force whereas the share of the IT industry was of the order of one or two percent. What impact on global productivity has had the development of these sectors? Table 1 shows that healthcare's and IT's productivities were one half and twice the national average respectively.

A case in point: healthcare versus infrastructure development Across nations there are great disparities in the extension of the healthcare sector. For countries with an aging populations (as is the case of all developed countries) it is of course natural to have an expanding healthcare sector but it must be recognized that its actual extent is determined by political decisions. Thus, in the United Kingdom which has a nationalized medical system the weight of healthcare in the economy is only one half of what it is in the US 16 .

The fact that through its own poor productivity level, the healthcare sector drags down overall productivity is not its only liability. Because most of its patients are elderly persons beyond retirement age, health care has little synergy with other activities.

Completely different is the case of infrastructure expenses. Many other sectors will benefit from better transportation infrastructure. Clearly, healthcare based development and infrastructure oriented development constitute two different models. As one knows, the infrastructure model is promoted by the Chinese government not only domestically but also for the rest of the Asian continent. Regarding healthcare, at this point it is too early to say which system China will choose. Will it be the US or the UK model17 ? Clearly this choice will affect the productivity of the whole Chinese economy. Too much resources and investments sunk in healthcare will be a drag on the economy. At the beginning of the paper we said that one would expect a 8% growth trend until 2025 but an over extended healthcare industry may well slow down this expectation to 6% or 5%.

What fraction of growth does rural flight explain?

In this section we compare the changes in GDP per employee actually observed to those predicted by the rural flight effect in three different ways.

Correlation of relative variations

Firstly, following equation ( 3), one may wish to see if there is a connection between the ups and downs of e 2 on the one hand and the wage changes on the other hand. Obviously, cases such as China in which the two variables grow steadily will not be appropriate for this test. The test can be done in better conditions for the United States in the period 1900-2010. The corresponding graph can be found in the arXiv version of the paper. There is a correlation of 0.64 between actual wage changes and those predicted by the two-sector model based on changes in e 2 .

Percentage of growth in China directly due to rural flight in 1990 and 2015

We wish to determine what proportion of the increase in GDP per employee is directly produced by the rural flight effect. For this test one needs a case in which the rate of change of the rural population is as large as possible. China is well suited for this purpose. We will compute the expected changes at the two ends of the time interval 1990-2015. For this purpose we will use the data given above (Table 3 and additional data).

As already explained the rural flight effect is only one of a number of transfer effects which contribute to GDP growth. One of the clearest manifestations of the effects of these transfers are the productivity increases within the two sectors. This effect cannot be explained by rural flight. Indeed, rural flight can only explain the global growth of G due to the interaction between agriculture and the rest of the economy. The productivity increases within the two sectors are due to interactions between their various sub-sectors.

• Tractors, trucks instead of horse driven carriages, engines, pumps, motorcycles, mobile phones and many other items that are produced in sector 2 progressively came into use in the country side, thereby lifting p 1 . These changes would happen independently of any transfer of labor force.

• At the same time, in sector 2 outdated textile factories were equipped with modern spinning and weaving machines manufactured in other factories of sector 2, newspaper printing machines were replaced by computerized systems, supermarkets replaced small stores. As above, these changes would happen independently of any transfer of labor force. Because sector 2 is more diversified than sector 1 it experiences more synergy and that is probably why the endogenous growth of sector 2 is faster than the endogenous growth of sector 1.

According to the comments following Table 3, we expect a greater effect of rural flight in 2015 than in 1990. Let us see if this is confirmed by observation.

Over the whole period 1990-2015 the labor force in sector 1 decreased by 170 millions which gives an average change of 34 millions over every 5-year interval. 1990-1995 Over this time interval, one gets (everywhere RMB means "RMB of 2015")

• The average of p 1 is p 1 = (5, 231 + 7, 434)/2 = 6, 332 RMB/employee • The average of p 2 is p 2 = (15, 380 + 27, 323)/2 = 21, 351 RMB/employee Thus, rural flight from 1 to 2 will increase G by: ∆G ′ = 34×10 6 (p 2 -p 1 ) = 511×10 9 RMB.

The actual increase in G was ∆G = G(1995)-G(1990) = 5, 627×10 9 RMB. Thus, the variation due to rural flight represents: 511/5627 = 9.1%.

2010-2015

A similar computation leads to: ∆G ′ = 2, 383 × 10 9 RMB, and ∆G = G(2015)-G(2010) = 5, 627×10 9 RMB. In this case the variation due to rural flight represents: 11.4%.

As expected we see that in 2015 the change due to rural flight is a larger proportion of the total increase than in 1990. We also see that the largest part of GDP growth must be attributed to endogenous increases of G 1 and G 2 which in turn are due to transfers occurring within these sectors.

In the arXiv version of the paper the previous computation is alsao presented in a more formal way based on equation (3). The calculation leads basically to the same estimates.

Indirect effects of rural flight

There are numerous indirect effects. We describe two of them below.

• When persons move from their village to a city their consumption style changes completely. Instead of living in a village house they will live in a multi-storage building. Whereas the village house was built mostly by hand, the contruction of the building relied of modern building techniques which allow a much higher productivity. Similarly, instead of buying from village markets once in cities the persons will buy in supermarkets which represent a more efficient form of distribution. In short, by moving to cities the persons will boost modes of production and distribution which have a higher productivity.

• Persons moving to cities will earn a higher income (that was probably their main motivation for leaving their village). By spending this income they will expand the domestic demand. For instance, by moving into an apartment, they will contribute to solve the problem of the "ghost buildings", that is to say newly built apartment which have remained inoccupied ever since they were built.

Although it is difficult to quantify these indirect effects, they explain why rural flight will continue to be the engine of Chinese economic growth in the years ahead.

Implications

The fact that rural flight accounts for less than 20% of the total growth has two important implications.

• A recession may temporarily stop employment shifts from sector 1 to sector 2. If this transfer would account for a high percentage (say some 80% or more) of economic growth, then its discontinuation would freeze further growth altogether and transform the recession into a depression. However, if employment transfer actually is only a secondary factor the synergy engine will continue to work and will pull the economy out of the recession18 . This is indeed what was observed in developed countries in the decades following World War II. There were only mild recessions. In other words, unless there is a political upheaval no major interruption of growth should be expected in China for at least 15 years, that is to say until it has become a service economy too.

• As seen earlier, in developed countries the growth of wages stopped or slowed down in the 1980s. This was due to the shift of their economies toward a service sector economy which is dominated by low productivity sectors of which healthcare is an important component. The fact that rural flight almost came to an end in the 1980s was due to two circumstances: (i) The labor force of sector 1 was already largely depleted. (ii) Because productivity growth in sector 2 was slowed down, this sector lost its attractivity in terms of higher salaries. Indeed, the growth of sector 2 was largely due to the introduction of so-called "odd jobs", "second class jobs" or "deskilled casual work".

Extent of the workforce reserve in rural China

In this last section before the conclusion, we wish to give a more precise description of the age structure of the rural population in China because this will directly affect the economic effect of rural flight.

Defining the question

The argument on which our previous argument was based assumes implicitly that the rural population comprises persons who can take up a job in the manufacturing or service sector once they have moved to cities. There are two situations in which such an assumption does not hold.

(a) The first case is when the rural population comprises only elderly persons beyond retirement age (Fig. 5b). This situation would occur when all middle-aged persons have moved to cities together with their children. In this case there would be no productivity reserve whatsoever in spite of a rural population which may be well over the 5% threshold.

(b) The second case is when the rural population comprises only grand parents and their grand children (Fig. 5a). This situation would occur when all middleaged persons have moved to cities but have left their children behind them in their villages 19 . In this case, there is no short-term productivity reserve but over a period of one decade the young segment of the rural population will contribute to productivity progress.

In former rural flights (described in Fig. 6 for industrialized countries) the situations (a) and (b) occurred only marginally and, as a result, productivity progress was not substantially slowed down. Why should the picture be different in China?

One obvious reason can be mentioned which is the pace of the rural flight in China. The very same evolution that took one century and a half in western countries is taking place in China in less than 50 years. So, in order to make sure that the rural flight mechanism will have the effect that we expect we must consider more closely the changes in the composition of the rural population. We will do that in two steps: first we give a fairly qualitative picture, then we will show two graphs which provide estimates for age-specific composition changes.

Qualitative view

This subsection is based on a paper in Chinese by Zong and Xiang (2013). As this paper provides many interesting tables and graphs one may wonder why we use it here to give a qualitative picture. It is because the paper is not based on census data but rather on a survey of their neighbors carried out by Chinese graduate students when returning to their home place during their term break20 . As a result, the data are based on fairly small samples of one or two thousands. However, they provide a much more detailed view than could be obtained from census data. The following points are of particular interest.

• Instead of a simplistic binary picture the paper considers several cases: persons who moved away and are no longer registered in the village (A); persons who are still registered but are present in the village during less than 3 months per year (B 1 ); this category would correspond to students or young people who return to their village a few times every year. Three similar categories (B 2 , B 3 , B 4 ) correspond to persons who stay in the village more than 3 months but less than 6 months, more than 6 months but less than 10 months, and more than 10 months. Around 2010 the percentage distribution was as follows:

A : 29%, B 1 : 18%, B 2 : 3.2%, B 3 : 2.7%, B 4 : 47%

• If one considers children under 15, about 50% lived with their two parents, 22% lived only with their mother, and 25% lived with their grandparents21 .

Quantitative picture

The age distributions shown in Fig. 5a,b are based on the censuses of 1982, 2000 and 2010. They confirm the picture given in the previous subsection in the sense that the demographic situation in rural areas is still fairly remote from the idealized cases represented by the dotted curves. Can we make comparisons with other countries? In the United States around 1930 the rural population represented 44% of the whole population. In the rural population the share of the group under 15 was 35%. For China around 2010 the corresponding figures were 55% and 13%. The first number confirms what we already emphasized namely that rural flight is only at its beginning in China. Comparing the shares of the age-groups under 15 makes little sense because it simply shows that in the US the birth rate and immigration rate were much higher than presently in China.

In conclusion, we can say that there is still a substantial manpower reserve in rural The graphs compare two idealized situations (dotted curves) with the actual age distributions. The expression "grandparents" designates persons over the age of 55 that is to say persons who can no longer be counted in the manpower reserve susceptible of moving to cities. The curve for 2028 is a linear projection based on the data of 1982 and 2005. It can be seen that although closer to the "grandparents only" picture, it is still fairly remote from it. Note that because of the y log scale the flat parts of the dotted curves that should be at zero percent had to be set to a low but non-zero percentage. Sources: [START_REF] Kasperkevic | The demographic crisis is going to hurt most in rural China[END_REF], [START_REF] Zhong | A regional comparison of the age distribution in the rural Chinese population and its implications to policy making [paper in Chinese, original title is: Woguo nongcun renkou nianling jiegou de diqu bijiao ji zhence hanyi[END_REF], [START_REF] Yiliminuer | La Chine, championne du monde de la gérontocroissance?[END_REF].

areas that will become available for moving to cities as soon as higher agricultural productivity will make that possible.

Conclusion

The present paper investigates a mechanism, the wage saturation effect, that has no obvious explanation in the framework of standard economic theory. To start from an effect that the theory does not predict is uncommon in economics22 which is probably why this effect did not yet attract the attention of economists.

We have shown that in developed countries there is a saturation effect in the increase rate of wages. The timing of this effect is ruled by the end of rural flight. This can be seen by comparing Fig. 6 and Fig. A2 particularly for the case of South Korea. Moreover, we have seen that the direct and indirect effects of rural flight explain fairly well the high rate of economic growth in China over the past three decades. In contrast, in spite of similar initial conditions, the development of countries such as Brazil, Mexico or Thailand was hampered by a succession of serious financial crises which often were trigerred by fund withdrawals made by overseas investors.

Fig. 6 provides a comparative view for a broad sample of countries which includes both developed and developing countries.

Chinese economic growth over 2015-2035 in comparative perspective

Several interesting features are highlighted in Fig. 6.

• The transfer of labor force from agriculture to the industrial and service sectors has progressed unabated in all developed countries. Economic crises or even the two world wars may have slightly slowed down the evolution (as in the case of Austria for instance) but they did not have any lasting impact. (1975). After 1970: Trading Economics website and Saint Louis Federal Reserve.

• We have already suggested that South Korea may be a good predictor of the future of the Chinese economy. The development of South Korea followed the pattern set by developed countries. We see that in terms of proportion of the labor force working in the agricultural sector Finland was about 20 years ahead of South Korea which itself was 30 years ahead of China23 . If one uses the rate of South Korea to extrapolate the curve for China one arrives to the conclusion that in 2035 the percentage of the labor force in agriculture will be about 10%.

• Among developed countries the UK is a case apart. Its agricultural sector fell to a level of 10% some 60 years before the United States. In this sense, Britain was the first post-industrial economy; this may explain the fact (observed in Fig. 3) that its rate of wage increase was substantially lower than in other countries.

What was the evolution of agricultural employment in the USSR and later on in the Russian Federation? By collecting data from various sources [START_REF] Gaidar | Russia, a long view[END_REF][START_REF] Wädekin | Agrarian policies in Communist Europe. A critical introduction[END_REF], Lerman et al. 2003, Trading Economics website) we got the following picture: The table shows that the interruption of the fall of the share of agricultural employment coincided with the crisis of 1988-2000. So, once again, we see that this variable is a good indicator of long-term economic growth. We see also that the time interval 1930-1960 saw a massive reduction in agricultural employment and we know that it was accompanied by rapid economic development.

Rural flight seen as a good indicator of productivity growth

In the first part of the paper was shown that a wage transition occurred in most developed countries in the 1980s. After decades of rapid growth, wages started to slump. Rural flight appeared as a good candidate for explaining not only this wage transition but also the rapid growth observed in China in past decades. Incidentally, one should not think that there was no or little growth before 1983. According to Chinese GDP statistics, the real average annual GDP growth rate was 9.8% from 1952 to 1982 and 9.9% from 1983 to 2014. Even though national accounting methods may have been different before 1983, the idea of a stagnant economy before 1983 seems inappropriate. Actually, the most conspicuous difference between the two periods is that in the first one growth was much more irregular than in the second. The coefficients of variation of the annual growth rates were 194% and 27% respectively.

In order to test the idea of a connection between rural flight and economic growth we set up a model which allowed us to predict the change of income resulting from rural flight. It was seen that this model is in good qualitative agreement with observation.

As expected, rural flight accounts for only a fraction of total growth but it is also a good indicator of the dynamism of sector 2. If tomorrow the Chinese economic growth starts to create a lot of "second class jobs" (for instance by an over-extension of the healthcare sector) then, those young people who presently still remain in Chinese villages will certainly think about it twice before moving to cities. This, in turn, make economic growth more sluggish. So, the main issue is whether in the coming decades China will be able to avoid the "odd job trap".

Wage progression and labor inflow

In this paper, we gave only little attention to the immigration factor. As already observed, the cost of labor is affected by supply and demand changes and supply depends upon immigration. Here we will limit ourselves to three observations which suggest that for the cases that we considered immigration is a second-order factor.

• Due to the sheer size of its population foreign immigration will have little incidence in China. The only country whose population could match the population of China is India. However, whereas there are important Indian communities in the UK and US, immigrants to China would have to learn Chinese, quite a formidable challenge.

• The case of Japan suggests that at the level of a whole country (as opposed to specific sectors) labor inflow through immigration is rather a second-order effect. Indeed, despite a much lower immigration rate, Japanese wages leveled off in the same way as in Germany where immigration is substantially larger (see Fig. 3).

• In contrast, at the sector level, immigration may play a role. In this respect, as a case study, it would be interesting to investigate the impact on labor cost of the inflow of Filipino nurses into the US24 .

all workers

Notes: Broadly speaking these different incomes decrease from top to bottom. Average earning is similar to the macroeconomic variable called "personal income" (i.e. basically GDP minus capital depreciation minus corporate profit divided by employment). At the bottom of the table an additional distinction may be appropriate between hourly, weekly and monthly wages especially in case of large changes in weekly hours worked. All incomes are expressed in national currency and adjusted for inflation. The two countries are not at the same stage in terms of overseas investment and financialization of the economy; therefore, the fact that so far in China there has been no divergence between GDP/capita and wage level does not mean that it will be the same in the future. countries it has been decreasing over past decades.

As an illustration of the difference between median and average income, one can mention that in Singapore in 2014 the average monthly household income was 9, 176 Singapore dollars, whereas the median was only 6,500, i.e. some 30% less. In addition, it should be noted that most income statistics published by the Singapore statistics office include the "employer CPF contribution". The acronym CPF means "Central Provident Fund" and it designates a social security fund destined to cover the retirement, healthcare, and housing needs of the employees. Currently, it represents about 11% of the wages. A similar system exists in many countries.

When analyzing wages one must be very careful for this is not a standard macroeconomic variable like GDP per capita. In fact, for each country one must check (provided that information is indeed given) to what kind of wages the published series corresponds. This reduced our sample of countries to those which publish their statistical data in English (or in the other languages that we are able to read). In short, instead of blindly including in our sample, many countries whose wage series would not be well documented we made the methodological choice of including a fairly small sample of countries for which we were able to get appropriate information.

We hope that subsequently our study will be extended either by us or (and scientifically that would be more satisfactory) by other researchers.

Moreover, other historical wage transitions need to be examined. One which comes to mind immediately is the sharp increase in wages which followed the Black Death of 1348. It is only after several wage transitions have been investigated that we will get a clearer understanding of the mechanism which is at work.

Appendix B. Synergy: individual vs. social productivity

At the end of the paper it was observed that progress in productivity comes mainly from what we called a synergetic effect. In the present section we try to understand this effect at least in a qualitative way.

Productivity at individual level

The simplest measure of the productivity of labor is through the ratio of GDP to the total number of hours worked. According to this definition it is fairly clear that the transfer of an agricultural worker to a modern factory will result in his productivity being substantially improved. This was true in the 19th century, when Irish tenants came to work in Birmingham, Liverpool, or Manchester. This same mechanism operates when a Chinese worker moves from his (or her) village to a modern factory in Guangzhou or Shanghai, but in this case the effect is much stronger for indeed the productivity of a 21st century textile factory will be way higher than the productivity of a textile factory of the 19th century.

As demonstrated by Adam Smith's needle factory example, higher productivity can be obtained by decomposing the production process into simple steps that can then be standardized and mechanized. At the other end of the spectrum are tasks which so far have not been subjected to the same process. A classical example given by the French economist Jean Fourastié is the "production" of an haircut. Fourastié observes that the time required for an haircut, namely about 20 minutes, did hardly change over the past two centuries. It is important to observe that the reason of this stagnation is more social than technical. It would certainly be possible to build a machine able to perform a haircut in a few minutes. However, such machines would perhaps not be well accepted by customers, nor would they be welcomed by hair cutters. Similarly it would be fairly easy to set up online visits to the doctor, but it can be expected that such a move will not be welcomed by the medical profession because doctors in developed countries would have to compete with doctors from developing countries.

We mentioned the previous examples in order to emphasize that the improvement of productivity is not only a technical challenge but has also an important social dimension. This leads us directly to the notion of social productivity.

Social productivity

If we consider productivity not only at the level of a company or an industry but at the level of the whole society the picture changes completely. For the sake of the present discussion we assume that a capital C (say one million euros) is spent in different ways. Let us examine the possible effects on the productivity of the whole country.

• Type -1: Frozen capital, negative effect. In this first operation the capital C is kept at home by its owner and not spent in any way. Thus, C is simply withdrawn from the money in circulation. This reduction of the money supply will have the usual deflationary effect. From an economic perspective this operation is the most negative way of using (or rather not using) the capital. The same negative effect would be achieved if the capital is sent abroad without any return.

• Type 0: Capital re-injected into the economy but with no positive benefit. The classical example of such an operation is the broken window fallacy introduced by the French economist Frédéric Bastiat in 1850. Bastiat considers a shopkeeper whose careless son happened to break a pane of glass and he describes bystanders who say "Everybody must live, isn't it? What would become of the glaziers if panes of glass were never broken?". Bastiat comments that by paying the glazier the shopkeeper puts the money in circulation, but at the same time he emphasizes that, had the window not be broken, then this expense could have been affected to an usage of greater social usefulness for the society as a whole. This brings us to the case of an expense which has a positive effect on the society.

• Type 1: Capital outlay which has a positive effect on social productivity. Suppose that the owner of a firm spends the capital C on buying several new trucks which will allow easier delivery of the goods produced by the firm. Not only will the capital be re-injected into the economy but throughout the trucks' life-time, it will allow smoother and faster delivery. In short, the production and usage of the trucks will improve the productivity of the firm and of society as a whole. The same observation applies to other investments which will help doing things faster and better. As an illustration at household level, one can mention the fact that the usage of washing machines will save much time compared to hand washing. In contrast, using bigger plasma TV screens will have little effect on social productivity; actually it may have a negative effect in the sense that children will spend more time watching TV at the expense of their school work. As a concrete illustration of an investment that would considerably improve social productivity in China, one can mention the distribution of good quality tap water. Presently (in early 2016) most Beijing residents buy bottled spring water because they think that their tap water is not really drinkable. Not surprisingly, they give the same advice to foreign visitors. Clearly the distribution of millions of bottles means a huge waste of energy and resources. The only beneficiaries are the companies, part of them foreign, who sell the bottled water. Needless to say, the same problem exists in numerous countries where, in a general way, the bottled water industry25 tries to extent its market share.

In a general way, many devices produced by industry will at the same time enhance the productivity of the society. This is of course true for capital goods such as machine tools or tractors but also for many products bought by the public, e.g. clocks, computers, cars and so on. In these cases, there is a kind of synergy through which the technical and scientific capabilities of a population increase. On the contrary, most services provided by the tertiary sector are of type 0. It is true that many of them (e.g. healthcare) cannot be avoided and that others such as cultural services are enjoyable, but this does not remedy their weak (or sometimes negative) contribution to global productivity.

An additional word is in order regarding the computer and telecommunication industry. Whereas the production of computers and other telecommunication devices is naturally included in the manufacturing sector it is not always clear how the software industry is categorized. On account of the fact that software applications are sold along with computers, digital machine tools or mobile phones, it would be logical to include the software industry into the manufacturing sector. The synergy which links together software applications is another reason for including the software industry into the secondary sector rather than into the service sector.

Fig. 1

 1 Fig.1Demographic transition in western Europe. The thin lines are centered moving averages (over intervals of 5 years) of the differences between birth and death rates for 4 countries: Germany (black), Denmark (blue), England and Wales (green). Sweden (red). The thick line is the average of the 4 cases. The demographic transition consisted in an almost simultaneous fall of death rates (mostly due to a decrease in infant mortality) and birth rates; however, because the second effect was predominant the net effect was a decrease in the rate of natural increase. The graph shows that this transition was marked by several ups and downs. In addition, for some countries (e.g. the Netherlands or France) this rule did not apply at all. Source:Flora et al. (1987, vol. 2, chapter 6)

  Fig. 2 Wage transition in the United States.In phase 1 the mean wage, w, increased exponentially at an average rate of 2.0% per year whereas in phase 2 it stagnated. Simultaneously the proportion of the labor force employed in agriculture, f a , fell from 41% in 1900 to 4.4% in 1970. There is a high correlation, namely 0.987, between the two changes. The relationship between the logarithms of the two variables is: log w = -a log f a + b, a = 0.67 ± 0.09, b = 1.87 ± 0.06. Sources: Historical Statistics of the UnitedStates 1975, Liesner 1989, US Bureau of Labor Statistics, "Trading Economics" website)

  Fig.5a,bAge distribution in rural China. The graphs compare two idealized situations (dotted curves) with the actual age distributions. The expression "grandparents" designates persons over the age of 55 that is to say persons who can no longer be counted in the manpower reserve susceptible of moving to cities. The curve for 2028 is a linear projection based on the data of 1982 and 2005. It can be seen that although closer to the "grandparents only" picture, it is still fairly remote from it. Note that because of the y log scale the flat parts of the dotted curves that should be at zero percent had to be set to a low but non-zero percentage. Sources:[START_REF] Kasperkevic | The demographic crisis is going to hurt most in rural China[END_REF],[START_REF] Zhong | A regional comparison of the age distribution in the rural Chinese population and its implications to policy making [paper in Chinese, original title is: Woguo nongcun renkou nianling jiegou de diqu bijiao ji zhence hanyi[END_REF],[START_REF] Yiliminuer | La Chine, championne du monde de la gérontocroissance?[END_REF].

Fig. 6

 6 Fig.6Labor force in agriculture. Apart from the UK which stands apart, all developed countries experienced more or less the same evolution. The fact that the curves for Sweden and Germany are almost the same shows that wars had almost no impact. The curve for China was extrapolated based on the rates seen in other countries and particularly in South Korea. Regarding the special case of Britain see the explanation given above in relation with Fig.3. Sources: Until 1970:[START_REF] Flora | State, economy, and society in western Europe, 1815-1975[END_REF] and Historical Statistics of the United States(1975). After 1970: Trading Economics website and Saint Louis Federal Reserve.

  Fig. A1 Comparison of different metrics measuring income for the United States and China.All incomes are expressed in national currency and adjusted for inflation. The two countries are not at the same stage in terms of overseas investment and financialization of the economy; therefore, the fact that so far in China there has been no divergence between GDP/capita and wage level does not mean that it will be the same in the future. Sources: USA: Historical Statistics of the UnitedStates (p.224), Saint Louis Federal Reserve website,, TradingEconomics website; China: http://www.chinability.com/GDP.htm, TradingEconomics website.

Table 1 GDP per employee in various economic sectors (USA, 2012)

 1

	Sector	Contribution Employment GDP per employee
		to GDP
		[billion $]	[million]	[thousand $]
	1 Educational services	183	3.34	54.8
	2 Retail trade	932	14.9	62.5
	3 Health care, social assistance	1, 153	16.9	68.2
	4 Art, entertainment	157	2.09	75.1
	5 Agriculture, forestry, fishing	186	2.11	88.1
	6 Government (federal and local)	2, 197	21.9	100
	7 Transportation, warehousing	467	4.41	106
	8 Professional services	1, 912	17.9	106
	All tertiary sectors	11, 929	97.6	122
	All sectors	14, 509	112	129
	All non-agricultural sectors	14, 323	110	130
	9 Manufacturing	1, 983	11.9	166
	10 Wholesale trade	962	5.67	169
	11 Information	737	2.74	269
	12 Financial activities	3, 229	7.78	415
	13 Mining	411	0.80	514

Notes: The GDP per employee given in the last column can be seen as a measure of employee productivity. Despite the modernization of US agricultural production there is still a 1:2 productivity gap between agriculture and manufacturing. This table suggests that what is usually called the service sector is in fact a very heterogeneous category in which productivity covers a scale from 1 to 10. The ratio between the productivity in agriculture and non-agriculture sectors is equal to 130/88 = 1.47. The present table is not an exhaustive list of all sectors but it represents 90% of the total GDP. Sources: GDP: Bureau of Economic Analysis (interactive table); Employment: Bureau of Labor Statistics ("Table

2

.1 Employment by major industry sector").

Table 2 Contribution of different sectors to the Chinese GDP, 1990-2013

 2

	Sector	Share	Share	GDP per	Productivity
		of GDP	of employment	employee factor multiplier relative to 1

  Table 1 for the United States.

	USA, 2013		China, 2013
	Productivity scale
	Agriculture	Non-agriculture	Agriculture	Non-agriculture

Sources: GDP data:

[START_REF] Bajpai | China's GDP examined: a service sector surge[END_REF]

; employment data: World Bank, (Interactive table entitled "Employment in agriculture (% of total employment)").

Table 3 .

 3 In addition, intermediate values of the GDP per employee for 1995, 2000, 2005 and 2010 are as follows (expressed in 2015 RMB):

	p 1 : 7, 434; 7, 547; 10, 150; 20, 030
	p 2 : 27, 323; 42, 189; 60, 273; 75, 394

Table 3 : China: Changes in GDP per employee in agriculture and rest of economy, 1990-2015

 3

	1990	2015	Ratio
			2015/1990

Table 4 Russia: Employment in agriculture in percentage of total labor force

 4

	1930 1960 1978 1985 1990 2000 2010 2014
	87% 39% 21% 15% 14% 15% 9%	7%

Table A1 Different metrics for measuring personal income

 A1

	Indicator	Comment
	1 GDP/capita	Apart from income in the form of salary, the GDP also involves capital gains,
		such as dividends or profits. In recent decades this part of national income has
		been growing. Today in the US non-salary income represents around 50%
	2 GDP/employee	Corrects the fact that GDP/capita increases when
		housewives take up a full time job.
	3 Average earnings In contrast with the median, the average is highly sensitive to top earnings
	4 Median earnings
	5 Average wage	The terms "worker" or "manual worker" usually mean non-managerial employee;
	of workers	compared to services, manufacturing provides better protection to workers
	in manufacturing particularly because of remaining unionization.
	6 Average wage of Includes (non-managerial) service employees.

index (1995=1) GDP per capita Wage Japan South Korea Fig. A2 Comparison of different metrics measuring income for Japan and South Korea.

  All incomes are expressed in national currency and adjusted for inflation. The curves of GDP per employed person were omitted because labor force as a percentage of population showed no definite trend. Thus, in South Korea it fluctuated randomly between 58% and 60%. The big gap observed in Japan between GDP per capita and wage came as a surprise.

	Japan, index (1955=1)	3 4 5 6 7 8	GDP per capita Wage						South Korea,	2
		2
										1
		1
		1950	1960	1970	1980	1990	2000	2010	2020	1990	1995	2000	2005	2010	2015	2020
																Sources:
	USA: Historical Statistics of the United States (p.224), Saint Louis Federal Reserve website, Liesner (p.98-99),
	TradingEconomics website; China: http://www.chinability.com/GDP.htm, TradingEconomics website.
	of employees, (ii) operating surplus (i.e. mainly profits) and (iii) consumption of
	fixed capital (i.e. depreciation of equipment). Altogether these components usually
	account for 90% of the GDP; the first component is of the order of 50% and in most

Sources: Japan: Historical Statistics of Japan (website), Trading Economics website (GDP at constant prices in billion of yen); South Korea: Korean Statistical Information Service (KOSIS), statinfo.biz. It would be useful to find wage data series starting before 1995.

This spanish word refers to a medieval economic organization in which the a farmer would pay the miller's fee through a part of the flour produced. A more general expression is "Export processing zone" because the production of such zones is destined to be exported back to the country of the plant owners.

The role of this factor is demonstrated in a fairly dramatic way by the fact that the cities of Hong Kong, Macao and Singapore have fertility rates as low as 1.17, 0.93 and 0.80 respectively (the data are for 2014).

Detailed comparative data can be found in[START_REF] Flora | State, economy, and society in western Europe, 1815-1975[END_REF] but a broad view can be obtained just by comparing the

In his budget declaration of February 2015[START_REF] Shanmugaratnam | Budget speech given in Parliament[END_REF] the Deputy Prime Minister (and also Finance Minister) of Singapore, was very conscious of this contagion. He warned that wage stagnation had set in for the United States, Europe and Japan and that one should not be surprised that eventually it may also hit Singapore.

Another indicator is the weight of health care expenditures; according to World Bank data in 2012 it represented 17% of the US GDP.

The huge changes which occur in the course of time for p 1 and p 2 are a different question which will be discussed later.

In this case sector 1 would be the whole economy except healthcare and sector 2 would designate the healthcare sector.

In 2013 healthcare expenditure accounted for 8.8% of GDP in the UK[START_REF] Lewis | Expenditure on healthcare in the UK: 2013[END_REF] and

17.3% in the US(US Department of Health 2015, p. 293). In spite of that, in 2013 life expectancy was 2.3 years longer in the UK (81.1 years against 78.8 in the US according to the OECD data reproduced in the Wikipedia article entitled "List of countries by life expectancy"). Actually, in this comparison, the UK could be replaced by any other OECD country with only minor changes.

One can be sure that this kind of decision will be subject to lobbying efforts from many sides.

Needless to say, economic growth can be thwarted for many other reasons, e.g. deflation, capital flight, disruption of the banking sector and so on. In such cases the problem may not go away as easily.

In societies in which house wives are not supposed to take up a job, one could assume that they remained in their villages with their children. In this case there would be no short-term productivity reserve despite a substantial rural population.

At the geographical level it is limited to 5 provinces of central China, namely: Anhui, Henan, Hunan, Jiangsu and Sichuan. All results given below are averages over these provinces.

A negligible proportion of 1.7% lived only with their father.

In contrast, econophysicists are more open to this sort of investigation. Incidentally, this is why the paper was submitted to a physics journal.

In this respect one should not forget that, as in Taiwan, the Japanese occupation had resulted in a substantial industrialization not only in the north of Korea but also in the south; more evidence can be found in[START_REF] Roehner | Relations between US forces and the population of South Korea[END_REF].

Their immigration is facilitated by the fact that their curriculum integrates the requirements and specifications of the US healthcare industry which in particular includes practicing the English language.

With the support of the powerful "International Bottled Water Association" (IBWA) which was founded in 1958 as the "American Bottled Water Association" (ABWA).

Acknowledgments

We wish to express our gratitude to Ms. Corina Neuerer of the "Statistisches Bundesamt" (German Federal Statistical Office) and to Ms. Alyson Williams of the British "Office of National Statistics" for helping us to locate and retrieve some of the statistical series used in this paper.

Appendix A. Metrics for measuring income

Income can be measured by various indicators and as the findings reported in this paper are, at least to some extent, indicator-dependent it is important to keep in mind the differences between them. They are summarized in the table below. For a better understanding of the difference between GDP/capita and wages it is useful to remember that the GDP has basically 3 components: (i) compensation HIGHLIGHTS Explanation of the stagnation of wages in developed countries Prediction of the productivity progress in China (2015China ( -2030) )