Françoise Hay

Christian Milelli

The endless quest to strategic assets by Chinese firms through FDI: From Inward to Outward Flows

Keywords: FDI, strategic assets, Chinese firms JEL Classification: F23, L52, O33

The paper highlights the major role played by foreign direct investment/ FDI flows in two ways -inflows or outflows -for Chinese firms by securing strategic assets to enhance their competitive advantage. The underlying rationale of the acquisition of such assets through FDI is specific to China. Therefore, we scrutinize the characteristics and determinants of FDI in its two dimensions.

INTRODUCTION 1

The rise of Chinese firms in world rankings has been amazing since the beginning of the millennium whereas they have become major investors abroad. From now on, the incumbent multinational companies/ MNCs have to reckon with these new competitors. The world can anymore be viewed as a 'Triad' but as a multipolar and complex configuration endowed with numerous networks, whose, among others, Chinese firms are an integral part.

Here, we are trying to explain the tremendous growth of Chinese firms without referring to the standard micro approach of the growth theory because China has many idiosyncrasies, and we advance that the role played by foreign direct invest investment/ FDI flows and the support of the State requires a specific approach. Hence, we emphasize the pivotal role played by FDI -both flows received and issued by China -in such expansion. In particular, we highlight the critical vehicle FDI represented for Chinese firms to acquire or augment their resources and capabilities, at home and abroad, in order to boost their competitive edge. Of course, FDI was not the only channel for Chinese firms to get required assets inasmuch as Sino-foreign partnerships and diverse agreements were also used, among others modalities, whatever they were operated inside China or abroad. If the acquisition of strategic assets is not the exclusive motive for FDI outflows, we will show that they play a key role, especially in industrial countries.

The actual experience of the Chinese economy is probably unique in its magnitude and dynamic. What is also atypical, at least to such a level, is the extensive role played by Chinese authorities -through diverse channels -to support the growth of domestic firms, to facilitate the transfers of technology and know-how from foreign investors, and to promote the investments abroad to strengthen Chinese competitive advantage and performance.

The linking of the growth of Chinese firms, which is basically a micro issue, to aggregated data of FDI was motivated by the need to get a better understanding of their behavior in a rapidly changing environment. Further, this approach was completed by data compilation in the last section devoted to outward FDI flows due to its novelty and size. Last, we combined genuine data as turnovers or the amounts of investment, with qualitative data such as the modalities of investment.

The paper is structured as follows:

First, we explore the underlying forces and the meaning of the quest for strategic assets by Chinese firms.

Second, we show, through the FDI flows China received since its opening to the rest of the world in late 1970s, the channels that gave Chinese firms the opportunity to acquire skills and expertise, as well as the government endorsement to facilitate their implementation.

Third, we consider the investments made by Chinese firms towards industrialized countries and more specifically towards Europe since the beginning of the millennium in order to get and/ or augment strategic assets. And we provide illustrations from compiled data.

THE SEARCH FOR STRATEGIC ASSETS : AN ANALYTICAL PERSPECTIVE

In the management literature, strategic assets as a whole -i.e. R-D qualifications, managerial capabilities, organizational skills, marketing expertise, brands or reputation -are viewed as the core of the competitive advantage of firms. This is particularly visible in a growing number of sectors where competition is not only founded on prices but growingly on other factors, e.g. the differentiation of goods or services sold.

Strategic assets are not homogeneous as each component has particular characteristics and determinants: what they have in common is that they allow to operationalizing the competitive advantage of the firm and, for a large part, require to be protected through stringent intellectual property rights.

Strategic assets are obtained either through own cumulative experiences or through external modalities, i.e. the set-up of joint-ventures or the takeover of firms or subdivisions. The former is a long-lasting process and is often coupled with the search of strategic assets outside the company to move up the value chain. The latter is time-saving but requires firms to have substantial absorptive and learning capabilities.

The literature on multinational companies, from the pioneering work of [START_REF] Hymer | The International Operations of National Firms: A study of foreign direct investment[END_REF] to [START_REF] Dunning | Trade, Location of Economic Activity and the Multinational Enterprise: A search for an eclectic approach[END_REF][START_REF] Dunning | The Eclectic Paradigm of International Production: A restatement and some possible extensions[END_REF][START_REF] Dunning | Reappraising the eclectic paradigm in an age of alliance capitalism[END_REF], [START_REF] Porter | The Competitive Advantage of Nations[END_REF], [START_REF] Caves | Multinational enterprise and economic analysis[END_REF] or [START_REF] Buckley | Models of the multinational enterprise[END_REF], has stressed the pre-requirement for firms aiming at setting up units overseas to detain relative ownership-specific advantage. However, this constraint has recently been lessened to take into consideration globalization that allows firms from emerging or developing economies to accelerate their internalization move [START_REF] Mathews | Dragon multinationals: new players in 21st century globalisation[END_REF]. Indeed, the multifaceted globalization has extended and facilitated the ways firms can acquire critical assets.

When considering literature on development in general along with the impacts of FDI flows on developing host countries, scholars have evolved from a critical point of view, and in some case, rather a political stance, to a more accommodating view. Further, multilateral institutions such as the World Bank, IMF or the OECD have systematically advocated the coming of foreign companies in developing countries, stressing the numerous clear-cut impacts, such as capital infusion, new jobs and skills, and technologies along with more efficient manufacturing skills and managerial capabilities.

The notion of 'reverse FDI' is sometimes used to characterize the investments made by firms from emerging economies within developed countries. Two main motives are put forward: first, strategic asset-seeking along with the research of proximity with centres of excellence to improve their capabilities along the value chain; second, the access to new markets (Luo & Tung, 2007). It is sometimes underlined that emerging investors go abroad to overcome their own disadvantages, such as the lack of technology or management know-how [START_REF] Moon | Unconventional Foreign Direct Investment and the Imbalance Theory[END_REF]. Similarly, [START_REF] Filippov | Europeanization strategy of Chinese companies: Its perils and promises[END_REF] pinpoint the capacity of Chinese firms to convert their 'competitive disadvantage' (no brand, no fame, no efficient distribution networks and lack of organizational capabilities) into competitive advantage, and therefore to offset the incumbency advantages on the part of large MNCs.

However, one must keep in mind that FDI is a learning process which requires to following successive stages, especially for the investors from emerging countries at the beginning of their internationalization path (Cantwell 1990). The experience accumulated by a firm is a major determinant to invest abroad, and the hierarchy and the combination of its motives generally evolve over time through different steps [START_REF] Minin | Chinese foreign direct investment in R&D in Europe: A new model of R&D internationalization[END_REF].

In a first step, Chinese firms realized that they could not rely solely on their domestic forces and partnerships with foreign companies to develop and upgrade their existing products and activities. So, they made the decision to invest abroad in order to bridge the technological gap and also to become more familiar with the sophisticated standards of Western countries.

In a second step, they exploited in China the technologies acquired abroad, and tried gradually to go beyond imitation and promote indigenous innovation before mastering advanced technologies. By doing so, they got an edge on their competitors, whether domestic or foreigners. Such process is in phase with the two-stage theory proposed by [START_REF] Bin | Two stage theory: analysis modes of foreign direct investment[END_REF] for the newcomers with, first, an 'experience phase' and second, a 'get the profits stage'. During the former, the firms invest abroad to make use of the host country's advance technological resources and tap specific assets allowing them to gain experience and improve capabilities. During the latter, the investors become more mature and experienced. They also increased efficiency to reap economies of scale and make profits: so, they enter the 'get the profits stage'. A similar approach is analyzed by [START_REF] Wang | Seeking the Breakthrough of the Internationalization of Yu-tong Bus Company[END_REF] while considering the investments made by emerging investors in industrialized countries. They highlight two categories of FDI: one, 'learning-oriented', and the other, 'competitive strategy-based' aimed to reach a leading position in the home country or at the international level.

The case of China is particularly interesting to analyze as its own experience saddles the contributions of the two dimensions of FDI -inward and outward -in its quest for strategic assets. Indeed, FDI has been instrumental to the catching-up of Chinese companies. They have benefited both to their direct (partnerships and joint-ventures) and indirect contacts (spill overs) with foreign firms in China, and to their investments abroad, especially in industrialized countries, through mergers-and-acquisitions or even Greenfield investments (R&D facilities or production units).

If the process as a whole was unbalanced in the 1980s-90s with large inward FDI flows and small amount of outward FDI flows, the picture changed in the 2000s with OFDI flows sharply increasing, before becoming more and more balanced after the global financial crisis, while, in parallel, the scope of the determinants of OFDI was enlarged.

The ratio OFDI / IFDI jumped from 17 percent in 2005 to 70 percent in 2012. According to the Chinese authorities, it is expected to be close to 100 percent by 2015-2020 (Figure 1). Recently, the quest for strategic assets has become a major concern of public officials: it is linked to the willingness to foster the innovative capability of Chinese companies. Indeed, if Chinese companies excel in price ultra-competition strategies (Zeng & Williamson, 2007), it is not a sustainable strategy at a corporate level when sectors are getting mature and when time comes to make profit. In this respect, the orientation of the national economy towards a more knowledge-intensive economy put a focus on strategic assets as R&D expenditures, innovation skills or patents (OECD 2007). Last, Chinese firms are both the beneficiaries of competences or strategic assets, and involved in the quest of strategic assets. In this case, different strategies are at play, mirroring the real nature of their ownership. On the one hand, State-backed enterprises, particularly core State-Owned Enterprises (SOEs), except from the natural resources' sectors, which have largely benefited from inward FDI flows after China adopted a more liberal regime for FDI in 1992, are now chasing strategic assets overseas to keep increasing their competitive advantage. On the other hand, private enterprises, which access to strategic assets through inward FDI have been hampered due to the national specific context during the 1990s [START_REF] Huang | Selling China: FDI during the Reform era[END_REF], are now trying to catch-up by accelerating their presence abroad. The rationale is double: first, to lift their competitive advantage on international markets; second, to reinforce their strength on the internal market which presence is vital for their global reach. As a result, strategic assets are growingly targeted in developed countries in a context where incumbent multinationals or local companies are selling assets due to financial distress or restructuring necessities [START_REF] Deng | Why do firms tend to acquire strategic assets in international expansion[END_REF].

INWARD FDI: A TRADITIONAL LEARNING CHANNEL FOR CHINESE FIRMS

The acquisition of strategic assets by China and Chinese firms is not the only contribution of inward FDI, but we find it at distinct periods, except at the very beginning in the 1980s (Table 1). Source: Compilations by the authors

The acquisition of strategic assets

Besides substantial 'round-tripping investments'2 , the first genuine FDI flows received by China following the opening of its economy were made by ethnic small-and-medium enterprises from closed countries, i.e. Hong Kong and Taiwan. They operated assembly lines in labour-intensive industries (textile-clothing, household appliances), and were localized in tax-favoured Special Economic Zones where they benefited, for exports, from extensive open regulations and the exemption from duties on imported inputs [START_REF] Huang | Selling China: FDI during the Reform era[END_REF]. As a result, spill over effects were not significant.

The global landscape that emerged in the second half of the 1990s changed the international division of labor and encouraged large conventional MNCs to increase the fragmentation of their activities worldwide3 . As a result, a new business environment came out, involving an unprecedented expansion of productive network relations, as well as a major change of the strategic context of knowledge's ownership [START_REF] Sturgeon | How do we define value chains and production networks[END_REF], whether through transmission or dissemination (Saliola & Zanfei, 2009). Within this context, the firms from industrialized countries, traditionally well-endowed in advanced knowledge and know-how, have been conducted, both passively and actively, to disseminate parts of their knowledge. Chinese firms have largely taken advantage of this trend while China ranks among the top host country for FDI flows since 1993 It is the Southern country that has received the most technological capabilities through FDI and cross-border contacts established with foreign firms [START_REF] Luo | Coopetition in international business[END_REF][START_REF] Miesing | Towards a Model of effective Knowledge Transfer Within Transnationals: The Case of Chinese Foreign Invested Enterprises[END_REF]UNCTAD 2010).

Institutions such as the World Bank or the IMF have considered the FDI inflows as a main driving force behind the Chinese 'economic miracle' (World Bank 1997;[START_REF] Tsen | FDI in China: some lessons for other countries[END_REF], as much as numerous scholars [START_REF] Lardy | Foreign trade and economic reform in China, 1978-1990[END_REF][START_REF] Lardy | The role of foreign trade and investment in China's economic transformation[END_REF][START_REF] Naughton | China's emergence and prospects as a trading nation[END_REF][START_REF] Lemoine | FDI and opening up the Chinese economy, Cepii[END_REF] among others).

The diffusion of knowledge from foreign MNCs to Chinese firms

Multinational companies are recognized as being critical vehicles for the creation and the dissemination of technological knowledge and expertise through their various partnerships and investments with the local firms of the countries where they operate.

The 'Linkage, Leverage, and Learning' framework stressed by [START_REF] Mathews | Dragon multinationals: new players in 21st century globalisation[END_REF] fit particularly well the experience of Chinese firms. Thanks to their 'Linkage' through FDI or partnership with foreign firms, the latecomer Chinese firms have got the possibility to acquire knowledge, to compensate their limited resources, and to receive 'Leverage'. Repeated over and over, these sequences of 'Linkage' and 'Leverage' have enhanced the capabilities of Chinese firms through a path of somehow industrial 'Learning'. Furthermore, most scholars juxtapose this theory with the one of Dunning to characterise Chinese FDI abroad.

Chinese firms have shown a great ability to absorb, assimilate and apply for commercial purposes the technologies they acquired through their foreign contacts. They also resorted to copies and imitations, and exploited the inner workings of reverse engineering prior to innovate by themselves [START_REF] Bell | The development of technological capabilities[END_REF]. Although the art of copying is part of the Chinese civilization (Shanzhai culture4 ), foreign investors have great difficulties accepting it:

all the face-to-face meetings5 we made in China mentioned this fact as the main problem they encountered in China and the increased competition it resulted for them since the 2010s.

However, Chinese firms do not hide from having recourse to copying: they use it to recall that there is some ability to intelligently imitate the others, and that it is a behavior prevailing since the dawn of time. Before them, the US companies did the same at the end of the 19 th century, as well as the Japanese firms in the 1970s-80s, or the Korean firms in the 1980s-90s.

Shenkar (2012) reminds that: "firms such as Apple, Microsoft, Visa, Wal-Mart and

McDonald's have also copied and improved concepts".

To sum up, China has demonstrated the efficacy of what may be called a 'FDI-led industrial take-off' strategy [START_REF] Ozawa | The role of multinationals in sparking industrialization: From "infant industry protection" to "FDI-led industrial take-off[END_REF].

From Chinese assimilation of foreign technologies to indigenous innovations

Chinese firms have been particularly clever to develop a business model combining low prices, mass consumption, reduced margins and innovation (Zeng & Williamson, 2007).

Undeniably, they have successfully managed to improve the borrowed foreign innovations and started to make 'native' innovations or 're-innovations' [START_REF] Lazonick | Indigenous innovation and economic development: lessons from China's leap into the information age[END_REF].

At the beginning, they adapted foreign technologies to their environment, culture and purchasing power of their consumers. By doing so, they have contributed to "create new products" -i.e. goods responding to new needs, involving new production methods and implying undeniable performances in terms of value for money [START_REF] Lall | China's Manufactured Export Surge: A Threat to East Asian Manufactured Exports?[END_REF].

Also, they carried out experiments to support the development of their products: generally, they rapidly test the products on their huge market, before incorporate customer's feedback and improve them.

While the innovations of the MNCs, particularly from OECD countries, rather concern 'highend' products with high prices, a peculiar feature of Chinese firms is to target 'low-end' segments in novel ways, implying in many regards a new paradigm of innovation (Zheng & Williamson, 2007). If one can talk about innovation here, according to the criteria of Schumpeter, it is due to the fact that the new products fit the demand of new consumers -i.e. social groups who could not afford to buy similar items before.

For [START_REF] Mathews | Dragon multinationals: new players in 21st century globalisation[END_REF] a country or a firm arriving late on the road of the industrial development has nevertheless a potential advantage: that consists of direct access to advanced technologies, and of the capability to absorb them faster and at a lower cost than the very firms that first developed them.

Last, we can notice that the acceleration of technological progress was not problematic for these newcomers, but rather gave them the opportunity to assert in new sectors, such as Information and Communication Technology, for instance.

The major role played by the Chinese government to facilitate technology and know-how transfers from foreign firms

The capacity of governments to stimulate growth and to create an appropriate environment on which firms can construct their specific advantage is well documented [START_REF] Porter | The Competitive Advantage of Nations[END_REF]). Indeed, the technology transfers from first-world MNCs, have been possible thanks to the significant advantages China was able to provide them, namely, low-cost production, cheap sourcing options, or access to a large potential of an internal consumer market (Saliola & Zanfei, 2009). And the economic or political fragmented nature of it was more advantageous for foreign companies than for domestic firms, particularly small or medium companies, which faced huge transaction costs on factors or products markets.

On the whole, the Chinese priorities have evolved over time with a framework quite conducive to innovation which included different steps successively aimed to: catching-up, to get autonomy, to move upmarket and to step into world top enterprises (e.g. Fortune Global 500)6 .

A catching-up drive in the 1980s-1990s

In the aftermath of the Reform and Opening up of the Chinese economy put in motion in 1978 by Deng Xiaoping, the priorities of the officials have been to promote the development of the national economy, and to address the shortage of capital (domestic savings and foreign exchange reserves), and of technology.

A relevant industrial policy was implemented and planned by targeting priority sectors for the national development and the restructuration of the whole State sector launched in the second half of the 1990s. The obligation for foreign companies to set a joint-venture with local companies was used on a large extent to promote the transfer of knowledge and managerial capabilities (Buckley et alii, 2004). At the same time, different measures have been planned, aimed to improve the educational system, the innovation national system, and the industry.

The improvement of Chinese human capital was intended to benefit to the domestic firms and also to boost the attraction of foreign investors (Box 1).

Box 1. Main priorities of the Chinese government in the 1980s-1990s It became also imperative for the Chinese authorities to do away with the 'low cost and poor quality' era. If they had such idea in mind during the past years, they were not able to achieve it. Actually, the global financial crisis was somehow timely by providing them the opportunity either to rebalance the economic growth -from an export-driven regime to a more domestic consumption-driven one -or to switch from 'the factory of the world' to 'the laboratory of the 9 Set up in 2000, its goal was to help the western part of China to catch up with the coastal regions which greatly benefited from the Opening up of the economy and the Reforms of 1978. The pillar of this policy was twofold: first, the construction of infrastructure (e.g. transport, hydropower plants); second, the attractiveness of foreign companies.

10 For example, the French automobile company PSA had to switch to the production of electric vehicles to have its second joint-venture authorized in 2011.

world' along with from the 'made in China' to the 'designed in China'. As a result, Chinese firms were urged to climb in range or to increase their share in the global value chains.

Box Source: Compilations by the authors

OUTWARD FDI: A GROWING QUEST FOR STRATEGIC ASSETS

The motives of Chinese firms when they invest abroad are diverse, and evolve over time according to the context (international and domestic). They fit the common taxonomies of FDI motives, and, among others, that of [START_REF] Dunning | The Eclectic Paradigm of International Production: A restatement and some possible extensions[END_REF][START_REF] Dunning | Reappraising the eclectic paradigm in an age of alliance capitalism[END_REF][START_REF] Dunning | The Eclectic (OLI) Paradigm of International Production: Past, Present and Future[END_REF], that is: resourceseeking, strategic asset-seeking (or augmenting), market-seeking and efficiency-seeking.

However, we find occasionally some different hierarchies, priorities and mix of motiveswhen compared to those of the MNCs from industrialized countries -due to a specific background, especially at the beginning of their international expansion, and in the frame of a dynamic process of particular importance in the case of the rapid growth of the Chinese economy (Table 2).

We focus here on the quest for strategic assets by Chinese firms abroad through outward FDI, because it held an important place since the beginning of the millennium within FDI flows towards industrialized countries, as such, or combined with others motives. Such a quest corresponds either to their needs or to the shortages of the Chinese economy [START_REF] Deng | Investing for strategic resources and its rationale: The case of Outward FDI from Chinese companies[END_REF].

Obviously, it is a new strategy as this motive was rare for the incumbent MNCs which generally had ownership-specific advantages before investing abroad.

The search for strategic assets often goes hand-in-hand with the access to markets, particularly in Europe or in the United States.

The motives of Chinese outward FDI have evolved from its very beginning in the 1980s (Table 2). First, they reflected the needs of the national economy driven by a buoyant manufacturing sector, which basic needs in natural resources have escalated and diversified, and therefore could not be satisfied by local supply 11 . Second, they reflected the growing distinctiveness of Chinese companies according to their ownership, with quasi pure private companies and hybrid companies expanding along with large State-backed companies.

Indeed, if private Chinese companies are on a large extent more market seekers, Chinese

State-backed enterprises are generally more attracted by countries with large endowment in natural resources. Since 2002, the motives mirror more and more the will of the Chinese authorities to not only have 'national champions' but definitively world-class enterprises.

Actually, the rationale goes beyond pure economics as Chinese authorities increasingly use OFDI flows -which are planned to reach 150 Billions of dollars a year in 2015 -to bolster China influence around the world.

The quest for strategic assets includes to set up or to pick up in particular locations suitable facilities -R&D centres, production and distribution facilities -which help to improve the efficiency and the competitiveness of Chinese companies. Further, by dispersing design and production globally Chinese firms are following genuine global strategies [START_REF] Andreff | Maturing strategies of Russian companies: comparison with Chinese multinationals[END_REF]).

11 However, this motive is still central: indeed, reliable supplies of oil and gas are part of the 'core interests' of the current China development and foreign policy. Source: Compilations by the authors FDI flows received by China were generally not sufficient to meet the demand of the local firms in expertise and technologies for different reasons. First, due to significant knowledge exposure, foreign firms were often reluctant to transfer their superior technologies in China [START_REF] Nolan | China and the global economy[END_REF]Guan et alii 2006); interestingly, [START_REF] Ozawa | Japanese Multinationals and 1992[END_REF] advised Japanese firms not to transfer in their foreign affiliates up-to-date technologies. This general recommendation was exacerbated in the case of China due to fledging intellectual property rights, not to mention extended copying practices (Shanzhai culture). Second, the fact that Chinese authorities have continuously favored public companies as recipient of technology and know-how transfers from foreign companies encouraged private companies to go abroad to find better opportunities for their development.

Therefore, from the beginning of the millennium, numerous Chinese companies made the decision to invest overseas. They could afford to make such investments thanks to the process of technology accumulation following the FDI flows previously received [START_REF] Lall | The New Multinationals. The Spread of Third World Enterprises[END_REF], money in hand, and also the support of the Chinese government -'Go abroad' policy (1999), and the recommendations of the 12 th Five-Year Plan (2011-2015) encouraging OFDI and crossborders mergers-and-acquisitions12 . However, in some sectors they were pulled out due to crowded markets and cut-throat competition: for example, there are currently 170 automotive manufacturers in China.

Indeed, the experience Chinese companies had across Europe since the beginning of the millennium has evolved a little.

During the 2002-2007 period, Chinese firms were quite newcomers and lacked experience.

They chased strategic assets in order to compensate weaknesses at home, to close their technology gap with Western firms and to get international recognition. In particular, Chinese firms wanted to improve their capabilities in response to the exacerbated competition that prevails in the domestic market. Since 2008-2009, in the wake of the global financial crisis, new priorities have been set to end the paradigm of 'low and poor quality products', and to improve the share of China in the global value chains. This trend has even been reinforced since 2011-2012 although we lack set-back and compelling evidence. What is new is that Chinese investors start to search for profit. They are also more interested by the European market in order to get strategic assets, as regulations and political context are viewed as less stringent than in the United States [START_REF] Rosen | Multinational firms, global value chains and the organization of knowledge transfer[END_REF].

In parallel, Chinese companies continue to take advantage of the numerous technology and know-how transfers from the MNCs, which have intensified in China since 2009.

The acquisition of strategic assets in Europe by Chinese firms through M&As

At the beginning of the millennium, Chinese investments in industrialized countries were quite unusual, even if some European acquisitions of old flagships and premium brands struck the public opinion and the media as the buyers were newcomers [START_REF] Madsen | The Internationalization of Born Globals: an Evolutionary Process[END_REF].

This was the case for TCL which bought the French companies Thomson TV and Alcatel Cross-borders M&As are often viewed as a short-cut to enhance the global reputation of the purchaser, to improve its capacities and skills, and to accelerate its learning process (Luo and Tung, 2007). During the last years, many Chinese firms have acquired, totally or partially, an increasing number of European firms with plants, top of the range technologies and premium brands. Often, these acquisitions gave them access to R&D facilities: that was the case for the acquisitions made by China BlueStar. These units have generally been maintained or even reinforced over time to take advantage of their accumulated expertise through codified and tacit knowledge, and also extensive scientific networking. The Figure 2 shows that these M&As are on an ascendant trend with a contraction in 2006 following a need to take a break and also resulting to some failures (TCL, for example), 13 Commercial dataset on M&A deals worldwide from Thomson Reuters.

14 From Mainland and Hong Kong. It appears clearly that a previous partnership with a European firm is a privileged vehicle to rapidly gaining a foothold in Europe. That also minimizes the risks of failure resulting from the 'psychic distance' and an unknown target company. This characteristic may explain why

Chinese companies are commonly viewed as more risks-tolerant when compared with companies from other origin.

Main host countries and activities for Chinese M&As in Europe

Without surprise, the largest European economies according to their size -Germany, United Kingdom, France and Italy -are the main host countries for Chinese M&As in Europe (Figure 3). The relative importance of the Netherlands can be explained by the localization of numerous holding companies due to a favorable tax treatment. This geographical breakdown is in line with the two main motives of Chinese investors in Europe: to have access to large markets (Buckley et alii, 2007), and to pick up specific assets in different activities or localizations: manufacturing in Germany, services in the United Kingdom, design in Italy, or luxury brands in France [START_REF] Hay | The Impact of the Global Financial Crisis on the Presence of Chinese and Indian Firms in Europe[END_REF]. The sector of equipment as a whole is predominant with nearly half of the deals made since 2009. The rationale of these acquisitions is to facilitate and expand the access to markets overseas on one side, and to tap strategic assets on the other (Figure 4). The automotive sector comes behind with half of the deals made since 2010. Likewise, the rationale is to pick up strategic assets with different strategies when taking into consideration auto-parts maker such as Johnson Electric, when acquiring Saia Burgess (Switzerland) on the one hand, or lead contractors such as Geely, when acquiring Volvo, on the other. Whereas the former is reinforcing its presence both at home and overseas, the latter brings back home the strategic assets to differentiate in a very crowded market.

The acquisitions made in the fashion sector, essentially clothing, are generally older, but involve companies willing to integrate upward (design) and/ or downward (marketing skills) competences. By doing so, they search to grab a largest share of the value-added and more profits.

The acquisition of strategic assets in Europe by

Main host European countries and activities for the set-up of R&D facilities by Chinese firms

The location choices for the set-up of R&D facilities are particularly appropriate to identify the attractiveness of a particular country.

The number of European countries for the establishment of R&D facilities by Chinese companies is expanding, even if five countries are coming up and reinforcing. The result was expected for four countries -United Kingdom, Germany, France and Italy -as there are the largest European countries, having, a priori, more opportunities in terms of localization, diversity of research domains, or qualified human resources (Figure 6). However, the United Kingdom is well ahead because of the quality of its academic institutions, the extensive networking between companies, be nationals or foreigners, and research bodies, and last but not least, the practice of English language. The attractiveness of Sweden is unexpected at first.

Actually, it is due to a mix of factors: the presence of numerous scientific parks in dedicated fields (Kista Park in telecom), government policy openly supporting foreign R&D facilities, and a pool of qualified human resources.

15 Commercial dataset on greenfields investments realized worldwide from Financial Times. The preferred activities for the creation of R&D facilities in Europe concern the following sectors: telecommunications, equipment, automotive industry and pharmacy (Figure 7). The primacy of the telecom sector is due to the presence of the two main Chinese companies from the equipment telecom sub-sector, Huawei and ZTE, which have already together around twenty R&D facilities across Europe.

Equipment also holds a significant share due to the dynamism of Chinese companies such as Haitian (injection molding machines), Haier (consumer electronics), Hisense (consumer electronics), Sany Heavy (construction machinery) or Xuzhou Construction Machinery Group (construction machinery), among others. All these investments are seen by Chinese companies as opportunities to create synergies and to found new technical partners across Europe, and, at the end, to expand their business, both in China and overseas.

The best use of the European advantages

CONCLUSION

The investments received and issued by China allowed its firms to get strategic assets they need for their development, resulting in increased market shares and overall sales either on domestic market or world markets.

If inflows FDI were the main channel for the acquisition of strategic assets up to the 1990s, Furthermore, motives of Chinese firms when they invest abroad are increasingly closer to those of incumbent MNCs except, to some extent, the importance of the quest for strategic assets. Indeed, they are still lacking specific assets -e.g. superior technology, world-class brands or international managerial capabilities -but they can rely on a large surplus of domestic savings and foreign exchange reserves to reduce the gap.

Chinese authorities are playing a leading role: indeed, they still have a heavy hand on economic policies, particular through the Five-year plans, State-backed enterprises, Sovereign

Wealth Fund or policy banks. They put priority on national development and favor their domestic firms when possible, particularly in strategic sectors (defense, telecommunications, etc.). That may explain why, paradoxically, the FDI's regime for inflows is getting increasingly regulated despite the acceptance of the obligations to the WTO in 2001.

As the Chinese economy and Chinese firms are developing and maturing, both aspects of FDI are getting interrelated, particularly through the acquisition of strategic assets. Likewise, FDI is growingly intertwined with the Chinese system of innovation. Indeed, the increase of R&D There are other effects that go beyond the economic domain, particularly in the political or geopolitical fields. Interestingly, the experience of China in opening up its economy in the late 1970s and the resulting investments made by foreign companies which contributed to its development is now put forward by the Chinese authorities when talking with African governments about the Chinese presence in Africa and its effects on African host economies.

Figure 1 .

 1 Figure 1. Chinese FDI Inflows and Outflows, 2005-2012 (Millions of dollars)

Foreign

  companies have, willy-nilly, agreed to play according to the rules set up because of the promising Chinese market. By devoting an irreversible opening of the country, China's accession to the WTO in 2001 marked a new milestone for foreign companies willing to enter or expand activity in China. More selectivity for inward FDI since 2002 to 2008, more autonomy after The increase selectivity of Chinese authorities towards FDI flows was accompanied by the rapid development of the national economy and the intent of foreign firms to have a presence on the Chinese market 'at any cost'. With the passing years, Chinese authorities have taken advantage of their favorable position to raise their requirements. As a consequence, they have fostered Sino-foreign partnerships and the upstream technology transfers by foreign MNCs, as well as the set-up of R&D facilities in China. They have also instilled competition between foreign firms to pick up the most 'cooperative' of them. Even if the global financial crisis of 2008 hit severely the Chinese economy through its exports and induced a swift reaction by Chinese authorities (Box 3), it also provided an opportunity to lift up the preconditions while the traditional industrial markets of the foreign investors were collapsing, in very contrast with the resilient Chinese market.The solicitation of the Chinese government for technology and know-how transfers from foreign companies willing to invest in China has been coupled with other requests related first, to their localization and incentives to fit with the 'Go West' policy 9 , and second, to their activities that had henceforth to match the priorities of Chinese authorities, put forward in the 12 th Five-Year Plan (2011-2015) 10 -i.e. new energy, environmental protection, hightech/software, agriculture, new materials, etc.

  Mobile, and the German Schneider TV in 2003-2004, for Weichai Shandong buying Ferretti yachts (Italy) in 2004, or China Bluestar acquiring the French Adisseo (animal nutrition) and Rhodia Silicone (silicone) in 2005, or Fibers Worldwide in the United Kingdom in 2006.

Figure 2 .

 2 Figure 2. Number of European acquisitions made by Chinese firms in manufacturing, 2002-2012

  in 2008 due to the global financial crisis and the resulting uncertain expectations and environment. However, the trend took a new orientation in 2009 as more of the half of the analyzed M&As have been made since then. Overall, the increasing number of Chinese M&As in Europe can be explained by the evolution of Chinese firms and their access to abundant supply of capital -particularly Statebacked companies -in a context of economic crisis which provides opportunities to acquire financial distress European companies or subdivisions. Interestingly, the acquisitions made by Chinese firms in Europe often follow former partnerships as it is illustrated by the following examples: China BlueStar for Rhodia Silicone (France), Chalkis for Conserves de Provence (France), Shengyang Machine for Schiess (Germany), Zoomlion for CIFA (Italy), Haitian for Zhafir Plastics (Germany), Sany Heavy for Putzmeister (Germany), YGM for Aquascutum (UK), or Lenovo for Medion (Germany), among others.

Figure 3 .Figure 4 .

 34 Figure 3. Main host countries for Chinese M&As in Europe, 2002-2012

  Chinese firms through the creation of R&D facilitiesSince 2002, a growing number of Chinese companies got strategic assets in Europe through the set-up of R&D facilities, combined or not with a productive activity. This move was driven by Chinese firms willing to upgrade their products and improve competitiveness while rubbing shoulders with qualified personnel or initiating collaborations with Chinese research staff.We listed about 100 creations of R&D centres in Europe for the 2002-2011 periods. Half of them have been created since 2008 and one third since 2010, with a record number of investments in 2011 (Figure5).

Figure 5 .

 5 Figure 5. The number of creation of R&D centres in Europe by Chinese firms, 2002-2011

Figure 6 .

 6 Figure 6. Main European countries for R&D facilities established by Chinese firms, 2002-2011

Figure 7 .

 7 Figure 7. Main activities for R&D facilities established by Chinese firms in Europe, 2002-2011

For

  the set-up of their R&D activities Chinese firms generally choose countries or areas endowed with the required resources, such as plenty of scientific connections, talented people or open-minded policies. For instance, Huawei and ZTE set-up their Swedish R&D facilities in the phone-mobile cluster created around Ericsson headquarters in Kista (Stockholm), Beijing ROSE set up its R&D centre in the Hoechst pharmaceutical industrial park (Frankfurt), Jac Anhui and Chang'an have created their first R&D centres abroad in Torino, the Fiat stronghold, and Chinamex established R&D facilities in Wigan (UK), an illustrious heart in the United Kingdom for the traditional cotton and textile industry.

  outflows FDI -essentially towards developed economies -have been combined with them since the 2000s. The context of crisis in industrialized countries prevailing since the end of 2008 has still stimulated FDI in both directions for China. And contrary to the 'Investment Development Path' proposed and revisited by[START_REF] Dunning | the investment path revisited: some emerging issues[END_REF], there is enough factors at play for both trends, with Chinese firms continuing to put a high priority on the acquisition of strategic assets in the coming years. However, such a focus combined with a high level of competition may hamper for the coming years the diffusion of the required know-how and technologies within the Chinese economy, which have still plenty of inefficient sectors or firms.

  expenditures at firm level and the implementation of new public institutions for research by the Chinese authorities since 2006-2007 had two distinct effects on FDI flows. On the one hand, they stimulated FDI outflows and contributed to increase the capacity of Chinese firms, to better identify their technological needs, and to absorb innovations made outside. On the other, they encouraged FDI inflows, attracted by a pool of qualified engineers and scientists and the government endorsement, especially for very new research fields reflecting the challenging issues of the sustainability of the Chinese economy for the coming years.

Table 1 . Contribution of FDI to the Chinese economy and domestic firms Period and Context FDI contribution to the Chinese economy and domestic firms 1980s: Opening Permitting FDI

 1

	Very beginning of FDI in Special Economic Zones
	(test, FDI seen in a cautious way)

Capital Support to the development of China Support to international trade / foreign currency reserves Basic know-how and staff training 1990s: Take-off, restructuration of SOEs, more liberal preferential treatment for foreign firms

	Technologies, know-
	FDI become significant
	A way to foster and accelerate the catch-up of the
	Chinese economy
	Sino-foreign JVs and partnerships encouraged
	Deal "Technology transfers/ Access to the vast
	potential of China consumer market"
	Many incentives to FDI up to 1996

how and capabilities Employment and staff training Productivity and efficiency improvement Growth opportunities International integration of the Chinese economy

(support to exports, foreign currency reserves) 2010s: The second largest economy worldwide More selectivity on FDI Selective FDI (quality investments favoured), in phase with Chinese governmental priorities and selfsufficiency: priority sectors and areas (Go West policy) Incentives for high-level technology transfers and creation of R&D centres by foreign firms Deal "Technology transfers/ Access to Chinese market" increasingly prevailing Strategic assets augmenting: technologies, know-how, capabilities, productivity improvement, etc. New top of the range activities in China (that Chinese firms don't yet master) International integration of the Chinese economy (global supply chains…)

  Legend (computers, future Lenovo) was created by 11 researchers from the Chinese Academy of Social Sciences. Founder (computers, since restructured company) was established around the Institute for Computer Science, Social Informatics and Telecommunications. Zoomlion (mechanical engineering) has been created from Changsha Construction Machinery Research, a research institution specialized in mechanical, etc.

	Education and R&D
	-Significant efforts devoted to educational and research infrastructures
	-Role of science and technology highlighted in the national development
	-A specific plan (1994) to support 100 R&D private centres, in partnership with universities 7
	-Incentives and subsidies to buy foreign patents
	Industry
	-Restructuration of SOEs
	-Priority sectors

-Stimulate the collaboration of enterprises from the same industry, and the standardization of the inputs -Support to 'national champions' (subsidies, soft loans, etc.) -Public investments in the industry Infrastructure -Significant efforts to develop transport infrastructures (by air, rail and road) Source: Compilations by the authors By early-mid 1990s, Chinese authorities have capitalized on the comparative advantages of the Chinese economy -low labor cost and emergence of a large internal market -to exercise a bargaining power and stimulate FDI flows 8 , and to increase the requirements to get appropriate technologies from foreign firms.

FDI authorizations to foreign companies have started to be conditioned to substantial technology transfers towards Chinese firms, mostly State-backed enterprises. That was supposed to be a 'win-win' scheme for foreign firms where each deal was managed in the following terms: 'your technology against an access to our large potential market'. 7

8 From the 1980s, Special Economic Zones were established on the coastal front in order to attract foreign investors with many incentives: a very attractive taxation, an unprecedented administrative flexibility, and big facilities to export. Soon, foreign investors have begun to invest massively in China, attracted by these new opportunities together with low Chinese labor costs. This policy has encountered quite positive results and since 1984-85 has been intensified and extended to news areas (coastal cities, Shanghai, Beijing, etc.).

2. Main priorities of the Chinese government since 2002

	Economy
	-To install a sustainable and robust economy
	-To encourage Chinese firms to embrace a global view, and to compete with incumbent multinational
	companies
	-To support the 'national champions'
	-To build a full-fledged, high-performing national innovation system. The goal of the Medium to
	Long-Term Strategic Plan for the Development of Science and Technology (2006) was to make China
	an 'innovation-oriented' society by the year 2020, and one of the world's leading 'innovation
	economy'. The plan also emphasized the need to develop capabilities for 'home-grown innovation'
	-To stimulate 'high-end' products
	-Increasing wages
	-Emerging of a consumer society
	Infrastructures
	-Expansion of the number ok kilometers of highways: from 0 km en 1990, 10,000 km at the beginning
	of 2000, 40,000 km at the end of 2005 to 85,000 km at the end of 2011
	-Expansion of the railway network: 120,000 km by 2015 (including 16,000 km of high-speed
	railways)

-To pursue the Go West policy for a more balanced growth at a regional level -To pursue the Go abroad policy: to improve the quality and the brand image of Chinese products, to get natural resources, new markets and new technologies Following the global financial crisis -The stimulus package of January 2009: economy refocused on domestic consumption -The 12 th Five-Year Plan: quality growth, welfare, accelerated development of innovation and 'hightech' activities -Chinese market for Chinese firms when possible -New activities

(environment, software, finance, etc.)

Table 2 . Contribution of OFDI to the Chinese economy and domestic firms Period and Context OFDI contributions to the Chinese economy 1980s: Opening

 2

		Access to natural resources (mainly in developing
	OFDI almost non-existent	countries)
	1990s: Take-off, restructuration of SOEs	Access to natural resources
	OFDI almost non existent
	2000s: Booming economy	Access to natural resources
	Chinese firms assert themselves, SOEs lead the way	Access to strategic assets (mainly in industrialized
	1 st significant OFDI flows (Go abroad policy,	countries) that can't obtain through IFDI: new
	access to WTO)	technology, brands, skills, patents, IP rights; to be the
		best in China
		Access to new markets and sale networks (mainly
		in industrialized countries): to support exports, to
		circumvent trade barriers
	2010: Second world economy
	Chinese firms are increasingly qualified and mature,
	aggressive and ambitious
	OFDI encouraged and always more diversified
	Normalisation of Chinese OFDI
		More efficiency -higher margins, lowest
		operational costs -(industrialized & developing
		countries)

Access to natural resources (developing countries)

Access to strategic assets (industrialized countries) to always go up in range, to be the best in the world: more asset-augmenting than asset-seeking (high-end goods and own brands)

Access to new markets (industrialized & developing countries) to circumvent trade barriers (rising protectionism against China)

Paper presented at the XV World Economy Meeting -Shifting Wealth in the World Economy, 6-7 th June

2013, Santander, Spain.

By establishing an affiliate in Hong Kong they get the status of 'foreign-invested enterprise' when they make investments back in mainland China.

Back then, many multinationals have developed their operations of outsourcing, subcontracting agreements, partnerships, in developing countries such as China in order to get lower production costs.

Literally, it means 'mountain stronghold', i.e. the mountain stockades of bandits that is far away from official oversight. Nowadays, it relates to a counterfeiting subculture.

Realized in Beijing, Chengdu and Wuhan, in the second half of 2011.

It is the case in the automotive industry where Chinese authorities have explicitly put a target of 40 % for 2015 for the domestic market share of Chinese companies.

In October 2004, two influential government bodies, the National Development and Restructuring Committee, and the Export-Import Bank issued a circular to especially promote cross-borders M&As that could enhance the competitiveness of Chinese firms[START_REF] Deng | Why do firms tend to acquire strategic assets in international expansion[END_REF].

World Bank (1997), China engaged, Integration with the global economy, Washington D.C. Zeng M. and P. J. Williamson (2007), Dragons at our door: how Chinese cost innovation is disrupting global competition, Harvard Business School Press.


Menzie Chinn
email: mchinn@lafollette.wisc.edu

Laurent Ferrara
email: laurent.ferrara@banque-france.fr

Valérie Mignon
email: valerie.mignon@u-paris10.fr.

Anindya Banerjee

Nicolas Coeurdacier

Dick Van Dijk

James D Hamilton

Matthieu Lemoine

Hervé Le Bihan

Antonia Lopez-Villavicencio

Anne Peguin-Feissolle

Post-recession US employment through the lens of a non-linear Okun's law 

Keywords: Okun's law, trend employment, non-linear modeling. JEL codes: E24, E32, C22

This paper aims at investigating the relationship between employment and GDP in the United States. We disentangle trend and cyclical employment components by estimating a non-linear Okun's law based on a smooth transition error-correction model that simultaneously accounts for long-term relationships between growth and employment and short-run instability over the business cycle. Our findings based on out-of-sample conditional forecasts show that, since the exit of the 2008-09 recession, US employment is on average around 1% below the level implied by the long run output-employment relationship, meaning that about 1.2 million of the trend employment loss cannot be attributed to the identified cyclical factors.

Introduction

One of the central puzzles following the financial crisis and the ensuing Great Recession has been the sluggish growth in employment during the recovery which began in June 2009, according to the NBER business cycle dating committee. It is somewhat surprising that analysts have worried about how employment growth has recently outpaced GDP, according to Okun's law [START_REF] Okun | Potential GNP: Its Measurement and Significance[END_REF], while others have bemoaned the slow pace of employment growth. Underpinning these discussions is a view that there is instability in this relationship between changes in employment and GDP growth. 1 From 2008Q4 onward, employment growth was below that predicted by a simple regression of employment growth on GDP growth over the 1987Q1-2007Q4 period [START_REF] Chinn | Okun's law, the jobless recovery, and unexpectedly fast net job creation[END_REF]. This outcome continued on into the recovery period, although the most recent observations have been above the regression line. There does seem to be a consistent pattern wherein contractions are associated with employment growth below that implied by the relationship that obtains over both upswings and downswings.

Our analysis is related to the issue of whether structural unemployment has risen in the wake of the Great Recession. This issue is of major importance for policy-makers, and biased estimation of natural levels of employment and unemployment can lead to inadequate economic policies. For example, in terms of monetary policy-making, over-estimated unemployment gaps can imply an underestimation of optimal monetary policy rates through standard Taylor equations. Within this context, disentangling structural and cyclical employment components is a key question.

In this paper, we estimate a model based on Okun's law, so that we can specify a decomposition of employment between trend and cyclical factors, wherein one could potentially interpret the trend factors as structural in nature. This caveat is necessary because statistically defined trend factors could be structural in origin, but might also conceivably incorporate factors that are not long term in nature, such as enhanced unemployment insurance benefits. 2One key problem that arises when dealing with the Okun's law is that several specifications co-exist in the empirical literature3 , rendering comparisons difficult. The relationship between output and employment can be estimated in differences, in gaps or in levels. Here, we implement a non-linear Okun's law for the US that simultaneously accounts for long-term relationships between output and employment as well as instability over the business cycle.

Relying on a non-linear error-correction specification over the 1950-2012 period, our main findings can be summarized as follows. First, if one does not account for the long-term relationship between GDP and employment within the Okun's framework (i.e. if one focuses only on the relationship in differences), then we obtain unrealistic results by overestimating employment by a substantial amount. Second, a standard error-correction model is able to reproduce the general evolution of employment, but underpredicts the decline in employment during the recession, and therefore overpredicts employment during the recovery. Third, accounting for the US business cycle by using an innovative non-linear smooth transition error-correction model enables a better reproduction of stylized facts, especially by taking the business cycle into account without integrating any exogenous information. Fourth, according to our estimated model, we show however that employment is still on average 1.05% below its potential level after the recession, meaning that the level of employment is 1.17 million lower than would have been predicted on the basis of the historical co-movement of employment and GDP.

The rest of the paper is organized as follows. Section 2 briefly reviews the recent literature. Section 3 describes the econometric framework, and Section 4 presents and discusses the results. The last section concludes the article.

A brief review of the recent literature

On the one hand, some papers have concluded that the cyclical component cannot account for the entire change in employment. In this respect, [START_REF] Stock | Disentangling the channels of the 2007-2009 recession[END_REF] argue that the slow recovery is mainly explained by a decline in the trend growth of the labor force.

Several explanations have been proposed regarding the effect of factors affecting structural employment. [START_REF] Estevão | Has the Great Recession raised US structural unemployment?[END_REF] estimate that about 1.75 percentage point of the increase in unemployment between 2006 and 2010 is due to negative interactions of mismatches between demand and supply on the labor market with weak housing conditions. In a multi-country framework, [START_REF] Chen | New evidence on cyclical and structural sources of unemployment[END_REF] show that sectoral shocks specific to the Great Recession-namely in the construction sector and to a lesser extent in finance-have contributed to increase the long-duration unemployment rate. Various other explanations include the extension of unemployment benefits and high uncertainty about future economic outlook; however these explanations seem to have less explanatory power (see e.g. [START_REF] Daly | A Rising Natural Rate of Unemployment: Transitory or Permanent?[END_REF].

On the other hand, others argue that there is no evidence of structural impediments on the labor market, given that modest recoveries are commonplace after balance sheets crisis. According to this view, the lack of aggregate demand is the main driver of the current high unemployment rate and consequently the job market will come back to its pre-recession equilibrium when economic conditions will improve. [START_REF] Lazear | The United States Labor Market: Status Quo or A New Normal?[END_REF] conclude that "neither industrial nor demographic shifts nor a mismatch of skills with job vacancies is behind the increased rates of unemployment". They recognize that job market mismatches increased during the recession, but they argue that those mismatches diminished at the same pace just after the recession exit.

In a recent work, [START_REF] Ball | Okun's law: Fit at fifty?[END_REF] defend this point of view and argue that there is no jobless recovery in the US, but only a sluggish economic growth that weights on the labor market. To support their analysis, they estimate the Okun's law for a sample of 20 advanced countries and show that there is a strong and stable relationship between output and employment. Based on empirical findings, [START_REF] Rothstein | The labor market four years into the crisis: Assessing structural explanations[END_REF] dismisses any structural factors to explain the low labor market activity. Also [START_REF] Farber | Unemployment in the Great Recession: Did the Housing Market Crisis Prevent the Unemployed from Moving to Take Jobs?[END_REF] estimates mobility rates and does not find any evidence that low geographic mobility, due to a deteriorated housing market, explains the weak labor market.

Given this lack of consensus regarding the decomposition of employment between structural and cyclical factors in the wake of the Great Recession, we propose an econometric model based on the Okun's law which enables us to decompose movements in employment into trend and cyclical components. Indeed, to evaluate the relationship between output and employment, the empirical Okun's law turns out to be a valuable tool as pointed out by [START_REF] Ball | Okun's law: Fit at fifty?[END_REF] among others. [START_REF] Knotek | How useful is the Okun's law?[END_REF] also suggests evidence that Okun's relationship between changes in the unemployment rate and output growth can be a useful forecasting tool, in spite of considerable instability over time and over the business cycle (see also Owyang and Sekhposyan, 2012, on this point). However, this instability in the relationship is not confirmed by [START_REF] Ball | Okun's law: Fit at fifty?[END_REF], who also reject evidence of non-linearity based on sub-samples investigations.

An econometric approach to estimating Okun's law

Arthur Okun documented the evidence for his eponymous law, the empirical relationship between the unemployment rate and output growth, in 1962. Since then, several versions of Okun's law have been developed. Some are expressed in levels, some in deviations from natural levels (gaps), and some in growth rates. For example, the original Okun's law was expressed in differences such as:

∆ ∆ , ( 1
)
where ∆LGDP is the change in the logarithm of real GDP and ∆UNR is the change in the unemployment rate. The parameter β is sometimes referred to the Okun's coefficient and is expected to be negative, reflecting thus the negative correlation between changes in unemployment and output growth. The ratio -α/β is an estimate of the rate of output growth necessary to stabilize the unemployment rate.

Alternatively, the gap version of the Okun's law linearly relates the unemployment rate with the output gap, as defined by the difference between the observed GDP and its potential value, such as: * ,

where LGDP* is the potential of log-GDP, which has to be estimated by a given econometric method, and (LGDP -LGDP*) is the output gap. The parameter δ can be seen as the unemployment rate consistent with full employment. Alternatively, the natural unemployment rate U* can be estimated exogenously before entering into equation ( 2). In that case, the left-hand side of equation ( 2) becomes (UNR -UNR*), referred to as the unemployment gap, and δ is set to zero. This gap specification is generally easier to estimate than the differences specification as variables involved are smoother. But the main drawback is that potential GDP and natural unemployment rate are unobserved values and have to be previously estimated using econometric methods, such as filtering techniques (Hodrick-Prescott or band-pass filters). As there is no consensus on the way to estimate such quantities,4 measurement error exacerbates the imprecision in estimating the relationship.

Departures from those original versions of Okun's law given by equations ( 1) and ( 2) are motivated by two observations. First, those equations do not include any long-term effect between the two variables as the low-frequency information is eliminated by the differentiation operation or by subtracting potential log-GDP. Yet, it is generally observed in econometrics that accounting for longterm effects can lead to fruitful results. In this respect, we decide to focus on the long-term relationship between employment and output in the framework of error-correction models, as both log-GDP and log-employment series are obviously integrated. We show in the following section how this choice is validated by the results. Using employment data instead of unemployment data also presents the great advantage of neglecting the participation rate that can lead to spurious measurement effect. Indeed, it has been shown [START_REF] Stock | Disentangling the channels of the 2007-2009 recession[END_REF] that the participation rate decreased from 66% in 2007 to less than 64% in 2012, implying thus a lower unemployment rate for a given level of unemployment in the years 2011-12.

Second, some authors have detected evidence of instability in Okun's law over time. Using standard rolling regressions, and allowing the estimation of the relationship over many different samples, [START_REF] Knotek | How useful is the Okun's law?[END_REF] underlines a great variation overtime of the estimated parameters of the Okun's law.

In particular, he shows that the Okun's law is sensitive to the state of the business cycle. Other authors have also investigated the non-linear dynamics of the Okun's law, including [START_REF] Lee | The robustness of Okun's law: evidence from OECD countries[END_REF], [START_REF] Viren | The Okun curve is non-linear[END_REF] and [START_REF] Harris | Testing for asymmetry in Okun's law: a cross-country comparison[END_REF]. According to [START_REF] Harris | Testing for asymmetry in Okun's law: a cross-country comparison[END_REF], four factors may explain the presence of non-linearity in the Okun's relationship: capacity constraints, signal extraction, costly adjustment and downward nominal wage rigidity. In addition, McCarthy, Potter and Ng (2012) underline that the Okun's law has not been a consistently reliable tool to forecast the amplitude of decline in the unemployment rate during the last three recessions.

In this paper, our aim is to account simultaneously for those two stylized facts described above, namely long-term and instability effects. In this respect, we consider a non-linear, smooth transition error correction model (STECM) whose parameters are allowed to evolve through time. More specifically, we retain the following non-linear specification with two regimes:

∆ ∆ ∆ ∆ ∆ ∆ ∆ , ,  , (3)
where LEMP denotes private non-farm payroll employment in logarithm, LGDP the logarithm of GDP,  t is a Gaussian white noise process, G denotes the transition function, γ is the slope parameter that determines the smoothness of the transition from one regime to the other, c is the threshold parameter, and Z denotes the transition variable.

This non-linear ECM takes the long-term relationship into account, as well as two regimes for the short-term relationship-the long run relationship remaining invariant to the regime. The economy can evolve in two states, but the transition between those two regimes is smooth: the two regimes are associated with large and small values of the transition variable relative to the threshold value, the switches from one regime to the other being governed by the transition variable Z (here, lagged GDP growth). The smooth transition function, bounded between 0 and 1, takes a logistic form given by: 5

, , 1

It is noteworthy that when the function G(.) is equal to zero, it turns out that the non-linear STECM equation collapses to a standard linear ECM.

Further, inspection of equation ( 3) highlights the fact that we impose the strong assumption that the long-run relationship between employment and GDP is constant over the 1950-2012 period (the employment predicted by this long run relationship is the trend employment which we refer to). We attempt to relax this assumption in robustness tests.

Results for the US economy

In this section we implement the previous non-linear ECM given by equations ( 3) and ( 4) until the beginning of the Great Recession, then we use the estimated model in an out-of-sample conditional forecasting approach in order to assess losses in US trend employment.

In-sample analysis

We estimate the model given by equations ( 3) and (4) over the period 1950Q1 -2007Q4 for US data of log-GDP and log-employment as presented in Figure 1. 6 This graph clearly highlights a long-term co-movement between both variables as well as evidence of non-stationarity, suggesting thus a cointegrated system. Formally, the implementation of Johansen's cointegration test leads to conclude to the existence of a cointegrating relationship between LEMP and LGDP. 7

5 See [START_REF] Teräsvirta | Characterizing nonlinearities in business cycles using smooth transition autoregressive models[END_REF]. 6 As previously mentioned, we do not estimate the equations over our entire sample, as we reserve the 2008Q1-2012Q3 period for out-of-sample forecasts. 7 We adopt a specification with one lag of first differences for the Johansen's test. The non-stationarity of employment and GDP series is also confirmed by the usual unit root tests (results are available upon request to the authors). First, we estimate the long-term linear relationship through ordinary least-squares over the period 1950Q1 -2007Q4. 8 The residuals from the long-term equation are obtained from the following estimated relationship:

5.8501 0.6155 , and are presented in Figure 2.

8 As a robustness check, we have also estimated the cointegrating relationship using the Dynamic OLS (DOLS) procedure, leading to very similar results. In addition, to address the issue of stability of our long-run relationship-a question that may be important as regards to the IT productivity shock initiated in the mid-1990s-we have applied various usual break tests. Our results were not convincing, a finding that is not surprising given that such tests are not suitable when dealing with productivity shocks. Indeed, as pointed out by [START_REF] Benati | Drift and breaks in labor productivity[END_REF] and [START_REF] Turner | Recent Trends and Structural Breaks in US and EU15 Labour Productivity Growth[END_REF] among others, those shocks are generally gradual. We have thus followed an alternative way by introducing the total factor productivity in the long-run relationship. Our results (available upon request to the authors) are very similar to those presented here.

LEMP

Once the estimation of this long-term relationship is realized, we integrate the lagged residuals into our main non-linear equation (3). To account for the business cycle in the short-term relationship, we select as transition variable the average GDP growth over 2 quarters, lagged by 2 quarters, i.e.:9 0.5 ∆ ∆ The estimation of the non-linear specification follows the methodology proposed by [START_REF] Teräsvirta | Specification, estimation, and evaluation of smooth transition autoregressive models[END_REF]. We start by testing for the null hypothesis of linearity using the test introduced by [START_REF] Luukkonen | Testing linearity against smooth transition autoregressive models[END_REF]. Once the null of linearity has been rejected, we select the specification of the transition function using the test sequence presented in [START_REF] Teräsvirta | Specification, estimation, and evaluation of smooth transition autoregressive models[END_REF]. 10 We then estimate the non-linear ECM, leading to the results presented in Table 1.11 The estimated value ̂ of the threshold c is close to zero, delimiting thus periods of expansion and periods of recession, as shown by the transition function displayed in Figure 3. The transition function clearly highlights the existence of two regimes in the short-term relationship between employment and output, which are strongly related to the business cycle phases, though slightly lagged. There is one regular regime that occurs most of the time, with an unconditional probability of 89%, while the second regime is more exceptional and appears only 11% of the time (i.e. when the transition function exceeds the natural threshold of 0.50). It is striking to observe that the second regime always begin at the end of recessions, generally one quarter before the end. The average duration of this recession regime is slightly greater than 3 quarters. In fact during this specific period of time, the persistence of the growth rate of employment tends to increase, as the first-order autoregressive estimate jumps to 0.589 from 0.215 in the regular regime. In addition, the contemporaneous elasticity dips from 0.644 to 0.308 and the lagged elasticity dies out. Thus, in this second regime, the dependence of employment growth on output growth is reduced. One explanation may be due to the fact that GDP growth tends to strongly bounce-back after recessions before returning to a "normal" expansion regime. Evidence of such behavior is documented in the papers of [START_REF] Bec | The possible shapes of recoveries in Markov-Switching models[END_REF] and [START_REF] Morley | The Asymmetric Business Cycle[END_REF]. Yet, during this bounce-back period, employment growth does not follow at the same pace, leading to a reduction in the dependence on output growth and an increase in its persistence.

It is notable that the point estimate for the coefficient on the lagged error term is equal to -0.0123 (= 0.0070 -0.0193) in the second regime. In other words, the extent of disequilibria has minor impact on the pace of net job growth when GDP growth is negative.

In order to compare those latter results stemming from our model, we need to consider benchmark models. To this end, we also estimate over the same period (i) a standard ECM given by equation ( 3) with function G(.) being equal to zero and (ii) an Okun's law expressed in differences as given by equation ( 1). Series in log-differences over one quarter are presented in Figure 4. As regards the specification of the linear ECM, we impose for short-term dynamics a similar structure to the one given in equation ( 3). Results of parameter estimation are given in Table 2. It is noteworthy that those estimates are rather close to the sum of the corresponding parameters in Regime 1 and Regime 2 (Table 1). The lagged log-difference GDP is not significant at usual levels.

The estimated equation in differences is given by: ∆ 0.0003 0.5400 ∆ .

The estimated parameter associated with GDP is significant at the 5% level, but residuals appear to be serially correlated according to usual whitening tests. In order to improve the goodness-of-fit, we include short-term dynamics into the regression model. The estimated model is the following:

∆ 0.0012 0.3846 ∆ 0.5729 ∆ .
All estimated parameters are significant at the 5% level, and we do not reject the null of noautocorrelation within residuals.

Conditional forecasts

We now compare the previous models on the basis of conditional dynamic forecasts of the variable LEMP over the period 2008Q1 -2012Q3. This means that we forecast employment based on the knowledge of the ex post path for LGDP. Those conditional forecasts are dynamic in the sense that, for each step, we use previously forecasted employment value instead of the observed value.

First we compare the three linear models, namely the model in differences, the model in differences with dynamics and the ECM. Conditional forecasts are presented in Figure 5.

Both models in differences largely miss the drop in employment during the Great Recession. In particular, conditional forecasts stemming from the Okun's law in differences exceed the prerecession values of employment by end of 2010. Those results are clearly at variance with reality and point to a failure in the employment version of Okun's law. If we integrate dynamics in the equation in differences, conditional forecasts are shifted downwards due to the presence of lagged differences of employment. We observe that at the end of 2012, conditional forecasts are close to observed values of employment, meaning that, at this date, the level of employment would be consistent with its historical equilibrium. Yet, this hardly makes this model convincing as an explanation for employment dynamics during the Great Recession.

When taking the long-term relationship into account, conditional forecasts partly reproduce the dip in employment due to the large decrease in GDP level during this specific period of time. However, there is still a wide gap between observed values of employment and conditional forecasts stemming from the ECM. In addition, this gap tends to persist after the end of recession.

Figure 5: Conditional forecasts of log-employment stemming from linear models

Note: Conditional forecasts stemming from the model in differences (red), the model in differences with dynamics (dotted red) and the ECM (blue). Observed values are presented in the dark line.

Let us now turn to the comparison of the ECM and the non-linear ECM based on those conditional forecasts. Figure 6 presents the observed employment (dark line), as well conditional forecasts from a standard (linear) ECM (blue line) and from the non-linear ECM (green line).

Both ECMs are able to reproduce the main movements in employment during and after the recession. However, there is a persistent gap between the observed employment (dark line) and the conditional forecasts from both models (blue and green lines), meaning that the employment is currently well below what it should be according to the models. When comparing both ECMs, taking the non-linear business cycle into account through the non-linear ECM (green line) leads to an important reduction in the gap. The contribution of the non-linear cycle to the employment is quite high (the average difference between the blue and the green lines is around 2.6 % in 2010) but tends to diminish (the green line slightly tends to the blue line), the average difference being only of 1.6% during the first three quarters of 2012. Our findings lead us to conclude that there has been indeed an effect of the Great Recession on the long-term private employment. Specifically, on average, since the exit of the recession (2009Q2), we find that employment is 1.05 % below predicted levels (according to the non-linear ECM), meaning that about 1.17 million of jobs have been lost due to non-cyclical reasons. This interpretation is in line with the recent literature on this topic, as pointed out for example by [START_REF] Chen | New evidence on cyclical and structural sources of unemployment[END_REF] or [START_REF] Stock | Disentangling the channels of the 2007-2009 recession[END_REF].

Robustness checks

As robustness checks, we compute confidence intervals for conditional forecasts and evaluate the sensitivity of our results to alternative measures of employment.

 Confidence intervals

To assess the quality of conditional forecasts, we compute confidence intervals based on a re-sampling bootstrap approach. As previously mentioned, residuals ̂ stemming from equation (3) over the sample 1950-2007 are proved to be non-correlated for low lags. In addition, they are not far from being normally distributed, according to the Jarque-Bera test of Normality at the 1% level 12 . Thus, we choose to implement a bootstrap resampling approach based on those residuals in order to estimate confidence bounds around conditional forecasts ∆ over the period from 2008Q1 to 2012Q3. As new residuals based on the difference between observed and conditional forecasts become available, we integrate them in the re-sampling approach. The number of bootstrap replications is fixed at B=1000. Figure 7 displays the 95% confidence interval. This confidence interval is quite narrow, due to the low standard deviation of residuals (equal to 0.0029), and illustrates the reliability of our forecasts. 13 Starting from the exit of recession, the realized employment stays clearly below the lower bound of the confidence interval until the end of the sample.

 Robustness to the employment series

We now assess the sensitivity of our findings to the choice of the employment series. To this end, we focus on total non-farm payroll employment (LEMPTOT) instead of only private nonfarm payroll employment. First, we estimate the long-term linear relationship over the period 1950Q1 -2007Q4, leading to the following residual series: u LEMPTOT 5.9296 0.6273 LGDP .

13 Note that we have assumed that parameters in equation (3) are known. Obviously, as in any other empirical applications, parameters need to be estimated, which leads to an additional uncertainty in predicted values. To our knowledge, there is no available clear procedure when dealing with a STECM, in spite of papers dealing with other types of non-linear models (see for example Li, 2011, or Bec, Bouabdallah and[START_REF] Bec | The way out of recessions: A forecasting analysis for some euro area countries[END_REF], in the case of univariate threshold models). As shown, the long-run elasticity is very close to the one estimated with private employment (0.6155). We then estimate a linear ECM over the same period, as well as the STECM given by equation (3).14 Parameter estimates of both models are given in Table 3; they are consistent with those obtained when dealing with private employment. The speed of adjustment to the long-term target is lower here and even non-significant, reflecting a less cyclical pattern. The transition function also describes very precisely the business cycles, though the probabilities do not reach one in this framework. This likely reflects the fact that the public employment is counter-cyclical during these specific periods (see Figure 8). Based on those estimates, we compute dynamic conditional forecasts for both linear and non-linear ECMs. Results are presented in Figure 9. Confirming our intuition, it is interesting to note that total employment is much less sensitive to the business cycle. This result is expected because total employment also includes government employment which tends to be less pro-cyclical. Average losses of employment since the exit of the recession amount to 3.9% with the ECM and 1.8% with the STECM. Based on this latter model, this corresponds respectively to an average loss of 2.4 millions of jobs. If we assume that our estimation of the private employment loss at around 1 million is correct, thus it means that the long-run loss of government jobs is likely to be close to 1.4 million on average since the exit of the recession.

Conclusion

Addressing the issue of whether structural unemployment has risen in the wake of the Great Recession is of crucial importance for policy makers. Within this context, this paper aims at investigating the links between employment and GDP in the United States. From a statistical perspective, we disentangle trend and cyclical components in US employment based on an innovative non-linear error correction model that accounts for both a (constant) long-term relationships between output and employment and short-run non-linearities in dynamics over the business cycle. Based on this estimated non-linear Okun's law, a conditional forecasting approach shows that the level of US private sector employment is on average around 1% below the level implied by the long run output-employment relationship, meaning that around 1.2 million of the trend employment loss cannot be attributed to the identified cyclical factors. 15 To the extent that trend employment depends on structural factors, eliminating this shortfall will depend upon the 15 The misprediction incorporates both estimated trend factors and prediction error due to model uncertainty.

Figure 1 :

 1 Figure 1: Log-GDP (top) and log-employment (bottom) over the period 1950Q1 -2012Q3

Figure 2 :

 2 Figure 2: Deviations to the estimated long-term relationship between log-employment and log-GDP

Figure 3 :

 3 Figure 3: Estimated transition function and US recessions until 2007Q4

Figure 4 :

 4 Figure 4: Log-GDP in differences over 1 quarter (top) and log-employment in differences over 1 quarter (bottom)

Figure 6 :

 6 Figure 6: Conditional forecasts of log-employment stemming from linear and non-linear errorcorrection models

Figure 7 :

 7 Figure 7: Confidence interval at 95% for conditional forecasts based on the STECM

Figure 8 :

 8 Figure 8: Estimated transition function for the total employment and US recessions until 2007Q4

Figure 9 :

 9 Figure 9: Conditional forecasts from linear and non-linear ECMs for total payroll employment

Table 1 : Estimation results of the non-linear error-correction model

 1

		Regime 1	Regime 2
	Constant -0.0071*** 0.0067***
	LEMP t-1 0.2149	0.3741***
	LGDP t	0.6439*** -0.3361***
	LGDP t-1 0.1932*	-0.1976
	Resids t-1 -0.0193** 0.0070
		5.1624
	̂ 0.0001
	Note: *** (resp. **): significant at the 1% (resp. 5%) level.
	In order to obtain the relevant coefficients in Regime 2, add the
	Regime 2 coefficient to the corresponding Regime 1 coefficient.

Table 2 : Estimation results of the linear error-correction model

 2

		Estimates
	Constant	-0.0013***
	LEMP t-1	0.5402***
	LGDP t	0.3733***
	LGDP t-1	0.0358
	Resids t-1	-0.0133**
	Note: *** (resp. **): significant at the 1% (resp. 5%) level.

Table 3 : Estimation results of linear and non-linear ECMs for total payroll employment Linear ECM Non-linear STECM

 3 : *** (resp. **): significant at the 1% (resp. 5%) level. In order to obtain the relevant coefficients in Regime 2, add the Regime 2 coefficient to the corresponding Regime 1 coefficient.

			Regime 1	Regime 2
	Constant	0.0006**	-0.0055*** 0.0055**
	LEMP t-1	0.5763***	0.2640	0.3763***
	LGDP t	0.3206***	0.6502*** -0.4094***
	Resids t-1	-0.0104	-0.0131	0.0057
			2.5041
	̂		-0.0015

Note

See e.g.,[START_REF] Knotek | How useful is the Okun's law?[END_REF][START_REF] Mccarthy | Okun's law and long expansions[END_REF] and[START_REF] Owyang | Okun's law over the business cycle: Was the Great Recession all that different?[END_REF].

For instance,CBO (2012) estimates both a long term natural rate of unemployment, and one accounting for short run factors. The former is driven by demographics and skill attributes, while the latter is determined in part by extended unemployment insurance benefits. For the sake of completeness, it should also be noticed that regarding hysteresis effects, part of trend employment will depend on long-lasting cyclical effects.

See Section 3.

In particular,[START_REF] Lee | The robustness of Okun's law: evidence from OECD countries[END_REF] has shown that the estimated Okun's relationship is sensitive to the method used for extracting the cyclical component.

Note that we have also tried other transition variables, such as changes in the employment rate and other lags for GDP growth rate. Using the average GDP growth over 2 quarters leads to the strongest rejection of the null of linearity, justifying our choice from an econometric viewpoint.

We refer for example to van Dijk,[START_REF] Van Dijk | Smooth transition autoregressive models -A survey of recent developments[END_REF] for details on smooth transition models.

that estimated model has successfully passed the usual misspecification tests: test of no residual autocorrelation[START_REF] Teräsvirta | Modeling economic relationships with smooth transition regressions[END_REF], LM-test for no-remaining non-linearity[START_REF] Eitrheim | Testing the adequacy of smooth transition autoregressive models[END_REF] and ARCH-LM test.

The null of Normality is accepted at the 1% level but rejected at the 5% level (p-value of 0.013). 2007 2008 2009

Note that the STECM is estimated without any lagged GDP given that the null of linearity was more strongly rejected when not including lagged GDP. As for the estimation with private employment, the lagged GDP is also non-significant in the linear specification.

implementation of measures that improve the workings of the labor market, as well as other government policies that raise the natural rate of unemployment.