Keith Head
email: keith.head@ubc.ca

Thierry Mayer
email: tmayer@univ-paris1.fr

John Ries
email: john.ries@ubc.ca

Revisiting Oligopolistic Reaction: Are FDI Decisions Strategic Complements?

Keywords: JEL classification: F23, R3 Oligopolistic reaction, spatial Cournot competition, uncertainty

introduced "oligopolistic reaction" to explain why firms follow rivals into foreign markets. We develop a model that incorporates the central features of Knickerbocker's story-oligopoly, uncertainty, and risk aversion-to establish the conditions required to generate follow-the-leader behaviour. We find that rival foreign investment will make risk-neutral firms less inclined to move abroad once its rivals have done so. We show that risk aversion can generate the Knickerbocker prediction and derive an expression for the minimum amount of risk aversion needed to generate oligopolistic reaction.

Introduction

Research on foreign direct investment (FDI) has long recognized two important motives for choosing a particular country as the site for a new facility. First, firms wish to gain improved access to that country's market. A local plant can lower transport costs or circumvent barriers to trade. Second, firms want to deploy the relatively abundant factors located in the country.

That is, they seek a low-cost production platform. In his 1973 book, Frederic Knickerbocker proposed a third motivation in location choice: firms might invest in a country to match a rival's move. In particular, Knickerbocker argued that firms in industries characterized by oligopoly would tend to follow each other's location decisions.

We define oligopolistic reaction (OR) as follows: The decision of one firm to invest overseas raises competing firms' incentives to invest in the same country. Essentially, we want to know whether, within the structure proposed in Knickerbocker, FDI decisions are strategic complements. Following the terminology of the field of industrial organization, firms' actions are strategic complements when an increase in the action of one firm raises the marginal profitability of an increase in the action for another firm.

Despite the strong recognition that Knickerbocker's hypothesis has attracted in the international business and strategy literature, there is surprisingly little formal examination of the conditions that give rise to OR. This paper develops a model that sequentially incorporates the important elements of the Knickerbocker framework-oligopoly, uncertainty, and risk aversionto evaluate the conditions required for OR to hold. We show that in the case of certainty, an oligopolist will be less likely to establish a manufacturing facility in a foreign country once its rivals have invested there, i.e. FDI decisions are strategic substitutes. Moreover, introducing uncertainty about costs in the foreign market reinforces this "reverse" Knickerbocker effect. We proceed to establish if firms are sufficiently risk adverse, they may benefit from matching a rival's move abroad. We are able to define the level of risk aversion necessary for the Knickerbocker hypothesis to hold in terms of the parameters of the model and show how it is influenced by changes in the number of firms as well as transport costs.

The persistent influence of oligopolistic reaction is underscored by the 89 citations to [START_REF] Knickerbocker | Oligopolistic Reaction and Multinational Enterprise[END_REF] in journals published between 1989 and 1999 according to the Social Science and Humanities Citation Index. A number of papers cite Knickerbocker as a motivation for adding specific covariates in regressions explaining FDI. Kogut andChang (1991, 1996) use the 8-firm Japanese concentration index in their analyses of Japanese FDI. They interpret the positive and significant coefficient of this variable in their 1991 study as evidence of follow-the-leader behaviour. 1 Hennart and Park (1994) and Yu and Ito (1988) add a measure of previous rival investment in their analyses of Japanese FDI in the United States. It has a significant positive effect in latter paper but an insignificant effect in the former.

We construct our model to reflect the main features of Knickerbocker's argument. The first important aspect is oligopoly. We model Cournot oligopolists that choose between producing at home or abroad. A second feature of Knickerbocker's framework is uncertainty about economic conditions in the foreign market. The follower is "uncertain of the production economies, if any, that it [the leading firm] might gain by manufacturing locally" [START_REF] Knickerbocker | Oligopolistic Reaction and Multinational Enterprise[END_REF], page 26).

Accordingly, we allow for uncertainty about production costs in the foreign market. Finally, Knickerbocker points to the role of risk aversion: "firms minimized their risk by matching the foreign direct investment of rivals" [START_REF] Knickerbocker | Oligopolistic Reaction and Multinational Enterprise[END_REF], page 23). We consider a firm objective function in which variation of profits enters negatively.

To our knowledge, no formal mathematical models of oligopolistic reaction exist that incorporate these central features of the Knickerbocker thesis. However, some authors have worked on related models. [START_REF] Caves | Corporate Mergers in International Economic Integration[END_REF] introduces the idea of mergers as strategic complements, an idea formalized in Fauli-Oller (forthcoming). Fauli-Oller shows that in a Cournot oligopoly, a firm's incentive to merge is decreasing in the number of outside firms. Thus, mergers between two firms will increase the likelihood of subsequent mergers. [START_REF] Flaherty | Local Presence and International Manufacturing in Technology-Intensive Industries[END_REF] show that follow-the-leader behaviour will occur when the leader's investment lowers the fixed costs of subsequent investment of rivals. [START_REF] Motta | International Trade and Investments in a Vertically Differentiated Industry[END_REF] examines sequential FDI location decisions of oligopolists when products are vertically differentiated. He shows that both oligopolists in a country may choose FDI over export to serve foreign customers, a result he states is consistent with the Knickerbocker hypothesis. He acknowledges, however, that his model does not demonstrate that follower investment is in response to the FDI of the leader firm. Aussilloux (1998) also relates the FDI/export decision in a sequential entry Stackelberg game to the Knickerbocker hypothesis. Here again, however, the incentive to invest is not positively related to the number of firms that previously chose to invest. [START_REF] Graham | Market Structure and the Multinational Enterprise: A Game-Theoretic Approach[END_REF] develops a model with rivalistic behaviour that he refers to as "exchange-of-threat." This model, however, gives rise to reciprocal FDI by oligopolists based in different countries, a phenomenon that differs from the follow-the-leader behaviour contemplated by Knickerbocker.

The following section outlines the set of plant location strategies available to the oligopolists and positions oligopolistic reaction in relation to the industrial organization literature on strategic substitutes and complements. Section 3 specifies the imperfect competition model we employ and calculates the profits associated with the strategy of maintaining home production and the strategy of relocating production abroad. We establish the main results about FDI being strategic complements or substitutes in three propositions in section 4. We examine equilibrium location in section 5. In the final section, we summarize our results and discuss their implications for observed patterns of FDI.

Framework

Multinational operations may have a number of different structures depending on characteristics of demand, production, and costs. For example, consider a firm that initially produces only at home and serves foreign markets by exporting. As economic conditions change, this firm may choose to relocate its single production plant to a low-cost foreign market, closing down its home plant. Alternatively, it may wish to establish production facilities in each major market to serve local demand. We refer to the first strategy as R to indicate "relocate" and the second strategy as A to represent "add location." The alternatives are shown in Figure 1. First, home firms decide whether to stay at home, S, or invest abroad. If they invest, they can either choose

R or A.
The focus of this paper will be on the relocation strategy R versus the strategy of staying at home S. R will be preferred to A when single-plant production is preferred to multi-plant production. We analyze strategy A in the appendix where we show a) the conditions on fixed production costs that make R preferred to A, and b) that the qualitative results are robust to whether S is compared to either R or A. Our reasons for concentrating on R is that, as shown in the appendix, strategy A contains a subset of the effects that influence strategy R. When a firm chooses R, it changes profits both at home and abroad. If the firm chooses A, however, only foreign profits are affected as it continues to serve home demand with home production. A model where FDI influences home profits seems most consistent with Knickerbocker's argument (p. 30) that "risk might not apply to a single market; the firm's market position might be in jeopardy in a number of foreign countries and even, perhaps, in the United States [the home country]."

The structure of the model is a two country, N -firm oligopoly. Firms operate a single plant and initially there are n h plants (or firms) located in the home country and n f plants in a foreign

∆n h = -1, ∆n f = +1 Relocate (R) ∆n h = 0, ∆n f = +1 Add Location (A) " " " " " "
country (thus a total of N = n h + n f firms). We consider a representative firm that operates in the home country but contemplates relocating production to the foreign country. If it were to do so, as expressed in Figure 1 the number of home firms would decrease by one while the number of foreign firms would increase by one. We are interested in the benefit associated with relocating production to f and how a rival's investment affects this benefit.

We begin with a certainty model where the representative home firm considers the benefit of relocating as the difference in the profits it obtains by staying at home versus the profits associated with relocating. Recall that Knickerbocker indicated that uncertainty as well as risk aversion were sources of oligopolistic reaction. Accordingly, we sequentially add these elements to the basic model. First, we introduce uncertainty about marginal costs in the foreign market and specify the benefit function defined in terms of the difference in expected profits for each alternative. Finally, we allow risk to enter negatively in utility and examine benefits in terms of differences in expected utility. Thus, in the succeeding analysis we consider the following three benefit functions which are functions of the number of firms, N , and the share of firms in the foreign market, x ≡ n f /N : 1. B 1 = π Rπ S : the difference in profits associated with choosing country f instead of staying in country h.

2. B 2 = E[π R ] -E[π S ]
: the difference in expected profits.

3. B 3 = EU (π R ) -EU (π S ): the difference in the expected utility of the profits associated with each strategy.

As mentioned earlier, oligopolistic reaction can be thought of in terms of FDI decisions being strategic complements. [START_REF] Jeremy | Multimarket Oligopoly: Strategic Substitutes and Complements[END_REF] define strategic complementarity as the case where the cross partial of the profit function with respect to each firm's strategic variable is positive, i.e. π ij > 0 where i is the strategic choice of firm i and j is that of firm j. The benefit functions defined above depict changes in profits associated with choosing to invest abroad. We analyze how the benefit function is influenced by an increase in the share of firms that have invested abroad. Thus, we view our approach as the discrete-choice, N-firm analogue of the condition proposed by Bulow et al. Oligopolistic reaction obtains when FDI decisions are strategic complements, i.e. when ∂B ∂x > 0. "Reverse" oligopolistic reaction occurs if ∂B ∂x < 0.

Bulow et al. examine a duopoly where a shock occurs that directly affects the level of a strategic variable chosen by Firm 1. They show that when the strategy variables are complements, a positive shock to one firms choice of strategic variable will increase the equilibrium level of the other firms strategy variable. In our framework, we also have in mind the existence of shocks that influence the strategic variable-whether to relocate production abroad-of particular firms. Suppose there are sunk costs of relocation that vary across firms and time.

For example, information advances may reduce relocation costs and some firms may be better equipped to take advantage of these lower information costs. These changes will make it profitable for some firms to relocate, thereby increasing x. As x changes, the expected benefits of FDI for remaining firms will rise or fall depending on whether FDI decisions are strategic complements or substitutes.

Linear Cournot Segmented Markets Model

Throughout the analysis, we will assume that for i = h, f , inverse demand functions are given by

P i = a i -b i Q i .
If firms in the same location behave identically, we have:

Q i = xN q f i + (1 -x)N q hi ,
the first subscript denoting location of the firm while the second subscript denotes the country where the output is sold.

We allow for different unit costs of production c i between countries and for trade to be subject to a transport cost t. We also assume fixed production costs per plant equal to G and a sunk cost F of setting up a new plant. The profit function of a representative firm depends on whether it is located in country h or f :

π R = (P f -c f )q f f + (P h -c f -t)q f h -G -F, π S = (P f -c h -t)q hf + (P h -c h )q hh -G.
Firms are Cournot competitors in segmented markets as in [START_REF] Brander | A Reciprocal Dumping Model of International Trade[END_REF] or [START_REF] Horstmann | Endogenous Market Structures in International Trade (Natura Facit Saltum)[END_REF]. Equilibrium quantities to each market for a firm choosing strategy S are

q hh = a h -c h -N x(c h -c f -t) b h (N + 1) , ( 1
)
q hf = a f -c h -t -N x(c h -c f + t) b f (N + 1) . ( 2
)
Profits earned from this strategy are

π S = b h q 2 hh + b f q 2 hf -G. ( 3
)
Now consider strategy R. If a home firm were to move to the foreign country, it would increase the number of firms operating there by one. Equilibrium quantities shipped to each market by a firm producing in the foreign market are given by

q f h = a h -c f -t + [N (1 -x) -1](c h -c f -t) b h (N + 1) , ( 4
)
q f f = a f -c f + [N (1 -x) -1](c h -c f + t) b f (N + 1) . ( 5
)
Profits earned from this strategy are

π R = b h q 2 f h + b f q 2 f f -G -F. ( 6
)
We assume that outputs q hh , q hf , q f f , and q f h are positive for all distributions of firms, x, across the two countries. 2 This assumption allows us to take derivatives of profits with respect to x without running into corner conditions on outputs.

Having specified profits associated with strategies S and R in the case of cost certainty, we can determine the benefit function's, B 1 = π Rπ S , derivative with respect to the share of firms abroad, x. This calculation yields our first proposition:

Proposition 1 In the Cournot segmented markets model with no uncertainty, the decisions to invest abroad are strategic substitutes, i.e. these conditions yield reverse oligopolistic reaction.

Proof: The mathematical version of the definition of oligopolistic reaction given above involves taking the derivative of B with respect to x, ∂B ∂x = ∂π R ∂x -∂π S ∂x , and determining its sign.

The derivatives of the profit functions with respect to the locations of rivals are given by

∂π S ∂x = 2b h q hh ∂q hh ∂x + 2b f q hf ∂q hf ∂x , ( 7
) ∂π R ∂x = 2b h q f h ∂q f h ∂x + 2b f q f f ∂q f f ∂x . ( 8
)
Note that

∂q hh ∂x = ∂q f h ∂x = N (c f + t -c h ) b h (N + 1) , ( 9
)
∂q f f ∂x = ∂q hf ∂x = -N (c h + t -c f ) b f (N + 1) . ( 10
)
Subtracting ( 7) from ( 8) and substituting in ( 9) and ( 10) yields

∂π R ∂x - ∂π S ∂x = -2N N + 1 [(c f + t -c h )(q hh -q f h ) + (c h + t -c f )(q f f -q hf )] . ( 11
)
Substituting equilibrium quantities into equation ( 11), we have

∂B 1 ∂x = -2N 2 (N + 1) 2 (c f + t -c h ) 2 b h + (c h + t -c f ) 2 b f < 0 (12)
An increase in x (the proportion of firms producing in f ) makes the R strategy (relocate the plant to the foreign country) less profitable relative to the S strategy (maintain single home plant). This model therefore yields reverse oligopolistic reaction.

•

Proposition 1 shows that the strategic interdependencies associated with oligopoly actually reduce the likelihood that firms will follow their rivals' investment decisions. Knickerbocker's original story of oligopolistic reaction involved more than oligopolistic interactions. He also identified uncertainty about the competitive advantage to be gained from investing abroad as a motivating factor. We now extend the relocation model to incorporate such uncertainty. We do so by making the cost of production in the foreign country uncertain. We assume that c f is a country-specific random variable with mean cf and variance σ 2 . This assumption is the simplest way to capture the realistic idea that firms are able to predict costs at home without much difficulty but cannot accurately predict their costs in a foreign environment. It also makes the strong assumption that firms' costs in the foreign country are perfectly correlated with each other. The latter aspect of the model is designed to make a point with minimal algebra rather than to reflect reality. However, many types of uncertainty such as real exchange rate risk or the risk of political upheaval would cause costs of all foreign firms to shift in common way. We also assume that firms learn c f following the relocation decision but prior to setting outputs.

We may now calculate the expected profits associated with staying at home versus those of moving abroad. Applying expectations to equations ( 3) and ( 6) and exploiting the rule that

E[q 2 ij ] = V[q ij ] + (E[q ij ]) 2 ,
where E and V are the mean and variance operators, we obtain

E[π S ] = x 2 N 2 σ 2 (N + 1) 2 1 b h + 1 b f + πS (13)
11

Cahiers de la MSE -2000.49

E[π R ] = (1 -x) 2 N 2 σ 2 (N + 1) 2 1 b h + 1 b f + πR (14)
The new terms πS and πR are simply the original profit functions from equations ( 3) and ( 6)

with cf substituted in place of c f . Subtracting the expected profit of locating in country f from that of keeping one's plant in country h, we obtain the benefit (

B 2 = E[π R ] -E[π S ]
) to be gained by choosing country f as

B 2 = N 2 (1 -2x)σ 2 (N + 1) 2 1 b h + 1 b f + πR -πS . ( 15
)
Proposition 2 The introduction of cost uncertainty leads to more pronounced reverse oligopolistic reaction.

Proof: Differentiating with respect to x we obtain

∂B 2 ∂x = -2N 2 σ 2 (N + 1) 2 1 b h + 1 b f + ∂ πR ∂x - ∂ πS ∂x < 0. ( 16
)
The first term shows that the higher the share of one's rivals that are already affected by the random foreign cost, the lower the expected benefits a prospective mover obtains by also subjecting itself to the random foreign costs. The remaining part of the equation, ∂ πR ∂x -∂ πS ∂x is just the ∂B 1 ∂x defined in equation ( 12) with cf replacing c f . This result shows that, far from generating oligopolistic reaction, the introduction of cost uncertainty further reduces the incentive to follow a rival's move abroad. •

The intuition for this result comes from the convexity of the profit functions. Since profit is proportional to quantity squared, an increase in the variance in quantity (caused by increase in the variance of costs) will also increase the expected level of profits. This is because firms adjust quantity after they learn costs. If costs are high, they produce less and vice-versa when costs are low. In general, a firm increases the variance of its output by locating in the country with fewest firms. What we are concerned about, however, is how rivals' relocation abroad affects a home firm's incentive to relocate. When x increases, the foreign country has more plants and the home country has fewer plants. Thus the variance of output associated with producing in the foreign market falls and, correspondingly, the variance of home output rises. Hence, the benefit of following is reduced by the increase in x.

We have shown that oligopoly interactions combined with uncertainty generate reverse oligopolistic reaction. However, there is one more element of the Knickerbocker story-risk aversion-to which we now turn. We will employ a specific formulation of expected utility and utilize other assumptions that allow us to generate a closed form expression for how the benefits associated with relocation change with increases in x. This enables us to establish oligopolistic reaction, define the minimum degree of risk aversion that generates oligopolistic reaction, and

show how this minimum level of risk aversion is influenced by changes in key parameters.

We suppose that the decision makers in the firm maximize a concave utility function of their income in which profits from the MNE's activities constitute a substantial part of income. In that case, they will care about expected profit in a positive way but view increases in the variance of profits negatively. We consider the special case of negative exponential utility defined over a normally distributed monetary wealth, i.e. suppose that utility over profits can be expressed as

U = -exp(-λπ),
where λ is the coefficient of absolute risk aversion. If π were normally distributed then, expected utility (after a monotone transformation, see [START_REF] Varian | Oligopolistic Reaction and Foreign Direct Investment: The Case of the U.S. Tire and Textiles Industry[END_REF]) can be expressed as

EU = Eπ - λ 2 V(π).
We use this result to redefine B as the gain in expected utility (rather than expected profits) associated with moving relative to staying:

B 3 = E[U R ] -E[U S ] = E[π R ] -E[π S ] + λ 2 V[π S ] -V[π R ] (17)
Since we have already calculated the first part of this expression in equation ( 15), we now need only calculate the difference in the variance of profits between moving and staying. To express these variances in terms of x and σ 2 is not easy since profits are a quadratic function of foreign costs. Greene (1993) provides a useful approximation. For Y = f (X) the variance of Y is

approximately 3 equal to [f (E[X])] 2 V[X].
Application of this rule yields

V[π S ] ≈ 4x 2 N 2 (N + 1) 2 [q hh + qhf ] 2 σ 2 , (18) V[π R ] ≈ 4(1 -x) 2 N 2 (N + 1) 2 [q f h + qff ] 2 σ 2 . ( 19
)
In each case above, the qij correspond to the results of substituting cf for c f in equations ( 1),

(2), (4), and (5). Increases in the variance of foreign costs (σ 2 ) also increase the variance of profits. The difference in variances is given by

V[π S ] -V[π R ] ≈ 4N 2 σ 2 (N + 1) 2 [x(q hh + qhf )] 2 -[(1 -x)(q f h + qff )] 2 . ( 20
)
What is the effect of shifting rivals to the foreign country on this difference? If relocation of rivals lowers the variance of profits of production in the foreign market relative to that of the home production, then for a sufficiently large amount of risk aversion we will obtain strategic complementarity. However, the following expression shows that this derivative cannot be signed without further restrictions:

sign ∂(V[π S ] -V[π R ]) ∂x = sign xq 2 h + (1 -x)q 2 f + D(x 2 qh -(1 -x) 2 qf ) ,
where qi ≡ qih + qif . The first two terms in this derivative may be viewed as the "direct" effect of changing x while holding outputs constant. This effect is unambiguously positive and reveals that when rivals move abroad and outputs remain constant, the variability of profits is reduced for a firm located in the foreign market and increased for a firm located in the home market.

The third term considers the effect of a change in x on outputs of stayers and relocators. It employs term D, defined as

D ≡ N N + 1 (c f -c h ) 1 b h + 1 b f + t 1 b h - 1 b f .
This "indirect" effect cannot be signed. Furthermore, under certain extreme parameter values, the indirect effect may be a large enough negative number so that it fully offsets the direct effect. In that case, risk aversion does not generate OR. The circumstances under which this occurs involve differences between the two countries in the slopes of the demand curves (b h and b f ) and expected costs (c h and cf ). By eliminating such differences, we remove the indirect effect and retain only the unambiguous positive direct effect in order to identify situations where oligopolistic reaction can actually occur. Thus we proceed to add a parameter condition:

Similarity Condition: b h = b f = b and cf = c h = c.
This condition is sufficient to yield the main proposition of the paper.

Proposition 3 Oligopoly, uncertainty, and large amounts of risk aversion can combine to generate oligopolistic reaction in the Cournot segmented market model. Under the Similarity Con-dition, FDI decisions are strategic complements for a sufficiently high degree of risk aversion.

Proof:

We now can substitute equations ( 15) and ( 20) into equation ( 17) and take the derivative with respect to x, which yields

∂B 3 ∂x = ∂B 2 ∂x + 4λσ 2 N 2 (N + 1) 2 xq 2 h + (1 -x)q 2 f , ( 21
)
where ∂B 2 ∂x is negative as defined in equation ( 16). Oligopolistic reaction will obtain if the positive second term is large enough to dominate the negative first term (carried over from proposition 2). Thus, it will occur in this framework for sufficiently large values of λ. •

The proposition shows that under particular conditions, the relocation of rival production to the foreign market reduces the variability of profits of firms located in that market and increases the variability of profits of firms remaining in the home market. With the introduction of risk aversion, there is now a reason to dislike increased variation in profits. Thus, a sufficiently large degree of risk aversion will make the negative effect on utility of profit variation dominate the positive effect of profit variation on expected profits.

We are able to define the minimum amount of risk aversion necessary to generate oligopolistic reaction by setting equation ( 21) equal to zero:

λ min = b(N + 1) 2 (1 + t 2 /σ 2 ) (a h + a f -2c -t) 2 . ( 22
)
Equation ( 22) allows us to explore how the minimum level of λ required to generate oligopolistic reaction varies according to the exogenous model parameters. First, it is decreasing in σ 2

indicating that the level of risk aversion inducing firms to want to match rivals' moves falls when there is more uncertainty about costs in the foreign market. Second, λ is increasing in transportation costs, t. High transport costs makes foreign goods relatively uncompetitive with goods produced at home. Thus, when transport costs are high, firms are less concerned that different realizations of the random foreign cost variable will have a strong impact on profits at home. Hence, there is less incentive to match the moves of rivals. Finally, the expression shows that when the total number of firms (N ) increases, the parameter measuring the degree of risk aversion must also rise to yield the same incentive to invest. If managerial risk aversion is randomly distributed in the investor populations, these comparative statics indicate that oligopolistic reaction will be more likely when there is great variability in foreign costs and less likely in highly atomistic industries.

The results of two-stage games often depend on whether the firms' choices in the second stage of product market competition are strategic substitutes or complements. We have used

Cournot competition with linear demand where outputs are strategic substitutes. This raises the issue of whether our results would generalize to Bertrand competition with differentiated products in which prices are strategic complements. We applied [START_REF] Ottaviano | Agglomeration and Trade Revisited[END_REF] model of price competition with linear demands for differentiated products to our two-stage game of location choice followed by competition in segmented product markets. Our resultsavailable by request-are that all three propositions continue to hold in the Ottaviano-Thisse model. The intuition is that proximity of rivals is bad for profits in most imperfect competition models. As a result, even when product market choices are strategic complements, location choices are strategic substitutes unless the firm is quite risk averse. Interestingly, we found that the more differentiated the products made by each firm are, the less risk aversion is required to generate oligopolistic reaction.

The relationship between oligopolistic reaction and market structure was a focus of the empirical analysis of Knickerbocker. Oligopolistic reaction predicts the clustering of FDI. Consequently, he derived a measure of spatial and temporal clustering of FDI by industry. There are, of course, other sources of FDI clustering. Firms would choose the same locations if cer-tain countries were particularly attractive due to low costs or high demand. Positive spillovers between firms (agglomeration economies) would also generate concentration. To address the issue of distinguishing oligopolistic reaction from other sources of clustering, Knickerbocker related his measure of FDI concentration to industry Herfindahl indexes. His claim was that the more concentrated the industry, the more likely it would be to exhibit oligopolistic reaction. 4Knickerbocker discovered a positive but non-monotonic relationship between FDI and industry concentration. Specifically, he found that clustering increased with industry concentration except at extreme levels of concentration. "Tight" (highly concentrated) oligopolies were less likely to concentrate FDI than "loose" (less concentrated) oligopolies. He explains this finding as resulting from the collusive behaviour of tight oligopolies.5 Our model suggests a positive relationship between industry concentration and oligopolistic reaction. It does not, however, predict the non-monotonic relationship found by Knickerbocker.

Equilibrium Location Choice

Thus far, we have examined how a rival's FDI affects the expected benefit of relocating production abroad. In this section, we consider the Nash equilibrium in location choice. A share x * in country f is a Nash equilibrium if there is no incentive for a firm in either country to switch locations unilaterally. For large numbers of firms, interior equilibria occur where B(x * ) = 0.

However, we are interested in oligopoly situations and must adapt the equilibrium condition accordingly. For no firm in country h to want to relocate to country f it must be the case that B(x * ) ≤ 0. For no firm in country f to regret its relocation choice (and therefore wish to return to country h), we require B(x * -1/N ) ≥ 0. For a corner solution with all firms at home, i.e.

x * = 0, we drop the second condition and require only B(0) ≤ 0. Correspondingly, a corner solution with all firms abroad, x * = 1, requires only the second condition that B(1 -1/N ) ≥ 0.

Allowing for uncertainty and risk aversion while imposing the Similarity Condition, we solve for the difference in expected utility for a firm in h between staying in the home country and relocating to f and express it as

B 3 = 2N (N + 1) 2 b [N (σ 2 + t 2 )(1 -2x) + t(a f -a h -t)] - λσ 2 N (1 -2x)(a h + a f -2c -t) 2 (N + 1) 2 b -F. ( 23
)
We plot equation ( 23 The figure also indicates the types of equilibria that are possible in this four firm example.

For λ = 0, the unique equilibrium occurs at x * = 1/2 where it is evident that B(x * ) < 0 and B(x * -1/4) > 0. Thus, there will be two firms in each country. The intuition is that, under risk neutrality, firms have an incentive to operate in the less concentrated market, resulting in an equilibrium where each market is equally concentrated. This is consistent with the result in the location theory literature showing that spatial proximity of competitors reduces prices and profits (for a model with Cournot competition see Anderson andNeven (1990, 1991)).

As risk aversion increases, it will eventually be the case that B(1/4) < 0, resulting in a unique equilibrium of three firms at home and one abroad. Further increases in λ will generate

x * = 0 as the unique equilibrium and then cause the slope to switch from negative to positive.

Eventually, higher λs will make the slope steep enough to set B(3/4) ≥ 0, resulting in an equilibrium of x = 1. In this case, if a firm believed that its three rivals would choose country f , then it would want to do so as well. Thus, two different equilibria are possible. In the first, all firms remain at home while, in the second, all firms migrate to the foreign country. This is the most interesting parameter range since it predicts either a large cluster of FDI in the foreign country or none at all. Two otherwise equal countries might have very different levels of success in attracting investment. This is despite the fact that there are no agglomeration economies-the direct effect of clustering is still to lower expected profits.

How realistic are the values of λ required to generate OR? [START_REF] Kocherlakota | The Equity Premium: It's Still a Puzzle[END_REF] survey article on the equity premium puzzle discusses the plausible range for the coefficient of relative risk aversion (CRRA). He argues that there is a consensus that the CRRA should be less than 10 but that only values of 18 or more can explain why equities have historically earned a 6% premium over risk-free Treasury bills. In the mean-variance expected utility function we have used, λ is the coefficient of absolute risk aversion. We can obtain the implied CRRA by multiplying λ by profits. For the numerical example in the figure, OR obtains for a CRRA of about 10 and two equilibria (x = 0 and x * = 1) exist for a CRRA above 15. We also simulated the model using the utility function (1 -γ) -1 π 1-γ where γ is the CRRA. We calculate expected utility based on 10000 draws of c f . For 20 simulations, we find on average that γ ≥ 17 yields OR for all x and γ = 22 is the minimum value of the CRRA required for two equilibria. These values, while large, are in line with values required to explain the equity premium puzzle.

Conclusion

Knickerbocker's oligopolistic reaction hypothesis can be formalized in terms of FDI decisions being strategic complements, a concept that is clearly defined in the industrial organization literature. The idea that the principal elements of the Knickerbocker story-oligopoly, uncertainty, and risk aversion-can combine to generate follow-the-leader investment behaviour has intuitive appeal.

The Cournot, segmented market model we develop shows that the requirements for oligopolistic reaction are rather strict. The cases of certainty and uncertainty with risk neutrality generate the opposite result-the benefits of relocating a plant to a foreign location are reduced when rivals invest there first. Only when a large amount of risk aversion is introduced does oligopolistic reaction occur. Even with risk aversion, we show that parameter values in the model must be restricted to guarantee the result.

Our investigation of equilibrium patterns of location reveals that under reverse oligopolistic reaction, there will be a tendency for investments of rival firms to be dispersed across the two locations. Oligopolistic reaction, on the other hand, will tend to cause the clustering of all investment in one location or the other. On the surface, this suggests that observations of concentrations of FDI in particular locations lend empirical support for the Knickerbocker hypothesis. However, such a claim would require distinguishing clustering due to oligopolistic reaction from other sources of clustering such as agglomeration economies.

Appendix: Relocation vs. Additional Location

The analysis in the body of the paper focuses on the potential relocation of a single plant, thereby abstracting from the option of establishing a new plant while retaining production at the old plant. Here, we begin by determining the critical level of fixed production costs, G, around which establishing an additional location (strategy A) or the relocation of the home plant (strategy R) is optimal. We then proceed to show that our three propositions continue to hold when FDI is associated with strategy A rather than strategy R.

Strategy A only makes sense when t <| c hc f |. If this condition does not hold, a firm will only produce in the low cost location. Thus, we maintain this restriction throughout the analysis in this appendix which implies that a firm with plants in each country will serve each market with the local plant.

Under both strategy A and R, a firm will serve foreign consumers with goods produced in the foreign market. Thus, profits in the foreign market will be the same under either strategy. The choice between these alternatives, therefore, involves whether it is more profitable to serve home consumers with foreign production or maintain the home plant, thereby saving transport costs but incurring fixed costs of production both at home and abroad. The difference in profits is

π A -π R = (P h -c h )q hh -(P h -c f -t)q f h -G .
Suppose that xN firms already invested in country f and all kept their h plant active. This implies the following equation for the difference in profits:

π A -π R = (a h -c h ) 2 -[a h -c h -N (c h -c f + t)] 2 b h (N + 1) 2 -G
For the considered firm to prefer keeping its plant in h we therefore need sufficiently small fixed costs, precisely:

G < N (c h -c f + t)[2(a h -c h ) -N (c h -c f + t)] b h (N + 1) 2 . ( 24
)
The condition on fixed costs is independent of x, the proportion of firms that already chose strategy A. We therefore know that if this condition is met all firms will prefer an additional location to a relocation and conversely. The model developed in body of the paper considers fixed costs that are high enough to justify treating only the relocation case. We now proceed to show that if firms choose to keep their home plants, our propositions continue to hold. If inequality ( 24) is met, the firms will consider the choice between strategy S and strategy A. As mentioned above, the firms serve consumers in h with their most proximate producing unit, their plant in h. Assuming that plants of a same firm do not compete with each other, that markets are segmented and that marginal production costs are constant, the only variable profits relevant in the choice are therefore the profits made in country f .

B = π A -π S = (P f -c f )q f f -(P f -c h -t)q hf -(F + G)
Differentiating, we obtain the following negative slope for the certainty case:

∂B 1 ∂x = -2N 2 (N + 1) 2 (c h + t -c f ) 2 b f .
Thus, we have reverse oligopolistic reaction and Proposition 1 obtains. We must consider the timing of decisions when firms are uncertain about foreign production costs, c f . As shown by inequality (24), the choice between R and A depends on foreign costs, which are unknown until after the firm makes the investment decision. Thus, the decision is based on the expected value of c f . Having invested and learned foreign costs, a firm decides whether to shut its home plant down and then sets outputs. In what follows, we focus on cases where inequality (24) holds once foreign costs are known.

In the uncertainty case with risk neutrality, we obtain

∂B 2 ∂x = -2N 2 (N + 1) 2 σ 2 + (c h + t -c f ) 2 b f < 0,
and Proposition 2 holds.

For the risk aversion case, we can re-express the difference in variances as

V[π S ] -V[π A ] ≈ 4N 2 σ 2 (N + 1) 2 [xq hf ] 2 -[(1 -x)q f f ] 2
The derivative of the benefit function is now

∂B 3 ∂x = - 4N 2 (N + 1) 2 σ 2 + t 2 2b -λσ 2 xq 2 hf + (1 -x)q 2 f f + tN b(N + 1) [x 2 qhf + (1 -x) 2 qff .
We will thus obtain oligopolistic reaction in this A framework for sufficiently large values of λ, namely:

λ > b(N + 1) 2 (1 + t 2 /σ 2 ) 2[6(N tx) 2 -6tN (a f -c h + t(N -1))x + (a f -c h + t(N -1))(a fc h + t(2N -1))] .

Thus, we have shown that the choice of strategy A or R depends on the level of fixed production costs G. Regardless of which strategy is adopted by firms, reverse oligopolistic reaction obtains in the case of certainty as well as the case of uncertainty with risk neutrality. A critical level of risk aversion is necessary to obtain oligopolistic reaction.

Figure

  Figure 1: Choice Structure

  ) for different levels of λ, the risk aversion parameter in figure2. This plot sets N = 4, a h = a f = b = 1, c = .25, t = .1, F = 0, and σ = .025. The values of λ chosen in the plot are those where the equilibrium pattern of firms location change given the parameters values stated above. In the case of risk neutrality, λ = 0, the slope is negative indicating that FDI decisions are strategic substitutes.

Figure 2

 2 Figure2illustrates the effects of increases in risk aversion on both the magnitude and sign

Figure

  Figure 2: Risk Aversion and Oligopolistic Reaction

[START_REF] Kogut | Technological Capabilities and Japanese Direct Investment in the United States[END_REF] report that studies of U.S. investment in Canada yield similar findings on the influence of the degree of concentration.

Cahiers de laMSE -2000.49

The fact that all quantities are positive requires some conditions on the values that the parameters of the model can take. These conditions will always be assumed to be fulfilled during the paper and all numerical examples respect these conditions.

This formula is derived from a linear Taylor series expansion where the expansion point is the average value of the uncertain variable, here cf . Using simulations (available upon request), we found the approximation of the variance to be accurate within 2%.

In fact, this test does not discriminate against FDI clustering due to other reasons.[START_REF] Head | Market Size Effects and Agglomeration[END_REF] show that clustering increases with industry concentration in a Cournot model with complete information and asymmetric demand. This model does not contain the risk aversion which we have shown is required to generate oligopolistic reaction but yields the relationship between FDI clustering and industry concentration that Knickerbocker argues identifies OR behaviour.

This explanation is, however, not easy to justify theoretically. As we have seen in our model and as is widely accepted in location theory, avoidance of cutthroat price competition is a major explanation for spatial dispersion of firms. The clustering of firms raises the incentives to undercut the competitor and makes competition fiercer through lower prices. If firms are colluding, they are able to maintain high prices despite spatial proximity using trigger strategies. Thus, as opposed to Knickerbocker's argument, colluding firms should exhibit more concentration than non-colluding firms. This has been shown by[START_REF] Friedman | Partial Collusion Fosters Minimum Product Differentiation[END_REF] who reverse the usual maximal dispersion result of price competing firms by allowing them to collude in the price subgame.


Matthieu Crozet
email: crozet@univ-paris1.fr

Thierry Mayer
email: tmayer@univ-paris1.fr

Jean-Louis Mucchielli

How do Firms Agglomerate? A Study of FDI in France

Keywords: JEL classification: F23, R3, R58 Industrial location, conditional logit, FDI, regional policy

This paper studies the determinants of location choice by foreign investors in France. A new sample of almost 4000 location choices over 10 years and 92 administrative locations is used to measure two important issues: To what extent do foreign investors cluster spatially and are the decision makers sensitive to investment incentives? Concerning the agglomeration effects, we find very strong evidence of positive spillovers between firms and identify the countries of origin and the industries for which those spillovers are the most substantial. Concerning promotion policies, we find very little evidence of any positive impact of either the national or European regional policy on location choices. Finally, we identify for some European countries a "learning process" of foreign direct investment, the location decisions gradually becoming more remote from the country of origin during the period we study.

Introduction

Promotion policies are largely used by local, national or European authorities in order to try and influence the location of economic activity in favor of lagging regions. Public authorities are particularly anxious to attract foreign investors often thought to be source of productivity increases by local firms in addition to creating new jobs. Related to these practices, is the now well documented finding that firms cluster in space (see Henderson and Kuncoro,1996 ;[START_REF] Ferrer | Patterns and Determinants of Location Decisions by French Multinationals in European Regions[END_REF][START_REF] Devereux | Taxes and the Location of Production : Evidence from a Panel of US Multinationals[END_REF][START_REF] Mayer | La localisation à l'étranger des entreprises multinationales : une approche d'économie géographique hiérarchisée appliquée aux entreprises japonaises en Europe[END_REF][START_REF] Head | Agglomeration Benefits and Location Choice : Evidence from Japanese Manufacturing Investment in the United States[END_REF][START_REF] Rauch | Networks versus Markets in International Trade[END_REF], for recent results on that topic). The decision makers implementing promotion and regional policies often have this idea in mind that being successful in attracting a first critical set of firms will generate a virtuous mechanism of self-reinforcing agglomeration of firms in the territory targeted. This paper analyzes location choices of foreign investors in France. It is particularly focused on the measurement of agglomeration effects -the positive influence of a firm's location choice on the probability that the subsequent firms make the same choice-and the identification of the effect of promotion policies used by local authorities to attract firms.

The existing empirical literature on agglomeration effects has mainly consisted of national level studies [START_REF] Wheeler | International Investment Location Decisions[END_REF]Mody, 1992, Devereux and[START_REF] Devereux | Taxes and the Location of Production : Evidence from a Panel of US Multinationals[END_REF] or choices of states in the USA [START_REF] Carlton | The Location and Employment Choices of New Firms : an Econometric Model with Discrete and Continuous Endogenous Variables[END_REF][START_REF] Friedman | What Attracts Foreign Multinational Corporations[END_REF][START_REF] Head | Agglomeration Benefits and Location Choice : Evidence from Japanese Manufacturing Investment in the United States[END_REF][START_REF] Rauch | Networks versus Markets in International Trade[END_REF]. The preceding work on location choices in Europe at a lower geographical level than countries has considered choices of regions by foreign investors on the European territory [START_REF] Ferrer | Patterns and Determinants of Location Decisions by French Multinationals in European Regions[END_REF]. [START_REF] Mayer | La localisation à l'étranger des entreprises multinationales : une approche d'économie géographique hiérarchisée appliquée aux entreprises japonaises en Europe[END_REF] considered in an integrated way the national and regional choices of Japanese investors in Europe. Some papers considered location problems at a very thin geographical level for Brazil [START_REF] Hansen | Industrial Location Choice in Sao Paulo, Brazil, a Nested Logit Model[END_REF], China [START_REF] Head | Inter-city Competition for Foreign Investment : Static and Dynamic effects of China's Incentive Areas[END_REF] or Indonesia [START_REF] Henderson | Industrial Centralisation in Indonesia[END_REF].

However, nobody has yet to our knowledge studied the determinants of location choice at a 2 Cahiers de la MSE -2000.50 very detailed level for a European country that would be a major receiver of FDI (see however [START_REF] Guimarães | Agglomeration and the Location of Foreign Direct Investment in Portugal[END_REF] for a very thin analysis of location choice of FDI within Portugal). This paper is the first to consider individual firms' decisions for over 90 territorial units in France.

One of our objectives is to study in more detail the characteristics of agglomeration effects.

Due to a very large dataset, we are in particular able to differentiate the determinants of location depending on the country of origin of the investor and the industry of the plant located in France.

Our results give insights for the following questions that are likely be important for the policy maker: Does the nationality of the firms matter for agglomeration effects? Do firms cluster more with other firms from the same country? Do firms show a preference for regions within France that are near to their home market? Do all industries exhibit the same pattern of geographic concentration? We show that the nationality of the investor is of crucial importance in location patterns. There are certain countries sharing a border with France for which investors show a very strong tendency to locate near their country of origin. However this tendency is declining over time which suggests some learning process in the difficulty of operating a plant abroad.

We also observe very different behaviours depending on industries. Concerning agglomeration effects, it is shown that firms cluster with their competitors but that this behaviour depends on the nationality of both the competitors and the investor.

We then analyze the effect of both French and European regional policies on location choice.

We show that foreign investors are, to a large extent, not sensitive to investment incentives. Even when promotion policies appear to have a statistically significant positive effect, the magnitude of this effects is very low compared to other determinants.

The remainder of the paper is as follows: Section 2 presents the theoretical determinants of location choice using a very simple oligopolistic competition model that yields an estimable equation for the location choice of firms. Section 3 describes the econometric model and the data used. Section 4 presents results on general and industry level location patterns, focusing 3 Cahiers de la MSE -2000.50 on agglomeration effects. Section 5 presents results on the impact of promotion policies and section 6 concludes.

Theoretical foundations

Location choice determinants can be broadly classified in four large groups: Demand that can be expected on the chosen location, factor costs that would be faced, the number of "local" and foreign firms active in that same location and public policies designed to attract firms.

The sign expected on the two first variables is very widely accepted to be respectively positive and negative. The influence of the number of firms is more complicated and results from a trade off between agglomeration and dispersion forces. On the one hand, location theory generally finds that geographic distance isolates firms from competition. A rise in the number of firms in a given location shifts prices down in that location and therefore decreases incentives to locate there. On the other hand, positive externalities between firms can emerge from technological spillovers or other mechanisms recently celebrated by the economic geography literature [START_REF] Krugman | Geography and Trade[END_REF][START_REF] Venables | Equilibrium Locations of Vertically Linked Industries[END_REF]. These forces contribute to the geographical clustering of firms and the sign of this determinant will therefore depend on the relative strength of the two forces.

Investment promotion policies can take various forms: job creation subsidy, temporary exemption from local taxes, low levels of corporate taxation... Everything else equal, firms should be positively influenced by this determinant in their choice.

All those determinants can be synthetized in a very simple formal framework yielding an estimable equation describing the profitability of choosing a particular location. Suppose firms use quantity as their strategic variable and let demand take a generalized Cobb Douglas form where price and income elasticities can differ from 1:

4 Cahiers de la MSE -2000.50 Q = αm γ p β .
(1) α is the share of income spent on the particular good considered, m is income (exogenous here) of consumers, β is price elasticity and γ income elasticity. Q is total quantity demanded at price p, this demand being satisfied by locally producing firms 1 . Suppose that firms have identical production costs when producing in the same location, ensuring the individual quantities will be equal in equilibrium: Q = Nq, N being the number of active firms on the market.

After tax profits of a representative firm willing to produce and sell at this location is:

π = (1 -t)(p -c)q, ( 2
)
where t is the corporate tax rate (representing promotion policies in a large sense) and c is a unit production cost function. First order condition for profit maximization is:

p 1 - q βQ -c = 0.
Using (1) and adding first order conditions over the N firms, we obtain the following expression for total equilibrium quantity:

Q = Nq = αm γ N β Nβ -1 cβ β ,
which gives equilibrium price: p = Nβ Nβ-1 c. Substituting q and p in the profit function, we obtain the following expression:

1 This assumption is of course not realistic as firms in each location usually serve consumers in several locations. It is however only made for analytical clarity and our demand variable will take into account the fact that firms serve several locations.

5

Cahiers de la MSE -2000.50

π = (1 -t) αm γ N (β+1) β Nβ -1 c 1-β
Supposing that price elasticity is superior to 1 (β > 1), profit is a decreasing function of corporate tax rate, production costs and number of active firms, that is competition intensity (a traditional effect in location theory, see d [START_REF] Aspremont | On Hotelling's Stability in Competition[END_REF]. Profit is also an increasing function of consumers' expenditure, i.e. of market size.

Let us specify a bit more the unit cost function such that unit cost is a function of ongoing wage (w) and includes a positive externality related to the number of firms2 :

c = w θw N -θ N , θ w > 0, θ N > 0.
The influence of the number of firms is then ambiguous. Suppose the number of firms is such that Nβ constitutes a reasonably good approximation of Nβ -1. The profit function can then be written as: β+1) .

π = (1 -t)αm γ (w θw ) 1-β N (-θ N -1)(1-β)-(
(3) Equation ( 3) is log-linear and gives us the theoretical foundations of our empirical estimation of location determinants. The signs of the first three variables are still clearly determined, but the sign of the count of firms variable is now depending on the importance of the externality parameter relative to the negative impact of competition.

3 Implementation of the location choice model There is a set I = (i, j, ...n) of possible location sites and the location i offers a profit π i to investors according to a set of variables U i = [ln X i1 , ......, ln X ik ], X i = [X i1 , ......, X ik ] being the vector of observable characteristics of location i.

π i = bU i + i
Where b is the vector of unknown coefficients to be estimated and i is the unobservable advantage of location i. All characteristics vary among locations, some fluctuate among industries as well but they are constant across firms. It is assumed that an investor chooses location i if it yields higher profits than any other possible choice. The probability of choosing i is thus :

Prob(π i > π j ) = Prob( j < i + U i -U j ) ∀j = i.
This probability of choosing location i was shown to take the following form [START_REF] Mcfadden | Econometric Analysis of Qualitative Response Models[END_REF] under a type I extreme value distribution of the error term:

P i = e bU i n j=1 e bU j .
Using this formula for the probability of investing in each location, the coefficient on each variable is then estimated by maximum likelihood. The expected signs and magnitudes of those coefficients are dictated by equation (3).

The data

The dependent variable

We consider location decisions by foreign investors in France. The left hand side variable needed is the location choice of each investor over all the 92 French départments 3 with its nationality, date of investment and industry. The main database (IEF) comes from the Direction du Trésor and was constructed based on the (now softened) legal obligation for foreign firms to ask for an administrative authorization to invest in France. This database reports many information on foreign affiliates operating in France including date and town of investment, employment, the different shareholders, their nationality and respective shares... We use the 1996 version of the database and consider investments from 1985 to 1995 mainly because of data limitations on the right hand side variables. We consider only firms for which the industry reported is manufacturing. We sum up the shares of foreign investors by country of origin and then keep only the firms for which the largest share is held by a foreign country and for which this share is at least 10%. We attribute the firm to the first country of ownership when several countries have shares in a given firm.

The main problem of this database is that only the location of the headquarters is reported.

However using the identification number of the firm, it is possible to track the producing units belonging to the firm and then get its precise location using a different database made available by the Ministry of Industry. The procedure has therefore been the following : take all investments with their dates in IEF and keep all producing units that belonged to a firm in IEF and were "born" the same year or after the date reported in IEF. The date of creation of the plant is inferred by looking at the first year where that establishment was reported by the French Ministry of industry. This gives us our sample of location choices which consists of a close to exhaustive list of producing units owned by foreign companies in France and established during that period. The sample contains 3902 observations over 206 industries.

Agglomeration variables

The agglomeration variables consist of cumulated counts of firms based on that sample. The calculation follows [START_REF] Head | Agglomeration Benefits and Location Choice : Evidence from Japanese Manufacturing Investment in the United States[END_REF] and consists of the count of firms belonging to the same industry (but not belonging to the same parent company) that were located in each département a year before the considered investment.

We here introduce new dimensions in the measurement of agglomeration effects. We first try to identify the "nationality" of the agglomerative force. We try to answer the following question: Does a firm exhibit a tendency to cluster equally with other firms from the same origin country, other non-French firms and/or French firms? There will therefore be three agglomeration variables: NH, NO and NF accounting respectively for the effect of the presence of same home country firms, other foreign firms and French firms. The sign and magnitude of each coefficient on those variables is dependent on the relative strengths of the competition effect and positive externalities exposed in the theory section. The comparison of coefficients on those variables will enable us to draw insights on the possibly different effects depending on different nationalities of the investors.

Second, we are able, due to the large size of the sample to differentiate between country of origin and industry in the location behavior of multinational firms. This is of course of primary importance for policy issues as it will appear that there is a large amount of heterogeneity calling for different measures by public authorities if they intend to attract FDI and conduct regional policies.

Demand variable

Unlike most of the empirical literature on location choice4 , the demand variable taken here is not local GDP. The French départements are of relatively little size and it seems clear that foreign investors target consumers far beyond the frontier of the département they choose to locate in. However, transport costs make distant consumers more difficult to reach and we must take this difficulty of access into account. We do so by using a variable inspired by the concept of market potential introduced by [START_REF] Harris | The Market as a Factor in the Localization of Industry in the United States[END_REF]:

MARK i = GDP i + j =i GDP j d ij .
Our demand variable, labeled MARK, therefore takes into account local GDP of the chosen location and adds the GDPs of all other locations weighted by their distance to the chosen location.

The source of the GDP data is REGIO, the Eurostat regional database that allocates French GDP between French départements. The distance variable consists of real road distances (fastest trip between the respective centers of the two départements) that have been collected using an electronic road atlas. MARK is of course only a proxy for the real demand perceived by firms. It is very difficult here to obtain data that could allow for more sophisticated demand variable at this geographical level. We believe that this proxy is however reasonable for a large proportion of the industries in the sample and the results seem to confirm this belief.

Labour costs variable

We were able to calculate a very precise wage per capita variable at the département and 4digit industry level. Using data on producing units operating in each département5 , we include the average wage per capita of the industry, département and year relevant for the investment considered. The variable is labeled W.

Distance to home country variable

As shown below, the location choices of FDI are also influenced by proximity with the investor's home market. We take into account this tendency of foreign firms to invest in locations near their country through a distance variable labeled DIS (the great circle distance between the economic center of the investing firm's country of origin and the center of each département available as a location).

Grants variables

The main instrument of regional policy available to the French government is called the Prime d'Aménagement du Territoire (PAT) and consists of labor related grants for creating or maintaining jobs in lagging regions. Both French and foreign investments are eligible for these grants and about half the annual funding goes to foreign investors. We estimate the influence of this policy instrument on location choice by introducing a variable called PAT which takes into account the funds granted to each region for the year of the considered investment.

Some French regions are also eligible to the European Commission regional policy involving grants that are sometimes used to attract FDI but most of the time consists of attempts to improve the economic environment with an expected indirect effect on attractiveness.

There are three main Objectives under which the Commission grants structural funds to European Regions. Objective 1 is aimed at promoting development and structural adjustments in regions that are lagging behind (defined as those with GDP per head below 75% of the Union average). No French region considered in this paper is in this case, due to the fact that we do not consider Corsica as part of the choice set. Objective 2 is aimed at promoting the conversion of areas affected by industrial decline. Objective 5b is aimed at rural areas affected by problems linked to the decline of agriculture. There are numerous French regions receiving grants under those two objectives, the two main receivers being Nord-Pas-de-Calais and Lorraine. We also include the "community initiatives" funds. The corresponding variables are the grants given to each region under each relevant objective, respectively : OBJ2, OBJ5B, HOBJ.

Results

Spatial patterns of investment

Figures 1 and2 show the spatial distribution of foreign affiliates in France for investors originating from other European countries (all affiliates in the département being attributed to the central city for this graph). It is readily apparent that the region around Paris has been a major recipient of investments for FDI from all origin countries. It is also striking that some investors have a preference for locations in France that are near the border with their origin country. This is particularly apparent for FDI originating from Belgium, The Netherlands, Germany and Switzerland. Similarities in culture, language, tastes, distribution networks... might therefore be an important determinant of location choices by investors originating from a country that has a common border with France. This behaviour is to be compared with other econometric relationships uncovered in international trade and FDI studies exhibiting a positive impact of cultural similarity on goods or factors flows. Concerning trade flows for instance, it is well known that a common language constitutes a powerful motivation for bilateral trade. It has furthermore been recently showed by [START_REF] Rauch | Networks versus Markets in International Trade[END_REF] that colonial ties had a strong positive effect on trade. Head and Ries (1998) also found a positive impact of migrants from the partner country on bilateral trade.

This pattern suggests that regions in France that share a border with the country of origin of the investor offer important advantages in the trade off between the costs of operating abroad and the access to French consumers: Whereas those locations might not offer an ideal access to the rest of French consumers, they present a whole set of features that are common with the country of origin of the investor and can therefore diminish the cost of operating abroad.

Results by country of origin

We now proceed to the estimation of the determinants of location choice of foreign investors in

France by country of origin. Tables 1 and2 present the results for the 8 main investing countries in France, that is the United States (21.3%), Germany (16.2%), the Netherlands (12.5%), Italy (10.9%), the United Kingdom (10.4%), Switzerland (9.3%), Belgium (6.4%), and Japan (2.1%).

The global regression shows, as expected, a positive influence of the market potential and a negative influence of wages. We also get a positive effect of competitors presence. This shows that agglomeration forces dominate dispersion forces on average, this finding being an indicator of spillovers that might exist between firms. It is noteworthy that the agglomeration with French firms is much higher than agglomeration with other foreign firms either of the same or a different country of origin. This might indicate that competition faced by a foreign investor in France is fiercer with other foreign firms than with French firms. This might also be the sign that the technological spillovers passing through informal communication or inter-firm mobility of qualified workers is substantially easier with French firms. Another interpretation of that result can be made in term of informational externalities (see [START_REF] Banerjee | A Simple Model of Herd Behaviour[END_REF][START_REF] De Coster | Spurious Agglomeration[END_REF][START_REF] De Coster | Spurious Agglomeration[END_REF], for theoretical models). Supposing that French firm have a better information than foreign companies on the "true" compared attractiveness of French départements, the location of French firms would therefore convey more information than the location of foreign affiliates for the prospective investor. As a consequence, foreign investors would be more willing to replicate French firms' choices than choices made by other multinational companies that might not have any better information than them.

The results show however a substantial variability depending on the country of origin of the firm. Some countries like Italy or the Netherlands show very low agglomeration effects compared to the rest of the sample. Those two countries, as Belgium, are also much more sensitive to the level of labor costs in their location choices. The American investors seem to search very productive workers despite their higher cost as shown by the positive coefficient on wages. Together with Swiss investors, they also show a less than average tendency to locate near final demand perhaps denoting the fact that the products sold are less tied to local demand than others.

This very large dataset enables to uncover important differences in firms' behaviour in terms of clustering behaviour. While on average firms tend to moderately follow the choices of competitors from the same country, there are large differences depending on the nationality of the investor. English firms for instance tend to follow English competitors as strongly as firms from the Netherlands tend to avoid other firms from the Netherlands. This is one of the first study where such heterogeneity, informative of relative strength of competition and agglomeration effects, is identified. It is also noteworthy that the coefficient on this variable, while it can be of either sign in theory, had never to our knowledge been significantly negative before this paper.

Finally, we observe in the regressions the impact of distance already seen in figures 1 and 2 for certain countries. The negative effect of distance from the country of origin is specially strong for Germany, Belgium and Switzerland and negative while insignificant for the Netherlands. We know focus for a moment on this determinant and its evolution over time.

The learning process of foreign investment

A possible explanation of the negative sign of distance from the origin country on location choice is that proximate départements share common characteristics with the origin country that make them particularly favorable sites for location6 . Behind the fact that some investors show a preference for regions in France contiguous with their home market might be a trade off between access to French consumers and ease of operation. The disadvantage faced by foreign affiliates with respect to local firms due to their lower knowledge of the characteristics of the local market is one of the oldest ideas in the theory of FDI (see [START_REF] Hirsch | An International Trade and Investment Theory of the Firm[END_REF] for instance). It is likely that locations in France near the German border share a sufficient amount of common "cultural" characteristics with Germany so that the cost of operating there (relative to local firms) is lower, ceteris paribus, than the cost of operating in more western locations in France.

The existence of transport costs however do not make those locations ideal basing points to serve the majority of French consumers. The trade off could then work as follows: Supposing that firms gradually learn the characteristics of the French market once they have an affiliate anywhere in France, the first waves of investment could then be concentrated near the German border in order to lower the disadvantage of being a foreign affiliate. The next waves could gradually move West in order to improve the access to consumers because firms have learned some of the characteristics of this market, reducing thereby their initial disadvantage.

Support for this intuition can then be found by looking at the evolution of the coefficient on distance and market potential. We expect a rise in both, the first becoming less negative with time and the second more positive. If following your rivals also participate in reducing your information gathering costs about the characteristics of the French market, we should then also expect a fall of the coefficient on NH.

Figure 3: The evolution of coefficients over time Figure 3 plots the three coefficients mentioned over the period of our sample and confirms the expected evolution for all three variables7 . The negative effect of distance is sharply declining over time, with a simultaneous increase of the coefficient on the market potential variable.

The coefficient on distance starts at -1.08 and ends at -0.35: At the beginning of the sample, decreasing distance by 50% from the country of origin increases the probability of receiving an investment by roughly 50%, only about 17% at the end. We interpret this as evidence of some learning process of foreign investors gradually moving from "familiar" locations near the country of origin to more central locations in France, where access to consumers is better. It is also to be noted that the coefficient on same country of origin competitors is shifting from a clustering behaviour to an avoiding behaviour (the coefficient is significantly negative at the end of the period)

Results by industry

We now proceed to regressions at the industry level to see which industries exhibit the most significant agglomeration effects and thus potentially constitute the most interesting targets for promotion policies as an initial advantage in the attraction of those industries could then result in self reinforcing agglomeration in the départements taking a good start. Due to the very large sample used we are able to conduct the analysis at the 4-digit level guaranteeing a very precise assessment of the industries that are more subject to agglomeration economies.

Tables 7 and8 in the appendix rank industries using the average value of the 3 agglomeration variables coefficients. Table 7 lists industries for which all three agglomeration variables have significant positive signs and table 8 lists the other industries. There are 76 industries for which estimation of all variables is possible. Of these, 8 have all three agglomeration variables significantly positive.

We see that industries often mentioned as characterized by strong positive spillovers appear in the first group of industries where we find very significant agglomeration effects. Computers is of course one of those as office machinery for which the coefficients are extremely large8 , a 10% increase in the number of firms in a département roughly increasing probability of investing there by 40%, for this industry.

Another interesting result is the fact that in the clothing industry, often referred to as characteristic of a low-skill labor intensive industry, the investors are very sensitive to wage differentials and much less to agglomeration economies (there is even a significant repulsion effect of other origins foreign investors in women's apparel). On the other hand, the industries with significant agglomeration effects do not seem to be sensitive to the level of labor costs.

We are therefore able to confirm here differences in the location decisions of investors across industries that were previously largely hypothesized in the literature without being rigorously tested due to lack of data. We found in particular that industries that where often thought to be characterized by strong agglomeration economies more than labor costs considerations (like computers, machine tools or car parts) indeed show this tendency. Conversely, low skill industries like clothing are not very sensitive to agglomeration economies but seem to favor costs differentials. Also, industries that are closely spatially tied to final consumption like magazine or newspaper editing show an overwhelming tendency to follow the spatial distribution of consumers rather than the spatial distribution of competitors.

The influence of promotion policies on location choice

The impact of the European Commission regional policy

In this section, we estimate the influence of Structural funds granted to French Regions by the European Commission. The data made publicly available by the Commission is surprisingly scarce. However we have the grants by Objective and region in France for the years 1989,1990 and 1991 which were the years where FDI in France was at its peak. We are therefore able to estimate the influence of those grants on location decisions of foreign investors for those three years because the number of observations remains substantial.

It appears in tables 3 and 4 that very few coefficients on the different grants of the Euro- pean Commission are significantly positive. Furthermore, when the impact of those grants is significantly positive, the size of the effect is lower than all other determinants by an order of magnitude. This means that, even in the few cases where some results of such policies are to be expected, they will be very largely outweighted by agglomeration or market potential considerations. Worse, the only significant coefficient that appears to be non negligible is a negative one for Japanese investors. This result is not the first to find little or even negative effect of European grants on attractiveness (see [START_REF] Ferrer | Patterns and Determinants of Location Decisions by French Multinationals in European Regions[END_REF]. This does not mean that those policies are inefficient generally speaking, but it casts doubts on the idea that the regional policy of the European Commission can actually influence or even reverse the "natural" location patterns of economic activity in Europe.

There is a problem with the evaluation of the influence of those funds which is often mentioned to explain the apparent poor and even sometimes negative influence of those grants.

The regional policies are designed to help the catching up of lagging regions or compensate a fall in their employment due to a structural crisis in the industries in which those regions are specialized. The fact that a region was not successful at attracting FDI is often a cause for its economic problems and the consequence of this can be a negative coefficient on the grant variable observed by the researcher. Our econometric implementation taking into account fundamental characteristics of regions, the market potential and wage variables should capture these structural issues and avoid any potential reverse causality problem when estimating the effect of grants on foreign investors.

We however evaluate the robustness of this apparent inefficiency of European grants on regional attractiveness by assessing the influence of past regional policy on present location choices. With some time, the funds might have improved the attractiveness of the region and the investors in subsequent years might be less repelled by this region. We therefore estimate the impact of the cumulated funds received by French regions between 1989 and 1991 on the choices between 1992 and 1995 and compare the coefficients with the preceding regression 9 . In order to save space, we do not include the results table here 10 but the results are strikingly similar. No coefficient is significantly positive and all significant coefficients are negative. All estimates of the impact of regional European grants are furthermore of very low magnitude.

We can therefore safely conclude that, if the European grants in French regions have had any impact on the location of FDI, this impact was very slightly negative for some origin countries.

In general there is simply no identified relationship between the amount given to a region by the European Commission and the probability that foreign investors choose to locate an affiliate in a département belonging to that region.

The impact of French regional policy

We now turn to the analysis of the impact of French regional policy on location choices by foreign investors. One can justify the extremely small consequences of European grants on FDI flows, saying they have for objective to promote the regional development and attractiveness but not to affect directly location choices. On the contrary, the PAT is explicitly a direct regional policy in favor of foreign investments. However, we see in the tables 5 and 6 that the impact of French regional policy (at least the PAT) is far from being as influential on location choices as 9 Such a test is only relevant if one supposes that past grants do not directly improve the current regional market potential, nor increase the wage and the number of local firms. We regressed these variables on the amount of grants received during the preceding period. We found no influence on the number of local firms and a very small negative impact on market potential and wage.

10 They are available upon request. the policy makers would like it to be. The global effect is significantly positive but again the magnitude of the effect is the lowest of all determinants. The only three countries for which we find a positive impact are The Netherlands, Germany and Italy. Even for those countries, the effect of grants on location choice is very marginal when compared to other determinants.

The Italian case is very interesting as it appears that investors from this country are very sensitive to monetary incentives compared to other investors. Indeed the positive effect of the grants is highly significant and the largest of all countries. Furthermore, Italian firms proves to be also among the most highly sensitive to wage differentials and show very little tendency to agglomerate relative to other nationalities. German and Dutch investors also show a much smaller tendency to cluster than the rest of the sample (even showing significant dispersion in the NH coefficient). Combined with the fact that those three countries are the ones which seems to be attracted by investment incentives, our study leaves therefore very little prospective for an efficient attractiveness policy. Indeed the investors that are sensitive to these measures, are only slightly so and do not cluster, hence the benefits of the grants to the region are likely to be very small. Succeeding in attracting initial investments from those countries is not sufficient to generate a self-reinforcing agglomeration of firms from those countries.

Conclusion

We assess in this paper the determinants of location choice of foreign investors in France. We focus in particular on the existence and magnitude of agglomeration economies and identify the countries of origin and industries for which positive spillovers suggested by the observed clustering between firms are the more pronounced. It appears that computers, car parts, machine tools and office machinery are instances of sectors characterized by the strongest agglomeration effects. A 10% increase in the number of competitors in a location can raise by up to 40% the average probability of investing in that location. On the other hand, firms originating from countries like Italy or the Netherlands and from industries like clothing are much less subject to clustering and more sensitive to the level of wages in their location patterns.

We also uncovered general patterns of FDI location that had not been, to our knowledge, the subject of rigorous empirical investigation. Among these, the location behaviour of foreign firms in France over time seems to suggest that a learning process is taking place in location choices over time: Firms tend to choose locations in France that are near their home market over the whole period, particularly when the investor is from Germany, Belgium, Switzerland and the Netherlands. However, this pattern gradually fades out over the period as the impact We provide here the complete list of industry level results. Tables 7 and8 list the coefficient on each variable or the 76 industries where estimation was possible.

Appendix: Location choice determinants by industry

32

Cahiers de la MSE -2000.50

Figure 1 :

 1 Figure 1: Patterns of foreign affiliates in France: FDI from Belgium, Germany and the Netherlands

3.1 The econometric model

	The economic decision studied in theoretical location models is by nature a discrete choice among
	several alternatives made by individual firms. Turning to empirical matters, the econometric
	model should therefore ideally have these features too. For this reason, models with a qualitative
	endogenous variable and particularly conditional logit models have been widely used in the
	preceding empirical work on industrial location.
	This model assumes that firms maximize a profit function subject to uncertainty when
	choosing a location. The deterministic component of the profit function consists of the various
	attributes of locations that can influence the profitability of building a plant in a particular
	location (equation 3). The random component consists of maximization errors, unobserved
	characteristics of choices or measurement errors. While the real underlying profit yielded by
	alternative locations cannot be observed, what is observed is the actual choice of each firm and
	the characteristics of the alternative locations.

Table 1 :

 1 Location choice of foreign investors in France.

	Dependent Variable: Location choice

Note: Standard errors in parentheses with * * * , * * and * respectively denoting significance at the 1%, 5% and 10% level.

Table 2 :

 2 Location choice of foreign investors in France.

		Dep. Var: Location choice
	Model :	USA	Japan	Switzerland
	ln Nb. of same	0.12	1.33 *	-0.27
	home country firms (NH) (0.10)	(0.70)	(0.19)
	ln Nb. of other	0.28 * * *	0.38	0.81 * * *
	foreign firms (NO)	(0.08)	(0.26)	(0.11)
	ln Nb. of French	1.18 * * * 1.50 * * *	1.07 * * *
	firms (NF)	(0.05)	(0.19)	(0.08)
	ln market	0.16 * * 0.53 * * *	0.17 *
	potential (MARK)	(0.07)	(0.20)	(0.10)
	ln wage (W)	0.86 * * *	-0.69	0.03
		(0.21)	(0.59)	(0.34)
	ln distance to	-0.95	1.03	-0.59 * * *
	home country (DIS)	(1.26)	(6.98)	(0.13)
	N. obs.	833	83	363
	Pseudo R 2	0.191	0.291	0.198

Note: Standard errors in parentheses with * * * , * * and * respectively denoting significance at the 1%, 5% and 10% level.

Table 3 :

 3 Location choice of foreign investors in France.

	Dependent Variable: Location choice

Note: Standard errors in parentheses with * * * , * * and * respectively denoting significance at the 1%, 5% and 10% level.

Table 4 :

 4 Location choice of foreign investors in France.

		Dep. Var: Location choice
	Model :	USA	Japan	Switzerland
	ln Nb. of same	-0.15	1.75	-0.48
	home country firms (NH)	(0.19)	(1.31)	(0.34)
	ln Nb. of other	0.53 * * *	0.37	0.91 * * *
	foreign firms (NO)	(0.14)	(0.49)	(0.20)
	ln Nb. of French	1.21 * * * 1.47 * * *	1.11 * * *
	firms (NF)	(0.10)	(0.36)	(0.14)
	ln market	0.24 *	0.34	-0.51 * *
	potential (MARK)	(0.14)	(0.38)	(0.23)
	ln wage (W)	0.81 * *	-0.55	0.26
		(0.38)	(0.95)	(0.65)
	ln distance to	0.37	15.45	-0.51 * *
	home country (DIS)	(2.49) (14.11)	(0.24)
	ln objective 2	0.00	-0.04	0.02
	grants (OBJ2)	(0.02)	(0.06)	(0.03)
	ln objective 5b	0.01	0.09	-0.07 *
	grants (OBJ5B)	(0.03)	(0.10)	(0.04)
	ln community	0.00	-0.23 * *	-0.04
	initiatives grants (HOBJ) (0.03)	(0.10)	(0.04)
	N. obs.	242	29	107
	Pseudo R 2	0.212	0.274	0.188

Note: Standard errors in parentheses with * * * , * * and * respectively denoting significance at the 1%, 5% and 10% level.

Table 5 :

 5 Location choice of foreign investors in France.

	Dependent Variable: Location choice

Table 6 :

 6 Location choice of foreign investors in France.

		Dep. Var: Location choice
	Model :	USA	Japan	Switzerland
	ln Nb. of same	0.10	1.30 *	-0.31
	home country firms (NH) (0.10)	(0.70)	(0.19)
	ln Nb. of other	0.28 * * *	0.39	0.82 * * *
	foreign firms (NO)	(0.08)	(0.26)	(0.11)
	ln Nb. of French	1.19 * * * 1.50 * * *	1.07 * * *
	firms (NF)	(0.05)	(0.19)	(0.08)
	ln market	0.12	0.50 * *	0.10
	potential (MARK)	(0.07)	(0.22)	(0.11)
	ln wage (W)	0.78 * * *	-0.76	-0.21
		(0.21)	(0.61)	(0.35)
	ln distance to	-0.41	1.35	-0.63 * * *
	home country (DIS)	(1.33)	(7.12)	(0.13)
	ln French regional	-0.02	-0.01	-0.04 * *
	policy grants (PAT)	(0.01)	(0.03)	(0.01)
	N. obs.	833	83	363
	Pseudo R 2	0.191	0.292	0.199
	Note: Standard errors in parentheses with * * * , * * and * respectively
	denoting significance at the 1%, 5% and 10% level.

Table 7 :

 7 Most agglomerated industries. Note: * * * , * * and * respectively denote significance at the 1%, 5% and 10% level.

	Industry	N. obs. NH	NO	NF	MARK W	DIS
	Office machinery	9	3.61 * *	3.85 * *	5.09 * * * -1.64 *	0.91	-1.9
	Lightning	19	2.44 * *	2.25 * * * 1.91 * * * -1.26 * *	0.79	-1.44 *
	Machine tools	23	1.64 *	1.36 * * * 1.29 * * * 0.76 * *	-0.32	-1.19 * *
	Misc. rubber	36	1.86 * * * 0.92 * * * 1.3 * * *	0.48	-0.65	-0.91
	Computers	71	1.16 * * * 1.05 * * * 1.35 * * * -0.35	0.99 * * 0.43
	Lifts	85	1.28 * *	0.44 *	1.61 * * * -0.27	-1.05 * -0.14
	Paints	65	0.93 * *	0.85 * * * 1.28 * * * -0.09	-0.12	-0.06
	Car parts	115	0.51 * *	0.29 *	0.93 * * * 0.19	0.75	-0.72

*

Table 8 :

 8 Location patterns of other industries. * * * , * * and * respectively denote significance at the 1%, 5% and 10% level.

	Industry	N. obs. NH	NO	NF	MARK W	DIS
	Springs	11	3.45 *	0.82	3.62 * * * 0.03	-4.03 * * 0.81
	Plaster for construction	7	4.16 * *	1.09	2.58 * * * -0.25	1.4	-0.93
	Paste and Glue	21	1.42	1.66 * *	3.28 * * * -0.85 *	2.9 *	-1.39 * *
	Transmission parts	17	2.71	1.93 * * * 1.68 * * * 0.25	3.25	0.03
	Basic plastics	17	2.31 * * * 0.53	2.31 * * * 1.01	0.35	-2.76 * * *
	Screws	7	2.28	1.36	1.33 * *	0.79	-0.18	-2.67 *
	Soap	17	2.35 * *	0.43	2.17 * * * -0.4	2.36	-1.58 *
	Small metal articles	10	1.41	1.91	1.49 * *	-0.03	0.22	-3.6 * * *
	Cardboards	11	2.68 *	0.36	1.69 * * * -0.14	1.76	-0.7
	Curved Glass	8	4.17 *	-2.4	2.68 * * * -1.94 * *	-5.63 * * -3.77 * *
	Industrial Gaz	50	2.09 * *	0.44	1.85 * * * -0.38	-1.05	0.3
	Cables and Wires	20	1.97 * *	0.69	1.33 * * * 0.1	-1.41	-0.18
	Agricultural Machinery	11	1.95	0.36	1.59 * * * 1.03 *	-0.71	1.2
	Navigation equipment	26	1.49	1.34 * *	0.94 * * * -0.38	-0.71	-1.25 * *
	Small gen, eng and transf.	9	0.04	1.38	2.26 * * * -1.79 * *	2.55	-3.01 * *
	Misc elec. mat	12	1.59	1.03	0.97	0.48	1.18	0.5
	Car bodies	21	1.22	1.1 *	1.08 * * * 0.52	1.33	-0.22
	Dom. elec. appliances	13	-0.24	1.86 * *	1.6 * * *	-0.68	3.5 * * *	-0.35
	Mechanical handling eq.	27	0.83	0.98 * * * 0.98 * * * 0.46	0.05	-0.51
	Active electronic comp.	21	-0.12	1.08 * *	1.74 * * * 1 * *	0.19	0.77
	Locks	19	1.08	0.31	1.19 * * * 0.75 * *	-1.61	-0.91
	Tabs	27	1.29	0.31	0.96 * * * 0.05	2.07	-0.04
	Office furniture	20	2.32 * *	-0.34	0.51	1.05 * *	-1.05	-0.88
	Essential oils	26	0.05	1.07 * * * 1.32 * * * 1.38 * * * -1.05	0.28
	Mechanical tools	51	0.84	0.83 * * * 0.63 * * * 0.12	-0.24	-0.21
	Industrial chemicals	47	0.06	0.93 * * * 1.25 * * * -0.03	2.38 * *	-0.79
	Shoes	19	1.21	0.4	0.6 * * *	1.33 * * * -1.31	-1.1
	Transmission equipment	20	0.33	-0.01	1.74 * * * 0.36	0.94	4.28 * *
		continued on next page
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		Cahiers de la MSE -2000.50

This externality takes a form comparable to the one specified by[START_REF] Belleflamme | An Economic Theory of Regional Clusters[END_REF]. For the foundations of such externalities and distinctions between different possible types of externalities, the reader can get back to the seminal work of[START_REF] Marshall | Principles of Economics[END_REF], recently inspiring a large number of papers including[START_REF] Krugman | Geography and Trade[END_REF],[START_REF] David | Marshallian factor market externalities and the dynamics of industrial localisation[END_REF],[START_REF] Arthur | Silicon Valley Locational Clusters : When do Increasing Returns Imply Monopoly?[END_REF][START_REF] Arthur | Increasing Returns and Path Dependence in the Economy[END_REF],Fujita and Thisse (1996, 1999).

Cahiers de laMSE -2000.50

Which correspond to the NUTS 3 level in the Eurostat geographical classification of regions for France.8Cahiers de laMSE -2000.50

A notable exception being[START_REF] Friedman | What Attracts Foreign Multinational Corporations[END_REF] who use a demand variable similar to the one used here in their analysis of foreign investment in the United States.10Cahiers de laMSE -2000.50

When data was missing because the département had no firm in the 4-digit industry, we used an average of the average national wage for this industry and the average wage across industries in this location.

One might also envision that this result reflects a relocation pattern of FDI: Investors look for a location in France near their home market to enjoy relatively low production costs compared with the ones they face in their own country, without increasing too much the transport cost to their home market. If this explanation might be plausible for Swiss or German investors, it does not seem credible for Belgian nor Dutch ones.

In order to improve stability and robustness of those estimations, we run logits for each couple of successive years(1985-1986, 1986-1987...).

All variables are taken in logs. As a consequence, all coefficients can roughly be interpreted as elasticities for an "average" investor of the change of each variable in a location on the probability of investing in that location.20Cahiers de laMSE -2000.50

* This research benefited from financial assistance of L'Istituto Affari Internazionali (Rome) and the Commissariat Général du Plan (Paris,

of the market potential gets bigger and clustering behaviour gets weaker. We interpret this evolution as evidence of learning of the French market characteristics by foreign firms: As time passes it becomes more and more important to be near final demand and less and less important to be in locations sharing common attributes with the home country.

We finally try to assess the impact of French and European regional policies through the inclusion of investment incentives and structural funds in the location choice but hardly find any positive impact of either measure on the actual choices of investors. Even if important agglomeration economies might be a favorable ground for effective attractiveness and regional policies, the evidence for France is very negative: We don't find any rise in the attractiveness of French départements when investing there is associated with grants from public authorities.