Oscar Joao Afonso
email: oafonso@fep.up.pt.

Henrique Rui

Alves

Rui Henrique Alves

Roberto Frias

Endogenous Growth and European Fiscal Rules

Keywords: Technological-Knowledge Gap, Monetary Union, SGP, Excessive Deficits, Numerical Computation. JEL Classification: O31, O38, H60, E62, C61

published or not. The documents may come

Introduction

With the creation of the European Monetary Union (EMU), the framework for the definition and implementation of macroeconomic policies has dramatically changed. Member-Countries have lost their exchange rate and money supply instruments and fiscal policy has been restrained by binding rules aimed at avoiding excessive public deficits.

The need for fiscal discipline was justified by the potential external negative effects that could result from excessive deficits run by any participant in the eurozone. These effects (e.g., De Grauwe, 2005) included a possible increase in the interest rate of the EMU, leading to possible pressures on the European Central Bank (ECB) to implement a more expansionist monetary policy, thus leading to an increase in inflation.

Fundamentally, European fiscal rules have been put in place because of the need to keep price stability (e.g., [START_REF] Baldwin | The Economics of the European Union[END_REF].

The above-mentioned rules included a maximum ceiling for the deficit to GDP ratio (3%) and for the public debt to GDP ratio (60%) and were consecrated by the Maastricht Treaty (1992). Further, the need for fiscal discipline has been improved by the rules of the Stability and Growth Pact (SGP), which assumed a budgetary equilibrium (or even a small budgetary surplus) as the fundamental goal in terms of the medium-run, in order to preserve some margin for manoeuvre for fiscal policy in the case of a negative shock. The SGP also established concrete sanctions to be applied to countries that maintain excessive deficits and do not comply with Council recommendations (European Council, 1997).

Since the beginning, these rules have been the main object of discussion among academics and politicians with regard to fiscal policy in the eurozone. Positions vary from strong support for the current framework to proposals for important changes in it or even to appeals for a radical change, which could include the federalisation of fiscal policy [START_REF] Alves | The 'New' Stability and Growth Pact: More Flexible, Less Stupid?[END_REF]. Among the arguments put forward in favour of major changes in the original SGP, we find the idea that fiscal rules would differ according to the level of development of the Member-Countries and their economic dimension.

The goal of economic and social cohesion would require higher rates of real GDP in the less developed countries, which in turn would require stronger public intervention and would be compatible with temporary public deficit and debt ratios higher than those proposed in the SGP. Moreover, several authors (e.g., [START_REF] Mills | The Case for Spending Rules[END_REF][START_REF] Brunila | Fiscal Policy: Coordination, Discipline and Stabilization, Bank of Finland[END_REF]Creel, 2003) suggested the substitution of current rules by the "golden rule" or the introduction of rules concerning public expenses (and not strictly the public deficit).

In particular, some expenses related to public investment would be excluded from the calculus of the relevant public deficit concerning the application of the "3 per cent" rule, following the idea, expressed in some literature (e.g., [START_REF] Milbourne | Public Investment and Economic Growth[END_REF] that public investment may help economic growth.

The other argument concerns external spillovers resulting from excessive deficits in one country, as they would only occur or be relevant if such country was big (like Germany), thus affecting financial markets and price stability in a relevant way.

The debate is not yet closed, but it may already have made a relevant contribution to the recent SGP reform (European Council, 2005). The "new" SGP allows for a growing number of circumstances that lead to a non-automatic application of sanctions, namely considering a diversified kind of public expenses that may justify the non-compliance to the "3 per cent" rule. As far as the present paper is concerned, it is relevant to note that, within that set, expenses regarding R&D are included.

In order to analyse whether or not such kind of public expenses should be treated differently and whether or not fiscal rules should differ between countries, we consider a standard economic structure in endogenous R&D-growth theory, for two countries that compose a monetary union. In each country, the production of perfectly competitive final The production function, in which the complementarity of inputs, in each country, is coupled with substitutability between countries, is adapted from the horizontal R&D growth models developed by [START_REF] Acemoglu | Productivity Differences[END_REF] as well as from the vertical R&D growth model presented by [START_REF] Afonso | Skill-biased Technological Knowledge Without Scale Effects[END_REF]. As a result of the close relationship between the production of intermediate goods and R&D, this one can be encouraged either by a direct subsidy or through a subsidy to the production of intermediate goods. Some empirical studies show a positive impact of public intervention on R&D (e.g., [START_REF] Falk | What Drives Business Research and Development (R&D) Intensity Across Organisation for Economic Co-operation and Development (OECD) Countries?[END_REF]. These policies have a negative impact on the fiscal budget of each country and that situation may lead to adverse consequences, such as those prevented by the SGP. However, they may reduce the technological-knowledge gap between countries and, through this, increase the competitiveness of the less developed one. In this case, they could be crucial for an increase in the economic convergence within the union and, in particular, for the economic growth performance of the poorer country, thus justifying a differentiation in fiscal rules. This will be the focus of the present work.

By assumption, countries differ in three features: (i) economic dimension, measured by labour endowments; the one with higher active population is called Big, the other one is called Small; (ii) domestic institutions, which are more advanced in the Big-country;

(iii) domestic quality indexes measuring technological knowledge, which are higher in the Big-country, as an endogenous consequence of the other two and measuring the level of development of each country.

The paper is structured as follows. Section 2 describes the model. Section 3 determines the equilibrium conditions. Section 4 analyses the effects of a governmental intervention. Finally, section 5 offers some concluding remarks. Each final good n [0, 1] is produced by one of two countries, the Small-country, S, and the Big-country, B. The former (latter) brings institutions, A S (A B ), and labour, L S (L B ), together with a continuum set of S (B) specific quality-adjusted intermediate goods, indexed by j [0, J] (j ]J, 1]). The output of n, Y n , at time t is,

+ = n B B J n t j k n S J n t j k n L A n j d t j k x q L A n - j d t j k x q t Y S , 1 1 , 0 1 1/ ) , ( 1/ ) , ( ) , , ( ) 1 ( ) , , ( ) ( . (1)
The integrals denote the contribution of intermediate goods to production. In the Schumpeterian tradition, the quantity of each j, x n , used in the production of the final good n is quality-adjusted; i.e., the quality upgrade is q > 1, and k is the top-quality rung at time t. The term 1-is the aggregate intermediate-goods input share.

The second and fourth terms on the right-hand side of (1) can be interpreted as representing the role of the labour to production, respectively, in S and in B. These terms include the labour levels of each country, where, by assumption, L B > L S . The term A is an exogenous variable representing the level of productivity, dependent on country's institutions. As B's institutions are, by hypothesis, more advanced, we consider (2) where: p n and p(j) are, respectively, the prices of n and j. A higher p n increases the marginal revenue product of the factors, encouraging firms to rent more intermediate goods. A higher L S,n or L B,n implies that more labour is used with intermediate goods, raising demand. Finally, a higher p(j) means lower demand, since the demand curve for intermediate goods is downward sloping. Plugging (2) into (1), we have the supply of n:

A B > A S >
+ = ) ( ) 1 ( ) ( ) , ( ) 1 ( ) ( ) ( , / 1 , / 1 1 t Q L A n t Q L A n t j p t p t Y S n S S B n B B n n , (3)
where: This result will allows us to analyse if a country specific governmental intervention may improve S's situation, thus questioning the existence of a "one size fits all" fiscal rule.

dj q t Q J t j k S = 0 ] / ) 1 ( [ ) , ( ) ( and dj q t Q J t j k B = 1 ] / ) 1 ( [ ) , ( ) ( , (4)
We define the aggregate output of the union, i.e., the composite final good, as:

= = n d t Y n d t Y n d t p n d t Y t p t Y n n n n n 1 0 1 0 1 0 1 0 ) ( ln exp ) ( ln exp ) ( ln exp ) ( ) ( ) ( , (

Intermediate-goods sector

Since Y is the input in the production of j [0, 1] and final goods are produced in perfect competition, the marginal cost of production of j [0, 1] is 1, regardless of the country.

Assuming that the government of each country can subsidise the production of j by paying an ad-valorem fraction, z x (more specifically, z x,S in S and z x,B in B), of each firm's cost, the after-subsidy marginal cost of producing j is (1 z x ); i.e., (1 z x,S ) in S and (1 z x,B ) in B.

Following [START_REF] Romer | Endogenous technological change[END_REF], j embodies a costly design (created in the R&D sector), which is recovered if profits at each date are positive for a certain time in future. This is assured by a patent law, which protects each leader firm's monopoly, while at the same time, almost without costs, spreading acquired technological knowledge to other firms.

The profit-maximisation price of the monopolistic firms yields the constant over t, across j and for all k mark-up

) 1 ( / ) 1 ( ) , , ( = = x z p t j k p
, which, with z x < , is in fact a mark-up over 1. Without any change in government intervention, this mark-up is stable over t, across j and for all k. This symmetry is thus dictated by the way in which each j enters (1) and by the fact that all intermediate good producers use the same input.

Since the leader firm is the only one legally allowed to produce the top-quality, it will use pricing to wipe out sales of lower quality. Depending on whether q (1-) is greater or lesser than the marginal cost, it will respectively use the monopoly pricing

) 1 ( / ) 1 ( = x z p or the limit pricing ) 1 ( x z q p =
to capture all the market. As in Grossman and Helpman (1991, Ch. 4), it is assumed that limit pricing strategy is used by all firms. Since the lowest price that the closest follower can charge without negative profits is (1-z x ), the leader can capture all the market by selling at a price slightly below q(1-z x ), because q represents the quality advantage over the closest follower.

R&D sector

The outcomes of R&D are designs, which improve the quality of intermediate goods and the quality indexes in (4), while creatively destroying the profits from previous advances (e.g., [START_REF] Aghion | A Model of Growth through Creative Destruction[END_REF], as the previous best quality loses that status.

As in [START_REF] Afonso | Skill-biased Technological Knowledge Without Scale Effects[END_REF], in j at t, a firm engaged in R&D that uses y(k, j, t) flow of Y is successful in upgrading the next quality, k(j, t)+1, with instantaneous probability ) , ( 1) , ( 1) , , ( ) , , (

t j k t j k q q t j k y t j k I =
, where: (6)

(i) the R&D activity is located in S (B) if 0 j J (J < j 1); (ii) 0 , ) , ( > t j k q
, is the positive learning effect of accumulated public technological knowledge from past R&D in j (e.g., [START_REF] Connolly | The Dual Nature of Trade: Measuring its Impact on Imitation and Growth[END_REF]

; (iii) , 0 , ) , ( 1 1 > t j k q
is the adverse effect caused by the increasing complexity of quality improvements in j (e.g., [START_REF] Kortum | Research, Patenting and Technological Change[END_REF]. 1 As mentioned earlier, we will allow each of the governments to subsidise R&D activities directly, by means of an ad-valorem subsidy z r , which can be country-specific (i.e., z r,S in S and z r,B in B).

Consumers

A time-invariant number of heterogeneous individuals continuously indexed by a [0, 1] decide the allocation of income, which is partly spent on consumption of the composite final good, and partly lent in return for future interest. For simplicity, we consider an exogenous threshold individual a , smaller than 0.5, since

= > = a 0 S 1 a B da L da L : individuals a a > are located in B, whereas individuals a a are located in S.
The infinite horizon lifetime utility of the individual a is:

dt t exp t a c t a U = 0 ) ( 1 1 ) , ( ) , ( 1 , (7)
1 As B is more developed, it can instead be considered > 0 is the inverse of the inter-temporal elasticity of substitution.

Savings consist of accumulation of financial assets -K, with return r -in the form of public debt owned by individuals and in the form of ownership of the firms that produce intermediate goods in monopolistic competition. 2 Thus, the budget constraint is:

> + = + a a t a w - a a t a w - t a K t r - t a c t a K B B w S S w K if , ) , ( ] 1 [ if , ) , ( ] 1 [ ) , ( ) ( ] 1 [ ) , ( ) , ( , , ! ! ! &
, where:

(8) respectively, which may be used by the government for fiscal policy purposes (in particular, as a means of financing, at least partially, the costs of the above mentioned subsidies); (iv) w and ! w may differ between countries, but not ! K ; (v) r is the same within the union, as a natural consequence of the monetary union.

(i) K(a,
Maximising (7) subject to (8) yields the growth rate of consumption, which is independent of the individual and is the standard Euler equation:

= = = ! ) ( 1 1 ) ( ) ( ) , ( ˆt r - t C t c t a c K , where a d t a c t C 1 0 ) , ( ) ( .
(9)

Government

The government of each country may intervene by imposing taxes on wages and/or on financial assets and by subsidising the production of intermediate goods and/or R&D activities. If necessary, the government may run a public deficit by issuing public debt sold to individuals. The budget surplus, BuS, of S and B is thus given respectively by:

2 The value of these firms, in turn, corresponds to the value of patents in use. We will be particularly interested in the effects of higher levels of subsidies in the less developed country, regarding an eventual convergence towards the level of development of the other country.

F

+ = + ! ! ; (10a) ) ( ) ( ) ( ) ( ) , ( ) , ( ) ( ) ( )) ( 1 ( , , 1 1 , t D t r t R z t X z da t a w da t a K t r t Bus t r B B w K B B B r B B

Equilibrium

The dynamic general equilibrium resulting from optimal decentralised behaviour can be described by the paths of Q S and Q B towards the steady state.

Equilibrium for given technological knowledge

The competitive advantage of either country on the production of the n th final good relies on the relative productivity related with the quality of national institutions, The endogenous threshold final good n follows from equilibrium in the inputs markets and relies on the determinants of the competitive advantage in final goods.

3 1 2 1 1 1 ) ( 1 ) ( " # $ + = S S B B L A L A t G t n . ( 11
)
It can be related to prices noting that it is indifferent to produce n in B or S. This yields the ratio of index prices of final goods produced in each country,

= ) ( ) ( ) ( ) ( t n 1 t n t p t p S B
, where: 12) Equation ( 11) shows that a higher economic development gap, G, a larger relative supply of labour, L B /L S , and/or a higher relative productivity concerning the quality of national institutions, A B /A S , results in a higher fraction of final goods produced in B, thus in a small n . By (12), small n implies a low relative price of final goods produced by B.

= = = = ) 1 ( ) ( exp ) ( exp ) 1 ( n n p p n n p p n B n S since 1 ln exp 1 0 = dn p n . (
In this case, the demand for B specific intermediate goods is relatively low, which discourages R&D activities aimed at improving their quality, as we can see below.

The equilibrium aggregate resources devoted to intermediate-goods production, X=X B +X S , and the equilibrium aggregate output, Y=Y B +Y S , i.e., the composite final good in the union (5), are expressible as a function of the currently given factor levels,

) ( ) 1 ( ) 1 ( ) ( ) ( ) 1 ( ) 1 ( ) ( ) , , ( ) ( / 1 / 1 1 0 1 0 ; ; t Q L z q A t p t Q L z q A t p dn dj t j k x t X B B B x B B S S S x S S n + = ; ( 13a
) ) ( ) ( ) 1 ( 1 ) ( ) ( ) 1 ( 1 ) ( ) ( ) ( / 1 / 1 1 , / 1 / 1 1 ; 1 0 t Q L A t p z q t Q L A t p z q n d t Y t p t Y B B B B B x S S

Equilibrium R&D

The expected current value of the flow of profits to the monopolist producer of j, V(k, j, t), 5 relies on: (i) profits at each t given by (equivalent equation for a producer in B) . The resulting expression for V(k, j, t) is:

S q q A t p q z L t j k t j k S S S x S in producer a for , ) 1 ( ) ( ) 1 ( ) 1 ( ) , , ( ) 1 ( ) , ( 1
) , , ( ) ( ) , , ( ) , , ( t j k I t r t j k t j k V + = % . ( 15
)
Hence, the expected income generated by the successful research on rung k th at time t, V(k, j, t) r(t), equals the difference between profit flow, %(k, j, t), which is paid out as dividends, and the expected capital loss, V(k, j, t) I(k, j, t), which will occur when rung k th is replaced by a new one. Thus, r + I is the effective discount rate of the successful R&D.

Under free-entry R&D equilibrium in each country the expected returns are equal to resources spent:

< < = + B j J t j k y z S J j t j k y z t j k V t j k I B r S r in i.e., ; 1 if , ) , , ( ) 1 ( in i.e., ; 0 if , ) , , ( ) 1 ( ) , 1, ( ) , , ( , , , (16)
The equilibrium can be translated into the path of the technological knowledge. The equilibrium country-specific technological-knowledge growth rate in S, for instance, is:

4 Since S is not too backward (i.e., an appropriate taxonomy for B and S would be developed versus developing, rather than developed versus underdeveloped), it is predictable that inter-country differences in prices of final goods are of second order. Moreover, in the context of a monetary union, with single currency and common market, prices of tradable goods tend to be very similar, as well as national inflation rates.

5 I.e., V(k, j, t) is the market value of the patent or the value of the monopolist firm, owned by consumers. .

$ = = 1 ) ( 1 ) 1 ( ) ( 1 1 1 ) ( ˆ) 1 ( 1 ) ( 1 , , , q t r z A t p L q q z z t Q t I S S x S S S S
(17)

In ( 17), the term in large brackets is the equilibrium country-specific probability of successful R&D, I S , given r and p S , which turns out to be independent of j and k, due to the removal of scale of technological-knowledge effects.

Equation ( 17) indicates that subsidies may improve technological knowledge and, through it, the country's level of development. Substituting p S in ( 17) and p B in the equivalent equation for B by expressions in ( 12) and equalling

) ( ˆt Q S to ) ( ˆt Q B ,
we find the equilibrium value of n . After that, the equilibrium levels of p S and p B are also revealed.

The equilibrium aggregate resources devoted to R&D, R, at each time t, are

) ( ) ( ) ( ) ( ) , , ( ) , , ( ) ( ) ( ) ( 1 0 1 1 t I L t Q t I L t Q dj t j k y dj t j k y t R t R t R B B B J S S S J B S + = + = + . (18)
Hence, (18) shows that more resources devoted to R&D in each country (and thus in the union) are needed to offset the greater difficulty of R&D when the technological knowledge in the country-specific range of intermediate goods rises.

Steady state

Since the aggregate output has constant returns to scale in inputs Q S and Q B , and Y, X, R and C are all multiples of Q S and Q B , the constant and unique steady-state endogenous growth rate, which through the Euler equation ( 9) also implies a constant steady-state interest rate,

) ( * * * B S r r r = = , designed by ) ( * * * B S g g g = =
is:

= = = = = = = = ! * K B S * r - c C R X Y Q Q g 1 1 ˆ* * * * * * * & 0 * * * = = = = n p p G B S . ( 19
)
Thus, * r is obtained by setting the growth rate of consumption in (9) equal to the growth rate of technological knowledge -see (17) -and using the equilibrium levels of p S and p B . Then, * g results from plugging * r into the Euler equation ( 9).

Government intervention

Now, we solve numerically the transitional dynamics towards the steady state to illustrate the effect of government intervention on the country-specific technological knowledge.

The stability properties of the transitional dynamics towards the steady state are block recursive, in the sense that we can first determine the stability of G and then recursively characterise the behaviour of all the other variables. 6 Using these results, we analyse whether different fiscal rules may be needed (or not) in order to offset divergences in development among member-countries within a monetary union.

Bearing in mind that r is always unique and using 17) -we can get the differential equation needed to obtain the path of the technological-knowledge gap between countries, G, and then the behaviour of other variables can be characterised:

) ( ˆt Q S and ) ( ˆt Q B -see (
" # $ + + × × = 1 1 1 1 1 1 1 1 1 1 2 2 ) 1 ( ) ( 1 1 1 1 ) ( 1 1 1 1 ) 1 exp( ) 1 ( 1 1 ) ( ˆ, , , , , , S S B B S S x S S r S x S S B B B B x B B r B x L A L A t G L z A z z L A L A t G L z A z z q q q t G . (20)
From ( 20) it is possible to give an intuition on how a governmental intervention affects equilibrium. Take for instance an increase in subsidies in S. It re-directs R&D towards designs that improve relatively more its technological knowledge, which increases the relative productivity of its intermediate goods. The development gap between S and B falls, but this intervention creates/increases public deficit in S -see (10a).

Using the fourth-order Runge-Kutta classical numerical method, which solves (20) with suitable precision, the time path of technological-knowledge gap is displayed, bearing in mind the baseline parameter values and labour endowments in Table 1. Table 1 (on separate page at the end of the paper) goes about here

We assume that initially G = 1.40, BuS = D = 0 in both countries. For simplification, we assume that there are no taxes and consequently there will be no effects on the budget surplus of one country resulting from changes in the fiscal policy of the other.

Figure 1 sums up the main results, by comparing paths of (1/G) and n under no public intervention (Scenario 0, Sc 0) with the ones resulting from an exogenous increase at t = 0 of: (Scenario 1, Sc 1) z x,S (to z x,S = 0.1); (Scenario 2, Sc 2) z r,S (to z r,S = 0.1);

(Scenario 3, Sc 3) z x,S and z r,S (to z x,S = z r,S = 0.1); and (Scenario 4, Sc 4) z r,B (to z r,B = 0.1).

Figure 1 also displays the path of the public deficit to product ratio for S in scenarios 1, 2 and 3, and for B in scenario 4. A governmental intervention in S, by way of an increase in z x,S and/or z r,S attenuates the inter-country technological-knowledge gap (Sc 1) or even makes it possible for S to reduce this gap (Sc 2 and Sc 3), as Figure 1a shows.

A greater z x,S increases the size of profits that accrue to the producers of intermediate goods in S -see ( 14) -, while a greater z r,S decreases the cost of R&D in S -see ( 16). In this way, an increase in z x,S and/or z r,S boosts the incentives to do R&D in S, thereby increasing the growth rate of its technological knowledge, Q S in (4), which in turn leads to (12). This path continues towards the constant new steady-state level of the mentioned variables, implying that 1/G is attenuated (Sc 1) or reverted (Sc 2 and Sc 3), but at a decreasing rate until it reaches its new higher steady state level, as depicted in Figure 1a.

As expected, the main adverse effect of the governmental intervention in S is a continuous increase in its public deficit and in the ratio between the public deficit and the GDP. 7 This increase is relatively under control in Sc 1, with an indirect subsidy to R&D through subsidising the production of intermediate goods, but assumes too high values in Sc 2 and 3, from a certain moment of time, as Figure 1c shows.

It is worth noting that the external negative effects of this governmental intervention in the small and less developed country, while in line with those expected [START_REF] De Grauwe | The Economics of Monetary Integration[END_REF], are of very limited importance: Table 2 shows slight increases in the price level index in B and in the interest rate within the union when compared to the scenario of nonintervention. In this way, it is possible to argue that financing the deficit running in the small country would have no major negative effects across the union.

Finally, we use Sc 4 to compare the effects arising from the same kind of governmental intervention in S and B, allowing us to highlight the importance of economic dimension on external effects of running a (probably) excessive public deficit.

As would be expected, the growth rate of the union, g, increases more significantly in the case of a direct subsidy to R&D given by B. This would mean a positive effect for the whole union, however such intervention would lead to an important increase in the technological-knowledge gap and to a significant decrease in competitiveness in S. The external negative effects of the governmental intervention would be clearly stronger in this case, associated with the creation of an excessive public deficit in B, which would be rapidly unsustainable, as the path of the public deficit to product ratio illustrates (Figure 1c). In this case, we observe a significant increase in the interest rate of the union, mainly driven by the need to finance an increasing public deficit, also as an important growth in the price level index of S. In this way, it is possible to argue that financing the deficit running in the big country would have major negative effects across the union.

From the results of our model it seems to be possible to consider that:

(i) a governmental intervention subsidising R&D led by a small country in a monetary union induces external negative effects of very little significance, but generates some relevant internal effects, promoting economic convergence within the union;

(ii) a governmental intervention subsidising R&D led by a big country in a monetary union induces strong external negative effects, raising the interest rate and the price level of the union, at the same time significantly reducing economic and social cohesion;

(iii) temporary differentiation of fiscal rules within the union, allowing less developed and small countries to have more margin for manoeuvre in order to implement temporary (direct and/or indirect) incentives to R&D, arises as a valid argument, as it may promote social and economic cohesion with very small costs;

(iv) in this sense, a direct subsidy to R&D works more rapidly, but has stronger negative effects on fiscal discipline, thus its use should be more restricted in temporal terms;

(v) one of the major aspects of the recent SGP reform, namely the consideration of an exceptional character of some public expenses related to the development of innovation and knowledge processes seems to be reasonable, possibly justifying an excessive deficit;

(vi) our results also point to the relevance of some criticisms made to the homogeneity of the European fiscal rules, which do not consider the composition of public expenses or the possibility of financing public investment through the increase of public debt.

Concluding remarks

The main purpose of this paper is to discuss one of the main questions raised by the emergence of the EMU, namely the homogeneity of fiscal rules for different countries. In particular, the paper focuses on the possibility for small and less developed countries to run temporarily excessive deficits, in order to improve their economic development and the social and economic cohesion within the union.

To this purpose, we develop a dynamic general-equilibrium growth model with two countries forming a monetary union. Growth is driven by Schumpeterian-R&D applied to intermediate goods which complement labour in each country. In this context, we analyse the effects of a governmental intervention through subsidising (directly or indirectly)

R&D activities and compare them to a situation with no governmental intervention.

An increase in such subsidies in the less developed and small country, S, re-directs R&D towards designs that improve the quality of the respective intermediate goods, increasing their productivity. This decreases the domestic relative prices of final goods produced in S. Thus, through the price channel, the inter-country technological-knowledge gap is reduced, but at a decreasing rate until it reaches its new steady state. By connecting government intervention with the technological-knowledge progress, we relate government intervention with the path of relative economic development.

Such an intervention would lead to the creation and increase of public deficits.

However, should they occur in a small country, their external negative effects would be of very little significance, while inducing some relevant internal effects, namely promoting economic convergence. Conversely, if an excessive deficit were run in the big country, strong external negative effects would occur, raising the interest rate and the price level of the union, and significantly reducing the level of economic and social cohesion.

These results suggest that temporary differentiation of fiscal rules within the union, increasing flexibility for the less developed and small countries, could promote cohesion with small costs. In particular, the consideration of an exceptional character of some public expenses connected to the innovation and knowledge processes would be justified.

This result goes in line with one of the major aspects of the recent SGP reform.

In future research, we intend to further develop the analysis in order to consider the impact on our results arising from issues such as: (i) the possibility of cheaper R&D imitation by the less developed country; (ii) the existence of taxation; (iii) the welfare analysis; and (iv) the possibility of other positive external spillovers from fiscal policies. Notes: (i) the baseline values are in line with our theoretical assumptions (for instance, A B >A S ), [START_REF] Acemoglu | Productivity Differences[END_REF], [START_REF] Connolly | A North-South Technological Diffusion: a New Case for Dynamic Gains from Trade[END_REF], and to calibrate the union growth rate around 2.5%; (ii) we consider S L a = = 0.42 and this value is normalised to 1; (iii) we start with no public intervention.

F

  and labour together with a continuum set of country specific quality-adjusted intermediate goods. Intermediate goods, in turn, use designs (resulting from R&D activities) under monopolistic competition.

  are aggregate quality indexes, measuring the technological knowledge in the countryspecific range of intermediate goods. Let us define G Q B /Q S . G accounts for the relative technological-knowledge level of B's specific intermediate goods, giving a measure of the technological-knowledge gap between countries or, in other words, of the economic development gap. An endogenous relevant result shown later is that G -1 < 1, since S has less labour and worse institutions.

  5)where we normalise its price at each time t to one (numeraire). Resources of the union, Y, that are not consumed, C, are used in the production of intermediate goods, X, and in the R&D sector, R; i.e., Y = X + R + C.

  i) X S (X B ) represents the resources devoted to intermediate goods production in S (B); (ii) R S (R B ) represents the resources devoted to R&D in S (B); and (iii) D S (D B ) represents the public debt in S (B). The first and second terms on the righthand side represent government tax revenue while the third and fourth terms represent government expenditure on subsidies for intermediate goods and for R&D, respectively, and the last term relates to interest paid on public debt.

  of the country-specific labour, as well as on the relative productivity and prices of the intermediate goods, because of complementarity in production.The prices of labour depend on the quantities, L B and L S . In relative terms, the productivity-adjusted quantity of L B in production of intermediate goods, they depend on complementarity with either labour, on the technological knowledge in the country-specific range of intermediate goods and on the mark-up. These determinants are summed up in Q B and Q S in (4).

  ) shows clearly that: (i) economic growth is driven by the technological-knowledge progress, reflected in the aggregate quality indexes; (ii) the3 The competitive equilibrium threshold n arises from profit maximisation by perfectly competitive producers of final goods and by monopolist firms producing intermediate goods, and full-employment equilibrium in factor markets. Thus, B produces final goods n > n and S produces final goods n n .

  of B for Y is higher, since, by assumption, L B > L S and A B > A S , and, as an endogenous result of the model, Q B > Q S -as will be shown later.4

  the given equilibrium interest rate; and (iii) the expected duration of the flow, which is the expected duration of the successful research's technological-knowledge leadership.Such duration, in turn, depends on

  G. Until the new steady state, such bias increases the supply of intermediate goods in S, thereby increasing the number of final goods produced in this country -see (11) and Figure1b-and lowering their relative price at least when compared to Sc 0 -see

1, which means that an absolute productivity advantage of L B over L S is

						Due to zero profit equilibrium by producers of n [0, 1], the demand for the top-
	quality of j by the producer of n is
	x	n	(	k	,	j	,	t	)	=	p	n	(	( ) p t	( j	, 1 t	)	)	1	/	q	k	(	j	,	t	)	[	(	1	)	/	]	(	1	n n	) A 1 A / 1 B S	/	) ( t t n ( , n L , L B S	)	, ,	if if	0 J	< <	j j	; ; 1 J	i.e., i.e.,	n n	is is	produced produced	in in	B S	.
											F o r
																			P
																						e
																											e r
																																		R
																																				e
																																					v i e
	accounted. A relative productivity advantage of either type is captured by (1-n) and n, w
	which implies that L S (L B ) is relatively more productive in final goods indexed by smaller
	(larger) ns. The parameter								]0, 1[ represents the labour input share.
						Finally, as we will see below, at each time t there is a competitive equilibrium
	threshold final good n , where the switch from one country to the other becomes
	advantageous. An increase in n would mean a larger space for production in country S,
	thus appearing as a measure of its relative competitiveness.
																																					5

Page 13 of 21 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	#
	"
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	12

  Table 2 compares initial and final steady-state values of the main variables and initial and final values for the deficit to product ratio in all scenarios.

	Figure 1 (on separate page at the end of the paper) goes about here
	Table 2 (on separate page at the end of the paper) goes about here
	Our results clearly indicate that with no governmental intervention (Sc 0) the inter-
	country technological-knowledge gap, 1/G, (and thus the divergence in levels of economic
	development) would grow significantly. That would cause a decrease in the
	competitiveness of the small and less developed country, measured by the decrease in n .

Table 1 . Baseline values of exogenous variables and parameters

 1 Variables Value Variables Value Parameters Value Parameters Value

	o r
	P
	e
	e r
	R
	e
	v i e
	w

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

We solve the model numerically because the differential equation describing the path of G is non-linear

-National Budget, Deficit, and Debt < H -Public Economics, E62 -Fiscal Policy|Public Expenditures, Investment, and Finance|Taxation < E6 -Macro Policy Formation, Macro Public Finance, Macro Policy, etc < E -Macroeconomics and Monetary Economics, C61 -Optimization Techniques|Programming Models|Dynamic Analysis < C6 -Mathematical Methods and Programming < C -Mathematical and † CEMPRE (Centro de Estudos Macroeconómicos e Previsão) is supported by Fundação para a Ciência e a Tecnologia, Portugal.


João ; Dias

Keywords: Organization, L22 -Firm Organization, Market Structure: Markets vs. Hierarchies; Vertical Integration < L2 -Firm Objectives, Organization, firm alliances, resource conditions, uncertainty

I. Introduction

A notable trend in recent years has been the swift growth in the intensity of firm alliance strategies 1 with a consequent proliferation in research studies on the subject. Among all the respective topics, one important question has merited particular attention from researchers: what motivates firms to enter into alliances with other firms?

The literature reveals a large number of motives for cooperative arrangements drawn from several approaches to firm behavior: transaction cost theory [START_REF] Williamson | Transaction cost economics: governance of contractual relations[END_REF], resource dependence theory [START_REF] Barley | Strategic alliances in commercial biotechnology[END_REF], resource-based view [START_REF] Das | A resource-based theory of strategic alliances[END_REF], organizational learning [START_REF] Kogut | Joint ventures: theoretical and empirical perspectives[END_REF], relationship marketing [START_REF] Arndt | Towards a concept of domesticated markets[END_REF], strategic behavior theory [START_REF] Kogut | Joint ventures: theoretical and empirical perspectives[END_REF], and so on. Each one of these approaches stresses specific aspects of alliance motivation. Transaction cost theory focuses on cost minimization, resource dependence theory on getting the resources to survive and the resource-based view on synergy. In turn, organizational learning rests on knowledge, relationship marketing on providing superior customer value and strategic behavior theory on profit maximization.

Despite the proliferation of motives, the most cited has been the desire to reduce transaction costs. Thus, transaction cost economics has 1 For the purposes of this paper, the expression "firm alliance strategies" designates any cooperative arrangement between independent firms that involves a level of integration between pure market exchange and full internalization, with the establishment (or otherwise) of a separate legal entity and the involvement (or otherwise) of minority investments by at least one participant firm. In this article, we analyze the impact of firm internal resources and perceived environmental uncertainty on the probability of a firm to establish an alliance. Thus, our theoretical framework is based on the resource dependence and resource-based view approaches, by one side, and on the literature about the role of environmental uncertainty on strategic alliances, by the other side.

Both the resource dependence theory and the resource-based view see firm resource conditions as prime drivers for alliance behavior: the probability of a firm entering into an alliance will be a function of the need to acquire external resources. However, according to our point of view, the first one is more adequate to explain alliances involving resource-poor firms while the latter fits better for firms that are relatively well resourceendowed. Our contribution is to show that results predicted by these two approaches should be moderated by perceived environmental uncertainty. Specifically, predictions of the resource dependence theory are more likely to occur in contexts of high perceived environmental uncertainty while the resource-based view fits better when this kind of uncertainty is not very high. The departing point of our study is the research made by [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF]. We take the challenge made by the authors when they suggest that future studies should consider managerial perceptions of the environment in order to better understand how firms react to environmental changes through strategic alliances. Our research and the above cited study have in common two basic assumptions: 1) alliance formation as a mechanism to adapt to environment is contingent on internal resources, and 2) resourcepoor firms and resource-rich firms can react differently in the same environmental context. However, our study differs from that of Park et al in a considerable number of points: a) the type of uncertainty used to explain the propensity of firms to enter into alliances; b) the expected behaviour of firms in different environmental contexts; c) the kind of firms included in the sample for empirical test purposes; and d) the achieved results. [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] consider the state of the market (stable, declining and growing) objectively measured as the sole environmental factor influencing the alliance behaviour of the firms. We don't question the appropriateness of this indicator for the purposes of the study, but the market is not the only source of uncertainty for firms. Hence, we followed the suggestion made by the authors themselves, and use several measures of perceived environmental context, that is, measures that reflect the way managers evaluate the external context of their firms. In particular, we aim to understand if different levels of perceived environmental uncertainty are [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] hypothesize that resource-rich firms are more likely to settle alliances when the market demand declines or grows, suggesting a U-shaped relationship between the level of environmental uncertainty and the propensity of firms to enter into alliances. They hypothesize also that resource-poor firms are more likely to enter into alliances when the market demand grows, suggesting a direct and positive relationship between the level of environmental uncertainty and the propensity to ally for this kind of firms. Based on the resource dependence theory and the resource-based view, we argue that the above cited relationship will be negative for the resource-rich firms and positive for the resource-poor ones.

In order to empirically test their hypotheses, [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] use a sample based on a sole industrial sector (semiconductor industry), recognizing that this is a limitation of their work. Additionally, they only consider start-up firms. We considered several industrial sectors as well as start-up and non-start-up firms. Hence, our study is more general, although recognizing that firm alliance behaviours can change across industries.

Finally, regarding the results, [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] conclude that resource-rich firms are more active in volatile markets while resource-poor firms are more active in relatively stable markets. We conclude that predictable environmental contexts while resource-poor ones have a higher propensity to ally in uncertain environmental contexts. However, these differences in the results will be moderated if we take into account that we use a different measure for the environmental context.

The paper is structured in two sections, in addition to this introduction and the conclusions. In section II, we conceptualize how perceived environmental uncertainty and resource conditions independently affect the propensity of firms to collaborate (model 1). Then, we let resource conditions and environmental uncertainty interact in order to obtain different resource condition impacts on the probability of firms engaging in alliances (model 2). In section III, the two models are formalized and applied to our sample in order to obtain a set of probabilities for alliance formation.

II. Theoretical framework and hypotheses

As said above, we agree with [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] that alliances can be viewed as an adaptive response to changes in the environment. However, All these questions were already discussed by [START_REF] Milliken | Three types of perceived uncertainty about the environment: state, effect, and response uncertainty[END_REF], whose point of view could be summarized as follows: a) environmental uncertainty is a multidimensional concept; b) there are three types of environmental uncertainty: state uncertainty, that is, unpredictability of particular components of the environment; effect uncertainty, that is, unpredictability about the impact on the organization of particular environmental events; and response uncertainty, that is, inability to predict the consequences of a choice; and c) environmental uncertainty should be distinguished as a descriptor of the state of organizational environments, that is, as a characteristic of the environment objectively measurably, and as a descriptor of the state of a person who perceives himself/herself to be lacking critical information about the environment, that is, as a perceptual phenomenon.

Based on [START_REF] Milliken | Three types of perceived uncertainty about the environment: state, effect, and response uncertainty[END_REF] classification, we deal with state uncertainty and adopt the notion of perceived environmental uncertainty, that is, the firms's perceived inability to predict something accurately. Our argument is that environmental uncertainty is perceptual in nature, that is, it is not unpredictable change per se that has implications on alliance decisions, but the perception of managers about the likelihood of such changes. At the same time, we consider that environmental changes have to Many researchers have studied the effects of environmental uncertainty on firm alliance strategies [START_REF] Beckman | Friends or strangers? Firm-specific uncertainty, market uncertainty, and network partner selection[END_REF][START_REF] Burgers | A theory of global strategic alliances: the case of the global auto industry[END_REF][START_REF] Dickson | Environmental determinants and individual-level moderators of alliance use[END_REF][START_REF] Robertson | Technology development mode: a transaction cost conceptualization[END_REF][START_REF] Sarkar | Alliance entrepreneurship and firm market performance[END_REF][START_REF] Steensma | The influence of national culture on the formation of technology alliances by entrepreneurial firms[END_REF]. According to these studies, the general conclusion is that firms enter into alliances in order to attain flexibility and enable prompt reactions to changes [START_REF] Child | Strategies of Co-operation: Managing Alliances, Networks, and Joint Ventures[END_REF]. The higher the level of environmental uncertainty, the greater the need a firm has to engage in collaboration with other firms. Thus, following these studies, the relationship between this factor and the propensity to alliance formation would be positive.

But the decision to ally is also contingent on the internal resource situation of the firm. The most adequate theoretical approaches to understand the role of resources in alliance formation are the resource dependence theory [START_REF] Pfeffer | Joint ventures and interorganizational interdependence[END_REF][START_REF] Pfeffer | The External Control of Organizations: A Resource Dependence Perspective[END_REF] and the resource-based view [START_REF] Das | A resource-based theory of strategic alliances[END_REF][START_REF] Dussauge | Cooperative Strategy. Competing Successfully Through Strategic Alliances[END_REF][START_REF] Faulkner | Cooperative Strategy. Economic, Business, and Organizational Issues[END_REF]. Both theories emphasize the internal resource situation of the firm as the prime driver for alliance formation. However, while the former emphasizes internal resource scarcity and the need to survive, the latter puts forward the internal resource capacities and the willingness to generate competitive advantages. Specifically, the resource dependence theory argues that some firms cannot internally generate all the resources they need. In a resource scarce context, the need for acquiring resources generates weaknesses. A fast and efficient mechanism to overcome these weaknesses is to establish alliances [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF]. Thus, cooperation is seen as a result of the desire of firms to acquire resources they lack internally but that are necessary for their survival.

Insofar as deficiencies in resources are viewed as driving forces for collaboration, alliance strategies are particularly relevant for resource-poor firms because they sharply experience resource dependency rather than any resource sufficiency [START_REF] Steensma | The influence of national culture on the formation of technology alliances by entrepreneurial firms[END_REF]. If a firm controls all the resources it needs, the desire to enter into an alliance will be very low, that is, resource shortages foster support for alliances whilst a situation of resource self-sufficiency ensures a lesser propensity to collaboration.

Compared to those resource-rich, resource-poor firms would be more motivated to enter into alliances [START_REF] Burgers | A theory of global strategic alliances: the case of the global auto industry[END_REF] so that the relationship between the probability of a firm engaging in an alliance and the resources it controls would tend to be negative according to the resource dependence theory.

The resource-based view also emphasizes the role of resources to explain inter-firm alliance strategies, but puts things in a different way.

Firms are supposed to be well endowed in resources that they want to capitalize on through alliances in order to generate value and reinforce their [START_REF] Stein | On building and leveraging competencies across organizational borders: A socio-cognitive framework[END_REF]. As a result, according to this theory, resource-rich firms would tend to be more active in creating alliances, unless they control all the needed resources.

If we combine the theoretical outcomes of both approaches, the result will be undetermined. According to the resource dependence theory, the relationship between the propensity to ally and the number of resources a firm controls would be negative, but the opposite is expected from the resource-based approach. Combining environmental uncertainty and firm resources in a model with no interaction (model 1), the hypothesis to be tested will be the following:

H1 -The probability of a firm entering into an alliance is directly and positively related to the level of environmental uncertainty it perceives and depends on the number of resources it controls.

However, our point of view is that this model is not adequate to fully explain alliance behavior. The adaptive response of firms to environment is conditioned by their internal situations, notably in terms of the resources they control, as [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] also point out. Our main argument is that if we want to make full use of the explanatory power of both approaches Resources obtained through alliances help firms to overcome resource shortages or to take the most from market opportunities. Resource shortages are particularly pressing in uncertain environmental contexts and market opportunities tend to arise more frequently in stable environmental contexts. So, external situation determines the kind of alliance that is more probable to occur: an alliance to fill a resource gap or an alliance to enhance a resource advantage. Hence, external situation determines also the kind of firms that set alliances with a higher probability: resource-poor or resourcerich firms, respectively. The use of the concepts of "exploitation alliance" and "exploration alliance" is useful at this point. [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF] define an "exploitation alliance" as a pull-oriented alliance, that is, "a need-based alliance to sustain a firm's survival", and an "exploration alliance" as a push-oriented alliance, that is, an alliance "to create new opportunities". The first type of uncertainty, when survival is the main objective of firms. When environmental uncertainty is not so high, this kind of alliances has a lower probability to arise because firms are more interested in taking advantage from the environment and the need to survive is less pressing. Alliances of the latter type, that is, "exploration alliances" are then more frequent. This is to say that the environmental context tends to determine the nature of the alliance.

Hence, environmental uncertainty determines also the type of firm more prone to settle alliances. Resource gaps and the need to survive are more frequent for resource-poor firms. As a consequence, resource-poor firms tend to engage more in alliances when environmental uncertainty is high (alliances enhance the short-term viability of these kind of firms) and less in relatively stable contexts. This is in accordance with the resource dependence theory. So, the hypothesis to test will be,

H2 -The probability of a firm entering into an alliance is negatively related to the number of resources it controls when the level of environmental uncertainty it perceives is high.

Resource advantages and the capability to take advantage from new opportunities characterize better resource-rich firms. This situation can not 12 be well understood using the resource dependence theory. In order to capture windows of opportunity, firms must be strong in internal resources, that is, they must be resource-rich, as postulated by the resource-based approach. Empirical results also support the view that these firms are more able to diversify products and activities [START_REF] Gourlay | The determinants of firm diversification in UK quoted companies[END_REF], creating new chances to ally.

Environmental opportunities are more probable to arise when uncertainty is not very high. As stated by [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF], "in a declining market, firms [that is, resource-rich firms] refrain from expanding or acquiring new resources, which further reduces opportunities for inter-firm collaboration". Following [START_REF] Park | When competition eclipses cooperation: an event history analysis of joint venture failure[END_REF], they argue that "any potential benefits of alliances would be offset by high costs and risks involved in setting up and managing strategic alliances". Hence,

H3 -The probability of a firm entering into an alliance is positively related to the number of resources it controls when the level of environmental uncertainty it perceives is low.

Summing up, the resource based view and the resource dependence theory have a strong explanation power for the behaviour of firms regarding strategic alliances. However, we contest the possibility of each one of these approaches being tested with models that do not allow for the interaction Thus, the conclusions of our integrative model support both the resource dependence theory and the resource-based view (table 1). The probability of a firm establishing an alliance rises when the number of resources it controls increases if perceived environmental uncertainty is not a serious constraint (the resource-based view). Otherwise, we have an inverse relationship (resource dependence theory).

[Insert Table 1. about here]

III. Data, econometric models and results

The data used in our models were collected through a survey made to a sample of Portuguese firms. The set of firms to be surveyed was selected from an official database (Base Belém) published by the Portuguese Statistical Institute (INE), containing the largest 10.000 Portuguese firms.

In order to select the firms to be inquired, we used as criteria the sub-sector In cases with no alliance, all data are for 1997. For firms with only one alliance created in the period 1995-1999, the data are for the year of the alliance. When two or more alliances were created in this period, we asked the CEOs to consider only the first one and to report all the relevant data for the year of the establishment of this alliance. logit specification was adopted.

Before presenting the results of the two models, a more accurate explanation and justification of the independent variables are needed.

As regards PEU, we have taken into account that our sample mainly includes SMEs, though they are among the biggest Portuguese firms.

Although this kind of firm may be just as sensitive to many types of to be especially sensitive to particular sources of uncertainty. So and following [START_REF] Burgers | A theory of global strategic alliances: the case of the global auto industry[END_REF], [START_REF] Dickson | Environmental determinants and individual-level moderators of alliance use[END_REF] and [START_REF] Sarkar | Alliance entrepreneurship and firm market performance[END_REF], we have considered technology, market and competition constraints as relevant sources of uncertainty for our sample of firms.

Technological complexity and volatility and increasing technological development costs threaten the relevance of existing competencies making alliances a source of advantages in the process of getting new technological knowledge. In the same way, demand uncertainty has been found to influence investment [START_REF] Caselli | Uncertainty and the slowdown of capital accumulation in Europe[END_REF][START_REF] Price | Aggregate uncertainty, investment and asymmetric adjustment in the UK manufacturing sector[END_REF]. In turbulent markets where customer needs evolve rapidly, collaboration helps firms to develop new products and services that satisfy emerging consumer needs and enhances their capacity to enter new markets and segments. As regards competition constraints, in rapidly changing competitive environments firms never know in advance whether or not their actions will invite retaliation or which moves by competitive rivals will bear a direct impact upon them [START_REF] Burgers | A theory of global strategic alliances: the case of the global auto industry[END_REF]. In this situation, firms can improve their positions by creating new networks with new partners or maintain them by reinforcing existing relationships through additional alliances in order to increase entry barriers and reduce the level of competitive intensity [START_REF] Sarkar | Alliance entrepreneurship and firm market performance[END_REF].

Therefore, and in order to test the influence of environmental constraints on the propensity of firms to engage into alliances, we have used In order to evaluate the extent to which resources controlled by the firm are important for engagement in alliance strategies, we have considered five critical resources: the existence of R&D activities in the focal firm, access to technology and general know-how, experience in internationalization processes, access to financial resources and access to a specialized work-force. The first item was objectively measured (the firm develops or not R&D activities) and for the latter four we have used fivepoint scale perceived measures. For each of these latter four items, we calculated the simple average of all responses at the sector level, in order to take into consideration sectoral specificities. Accordingly, we considered as weak those cases with worst situations than the sector average and as strong all other cases. The variable measuring resource strength was then graduated from 0 (the focal firm is weak in all items) to 5 (the focal firm is strong in all items). the variable PEU is linked to external conditions. As we can see in table 2, the correlation coefficient between these two variables is negative and equal to -0.32.

The choice of control variables (AGE, SIZE and EFF) aims to incorporate into the models the variables most often used in other studies 2 .

We do not expect specific results for these variables because the extant literature is not consensual in this field.

Summing up, the two models differ, not in their original explanatory variables (exactly the same in both models) but in the way they combine to produce results and test hypotheses. In model 1, no interaction between independent variables is assumed. In model 2, we let perceived environmental uncertainty and the number of resources interact and we admit a non-linear relationship between the probability of alliance formation and each of these independent variables.

Our expectation is that model 1 will produce increasing probabilities of alliance formation with the increase of PEU (hypothesis H1). As regards model 2, and having in mind H2 and H3, our expectation is that the probability of alliance formation will increase with the rise in PEU (NRES)

for low levels of NRES (PEU) and decreases with PEU (NRES) for high levels of NRES (PEU).

2 See, for example, [START_REF] Bishop | Collaboration and firm size: some evidence from the UK defense industry[END_REF], [START_REF] Gomes-Casseres | Alliance strategies of small firms[END_REF]), Rothweel (1983), Moenaert et al (1990), [START_REF] Steensma | The influence of national culture on the formation of technology alliances by entrepreneurial firms[END_REF], [START_REF] Foster | A regression model explaining predisposition to collaborate[END_REF], [START_REF] Baum | Institutional linkages and organizational mortality[END_REF], [START_REF] Stuart | Interorganizational endorsements and the performance of entrepreneurial ventures[END_REF], [START_REF] Levitt | Organizational learning[END_REF], [START_REF] Burgers | A theory of global strategic alliances: the case of the global auto industry[END_REF], [START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF]. positive and statistically significant. Regarding the variable NRES we see that the coefficient is also positive and statistically significant. This means that the probability of a firm entering into an alliance increases with the level of environmental uncertainty it perceives and the number of resources it controls.

The probability of alliance formation for all levels of PEU and NRES can be calculated using the results of model 1 (table 4). With a level 1 of perceived environmental uncertainty, the probability of a firm entering into an alliance when it controls none of the included resources is 1.45%. The probability rises to 88.9% when we consider a firm that controls all the five resources considered and has a level 5 of perceived environmental uncertainty.

In general, the results are in accordance with the predictions of the resource-based view, independent of the level of perceived environmental uncertainty. However, we can see that low levels of environmental uncertainty produce lower probabilities of alliance formation, regardless of the number of resources the firm controls. This already serves as a first indication that environmental conditions matter in the behavior of firms.

[Insert Table 3 3). All the estimated coefficients for the main variables are statistically significant.

In particular, we obtained negative estimates for the coefficients of PEUsquared and NRES-squared, indicating an inverted U-shaped relationship between the probability of alliance formation and the level of perceived environmental uncertainty, on the one hand, and this probability and the number of resources, on the other. This means that alliance events seem to be more common for conjointly intermediate values of these variables than for the conjointly extreme values. The interaction term is also significant indicating strong crossed effects of the two explanatory variables on the probabilities of alliance formation.

Both in models 1 and 2, the high value of the likelihood ratio (LR) rejects the hypothesis of joint exclusion of all the explanatory variables.

Furthermore, the joint exclusion of the additional variables in model 2 is clearly rejected by the data (the value of the LR test statistic is 27.0, quite above the critical value of 7.81 corresponding to a 2 (3;0.05) ), thus giving a clear preference for this model when we confront it with model 1.

The estimated probabilities (table 5) show that for the first three levels of perceived environmental uncertainty, the probability of alliance formation increases with the number of resources in accordance with the resource-based view. Conversely, for the highest levels of that variable, the probability of an alliance event tends to decrease with the number of

IV. Conclusions

The resource dependence theory and the resource-based view both emphasize the role of internal resource conditions on inter-firm alliance formation. The first one is more appropriate to explain cooperation involving resource-poor firms while the latter is more adequate to understand alliances between resource-rich ones. The main contribution of this article is to show that these results are contingent on environmental uncertainty perceived by firms. So, we let resource conditions and perceived environmental uncertainty interact in order to fully assess their impact on the probability of firms to engage in alliances.

We have argued that for high levels of perceived environmental where the survival of the firm is not threatened. These firms then show a low propensity to ally. On the contrary, resource-rich firms are interesting partners in a context where the benefits of allying exceed the costs.

Therefore, for low levels of environmental uncertainty, alliances are mainly developed by this kind of firms and "exploration" alliances are particularly relevant in this context.

Our empirical results support the theoretical arguments. Confronting the estimates obtained with models 1 and 2, the data give a clear preference to the model with interaction between resources and environmental uncertainty. That is, the impact of resources on alliance activity is moderated by perceived uncertainty. In fact, table 5 shows that, for high levels of environmental uncertainty, the probability of alliance formation tends to be negatively related to the number of resources a firm controls, a result that is in accordance with our hypothesis H2. For low levels of uncertainty, the probability of alliances increases with the number of resources, in line with our hypothesis H3. However, the limited number of alliances in our database does not allow us to exploit this type of analysis.

So, the main conclusion of this paper is that the resource-based view holds for low levels of perceived environmental uncertainty whilst the resource dependence theory fits better to severe adverse conditions. Our interpretation is that, in the first case, alliances are mainly explained by the capacity to find partners, that is, by the availability of internal resources. In the second case, they are activated by a lack of resources and the fear of bankruptcy within a context of great environmental uncertainty.

F

  often mentioned approach in theoretical and empirical studies seeking to understand the drivers of alliance formation. Other points of view, namely those related to the internal resource situation of the firms and their external environment, are not yet so frequently taken into account as the transactional approach.

  firm behaviours regarding inter-firm alliances. In our study, the level of environmental uncertainty is dependent on several external factors (subjectively evaluated by managers), including the state of the market.

  are more prone to settle alliances in relatively

  introducing environmental uncertainty as a key determinant factor of firm alliance strategies raises three important questions: 1) what are the sources of environmental uncertainty, 2) what type of environmental uncertainty dealing with, and 3) what measures of environmental uncertainty (objective or perceived) are most adequate.

  main fields: market, external resources (technology, human resources and so on) and competition.

  The main argument for alliance formation is that firms try to leverage their superior resources with complementary resources owned by other firms

  and resource-based views), we have to allow interaction between resource conditions and environmental uncertainty. The strong propensity of resource-rich (resource-poor) firms to engage in alliances predicted by the resource-based view (resource dependence theory) may be moderated by perceived environmental conditions, according to our line of reasoning. Therefore, a more complex explanation is needed and other hypotheses have to be tested in order to understand the role that resources and perceived environmental uncertainty interactively play in alliance formation (model 2).

  occur more frequently in contexts of high environmental

  of environmental uncertainty and the number of resources firms control. Regarding the resource dependence theory, what is surprising is that albeit the importance that resources and uncertainty separately play in the framework, they do not act interactively to explain alliances. If they do, theoretical results would be somewhat different.

  the size of the firm. Concretely, we selected only firms belonging to 29 industrial sub-sectors and, within each sub-sector, the 50% largest ones. The number of firms enquired was 2751 and the number of respondent firms with complete data for estimation purposes was 310, of which 83 correspond to effective alliances.The survey was put in place at the end of 1999 and was directed to the CEOs of the firms. Questions included the following categories: a) general information (sector of activity, size of the firm, year of establishment, R&D activities, level of internationalization); b) evaluation of the environmental context (market, technology and competition constraints); c) establishment of alliances with other firms during 1995-1999 and data related to them (main objective, number and nationality of partners, type of alliance).

  other company, we expect their engagement in alliances

  including items related to technology, demand and competition indicators. Each of these three items was expressed in a fivepoint response scale in order to assess manager perception of environmental constraints. Specifically, we asked CEOs to respond to what extent 1) the pace and complexity of contemporary technological developments, 2) consumer behavior and 3) the behavior of competitors, are constraining factors in the development of firm strategy. Then, for each firm we have calculated the simple average of the three results, thus obtaining a scale of 1 to 5 for our composite variable.

  variable NRES measures internal resources,

  the firm. Thus, as expected, the resource-based view holds for low levels of environmental uncertainty and the resource dependence theory can be applied when firms face sharply adverse external conditions.

  with those of[START_REF] Park | Firm resources as moderators of the relationship between market growth and strategic alliances in semiconductor start-ups[END_REF], although they work with a different concept of uncertainty and use only star-up firms in the semiconductor industry. In our case, we used data concerning 29 industrial sub-sectors. Sectoral specificities are partially taken into account by the way we defined the resources variable. It would be interesting to further differentiate between sectors and also particular types of alliances.

Table 2

 2

	shows descriptive statistics and the correlation matrix for the
	explanatory variables used in the econometric analysis.
	[Insert table 2 about here]

where PEU (perceived environmental uncertainty) and NRES (number of resources the focal firm controls) are the main variables, and AGE (age of the focal firm, in years), SIZE (size of the focal firm measured by number of employees), and EFF (efficiency of the focal firm measured by the ratio sales turnover / number of employees) are control variables. In both cases, a

Table 1 .

 1 Probabilities of alliance formation

	o r
	P
	e
	e r
	R e v
	i e
	w

Table 2 .

 2 Mean values, standard deviations and correlation matrix for the explanatory variables in models 1 and 2

		Mean Std Dev	Correlation coefficient
				AGE SIZE EFF PEU NRES
	AGE	29.4	24.0 1.00
	SIZE	391	1417 -0.09 1.00
	EFF	21.7	60.9 -0.05 0.03 1.00
	PEU	3.04	0.73 0.01 -0.16 0.03 1.00
	NRES	2.31	1.32 0.02 0.18 0.14 -0.32 1.00

Page 28 of 30 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

		Submitted Manuscript
		Table 3. Econometric results
			Model 1			Model 2
	Variable	Coefficient Standard-	p-value	Coefficient Standard-	p-value
			error			error
	Constant	-6.289	.9763	.000	-29.95	6.488	.000
	AGE	.0191	.0056	.001	.0210	.0063	.001
	SIZE	.00037	.00019	.050	.00051	.00026	.053
	EFF	.00002	.000008	.013	.000015	.000009	.097
	PEU	.9161	.2308	.000	10.39	2.848	.000
	NRES PEU 2 NRES 2 PEU*NRES F .5282 o r	.1298	.000	6.705 -.8456 -.2493 -1.465	1.557 .3340 .1092 .3331	.000 .011 .022 .000
	N Log-likelihood LR % of correct predictions	310 P -145.3 e 69.6 e r 77.7		310 -131.8 96.65 78.7
			R e v
				i e
				w
			29

Table 4 .

 4 Probabilities of alliance formation -model 1

							Number of resources
					0	1	2	3	4	5
				1	0.0145	0.0243	0.0405	0.0669	0.108	0.171
	Perceived	environmental	uncertainty	2 3 4	0.0354 0.0841 0.187	0.0586 0.135 0.280	0.0955 0.209 0.398	0.152 0.309 0.528	0.233 0.432 0.655	0.340 0.563 0.763
				5	0.364	0.493	0.623	0.737	0.826	0.889

Estimates based on mean values for the control variables

Page 29 of 30 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 5 .

 5 Probabilities of alliance formation -model 2

							Number of resources
					0	1	2	3	4	5
				1	.0000	.0000	.0000	.0031	.0915	.6680
	Perceived	environmental	uncertainty	2 3 4	.0000 .0052 .3120	.0004 .0393 .4510	.0077 .1630 .4750	.0882 .3610 .3770	.4240 .4980 .1970	.7730 .5140 .0572
				5	.8790	.7530	.4370	.1070	.0111	.0006
	Estimates based on mean values for the control variables

Page 30 of 30 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript