ESTUDIOS SOBRE LA ECONOMIA ESPAÑOLA

Xulia González Jordi Jaumandreu

EEE 45

http://www.fedea.es/hojas/publicado.html

Xulia González and Jordi Jaumandreu

May, 1998

Abstract

This paper integrates the analysis of the decision to undertake R&D activities with the analysis of the decision on the level of the R&D investment when this investment is carried out. The theoretical framework assumes the existence of minimum required R&D expenditures, brought about by the indivisibility of some resources. This assumption, combined with demand characteristics and technological opportunities, determine threshold levels of R&D expenditures under which firms do not find it profitable to invest. This framework leads naturally to a Tobit-type econometric model aimed at estimating thresholds, which we apply to a Spanish manufacturing representative micropanel sample that includes observations on more than 2,000 firms of all size, many without R&D expenditures. Our conclusions are that sizable thresholds exist, which are systematically related to a list of demand and technological factors. The results strongly suggest that there is an advantage of the biggest firms in undertaking innovative activites.

*We thank Manuel Arellano, Raquel Carrasco, Jose Vidal, Chelo Pazó and Daniel Miles for helpful comments and the audiences at EARIE 1997, XIII Jornadas de Economía Industrial and Fundación Empresa Pública seminar. We acknowledge financial support from CICYT, project SEC97-1368.

Xulia González. Universidade de Vigo. Dpto. Economía Aplicada. Apdo. 874, 36200 Vigo. Spain. E-mail: xgzlez@uvigo.es.

Jordi Jaumandreu. Fundación Empresa Pública. Pza. Marqués de Salamanca, 8. 28006 Madrid. Spain. E-mail: jaumandreu@funep.es.

1.- INTRODUCTION

Most analyses of R&D determinants overlook the fact that not all the firms perform actively innovative activities. However, in most industries there is some proportion of firms that do not report R&D expenditures. For example Cohen and Klepper (1992) find, in a sample of American manufacturers that overrepresents the biggest firms, that 16 percent of the total observations are zero R&D expenditures. Moreover, the proportion of business units that report zero expenditures range, for the two digit industries, from 5 to 50 percent. And according to the representative sample of Spanish manufacturing firms that we employ in this work, almost 15 percent of the firms with more than 200 workers, and 70 percent of the firms under this size, do not report to perform formal R&D.

If we take firms as rational, it seems natural to consider zero R&D expenditure as the result of a decision based on the (expected) market profitability of such activities, just like R&D performers are supposed to choose optimally their levels of expenditure. Therefore, if we ignore the analysis of the factors that impel or inhibit the undertaking of R&D activities, something important is lost in the general analysis of the mechanisms that determine the level of innovative activities. In fact, several authors have expressed their worries about the effects of the presence of sample selection biases in most of the samples used in the analysis of innovative activities (see, for example, Cohen and Levin (1989) and Griliches (1990)).

In this paper we try to integrate the analysis of the decision to undertake R&D activities with the analysis of the decision on the level of the R&D investment when this investment is carried out. With this aim, we develop a theoretical framework to explain simultaneously both decisions, and we discuss the corresponding suitable econometric model. The central idea is that firms can enlarge their demand by doing R&D quality enhancing, but this activity is subject to some technological constraints, summarized in a sales-R&D expenditures frontier (maximum sales at each expenditure level), that will differ by industries and even by firms . In particular, we consider that innovative activities are subject to the indivisibility of some R&D resources (and old and widely accepted idea, see, for example, Arrow (1962)). This implies that a minimum expenditure is required to improve product quality above a standard level in order to affect demand (i.e. the feasible set is not convex).

Most theoretical and empirical work has focussed on process R&D activities, but empirical evidence point to the dominance of product or mixed R&D expenditures. For example, Scherer (1984) reports that

Minimum expenditure, jointly with varying demand characteristics and technological opportunities, determine threshold R&D levels under which firms do not find profitable to invest. The reason is that, under the threshold, the output effect of performing R&D is not still big enough for R&D expenditures to be completely recovered with the profits derived from the investment. However, each firm not performing R&D faces its particular frontier, and hence has some shadow optimal level of investment, that we would observe if it were compelled (or subsidized) to undertake it. Accordingly we take R&D investment, and specifically the R&D intensity or effort (the ratio of R&D expenditures to sales), as a censored variable for which we do not observe the optimal values that have been discarded as non-profitable. Our econometric model is aimed at the identification of the common characteristics of the sales-R&D frontiers, in which performers and non performers identify their optimal (actual or shadow) values, and to the measurement of the thresholds and the uncovering of its determinants.

Our theoretical framework consists of a very simple model, where the focus is the individual decision, and we try to keep the restrictive assumptions reduced to a minimum. We consider the actions of one firm, that can be considered one competitor in a product differentiated market, where it takes as given the actions of the rivals. The demand of the firm depends on price and quality, and the firm chooses simultaneously the price of the product and the level of R&D expenditures to affect quality . The firm can choose not to spend on innovative activities, and then it will sell at the minimum standard quality given by the "state of arts". The framework can be seen as modelling an incremental decision in a moment of time, as in a recent model by Cohen and Klepper (1996) to explain the role of firm size . In our framework, market power (measured by the price-cost margin) interacts with demand characteristics (which give the willingness to pay for higher quality product) and technological opportunities (which give the ease to improve quality) to determine simultaneously R&D expenditures and the sales of the firm.

most industrial R&D is product-oriented (75.4% of R&D expenditures of American firms are allocated to product innovation activities). And according to a Spanish official survey of innovation activities referred to 1994 (INE (1997)), 65% of R&D firm's expenditures are allocated to product innovation activities and only 2% of firms perform exclusively process R&D activities.

This is the usual setting in modelling the R&D decisions with empirical purposes. See, for example, Levin and Reiss (1988) and their modelling of the simultaneous decision on R&D and output in the presence of spillovers.

The model predicts that the likelihood of spending on R&D and the amount of the investments increase with firm size (sales), which agrees with what has been empirically found elsewhere (see, for example, the most recent survey on empirical findings by Cohen (1996)). But the particular relationship between R&D effort and size for R&D performers depends on the assumptions on the form of the relevant part of the sales-R&D frontier. A concave frontier, which seems natural to assume, will imply a somewhat higher R&D intensity for the (otherwise equal) big performers, a feature that sometimes has been empirically found. In addition, if the frontier is concave, the inverse relationship which has occasionally been found at very small sizes (and is also apparently present in our sample) also has a misleading character .

This framework leads naturally to a Tobit-type econometric model (more specifically a type 2 generalized Tobit model, in Amemiya's (1985) terminology). The variable of interest (R&D effort) is only observed when it is stochastically greater than a threshold, which can be specified as a linear combination of explanatory variables. To estimate an effort determinants equation free of selection bias, we must specify the thresholds. And, at the same time, under the assumption that some identification conditions hold (see below), we can also estimate the thresholds and their determinants. This type of econometric model dates back to Gronau (1973) and Nelson (1977) , although the model we propose is particular in one aspect. The obtainable price-cost margins are a key variable for firms to evaluate the profitability of the investment and its optimal value, and hence for the identification of the model. But this variable must be treated as endogenous if firms set prices simultaneously to R&D expenditures. Our econometric model treats both the censoring of effort and the endogeneity of margins. To do so, a two stage procedure based in the conditional maximum likelihood approach of Smith and Blundell (1986) and Blundell and Smith (1989, 1994) is applied.

Although, in contrast to our framework, their model takes output as subject to an exogenous rate of increase.

Bound et al. (1984) for American firms, and Pavitt et al. (1987) for British firms, found that very small and very large firms appeared to be more R&D intensive than intermediate ones. However, Cohen et al. (1987), controlling for industry effects and distinguishing between the size of the firm and the business units, showed with the same American data that no size variable affected R&D effort.

The data set we use is an unbalanced panel of more than 2,000 Spanish manufacturing firms observed during the 6 year period 1990-95. The data come from a sample of Spanish manufacturing firms representative by industries and size strata. Representativity allows us to claim that results are valid for the whole manufacturing.

>From the estimation of the econometric model, a number of interesting conclusions are derived. Threshold effort exists and are not negligible, although they vary importantly according to definite demand characteristics and technological opportunities. Size has almost no impact on the relevant frontier for (the otherwise equal) performing firms, but strongly influences thresholds: the smaller the firm the bigger the threshold. This suggests the presence of size-related advantages to undertake innovative activities.

The rest of the paper is organized as follows. Section two explains the theoretical framework for the modelling of the individual decisions. Section three develops an example in terms of a product differentiated market, to show how the model can be cast in terms of a specific industry framework. Section four sets the econometric model and discusses the procedures of estimation. Section five briefly examines the data and explains the results of the estimation, and section six concludes. The paper includes two appendices, an appendix to explain in greater detail the econometric model and the estimation strategy, and a data appendix.

These authors modelled the housewives decision to enter the labor market depending on unobserved reservation wages. But, despite its use in labor economics and some pioneering experiments to introduce Tobit analysis in the examination of the innovative activities (see Cohen, Levin and Mowery (1987) and Cohen and Klepper (1996)), there has not been to our knowledge any previous intent to build a structural model along this lines to explain the R&D decisions.

2.- THEORETICAL FRAMEWORK

In this section we set a general framework to characterize the individual firm decision to undertake product R&D activities. For the sake of simplicity, we assume a representative firm which is a monopolist of its good variety, and we ignore the actions of the rivals, which can be thought of as given.

The demand faced by the firm, , depends on the price, p, and the quality of the good, s. It seems natural to assume that an increase in quality increases demand at a non-increasing rate . Therefore, the firm may enlarge its demand by augmenting the quality of the good that it produces.

Quality can be improved by incurring in R&D expenditures, denoted henceforth by x, according to some technological rules. Our analysis will be based on two features regarding the quality response functions that seem both natural and broadly accepted. Firstly, we assume that there is a minimum amount of investment below which R&D activities have no effect. We consider this characteristic derived from the indivisibility of some R&D resources (see, for example Arrow (1962), and for a more recent discussion, Metcalfe (1996)), and it will raise the existence of threshold effects. Secondly, we consider that the effectiveness of R&D expenditures is subject to diminishing returns. This is, in fact, the usual assumption in cost-reducing and demand-creating R&D (see, for example, Dasgupta and Stiglitz (1980) or Levin and Reiss (1988)).

According to these features we will assume that R&D expenditures below a certain level have no effect on quality, and the firm would simply attain the standard quality given by the current “state of arts”, . Otherwise R&D expenditures will affect quality according to the relationship , with , . In addition, we will assume that the production of the good implies a unit cost of c that, for simplicity, we will assume to be

independent of quality .

Suppose now that, taking into account the effects of innovative activities on quality, the firm sets simultaneously the price and the optimal level of R&D expenditure to maximize its profits. That is, the firm solves

\[\max _ {p, x} \Pi (p, x) = (p - c) q (p, s (x)) - x,\tag{1}\]

subject to

\[s (x) = \left\{ \begin{array}{l l} s (0) & i f \qquad x \leq \overline {{x}} \\ s (x) & o t h e r w i s e, \end{array} \right.\]

where the non-convexity of the constraint must be noticed.

The F.O.C. equations, conditional on some positive level of R&D expenditure, are

\[\frac {\partial \Pi}{\partial p} = q (p, s (x)) + (p - c) \frac {\partial q (p , s (x))}{\partial p} = 0\tag{2}\]

\[\frac {\partial \Pi}{\partial x} = (p - c) \frac {\partial q (p , s (x))}{\partial s} \frac {\partial s (x)}{\partial x} - 1 = 0\tag{3}\]

Notice that the condition implied by equation (3) can also be written as

\[p - c = \frac {1}{\frac {\partial q}{\partial x}}\]

Let us interpret the inverse of the slope as the (marginal) cost of increasing sales by one unit through an increase in the R&D expenditure. Then equation (3) can be read as saying that, at equilibrium, the unit profit derived from sales must equal the marginal cost of increasing them through R&D activities .

This is a rather usual assumption, that considers R&D a non-rival input of production. Klette and Griliches (1997) describe this assumption as “once a new product improvement is developed and introduced, no additional resources are needed to produce this improved product as compared to the older version”.

The model can be modified to accommodate some dynamics by assuming that quality depends on a stock of R&D expenditures K accumulated over time (a “knowledge capital”; see, for example, the classical approach of Griliches (1979) or the recent revision in Klette (1996)). If , where with representing depreciation, dynamic optimization under a discount factor r gives a rule on optimal K that can be approximated by the static solution (under a stationary environment).

[s = s(K_{t})]

Notice that the problem can be easily adapted to study the effects of both financial constraints or subsidies to R&D investments. Assume that x is measured in efficiency monetary units and let be effective cost, where represents a risk premium and a unit subsidy.

a

>From equations (2) and (3) we can derive an optimal pair , conditional on . For simplicity, we will assume that these equations have an interior solution, i.e. such a pair always exists . But the existence of this solution does not imply that it is the most profitable for the firm. This solution must be compared with the profits derived from not incurring in R&D expenditures, and hence providing the standard quality. Call these profits , the double asterisk on price stressing the fact that the price set can differ from . Then, the equilibrium for the firm can be characterized by the pair such that

\[\Pi (p ^ {e}, x ^ {e}) = \max \{\Pi (p ^ {*}, x ^ {*}), \Pi (p ^ {* *}, 0) \}\tag{4}\]

A particularly simple case emerges when the elasticity of demand with respect to price is independent of s; that is, we can write . In this case, equation (2) in isolation gives the optimal price in any situation, . Therefore, when the firm does not undertake any R&D activity, profits can be written simply . In what follows, we will analyze with some detail the firm equilibrium focusing, for the sake of simplicity and graphic convenience, in this case. In the empirical exercise we will test and accept this version of the model. We begin with a graphic analysis.

On the one hand, consider the isoprofit curves in the plane. They have the form

\[q = \frac {\overline {{\Pi}}}{(p - c)} + \frac {1}{(p - c)} x.\]

x = fgq

The x = fgq equilibrium solution of the model by Cohen and Klepper (1996) can be obtained as a particular case of this problem by setting the demand function equal to , and letting the firm set price and R&D expenditures. Then we obtain , where the exogenous output factor of proportionality g is replaced by the elasticity of demand with respect to price, .

1/

To ensure the existence of such a pair it suffices to assume that the unit profits are higher than the marginal cost at the point , where is the zero profits R&D expenditure point that the frontier can include (the point at which ).

Levin and Reiss (1988), for example, build their model on an assumption of this type. It can be understood as a situation in which quality improvements have no short-run impact on the price elasticity of demand. This elasticity, however, is likely to depend on past investments.

Therefore, the slope of a family of isoprofit curves depends on p-c and, hence, on the price set for a given production cost c. Panel A of Figure 1 depicts a family of isoprofit curves corresponding to a given optimal price . On the other hand, we have the set of feasible pairs for a given optimal price. The frontier of this set is jointly determined by the functions of demand and production of quality, according to the relationship . The set is not convex due to the requirement of a minimal R&D expenditure to improve standard quality, and hence demand. Panel B of Figure 1 depicts the frontier .

Now, put together the family of isoprofit curves corresponding to the optimal price and the frontier of the set of feasible points. The (conditional) optimal expenditure will correspond to the point of tangency of with the isoprofit curve that gives the highest profits. But this expenditure is not always the global optimum. The slope of the frontier, and hence the demand for quality and the technology to produce it, determine a level of R&D expenditure at which the firm will be “indifferent” between undertaking R&D activities or not. Investing in R&D by an amount less than is less profitable than not undertaking such activities. We will call this amount the threshold expenditure. Therefore, as far as the decision of the firm is concerned, we have two possible cases, depicted in Panel C and Panel D of Figure 1. In the first case, the firm does not undertake R&D expenditures because its conditional investment is lower than the threshold, and it finds it more profitable to supply the good at a standard quality. In the second, the firm invests in R&D by an amount greater than the threshold.

Formally, given the optimal (conditional) values of and , we will observe that the firm undertakes or not R&D expenditures depending on

\[\Pi (p ^ {*}, x ^ {*}) \gtrless \Pi (p ^ {*}, 0)\tag{5}\]

or

\[(p ^ {*} - c) q \left(p ^ {*}, s \left(x ^ {*}\right)\right) - x ^ {*} \geqslant \left(p ^ {*} - c\right) q \left(p ^ {*}, s (0)\right)\]

This frontier can be replaced, without any change in the basic analysis, by a differentiable one in which the R&D expenditure under a given value has an increasing and convex effect on demand. This can be seen as another way to model the effect of technological indivisibilities on the quality response function . Also, it can be assumed that there is a “jump” in the function at the point , i.e. .

This condition can be rewritten as where is the sales increase derived from the R&D expenditures. That is, the firm will undertake R&D activities if the output effect, evaluated at the unit profit that the firm obtains, is higher than the R&D expenditures. In other words, if the increase in profits derived from doing R&D exceeds the incurred expenditures.

Consequently, the level of expenditure, , at which the firm would be indifferent between performing R&D or not is given by a unit profit such that

\[p - c = \frac {\widetilde {x}}{\triangle q}\]

The firm will consider such an expenditure if its unit profit equals the inverse of the slope of the frontier at this point. Therefore, the threshold value is characterized by the following unit elasticity condition

\[\frac {\widetilde {x}}{\triangle q} \left. \frac {\partial q}{\partial x} \right| _ {x = \widetilde {x}} = 1.\]

R&D expenditure analyses are normally carried out in terms of the intensity or effort variable, i.e. the ratio of R&D expenditure to sales, . Equation (3) can be easily rearranged to give an optimality condition for the level of effort

\[{\frac {x}{p q}} = {\frac {p - c}{p}} \quad {\frac {s}{q}} {\frac {\partial q}{\partial s}} \quad {\frac {x}{s}} {\frac {\partial s}{\partial x}}\tag{6}\]

Optimal effort appears to be linked to the price-cost margin, the elasticity of demand with respect to quality and the elasticity of quality with respect to R&D expenditure . When equation (2) is then used to replace the price-cost margin by the inverse of the elasticity of demand, a rather familiar ratio of elasticities is obtained to explain effort (a Dorfman and

It is important to emphasize that, under the assumption of an elasticity of demand with respect to price independent of s, the demand for quality and the production of quality technology determine completely the threshold value, i.e. the threshold is independent of the price. Using the identity it can be easily verified that the elasticity condition is independent of price.

Under financial constraints or subsidies, condition (6) must be multiplied by (see note 8). Therefore, a log-linear version of (6) will include additively. This suggests that, in the absence of detailed information, the likely firms' heterogeneity in financial conditions can be treated introducing an additive random disturbance.

ρ

Steiner (1954) type condition). It can be easily shown that, given a frontier, optimal effort will be slightly increasing in q and that there is a well defined threshold value of effort . In the rest of the paper we will mainly refer to and use effort thresholds.

3.- AN EXAMPLE

In this section we develop an example in terms of a product differentiated market that, to simplify things, we consider monopolistically competitive. The demand specification corresponds to the well known Dixit-Stiglitz (1977) model, augmented to accommodate quality. In this framework, we introduce and specify a function of production of quality.

Let us consider an industry that is composed of n firms, each of them producing one distinct brand whose output is denoted by , each output presenting an associated level of quality . Assume there is a representative consumer that spends a fixed amount of income Y on the products of the industry, whose preferences are given by the utility function.

\[U (\widehat {q}) = \left[ \sum \left(q _ {i} s _ {i} ^ {\delta}\right) ^ {\rho} \right] ^ {\frac {1}{\rho}}, \qquad 0 < \rho < 1\]

where represent the quality enhanced quantities, and is a quality sensitivity parameter .

Utility maximization gives demands of the form

\[q _ {i} (p, s) = y p _ {i} ^ {- \eta} s _ {i} ^ {\varepsilon}\]

where , , is the elasticity of substitution between the quality adjusted goods, , and , where is a quality-adjusted price index. Note that , and that if we assume .

q)

q.

Given , the ratios corresponding to the points on the frontier that can occur as (conditional) equilibria, present a one to one correspondence with the levels x of R&D expenditure (notice that we have excluded the x values to the left of the point at which , therefore and the ratios are decreasing in x and q). Therefore, the possible effort equilibria can be expressed as a continuous monotone function of either x or q. This implies that we have a well defined threshold value of effort corresponding to the threshold R&D expenditures . In addition it can be checked that we expect the R&D effort to be an increasing function of sales.

The U( ) specification follows Dixit and Stiglitz (1977). Quality is introduced in a similar way in Levin and Reiss (1988), Sutton (1991), Motta (1992) and Sutton (1997), among others.

Suppose that the number of firms that operate in the industry is large enough to consider the effects of the price and quality decisions of a single firm on the aggregate p-index as negligible. Then, the price and quality elasticities perceived by every firm will simply coincide with and .

Assume that firms can affect the quality of their products according to the following function

\[s (x _ {i}) = \left\{ \begin{array}{l l} \overline {{x}} ^ {\theta} & \text {if} \qquad 0 \leq x _ {i} \leq \overline {{x}} \\ x _ {i} ^ {\theta} & \text {if} \qquad x _ {i} > \overline {{x}} \end{array} \right.\]

where . That is, quality can be increased, although at a decreasing rate, by incurring in additional expenditures beyond a minimum level required from the beginning to affect quality. On the other hand, we assume that every good can be produced at a unit cost c.

Let us consider the Nash equilibrium in prices and expenditures. According to (4) every firm chooses a pair such . To determine the optimal price , and the (conditional) optimal investment , it suffices to solve the program , subject to the production of quality relationship constraint. Optimal price is

\[p _ {i} ^ {*} = \frac {\eta}{\eta - 1} c,\]

and (conditional) optimal R&D expenditures can be written

\[x _ {i} ^ {*} = \left(\frac {\theta \varepsilon}{\eta \gamma}\right) ^ {\frac {1}{1 - \theta \varepsilon}} \overline {{x}},\]

where is the ratio of minimum R&D expenditures to the sales at optimal price and standard quality.

At the same time, it is easy to check that and

This is the usual assumption to produce a monopolistically competitive setting. See, for example, Dixit and Stiglitz (1977).

. Hence the threshold value, computed from (5), is

\[\widetilde {x} _ {i} = \frac {\overline {{x}}}{(1 - \theta \varepsilon) ^ {\frac {1}{\theta \varepsilon}}}\]

Accordingly, from the condition , it is easy to obtain

\[\frac {1}{\eta \gamma} > (\theta \varepsilon) ^ {- 1} (1 - \theta \varepsilon) ^ {- \frac {1 - \theta \varepsilon}{\theta \varepsilon}}\]

Therefore, the pair selected by every firm will be given by

\[(p _ {i} ^ {e}, x _ {i} ^ {e}) = \left\{ \begin{array}{c c c} (p _ {i} ^ {*}, x _ {i} ^ {*}) & i f & \frac {1}{\eta \gamma} > (\theta \varepsilon) ^ {- 1} (1 - \theta \varepsilon) ^ {- \frac {1 - \theta \varepsilon}{\theta \varepsilon}} \\ (p _ {i} ^ {*}, 0) & i f & o t h e r w i s e \end{array} \right.\]

Thus, the probability of undertaking innovative activities increases with market power (low ) and low minimum required expenditures relative to sales ( ), a high elasticity of demand with respect to quality ( ) or a high elasticity of quality with respect to R&D expenditures ( ).

In addition, it can be checked that optimal effort will be given similarly to (6) by

\[\frac {x _ {i} ^ {*}}{p _ {i} ^ {*} q _ {i} ^ {*}} = \frac {\theta \varepsilon}{\eta}.\]

This effort will be observed if it is higher than the threshold value, given by . In the simplest case developed thus far, every firm in the industry will take the same action, and hence we would observe only different R&D decisions in different industries. But the model can generate easily asymmetric outcomes. Suppose, for example, that firms are characterized by different abilities to increase quality from R&D expenditures (different ) or face different minimum expenditures (different ). Then, we can obtain equilibria where some firms do innovative activities and others do not in the same industry.

The equilibrium relationships for the price-cost margin (PCM) and technological effort (E) suggested by the theoretical framework can be summarized as follows

\[\begin{array}{r c l} {P C M _ {i}} & = & {1 \big / \left(\frac {p}{q} \frac {\partial q}{\partial p}\right) _ {i}} \\ {E _ {i} ^ {*}} & = & {P C M _ {i} \quad \left(\frac {s}{q} \frac {\partial q}{\partial s}\right) _ {i} \quad \left(\frac {x}{s} \frac {\partial s}{\partial x}\right) _ {i},} \end{array}\]

where the following observability condition holds for the optimal technological effort

\[E _ {i} = \left\{ \begin{array}{c c} E _ {i} ^ {*} & i f \qquad E _ {i} ^ {*} > \widetilde {E} _ {i} \\ 0 & o t h e r w i s e. \end{array} \right.\]

That is, the optimal technological effort will be observed whenever it is greater than a critical level or threshold value .

Let x be the vector of variables explaining the price and quality elasticities and z the vector of those variables in which we will condition the price-cost margin. If we write , , and , then the previous theoretical model can be cast in the following simultaneous econometric model

\[{e ^ {*}} = {\alpha m + x \beta_ {1} + u _ {1}}\tag{7}\]

\[m = z \beta_ {2} + u _ {2}\tag{8}\]

\[\widetilde {e} = x \beta_ {3} + u _ {3}.\tag{9}\]

where the variable is a latent variable that we will only observe according to

\[e = \left\{ \begin{array}{l l} e ^ {*} & i f \qquad e ^ {*} > \widetilde {e} \\ 0 & o t h e r w i s e. \end{array} \right.\tag{10}\]

Equation (7) explains the optimal effort in terms of the price-cost margin and the vector of determinants of the elasticities. According to the theoretical model, we expect to hold. However, we do not impose this constraint to use the estimation of as a test of the validity of the specification. In addition, will prove to be a key parameter in the identification of the model.

>From now on we reserve the asterisk to denote the latent or not fully observed variable optimal effort , to be distinguished from the observed effort E. The asterisk on the optimal PCM, always observed, is suppressed to simplify notation.

PCM,

Optimal effort is a censored variable, and equation (7) together with the rule of observability (10) constitutes a Tobit type model. The rule of observability specifies that the dependent variable is only observed if it is greater than a threshold.

Equation (9) specifies the thresholds. The variables that determine the threshold are supposed to be the same as those that explain the optimal effort, with the price-cost margin as the only exception. This follows closely the theoretical framework, where the thresholds result from the shape of the frontier defined by the set of feasible pairs sales-R&D expenditure. The dependent variable of this equation is not observed, and the estimation of predicted values for the thresholds will be a by-product of the model.

Finally, equation (8) specifies the price-cost margin conditional on z. This equation can be understood either as a reduced form equation or a structural equation. As a reduced form, it can be thought of as the result of solving a subsystem consisting of equation (7) and an equation like

\[m = \alpha_ {2} e ^ {*} + x _ {2} \beta_ {2} + u _ {2} ^ {\prime}.\tag{8'}\]

That is, a structural margin equation in which optimal effort would influence the price-cost margin. Identification of this subsystem would imply that and x each had at least one non-overlapping variable. In this case z should consist of all the common variables plus the non-overlapping ones.

But, if holds in equation , then the price-cost margin equation (8) can be thought of as a structural equation, where we have written z for and for . To adapt equation (8) to these two possible interpretations, we will start with the broadest specification, allowing the exclusions on z to be done by the estimation.

In any case, the hypothesis that we must test explicitly is whether the margin depends on the observed effort. This dependence, that might be considered somewhat likely, corresponds to the hypothesis of non-independence of the price elasticity of demand from the level of quality. If this were the case, it would have two main consequences. Firstly, the margin equation would be

\[m = \alpha_ {2} e + x _ {2} \beta_ {2} + u _ {2} ^ {\prime}.\tag{8"}\]

and the obtention of an explicit linear reduced form for the margin would be precluded (see Blundell and Smith (1994)) . This would have implications on the suitable econometric procedures. Secondly, the determination of the thresholds independently of price would be doubtful, and the exclusion of the margin in the thresholds equation would lose support creating an identification problem (see below).

Together, equations (7)-(10) define a variant of the Gronau-Nelson model (Gronau (1973), Nelson (1977)), that was created to explain participation decisions in the labor market, and where the censored variable is market wage and the thresholds are reservation wages. Alternative identification conditions for the parameters of this model are discussed in Maddala (1983) or Amemiya (1985), among others. One of the possible identification conditions is that at least one variable included in the equation for the censored variable is not included in the thresholds equation. This condition arises naturally in our model, because margins determine optimal effort but can be excluded, on theoretical and testable grounds, among the determinants of the thresholds. But margins cannot be considered exogenous. Therefore, the basic model must be amended to accommodate endogenous variables in the equation for the censored variable.

To estimate the model, we apply the conditional maximum likelihood approach developed by Smith and Blundell (1986) and Blundell and Smith (1989,1994). We start by assuming the joint normality of the disturbances , and . Then, we proceed in three steps as follows.

Firstly, we will check that we can reject the hypothesis that equation (8") represents the correct modelling, i.e. that observed effort e is a determinant of the margin. To do so we test, as Blundell and Smith (1994) suggested, this structural equation for the price-cost margin against the (non-nested) explicit reduced form for the margin that would arise in any other case. This is a Davidson and McKinnon (1981) test, that amounts to test in the IV estimation of the equation

The simultaneous model represented by equations (7) and (8") does not possess an explicit reduced form, because e is a censored variable.

\[m = \alpha_ {2} e + x _ {2} \beta_ {2} + \delta \widehat {m} + \widetilde {u} _ {2},\]

where . Once this specification is discarded, we can safely take our equation (8) either as a reduced form or as a structural form that does not include .

Secondly, we will consider the model conditional on the disturbance , replacing this disturbance by its least squares estimate from the margin equation (see Appendix A for details). Thus, we will be left with the following Tobit model

\[\begin{array}{r c l} {e ^ {*}} & = & {\alpha m + x \beta_ {1} + \rho_ {1} \widehat {u} _ {2} + v _ {1}} \\ & & \\ {\widetilde {e}} & = & {x \beta_ {3} + \rho_ {3} \widehat {u} _ {2} + v _ {3}} \end{array}\]

with the observation rule

\[e = \left\{ \begin{array}{c c} e ^ {*} & i f \qquad e ^ {*} - \widetilde {e} > 0 \\ 0 & o t h e r w i s e, \end{array} \right.\]

were we can apply standard procedures.

Finally, we will estimate the previous model by means of the Heckman (1976) two stage procedure (see Appendix A for details). That is, we will estimate by ML the probit model

\[I = \left\{ \begin{array}{l l} 1 & i f \qquad \frac {\alpha}{\sigma} m + x \left(\frac {\beta_ {1} - \beta_ {3}}{\sigma}\right) + \left(\frac {\rho_ {1} - \rho_ {3}}{\sigma}\right) \widehat {u} _ {2} > \frac {\nu}{\sigma} \\ 0 & o t h e r w i s e \end{array} \right.,\]

and we will use the computed inverse Mills ratio to estimate by OLS the optimal effort equation

\[e ^ {*} = \alpha m + x \beta_ {1} + \rho_ {1} \widehat {u} _ {2} + \beta_ {\lambda} \widehat {\lambda} + \xi .\]

>From the parameter estimates of this equation and the probit equation, it is possible to recover estimates for all the parameters of the model. Thus, we will use the estimates to compute thresholds.

5.- DATA AND RESULTS

The data set we use is an unbalanced panel of 2,020 Spanish manufacturing firms, observed during the 6 year period 1990-1995. For two thirds of the firms we have three or more time observations (see the details in Appendix B). The sample comes from a somewhat broader sample of Spanish manufacturing that can be considered approximately representative, with different degrees of representativeness, of two manufacturing subpopulations: firms with under 200 workers and firms with more than 200 workers. Our subsample consist of the set of firms for which the data required in this exercise are available. We pool together all the observations when we intend to estimate conditional expectation functions, but it is convenient to treat separately the subsamples in description .

Among the firms, almost 30% report R&D expenditure every year they are observed, 20% report positive R&D expenditures only part of the years in which they are observed, and 50% report zero R&D expenditures every year in which they are observed (see more details in Appendix B). The degree of permanence in the sample (years in which the firm is observed) does not seem to affect systematically either the probability to expend on R&D or the average R&D intensity. On the contrary, the occasional R&D performers show clearly lower average R&D intensities. We interpret these firms as crossing occasionally the threshold and we leave this fact, as well as their effort, to be explained by the model.

Before beginning with the econometric exercise, it is convenient to summarize some basic facts which must be explained. Table 1 classifies the sample of firms according to industry and size, and distinguishes between R&D performers (stable and occasional) and non-performers. Figure 2 reports the R&D distributions according to the size of firms. The probability of undertaking R&D activities changes dramatically by industry, ranging from 0.13 to 0.68 for the smallest firms, and from 0.46 to 1 for the biggest, and is notably higher for the latter within each industry. The average R&D effort of the performers changes equally across industries and sizes, ranging from a modest intensity of 0.35 per-centual points to 4.5 points. In two thirds of the industries, the average effort of the smallest firms is higher than the effort of the biggest. These patterns are more or less the usual, and reveal a great heterogeneity that goes beyond our rough classification by industries. We expect the econometric model to help in explaining this heterogeneity.

At the beginning of the period, firms with under 200 workers were sampled randomly by industry and size strata, retaining 5%. Firms with more than 200 workers were all requested to participate, and the positive answers represented more or less a self-selected 60% of firms with this size. To keep representativity, samples of newly born firms were added every subsequent year. Exits from the sample are both for death and attrition.

Our empirical model is defined by equations (7) to (9), and our main interest is the estimation of the effort equation (7) subject to the thresholds observability rule (10). However, as explained in section 4, the margins equation (8) must be estimated to deal with the endogeneity of the price-cost margin in the effort equation.

We begin by building up a classical margin equation (see, for example, Martin (1993)), where we add observed effort as a regressor (Table 1, first column of estimation I) . The equation includes, firstly, the log of the firms market share. This variable is included according to the insights given by any oligopoly model and its proven empirical importance in explaining margins in empirical analysis with firm data . Secondly, and according to a well known practice, we include the ratio of advertising expenditure to sales. Thirdly, we include the rate of the utilization of capacity and a set of time dummies to pick-up the cyclical and macroeconomic effects. Fourthly, we include two typical control variables. The ratio of capital to sales, to control for the lack of subtraction of the user cost of capital in computing the price-cost margin. And a measure of the importance of self-employment in the firm, to control for the lack of a proper deduction of some labour costs.

The equation is estimated by instrumental variables, taking both the effort and market share variables as endogenous . We treat as endogenous the firms' shares because they must be considered simultaneously determined with the price and R&D expenditures. Even if we are not specially interested in the underlying equation in which these shares are determined, this simultaneous determination must be borne in mind and taken into account. The estimated equation looks very reasonable: the coefficients agree with the expected impacts and have sensible values.

When effort is zero we adopt the usual solution of setting the log of the R&D variable iqual to zero, adding a dummy variable that takes the value one for these observations and zero otherwise (see, for example, Klette (1996)).

As there are firms with zero market share (meaning no significant market share) we apply to this variable a similar treatment to effort.

The instruments employed in the estimation are just the exogenous variables we are going to use in the specification of the effort equation (see below), and some additional variables which we guess they could

The second column of estimation I specifies the reduced form corresponding to the alternative hypothesis according to which the variable that must be included to explain margins is latent effort (see section 4). The specification test for non-nested models clearly rejects the structural form against this alternative. Therefore, we conclude that margins are not a function of observed effort.

Furthermore, the low significance of most of the effort determinants in the reduced form equation suggests that effort can probably be completely excluded from the margins equation (estimation II). To test this particular specification, we carry out an F-test on the exclusion of the effort determinants included in the reduced form. This is done by testing the reduced form specified in estimation II against the former one. As a result, we accept that margins can also be considered independent of current latent effort and, therefore, that the structural and reduced form equations of estimation II are the right model for margins. Consequently, we will use this last reduced form to estimate the residuals to apply the conditional maximum likelihood approach method, explained in section 4, to the estimation of the effort equation. Now, we switch to the specification of this equation.

According to the theoretical framework, optimal effort may be seen as determined, besides by the price cost margin, by two basic elasticities: the elasticity of demand with respect to quality, and the elasticity of quality with respect to R&D expenditures. The first elasticity is a characteristic of the demand function, given by the nature of the good and consumer preferences. The second elasticity is a feature of the function of production of quality, and depends on the ease to translate R&D expenditures to product innovations affecting quality.

enter a shares' equation. In particular, we use two dummies describing the extreme outcomes of a very concentrated market (less than 10 competitors) and a very atomized one.

Every non-overlapped exogenous determinant of shares and effort (the previous instruments) is included after the exogenous variables that were already included in the price-cost margin equation.

To account for the differences in the elasticity of demand with respect to quality we will use four variables, two direct indicators of product characteristics and two indirect indicators, related with the dimensions of the market. The first variable, quality sensitivity, indicates high product sensitivity to quality. The second variable, standard product, provides an indicator of whether the good presents a high distance from specific consumer preferences and needs, and hence can be considered an inverse indicator of quality of one specific dimension of quality. The third and fourth variables, extensive market and export intensity assume respectively that the higher the dimension of the market and the proportion of sales made abroad, the higher the sensitivity of the good to quality.

To give account of the ease of production of quality, or elasticity of quality to R&D expenditures, we will also use four variables. The first variable, skilled labor, is intended to measure firm ability to perform complex tasks. The second variable, geographical opportunities, takes into account that innovation is eased in big cities through the interaction of firms and research centres, the presence of strong spillovers and so on (see, for example, Audretsch and Feldman (1996)). The third variable, entrant firm, is included because younger firms possess superior processes and organization, specially adapted to product innovations. Finally, we will use the traditional indicator of “revealed” technological opportunities, the yearly average number of patents in each industry.

We include, in addition to these variables, a set of 18 industry dummies, 6 size dummies and a set of time dummies. The time dummies are included to control for any type of macroeconomic effects. The industry and size dummies are included to control for other unobservable determinants of optimal effort related with industry and size characteristics.

Now, we are going to analyze the results of estimating the optimal effort equation taking into account the censoring of the dependent variable and the endogeneity of margins. But, before turning to this estimation, it is worth looking briefly at the results of non treating or treating only partially the problems of endogeneity or censoring.

Table 3 reports the results of alternative estimations of an effort equation. The first column reports the results of running a simple OLS estimation across the whole sample, using as a dependent variable the log of effort or zero according to the positiveness of effort. The second column uses all the exogenous margins determinants (see the previously estimated reduced form) as instruments for the margin. The third and fourth columns report the result of a two stage procedure of estimation, using first a zero-one index of the values of the variables to estimate the probability of finding positive effort, and an OLS estimation of an effort equation for the forms with positive effort, that includes as a regressor the inverse Mills ratio computed from the previous estimation. We do not try any correction for endogeneity. These estimates show that the main difference between the OLS and IV estimation without treating censoring is the value of the coefficient on the margin variable, that rises when endogeneity is dealt with, and that the treatment of censoring reveals significant differences between the probability and effort intensity equations.

Table 4 reports the results of our two stage conditional estimation, that uses the residuals computed from the margins reduced form equation to control for endogeneity in a two stage procedure to treat censoring. The estimation improves greatly the coefficient of the margin that, if lower than unity, it cannot be rejected as being equal to one, while the rest of the coefficients remain close to the previous two stage estimation. We interpret the result as a validation of the theoretical underlying framework, in which margins enter the optimal effort equation with a unity coefficient .

All the variables aimed at explaining optimal effort as a function of the elasticity of demand to quality have the expected sign and a strong impact. Similarly, all the variables included to give account of the elasticity of quality production with respect to R&D expenditures have the expected sign and sensible coefficients. On the other hand, optimal effort presents an important additional heterogeneity by industries, given by the value of the industry dummies, while the time dummies do not detect significant differences across time. Interestingly enough, the size dummies are not significant and, if any, they tend to suggest an increase of the optimal effort at the biggest sizes. This contrasts sharply with the fact that the smaller firms tend in practice to present higher efforts. Our equation confirms that this is not a characteristic linked to the shape of the frontier sales-R&D expenditures that, if any, would justify an optimal effort increasing in size.

We attribute the lack of precision of the estimation to the inadequacies of our specification: the neglect of the dynamic aspects of the decisions, the use of a gross margin proxy, the effect of heterogeneity in financial conditions, etc... In any case, the optimal effort equation represents a notable estimation by itself, with sensible coefficient values, allows us to deduce the threshold determinants from the differences among the probability and intensity equations.

The most interesting result from the estimated equation is, however, the derived estimates for the parameters of the thresholds, reported in the last column. Again, signs and values look very reasonable. Recall that the thresholds give the value of effort under which firms will not find it profitable to undertake R&D expenditures. We can summarize the results as follows. If the product presents a high quality sensitivity the threshold is lower, but if the product has a low degree of standardization the threshold is higher. Extensive markets for the good increase thresholds, but the highly exported goods present lower thresholds. The product sophistication revealed by a high proportion of skilled labor increases thresholds, and the highest industry opportunities are associated to high thresholds. Interestingly enough, the entrant firms and the firms located outside the main industrial centres do not seem to face significantly higher thresholds, a fact that one can rationalize by the technological nature of the thresholds. Finally, the size of the firm influences the size of the thresholds. The bigger the firms the lower the threshold. This suggests that part of the size of the thresholds can be determined by the presence of some economies of scope, due to the presence of other investments, which increase with size. Figure 3 depicts the R&D effort distributions by industries and reports the thresholds.

6.- CONCLUSIONS

A number of interesting conclusions are derived from this paper. First, thresholds exist. That is, there are minimum statistically significant R&D intensities under which firms tend to not invest. Second, thresholds are not negligible. For example, thresholds range roughly across industries from 0.2 to 0.5 of the R&D intensity of the median performing firm. Third, thresholds vary importantly according to demand characteristics and technological opportunities. And they vary in a fashion that does not coincide necessarily with the role played by these demand characteristics and technological opportunities in inducing effort. We give some examples. A high sensitivity to quality of the product induces high effort, but lowers the thresholds. Product complexity, instead, induces high effort and increases thresholds. Entrant firms and firms located at the great industrial centres show higher effort, but they face more or less the same thresholds as the rest of the firms. Four, thresholds also vary by industry and firm size, reflecting the additional impact of unobserved variables.

The most interesting set of findings refers size. Very small R&D performing firms, once the effect of the other variables aimed at explaining effort is controlled, no longer show a size intensity effect. Only the biggest sizes tend to show an imprecisely estimated positive effect of size. These findings validate the idea of a concave frontier and suggest that it can possess a constant elasticity shape. On the other hand, size presents a strong and monotone inverse effect on thresholds (the bigger the firms the lower the thresholds). On average, the biggest firms show a threshold that amounts to half of the threshold of the smallest firms. Size thresholds therefore explain part of the variations by size in the likelihood to spend in R&D. This suggests the relevance of a particular version of the hypothesis of the advantages of size because of the presence of complementary activities. The greater are some activities consubstantial to size, the lower are the minimum requirements to start affecting quality spending on R&D.

In addition, our general joint modelling of the decision to undertake R&D and the intensity of these activities has been shown to give sensible results. Then, the determinants of threshold values can be employed to guide policy recommendations. For example, our estimates suggest that specific product campaigns to reinforce consumers' sensitivity to quality can increase the firm's likelihood of performing R&D. Furthermore, the theoretical model can be extended to analyze the implications of firms investment constraints and the effect of subsidies on the R&D decisions. Moreover, the modelling can be extended to firm decisions similar to the R&D decisions affected by thresholds (for example, exports).

Appendix A: Econometric model and estimation strategy.

The starting model is

\[{e ^ {*}} = {\alpha m + x \beta_ {1} + u _ {1}}\]

\[m = z \beta_ {2} + u _ {2}\]

\[\widetilde {e} = x \beta_ {3} + u _ {3},\]

where we assume that and and are jointly normally distributed disturbances, with variances and covariances .

Obtaining the conditional model

Following the conditional maximum likelihood approach, we can rewrite the first equation conditional on as

\[e ^ {*} = \alpha m + x \beta_ {1} + \rho_ {1} u _ {2} + \varepsilon_ {1},\]

where and . Due to the joint normality of and , with , and is independent of and .

Similarly, we can express the third equation conditionally on . This gives the following conditional model

\[\begin{array}{r c l} {e ^ {*}} & = & {\alpha m + x \beta_ {1} + \rho_ {1} u _ {2} + \varepsilon_ {1}} \\ & & \\ {\widetilde {e}} & = & {x \beta_ {3} + \rho_ {3} u _ {2} + \varepsilon_ {3},} \end{array}\]

with the following conditional censoring rule

\[e = \left\{ \begin{array}{c c} e ^ {*} & i f \qquad \alpha m + x (\beta_ {1} - \beta_ {3}) + (\rho_ {1} - \rho_ {3}) u _ {2} > \varepsilon_ {3} - \varepsilon_ {1} \\ 0 & o t h e r w i s e. \end{array} \right.\]

This model has the structure of the standard unobserved thresholds model.

To obtain an estimable model, must be replaced by its consistent estimator , where . Then, the disturbances become and , but the second terms of these expressions are asymptotically negligible for the consistency properties. Hence, the standard Tobit procedures of estimation can be applied.

Two stage estimation of the conditional model

Write the Tobit model as

\[e = \left\{ \begin{array}{l l} e ^ {*} & = \alpha m + x \beta_ {1} + \rho_ {1} u _ {2} + \varepsilon_ {1} \quad i f \qquad w \gamma > \frac {\varepsilon}{\sigma} \\ 0 & \text {otherwise,} \end{array} \right.\]

where , , and , with . Define the dichotomous variable . Then, using the probit model, substituting for , we can get estimates of , , , and compute the inverse Mills ratio .

The expectation of the nonzero observations of the first equation can be written as

\[E (e ^ {*} | w \gamma > \frac {\varepsilon}{\sigma}) = \alpha m + x \beta_ {1} + \rho_ {1} u _ {2} + E (\varepsilon_ {1} | w \gamma > \frac {\varepsilon}{\sigma}),\]

where . Therefore, the first equation can be rewritten as

\[e ^ {*} = \alpha m + x \beta_ {1} + \rho_ {1} u _ {2} + \beta_ {\lambda} \lambda (w \gamma) + \xi .\]

The estimation of this model, replacing by its estimation, provides directly an estimate of the parameters and . Using these estimates, together with the probit estimates of , we can obtain an estimation of , and hence of every parameter of the third equation. In particular, we have

\[\begin{array}{r c l} \widehat {\sigma} & = & \frac {\widehat {\alpha}}{\widehat {\gamma} _ {\alpha}} \\ \widehat {\beta} _ {3} & = & \widehat {\beta} _ {1} - \widehat {\sigma} \widehat {\gamma} _ {\beta}. \end{array}\]

On the other hand, we know that

\[E (\varepsilon_ {1} ^ {2} | w \gamma > \frac {\varepsilon}{\sigma}) = \sigma_ {1} ^ {2} + \frac {\sigma_ {1} ^ {2} - \sigma_ {1 3}}{\sigma} w \gamma \frac {\phi (w \gamma)}{\Phi (w \gamma)}.\]

This suggests to estimate as

\[\widehat {\sigma} _ {1} ^ {2} = \frac {1}{N} \sum_ {i} \left[ \widehat {\xi} ^ {2} - \widehat {\beta} _ {\lambda} (w \gamma) \widehat {\lambda} \right],\]

and, given an estimate of , it is possible to obtain estimates of and in the following way

\[\sigma_ {1 3} = \widehat {\sigma} _ {1} ^ {2} - \sigma \widehat {\beta} _ {\lambda}\]

\[\sigma_ {3} ^ {2} = \widehat {\sigma} ^ {2} + \widehat {\sigma} _ {1} ^ {2} - 2 \widehat {\sigma} \widehat {\beta} _ {\lambda}.\]

Appendix B: Sample and variable statistics and variable definition

Technological effort: ratio of total R&D expenditures to sales. Total R&D expenditures include the cost of inside R&D activities, the payments for outside R&D contracts, and the expenditures on imported technology (patent licenses and technical assistance).

Price-cost margin: approximated by the value of gross output minus variable costs of production, divided by the value of gross output. The gross output value is computed as sales + stocks variation + other revenues, and the variable costs of production as intermediate consumption (raw materials and services) + labor costs. R&D services have been excluded from cost, and an estimation of the costs represented by the R&D personnel has been deducted from the total labor costs.

Market share: the market share reported by the firm in its main market. In the surveys firms are asked to split their total sales by markets and report their market shares. If a firm reports that its share is not significant, we set zero market share.

Advertising intensity: ratio of advertising expenditures to sales.

Capacity utilization: average rate of utilization, as reported by the firm, of the normal capacity of production.

Relative age: difference between the age of the firm and the average age of the firms in the industry.

Capital intensity: ratio of non financial assets to gross output.

Self-employment: ratio of the number of relatives of the owner working in the firm to total workers.

Less than ten competitors: dummy variable which takes the value one if the firm reports that its main market has less than ten competitors.

Atomized market: dummy variable which takes the value one if firm reports that its main market is atomized.

Quality sensitivity: dummy variable which takes the value one if the firm reports that it carries out quality controls on a systematic basis.

Standard product: dummy variable which takes the value one if the firm reports that its products are highly standardized, as opposed to specifically designed for the customers, and that the rivals rarely change their products.

Extensive market: dummy variable which takes the value one if the firm reports that its main market is national and/or international, as opposed to local or regional.

Export intensity: ratio of exports to sales.

Skilled labor: ratio of the number of highly qualified workers (engineers and graduates), once the R&D personnel deducted, to total personnel.

Entrant firm: dummy variable which takes the value one if the firm is five or less than five years old.

Geographical opportunities: dummy variable which takes the value one if the firm has its main plant in a big city (more than 500.000 inhabitants).

Average industry patents: yearly average number of patents registered by the firms in the industry (excluding the patents registered by the firm).

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Table B1: Number of ...rms by time spells and type of R&D performers.

Firms reporting reports zero R&D expenditures every observed year Firms reporting reports positive R&D expenditures every observed year Firms reporting positive R&D expenditures some of the observed years

Table B2: Variable descriptive statistics

Table 1: R&D performers and R&D export by sectors

Table 2: A test on the dependence of pricing from the observed export Dependent variable: Price cost margin (in logs)

T- statistics in parentheses

Table 3: Alternative estimation of the R&D export equation Dependent variable: R&D export (in logs)

T-statistics in parentheses OLS standard errors in the two step estimation are robust. The dependent variable of the ...rst two columns is log of ((R&D expenditures/sales) * 1000) if e*ort >0 and zero otherwise

Table 4: Optimal R&D e and thresholds determinants Dependent variable: R&D e (in logs)

OLS standard errors in the two step estimation are robust

Table 5: Estimated export thresholds for product R&D activities

Figure 1: The determination of R&D expenditures