SMEs’ INVESTMENT DETERMINANTS: EMPIRICAL EVIDENCE USING QUANTILE APPROACH

This paper makes an important contribution to the literature on SMEs, namely investigating whether the relationships between determinants and investment are dependent on the level of investment. Based on a sample of Portuguese SMEs, using two-step estimation method, fi rstly using probit regression and secondly using quantile regressions, we fi nd signifi cant non-linearities in relationships formed between determinants and investment over the distribution of investment. In particular, we fi nd that: 1) sales, age and growth opportunities are restrictive determinants of investment for low levels of investment, but positive determinants of investment for high levels of investment; 2) debt and the interest rate are restrictive determinants of investment but only for low and intermediate levels of investment; 3) cash fl ow is a positive determinant of investment, but is more important for investment regarding low levels of investment; 4) GNP is a positive determinant of investment, but only for high levels of investment; and 5) investment in the previous period is a positive determinant of investment in the present period, but only for intermediate and high levels of investment. The relevance of the various theories explaining fi rm investment depends on SMEs’ level of investment.


Introduction
Various theories have tried to explain fi rm investment. Neoclassical Theory, Free Cash Flow Theory and Agency Theory are particularly important in this context. According to Neoclassical Theory (Hall, Jorgenson 1967;Jorgenson 1971;Chirinko 1993) investment is explained by fi rms' exogenous variables, sales being particularly important in this context. If sales increase, fi rms increase investment, and if sales fall, they reduce investment.
Based on the information asymmetry in relationships formed between owners/managers and creditors, the studies by Fazzari et al. (1988) and Fazzari and Petersen (1993) originated Free Cash Flow Theory. According to Free Cash Flow Theory, unlike what is proposed by Neoclassical Theory, investment depends on fi rms' endogenous factors, cash fl ow being particularly important in explaining fi rm investment. The high sensitivity of investment to variations in cash fl ow indicates the severe constraints felt by fi rms in fi nancing their investment.
Finally, Agency Theory bases its assumptions on the confl icts, on one hand between owners and managers, and on the other, between owners/managers and creditors. In this particular context, use of debt is particularly relevant with the aim of lessening confl icts between owners and managers and between owners/managers and creditors.
The various studies about fi rms' investment determinants (for example, Fazzari et al. 1988;Fazzari, Petersen 1993;Lang et al. 1996;Mizen, Vermeulen 2004;Aivazian et al. 2005;Bond, Van Reenen 2007;Junlu et al. 2009;Sun, Nobuyoshi 2009) consider the central tendency of investment, and do not check whether relationships between determinants and investment tend to be similar for low and high levels of investment.
In Europe in general, and Portugal in particular, SMEs are particular importance to the economy. In Portugal, SMEs represent 99.68% of total number of fi rms, and representing 72.5% of employment, 57.9% of turnover, and 59.8% of gross added value at factor costs, in relation to the total of fi rms (National Institute of Statistics 2010). SMEs in Portugal are special importance for employment and economic growth.
Given the importance of SMEs as agents of change and for creating employment and economic growth, this study aims to investigate whether the relationships between determinants and investment are identical in SMEs with low and high levels of investment. The study is particularly important since it allows us to suggest different guidelines for economic policy according to SMEs having low or high levels of investment.
To fulfi l the objective of this paper, we consider a sample of 1845 SMEs. To solve conveniently the problem of possible bias in the results obtained, due to the survival issue, we use the two-step estimation method proposed by Heckman (1979). At a fi rst stage, considering all SMEs, both surviving and non-surving, we estimate probit regressions. At a second stage, we use quantile regressions to determine relationships between determinants and investment. This paper makes important contributions to the literature on SMEs. Firstly, it is pioneering in applying quantile regressions to the study of SME investment determinants. Secondly, it shows there are signifi cant non-linearities in the relationships established between determinants and SME investment. Thirdly, it presents a wide range of SME investment determinants. Fourthly, it shows that the applicability of the different explanatory theories of investment depends, in the SME context, on the level of investment, i.e., if SMEs have high or low levels of investment. Fifthly, given use of the two-step estimation method, the paper makes an additional contribution to the literature, namely identifying the positive and restrictive determinants of SME survival.
After this introduction, the paper has the following structure: section 2 presents the hypotheses for investigation; section 3 presents the methodology used, namely the database, variables and method of estimation; section 4 presents the results obtained; section 5 goes on to discuss these results; and fi nally, section 6 presents the conclusion and implications of the study.

Investigation hypotheses 2.1. Sales
According to Neoclassical Theory, sales stand out in explaining fi rm investment. If sales increase, fi rms increase investment and if sales fall, they reduce investment (Hall, Jorgenson 1967;Jorgenson 1971;Chirinko 1993). Regarding the importance of sales as a central determinant in explaining investment, Eisner (1963) and Chirinko (1993) conclude that sales have clear statistical predominance over any other variable in explaining fi rm investment. Various studies, among which we could highlight those of McConnell and Servaes (1995), Lang et al. (1996), Aivazian et al. (2005) and Serrasqueiro et al. (2008), identify a positive relationship between sales and investment. These studies were made in the context of large fi rms.
In SMEs, the importance of sales is expected to be less than in the case of large fi rms. In multiple situations, for small fi rms, sales are more relevant for coping with occasional diffi culties in cash management than for making investment.
We can expect sales to have a limited effect on investment when SMEs have low levels of investment, a situation which should be reversed for SMEs with high levels of investment. Therefore, for SMEs that invest less, the sales variable should have little expression in the market, and as such an effect of apprehension and incapacity in relation to investment should result, as SMEs that make little investment jeopardize their survival in the market. For SMEs with high levels of investment, those higher levels of investment could be a consequence of a positive evolution of sales.
Based on the arguments presented, we formulate the following hypothesis: H1: he positive relationship between sales and investment is of a greater magnitude for SMEs with high levels of investment than for SMEs with low levels of investment.

Cash fl ow
The studies by Fazzari et al. (1988) and Fazzari and Petersen (1993) indicate that cash fl ow is a relevant determinant in explaining fi rm investment. According to the authors, the greater sensitivity of investment to cash fl ow indicates that fi rms are fi nancially restricted. The conclusions of these authors gave rise to Free Cash Flow Theory, a theory which disputes the arguments of Neoclassical Theory since it considers that fi rms' endogenous determinants, with special prominence for cash fl ow, are relevant in explaining fi rm investment. Fazzari et al. (1988) show that fi rm investment is dependent on cash fl ow, fi nding a positive relationship between the level of fi rms' cash fl ow and investment. The authors also show that the sensitivity of investment to variations in cash fl ow is greater in fi rms that are more susceptible to credit rationing, due to the information asymmetry in the relationships between shareholders/owners and creditors. In this context, Hoshi et al. (1991) conclude that in fi rms with a better relationship with creditors, and consequently subject to fewer problems of information asymmetry, investment is less sensitive to cash fl ow variations than in fi rms with a worse relationship with creditors, the latter type of fi rms being more dependent on cash fl ow for investment, given the greater information asymmetry and consequently lesser capacity to obtain credit. Fazzari et al. (1988), Hoshi et al. (1991), Fazzari and Petersen (1993), Hubbard et al. (1995), Zingales (1997, 2000), Cleary (1999), Vermeulen (2002), Mizen and Vermeulen (2004), Bond and Van Reenen (2007), Junlu et al. (2009) andSun andNobuyoshi (2009) fi nd empirical evidence of a positive relationship between cash fl ow and fi rm investment. The relevance of cash fl ow in determining fi rms' investment decisions is due to the information asymmetry in relationships between shareholders/ owners and creditors, with cash fl ow being more relevant in explaining fi rms' investment the smaller their size and the poorer the relationship with creditors. Fazzari et al. (1988) conclude that SMEs face greater restrictions in accessing external fi nance, and so become more dependent on internal funds as a means to fi nance investment. Gertler and Gilchrist (1994), Petersen and Rajan (1995) and Vermeulen (2002) argue that cash fl ow is a particularly relevant variable in explaining investment in SMEs, given the lesser possibility of obtaining credit due to the reduced capacity to provide collateral and greater likelihood of bankruptcy.
Considering that SMEs with low levels of investment are more affected by fi nancial constraints, we can expect their investment to be more sensitive to cash fl ow, compared to what happens in SMEs with high levels of investment and probably less affected by fnancial constraints.
Based on the arguments presented, we formulate the following hypothesis for investigation:

H2:
The positive relationship between cash fl ow and investment is of a greater magnitude in SMEs with low levels of investment than in SMEs with high levels of investment.

Debt
According to Jensen and Meckling (1976), there are two types of agency confl icts: 1) confl icts between owners/managers and creditors; and 2) confl icts between owners and managers.
In the SME context, agency problems between owners/managers and creditors are particularly important, since in the great majority of cases ownership and management of SMEs is in the same hands. Jensen and Meckling (1976) state that when a fi rm uses outside capital, confl icts of interest arise between shareholders/owners and creditors. A higher level of debt, whether to reduce the agency costs of equity or for any other reason, can lead the fi rm to face another type of cost: the agency cost associated with external capital. This cost, generated by the confl ict of interests between shareholders/owners and creditors, greatly limits fi rms' recourse to debt. Lenders restrict fi rms' level of credit, since shareholders/ owners can invest in high-risk projects aiming to increase the value of equity rather than the value of the debt. Therefore, if the project succeeds, owners receive most of the profits, but on the other hand, if it fails creditors bear most of the costs (Jensen, Meckling 1976). Based on agency problems, Myers (1977) and Zwiebel (1996), conclude that a negative relationship is to be expected between debt and the level of fi rm investment, given that creditors make access to credit more diffi cult in situations of greater information asymmetry concerning the profi tability and risk of projects, with fi nance only being channelled to more profi table and less risky projects. Myers (1977), Jensen (1986), Stulz (1990), McConnell and Servaes (1995), Lang et al. (1996), Aivazian et al. (2005), Ahn et al. (2006), Firth et al. (2008) Lee and Ratti (2008) obtain a negative relationship between debt and investment. In addition, Lee and Ratti (2008) fi nd that relationship to be of a greater magnitude in small fi rms.
As fi rms invest more, we can expect the possible negative effect of debt on investment to be weaker. This may happen because fi rms that invest more give a positive sign to lenders, in such a way that the agency costs arising from the confl ict between owners/ shareholders and creditors diminish. So the fi rms that invest most can resort to debt as a way to fi nance their projects, as creditors eventually make it less diffi cult tol access debt. On the contrary, the fi rms that invest least continue to give the market a sign of lack of vitality and confi dence, and so creditors increase the cost of capital as a way of minimizing the information asymmetry concerning the profi tability and risk of projects, preventing fi rms from investing in low-profi tability, high-risk projects.
Based on the arguments presented, we formulate the following hypothesis for investigation:

H3:
The negative relationship between debt and investment is of greater magnitude in SMEs with low levels of investment than in SMEs with high levels of investment.

Age
Authors such as Fazzari et al. (1988) and Johansen (1994) state that SMEs face greater obstacles in obtaining external fi nance. Beck et al. (2006) argue that fi rm age serves as a proxy for their fi nancial constraints, although this lessens as fi rms grow.
The SMEs that make least investment will be made up of young fi rms that invest less due to liquidity constraints and older SMEs that invest less due to having fewer growth opportunities. Therefore, if for SMEs that invest less the relationship between investment and age is negative, this means the reduction in young fi rms' fi nancial constraints does not get over the lack of profi table projects. If the opposite happens for fi rms that invest less, this means age reduces liquidity constraints. SME age can serve as an important proxy for reputation and credibility (Diamond 1989;Ang 1991), allowing access to external fi nance on more advantageous terms, which may contribute decisively to age leading fi rms to invest more. We can therefore expect the impact of age on investment to be greater in SMEs with high levels of investment than in SMEs with low levels of investment.
Based on the arguments above, we formulate the following hypothesis for investigation: H4: The positive relationship between age and investment is of a greater magnitude in SMEs with high levels of investment than in SMEs with low levels of investment.

Growth opportunities
Authors like Fazzari et al. (1988), Ascioglu et al. (2008), Carpenter and Guariglia (2008), Junlu et al. (2009) and Sun and Nobuyoshi (2009) fi nd a positive relationhip between investment and growth opportunities. Carpenter and Guariglia (2008) conclude that growth opportunities can be particularly relevant in explaining SME investment, due to these fi rms being more subject to fi nancial constraints arising from evaluation by creditors. Therefore, growth opportunities may contribute to lessening those fi nancial constraints, since they can serve as an important sign to creditors of vitality and possibilities for growth.
We can expect growth opportunities to have an effect of greater magnitude on investment in SMEs with high levels of investment than in SMEs with low levels of investment, as SMEs that invest most manage to take advantage of the growth opportunities that arise.
Based on the arguments above, we formulate the following hypothesis for investigation:

H5:
The positive relationship between growth opportunities and investment is of a greater magnitude in SMEs with high levels of investment than in SMEs with low levels of investment.

Interest rate
According to Neoclassical Theory, interest rates are an important determinant of fi rm investment. Bernanke and Gertler (1995) and Gilchrist et al. (2005) conclude there is a link between investment and monetary policy, stating that the cost of credit, and consequent effects on fi rms' investment, necessarily has an effect on the economy. Bernanke and Gertler (1995), Gilchrist et al. (2005Gilchrist et al. ( , 2006 state that increases in interest rates mean diminished investment. The more relevant the problems of information asymmetry associated with relationships formed between fi rms' owners/managers and creditors, the greater the possibility of creditors hindering fi rms' access to credit by increasing interest rates (Ghosh, Ghosh, 2006). In general, problems of information asymmetry are known to be more severe in the SME context, and so there is a greater possiblity of this type of fi rm having particular diffi culty in accessing external fi nance.
We can expect that interest rates, in defi ning the cost of capital, have a more negative effect in SMEs that invest less. SMEs with low levels of investment could be more restricted fi nancially due to the greater relevance of problems of information asym-metry, and so the negative impact of interest rates on investment could be of a greater magnitude, compared to what occurs in SMEs with high levels of investment.
Based on the arguments presented, we formulate the following hypothesis for investigation:

H6:
The negative relationship between interest rate and investment is of a greater magnitude in SMEs with low levels of investment than in SMEs with high levels of investment.
At times of economic recession, we can expect external capital markets to be more restrictive in granting credit, with SMEs also having less capacity to retain cash fl ow. In these circumstances, SME investment will be expected to diminish. In periods of economic growth, on one hand SMEs will have easier access to credit, and on the other be more able to retain cash fl ow, making it easier to increase investment.
The effects of economic growth on investment could be more relevant when SMEs have high levels of investment, since these are fi rms in a period of growth and so the marginal effect of economic growth could mean a greater increase in investment than in the case of SMEs with low levels of investment and consequently greater diffi culty in managing their fi nancial resources.
Based on the arguments presented, we formulate the following hypothesis for investigation:

H7:
The positive relationship between GNP and investment is of a greater magnitude in SMEs with high levels of investment than in SMEs with low levels of investment.

Database
This study uses the SABI (Iberian Balance-Sheet Analysis System) database supplied by Bureau van Dijks for the period 1999-2006 1 .
Aiming to analyze SMEs, we select fi rms based on the European Union recommendation L124/36, (2003/361/CE). According to this recommendation, a fi rm is considered an SME when it meets two of the following three criteria: 1) fewer than 250 employees; 2) annual total assets under 43 million euros; and 3) business turnover under 50 million euros.
The fi nal sample composition is presented in Table 1 below.

Defi nition of variables
The independent variables used in this study are as follows 3 : Sales, Cash Flow, Debt, Age, Growth Opportunities, Interest Rate and Gross National Product. To test the dynamics of investment over time, we also use lagged investment, to test whether the persistence of investment is identical for SMEs with low and high levels of investment.
The variables used in this study were measured as follows: -I i,t is net investment, given by the ratio of variation of fi xed capital less amortization and depreciation in the present period to fi xed assets in the previous period; -I i,t-1 is the lagged net investment; -SALES i,t-1 are sales in the previous period, given by the logarithm of business turnover in the previous period; -CF i,t is cash fl ow in the present period, given by the ratio of operational results after payment of interest plus depreciation divided by total assets in the present period; -LEV i,t-1 is debt in the previous period, given by the ratio of total debt in the previous period to total assets in the previous period; -AGE i,t-1 is fi rm age, given by the logarithm of the number of years fi rms have been in existence; -GO i,t-1 are growth opportunities in the previous period, given by the sales growth fi rm in the previous period; -IR t is the market interest rate in the present period, represented by the 3-month euribor rate; -GNP t is Gross National Product in the present period, given by the logarithm of Gross National Product.
All the monetary variables were defl ated using a defl ater constructed based on the GNP defl ator in each year. The base year considered for defl ation of monetary variables was 2006.
It should be noted that all estimations include annual dummy variables in order to measure other effects of the economic climate not measured by the interest rate and Gross National Product, on variations in SME investment. In addition, we consider sector dummy variables to measure the impact of possibly different relationships between determinants and investment according to fi rms belonging to different economic sub-sectors. Just as Blanco-Mazagatos et al. (2007), we consider the following sector dummy variables 4 : 1) agriculture; 2) forestry and fi shing; 3) construction; 4) manufacturing industry; 5) wholesale and retail; and 6) services.

Survival analysis
Construction of a sample of fi rm data including only fi rms that operate in the market during the entire period of analysis could create bias in the results, due to not considering the situation of fi rms that left the market during the period of analysis. Indeed, we would expect relationships between determinants and investment to be of a different nature for surviving and non-surviving fi rms. Not considering in the sample fi rms that leave the market could lead to bias in the relationships formed between determinants and investment. According to Heckman (1979), Calvo (2006) and Lotti et al. (2009) one way to eliminate this selection problem is to use the two-step estimation method proposed by Heckman (1979).
At a fi rst stage, and considering the total sample, both fi rms remaining in the market and those leaving the market, we estimate a model of probability of fi rm survival, based on the probit regression analysis.
The dependent variable takes the value of 1 when the fi rm survives and the value of 0 when it leaves the market. Just as Calvo (2006), we will consider as explanatory variables of the probit regression the determinants used at the second stage of estimation.
The probit regression to estimate can be presented as follows: , where: I i,t-1 is investment in the previous period; SALES i,t-1 are sales in the previous period; CF i,t is cash fl ow in the present period; LEV i,t-1 is debt in the previous period; AGE i,t-1 is age in the previous period; GO i,t-1 are growth opportunities in the previous period; IR t is the interest rate in the present period; GNP t is GNP in the present period; D s are sector dummy variables; d t are annual dummy variables; and z i,t is the error.
Based on the probit regressions, estimated in the fi rst step, we calculate the inverse Mill's ratio 5 , and use it as an additional explanatory variable in the second step when estimating relationships between determinants and investment through quantile regressions.

Quantile regression
Use of quantile regressions is normal when aiming to check whether relationships between the dependent variable and independent variables are dependent on the level of the dependent variable.
With the objective of testing whether the relationships between determinants and investment are identical as a function of the level of SME investment, we turn to quantile regressions. In this way, we can check whether relationships between SME investment and its determinants are different for low and high levels of investment. This type of model conditioned to a quantile regression has received considerable attention, as it leads to a more complete statistical analysis of the stochastic relationship between random variables (Knight 1989;Weiss 1991;Hasan, Koenker 1997;Rogers 2001;Koenker, Xiao 2004;Serrasqueiro et al. 2010).
Using the quantile regression estimator developed by Koenker and Hallock (2001), which considers that the conditional distribution quantile  of the dependent variable (Y i,t ) is a linear function of the vector representing the independent variables (Z i,t ), the regression conditioned to the quantiles can be presented as follows: and, with the following restriction: , , where: , In this way, we aim to study the determinants of SME investment, following a regression conditioned to the quantiles, in which  = 5°, 10°, 25°, 50°, 75°, 90°, 95°. Estimating the quantiles conditioned to the regression for the different values of , we will have the distribution of the variable Y i,t , conditioned to the corresponding values of Z i,t for the values of i ( 1,...,1845) So as to guarantee the robustness of results in relation to the parameters estimated for the different quantiles, we use the bootstrap matrix method proposed by Buchinsky (1995Buchinsky ( , 1998. Based on the Monte Carlo simulations, Buchinsky (1995) concludes that the bootstrap matrix method is most advisable for data samples with a rather low number of observations, being considered a valid method in the presence of the most varied forms of heterogeneity.
To test for possible non-linearity, over all investment distribution, for each of the determinants considered in this study, we use the Chow test. For each investment determinant, the null hypothesis indicates non-existence of non-linearities between determinants and investment over the distribution of investment, and the alternative hypothesis indicating the existence of non-linearities between determinants and investment over investment distribution.

Descriptive statistics and correlation matrix
The descriptive statistics of the variables used in this study are presented in Table 2 below.
Investment is found to have quite volatile behaviour, since the standard deviation is considerably above the mean. The variables of cash fl ow and growth opportunities are also volatile, the volatility of growth opportunities being greater, as the standard deviation of this variable is considerably above the mean. The behaviour of the other variables is not very volatile, the standard deviation of the variables being less than the respective means.
The results of the correlations between variables are presented in Table 3.   Aivazian et al. (2005) conclude that the problem of collinearity between explanatory variables may be particularly relevant when the correlation coeffi cients are above 30%. The correlation coeffi cients of the independent variables are not too high, despite those between cash fl ow, interest rate and GNP, and investment in the previous period, as well as between debt and the interest rate, being above 30%. In general, the correlation coeffi cients indicate the problem of collinearity between explanatory variables is not particularly relevant in this study. Table 4 presents the results of the survival analysis, referring to the fi rst step of the Heckman (1979) method. The empirical evidence obtained lets us conclude that investment in the previous period, cash fl ow, sales, debt, age and GNP are determinants stimulating SME survival. On the contrary, the interest rate is a restrictive factor of SME survival. Finally, we fi nd that growth opportunities neither restrict nor stimulate SME survival. Table 5 presents the results of the quantile regressions, corresponding to the second step of the estimation method proposed by Heckman (1979), with the aim of determining the relationships between determinants and SME investment, over the distribution of SME investment.   The multiple empírical evidence obtained allows us to conclude that: 1) The relationship between investment in the previous period and investment in the present period is not statistically signifi cant for low levels of investment, being positive and statistically signifi cant for moderate and high levels of investment. 2) For low levels of investment, we fi nd a negative and statistically signifi cant relationship between sales and investment. However, for high levels of investment, the relationship between sales and investment is positive and statistically signifi cant. 3) The relationship between cash fl ow and investment is positive and statistically signifi cant, whatever the level of investment. However, the relative importance of cash fl ow for SME investment seems to be greater for low levels of investment. 4) Except for particularly high levels of investment (95th quantile), whatever the level of investment considered, we fi nd a negative and statistically signifi cant relationship between debt and investment. We also fi nd that the negative infl uence of debt on investment diminishes over investment distribution. 5) A negative and statistically signifi cant relationship is found between age and investment for low levels of investment. On the contrary, for moderate and high levels of investment, there is a positive and statistically signifi cant relationship between age and investment. 6) We also fi nd a negative and statistically signifi cant relationship between growth opportunities and investment for low levels of investment, and the relationship being positive and statistically signifi cant in situations of moderate and high investment. 7) The relationship between interest rate and investment is negative and statistically signifi cant, except in situations of particularly high levels of investment (90 th and 95 th quantiles). We also fi nd that the relative importance of the interest rate on diminished investment becomes less as the level of investment increases. 8) Except in situations of low investment (5 th and 10 th quantiles), there is a positive and statistically signifi cant relationship between GNP and investment. The positive infl uence of GNP on investment becomes greater as the level of investment increases.

Investment determinants
Estimating relationships between determinants and investment with the OLS regression, we fi nd the variables of investment in the previous period, cash fl ow, sales and GNP infl uence investment positively. On the contrary, debt and the interest rate infl uence investment negatively. Finally, age and growth opportunities do not infl uence investment.
For all the quantiles considered, there is a negative and statistically signifi cant relationship between the inverse Mill's ratio and investment. We fi nd, therefore, that use of the inverse Mill's ratio in the quantile regressions allows effi cient solution of possible problems of bias of the estimated parameters measuring relationships between determinants and investment. Table 6 shows the result of the Chow test checking for the possibility of non-linearity between determinants and SME investment over investment distribution.
The results show that, for all the determinants of investment considered in this study, we reject the null hypothesis of non-existence of non-linearity between determinants and investment for different levels of investment. We also found, for all investment determinants considered, that the individual test of equality of estimated parameters between lower and higher quantiles of the SMEs investment distribution 6 , us to confi rm the existence of different relationships between determinants and investment in lower and higher quantiles. Which reinforces the idea that the level of SME`s investment infl uence the relationships established between determinants and investment over SMEs investment distribution.  F(1,11105) 21.08***

Discussion of the results
According to Neoclassical Theory, fi rms' investment decisions are independent of their fi nancial structure, and so cash fl ow and debt are irrelevant in explaining investment decisions, emphasizing sales as the central variable of investment.
As can be observed in Figure 1, sales have a special infl uence on SME investment, but only for high levels of investment, as they are a restrictive determinant of investment for low levels of investment. This empirical evidence lets us corroborate the previously formulated hypothesis H1, since sales are of greater relative importance for investment in SMEs with high levels of investment than for SMEs with low levels of investment. The difference identifi ed is reinforced by the Chow test, which lets us conclude there are signifi cant non-linearities in the relationship between sales and investment over the distribution of SME investment.
The empirical evidence obtained suggests that the assumptions of Neoclassical Theory (Hall, Jorgenson 1967, 1971Chirinko 1993), that fi rms adjust their investment as a function of sales, are only corroborated by the empirical evidence found here when SMEs have high levels of investment. Therefore, the empirical evidence obtained does not corroborate the assumptions of Neoclassical Theory when SMEs have low and moderate levels of investment. Contrary to what is stated by Eisner (1963) and Chirinko (1993), in the SME context, sales are not statistically predominant over other possible determinants in explaining investment. Besides, the empirical evidence only corrobo-rates that obtained by McConnell and Servaes (1995), Lang et al. (1996), Aivazian et al. (2005) and Serrasqueiro et al. (2008), evidence obtained in the context of large fi rms, when SMEs have high levels of investment.
The empirical evidence suggests that fi rms investing less do not adjust their level of investment as a function of sales, probably due to their reluctance to increase investment in market conditions which may be particularly adverse. For SMEs with high investment levels, possibly favourable market conditions may contribute to SMEs adjusting investment as a function of sales, aiming to increase their share of the market. It is also important to mention that the strategy of adjusting investment in SMEs with high levels of investment, as a function of sales, could be appropriate, since sales are a positive determinant of SME survival, so allowing them to conciliate strategies of survival with strategies of diversifi cation. Figure 2 presents the relationship between cash fl ow and investment over investment distribution.

Fig. 1. Estimated parameters of relationship between I i,t and SALES i,t-1
Notes: The relationship between cash fl ow and investment is positive and statistically signifi cant over all investment distribution. However, as observed in the fi gure presented above, that infl uence is greater when our subject of analysis is SMEs with low levels of investment. The result of the Chow test shows there are signifi cant non-linearities between cash fl ow and investment over investment distribution. Based on the results obtained, we can consider the previously formulated hypothesis H2 as valid, since cash fl ow is of greater relative importance for increased investment in SMEs with low levels of investment than in SMEs with high levels of investment.
Firstly, the fact that cash fl ow is a determinant stimulating SME investment lets us corroborate the assumptions of Free Cash Flow Theory (Fazzari et al. 1988;Fazzari, Petersen 1993), since investment is also dependent on fi rms' endogenous factors, and not only infl uenced by exogenous factors, as forecast by Neoclassical Theory.
Secondly, the fact there is a positive and statistically signifi cant relationship between cash fl ow and investment, over the whole distribution of SME investment, shows the particular importance of cash fl ow in fi nancing SME investment, corroborating the arguments of Gertler and Gilchrist (1994), Petersen and Rajan (1995) and Vermeulen (2002), as well as the empirical evidence obtained by Fazzari et al. (1988), Hoshi et al. (1991), Fazzari and Petersen (1993), Hubbard et al. (1995), Zingales (1997, 2000), Cleary (1999), Vermeulen (2002) Thirdly, the empirical evidence suggests that in the SMEs that invest least, investment is more sensitive to variations in cash fl ow, that sensitivity diminishing as SMEs invest more. This being so, the empirical evidence obtained in this study could agree with the conclusions of Fazzari et al. (1988) and Hoshi et al. (1991), since naturally, low SME investment could be affected by the greater importance of problems of information asymmetry in relationships between SME owners/managers and creditors. Therefore, the empirical evidence obtained in this study is seen to corroborate the conclusions of De Jorge Moreno and Castillo (2011), that investment is infl uenced by the corporate governance of fi rms. Fourthly, the fact that cash fl ow contributes to increased likelihood of SME survival also indicates the importance of cash fl ow in the activity of this type of fi rm.
Concerning the relationship identifi ed between debt and investment in SMEs, we fi nd a negative and statistically signifi cant relationship except in the highest quantile of investment distribution (95th quantile). Nevertheless, as can been observed in the following Figure 3, the magnitude of the negative relationship between debt and investment diminishes as we advance along the distribution of SME investment.
The results of the Chow test show there are signifi cant non-linearities in the relationship between debt and investment over the distribution of SME investment. Based on the empirical evidence obtained, we can consider the previously formulated hypothesis H3 as valid, since the negative relationship between debt and investment is of greater relative importance in SMEs with low levels of investment than in SMEs with high levels of investment.
Agency problems (Jensen, Meckling 1976;Myers 1977;Zwiebel 1996) appear to be particularly relevant in SME activity, being more important in SMEs that make least investment. Creditors may realize the particular diffi culties of SMEs that invest least, making terms of access to credit diffi cult for them, which could mean payment of high credit costs, making it impossible to take advantage of good investment opportunities and contributing to a negative effect of debt on investment. This conclusion may be a particular problem for SMEs with low levels of investment, since debt is a positive determinant of SME survival, possibly due to its importance in situations where SMEs lack suffi cient internal funding to fulfi l the multiple investment opportunities arising.
For the SMEs that invest most (95th quantile) the effect of debt is not diminished investment. This may happen because creditors can recognize the good investment opportunities presented to this type of SME, and grant credit easily. The fact that debt does not mean diminished investment in SMEs when they have particularly high levels of investment contradicts the empirical evidence obtained in other studies 7 (Myers 1977;Jensen 1986;Stulz 1990;McConnell, Servaes 1995;Lang et al. 1996;Aivazian et al. 2005;Ahn et al. 2006;Firth et al. 2008;Lee, Ratti 2008). The empirical evidence appears to corroborate the conclusions of Lee and Ratti (2008), since the SMEs that invest least may fi nd their growth particularly restricted, being smaller than the SMEs that invest most, with a consequently more negative effect of debt on investment, due to the fact that creditors do not recognize good growth opportunities in this type of SME and make terms of credit diffi cult.
The following Figure 4 presents the relationships identifi ed between age and investment, over the distribution of SME investment.
The empirical evidence obtained shows that age is a restrictive determinant of investment in SMEs with low levels of investment, but a determinant promoting investment  when SMEs have high levels of investment. The results of the Chow test confi rm there are signifi cant non-linearities between age and investment over the distribution of SME investment. We can therefore conclude that the positive relationship between age and investment is of a greater magnitude in SMEs with high levels of investment than in SMEs with low levels of investment, and so we can accept the previously formulated hypothesis H4 as valid.
Age may function as a proxy for the reputation and credibility of SMEs (Diamond 1989;Ang 1991), contributing to SMEs being able to obtain external fi nance on more advantageous terms, which allows them to increase investment and make effi cient use of their business opportunities.
It is important to mention that age is a determinant promoting SME survival. Therefore, the marginal increase in age may be fundamental in SMEs with high levels of investment, allowing signifi cant increase in investment due to creditors recognizing their good investment opportunities together with reputation and credibility, so contributing to their survival in their operating markets.
The following Figure 5 presents the relationships between growth opportunities and investment over the distribution of SME investment.
Growth opportunities are found to be a restrictive determinant of investment in SMEs with low levels of investment, but a determinant promoting SME investment when they have high levels of investment. The results of the Chow test show there are signifi cant non-linearities between growth opportunities and investment over the distribution of SME investment. We can therefore consider the previously formulated hypothesis H5 as valid, since growth opportunities are of greater relative importance for increased investment in SMEs with high levels of investment than for SMEs with low levels of investment.
Growth opportunities seem to be particularly relevant for increased investment in SMEs with high levels of investment, possibly due to creditors recognizing good business opportunities in this type of fi rm, diminishing the information asymmetry in relationships formed between owners/managers of these fi rms and creditors. The empirical evidence obtained corroborates partially the conclusions of Carpenter and Guariglia (2008), as well as the empirical evidence obtained in other studies 8 (Fazzari et al. 1988;Ascioglu et al. 2008;Carpenter, Guariglia 2008;Junlu et al. 2009;Sun, Nobuyoshi 2009), since growth opportunities are only a positive determinant of investment in SMEs with high levels of investment, being a restrictive determinant of investment when SMEs have low levels of investment. Indeed, creditors may interpret low investment as a sign of business diffi culties, and so make credit terms diffi cult, as a consequence of attributing a high business risk to growth opportunities in this type of SME. Figure 6 presents the relationships formed between interest rate and investment over the distribution of SME investment.
A negative relationship is found between interest rate and investment over the distribution of SME investment. However, that negative relationship diminishes in magnitude and statistical signifi cance, the relationship becoming practically nil and without statistical signifi cance when SMEs have high levels of investment (90th and 95th quantiles). The results of the Chow test confi rm the existence of signifi cant non-linearities in relationships between interest rate and investment over the distribution of SME investment. The previously formulated hypothesis H6 can therefore be considered valid, since the negative relationship between interest rate and investment is of a greater magnitude when SMEs have low levels of investment than when they have high levels of investment.
According to the conclusions of Bernanke and Gertler (1995) and Gilchrist et al. (2005), interest rates are found to infl uence fi rm investment in general, and that of SMEs in particular. SMEs in general being particularly affected by problems of information  asymmetry in the relationships they form with creditors, those problems seem to affect particularly SMEs with low and moderate levels of investment. When SMEs, through high investment, give signs to the market of the capacity to survive and good future growth, creditors, recoginizing those characteristics, may make terms of credit easier, compared to the case of SMEs with low and moderate levels of investment. The empirical evidence obtained in this study seems to corroborate the arguments of Ghosh and Ghosh (2006), since interest rates appear to harm essentially SMEs with low levels of investment and consequently greater information asymmetry associated with the relationships formed with creditors. Higher interest rates may jeopardize particularly the survival of fi rms with low and moderate levels of investment, since they are seen to be a restrictive determinant of SME survival. Figure 7 presents the relationships formed between GNP and investment over the distribution of SME investment. The empirical evidence obtained allows us to conclude that GNP is a determinant stimulating investment in SMEs when they have moderate and high levels of investment, but is neither a positive nor restrictive factor of investment in SMEs when they have low levels of investment. We also fi nd that the magnitude of the impact of GNP on investment is greater, the greater the investment. The result of the Chow test shows there are signifi cant non-linearities in the relationships formed between GNP and investment over the distribution of SME investment. We can therefore accept as valid the previously formulated hypothesis H7, since GNP is of greater relative importance for increased investment in SMEs with high levels of investment than for increased investment in SMEs with low levels of investment.
The results confi rm that changes in the economic climate in general (Kildienė et al. 2011;Valackienė, Virbickaitė 2011), and in GNP in particular, have an effect on SME activity, especially when fi rms have moderate and high levels of investment, corroborating in these circumstances what is stated by Bernanke and Gertler (1989) and Bernanke et al. (1996)., Gertler and Gilchrist (1994), Oliner and Rudebusch (1996) and Vermeulen (2002). However, that positive effect appears to be particularly relevant when SMEs have moderate and high levels of investment, suggesting that the marginal effect could be more relevant in SMEs with more investment, and consequently greater growth, than in SMEs with lower levels, and so the latter may not take advantage of the opportunities conferred by economic growth due to the particular fi nancial diffi culties they may be facing. GNP is also found to be a determinant promoting SME survival. This result combined with the effect of GNP on investment in SMEs with moderate and high levels of investment gives increased importance to a favourable economic climate for the activity of this type of SME.
Finally, we also fi nd signifi cant non-linearities in the relationships formed between investment in the present period and investment in the previous period over the distribution of SME investment. The results of the Chow test confi rm that situation. The relationships between investment in the present period and investment in the previous period are presented in Figure 8.  The fact that investment is persistent only when SMEs have moderate and high levels of investment indicates that investment is only of a continuous nature over time when SMEs do not have low levels of investment. When SMEs have low levels of investment, the particular diffi culties borne by fi rms may mean occasional, rather than continuous investment, which does not allow consolidation in their markets of operation. This aspect is all the more important, due to the fact of investment being a determinant promoting SME survival. Therefore, non-continuous investment in SMEs with low levels of investment may mean diminished likelihood of this type of SME surviving.

Conclusion and implications
Based on a sample of 1845 SMEs, and using the two-step method proposed by Heckman (1979) in estimation, we investigate whether the relationships between determinants and investment are of the same nature over the distribution of SME investment. The multiple empirical evidence obtained indicates there are signifi cant non-linearities between determinants and investment over the distribution of SME investment.
Firstly, sales are found to be a determinant promoting investment in SMEs when they have high levels of investment, but are a restrictive determinant of investment when SMEs have low levels of investment. This result shows that one of the assumptions of Neoclassical Theory, namely that of fi rms adjusting investment as a function of sales, is only applicable in the case of SMEs with high levels of investment.
Secondly, cash fl ow is a determinant promoting investment over all the distribuion of SME investment. This result contradicts the assumptions of Neoclassical Theory, corroborating those of Free Cash Flow Theory, since SME investment is not only dependent on exogenous determinants, fi rms' endogenous determinants being very relevant in explaining SME investment. In addition, we fi nd the relative importance of cash fl ow in explaining investment is greater when SMEs have low levels of investment than when investment levels are high. We can therefore conclude that Free Cash Flow Theory is particularly applicable in situations where SMEs have low levels of investment, i.e., when they may be particularly restricted in fi nancing their investment opportunities.
Thirdly, debt is a restrictive determinant of SME investment, except when investment levels are particularly high. Creditors may make access to debt diffi cult for SMEs with low and moderate levels of investment, since they do not recognize good business opportunities in this type of SME. We can conclude that Agency Theory, namely concerning agency problems between owners/managers and creditors, is particularly applicable in the investment decisions of SMEs when they have low and moderate levels of investment.
Fourthly, age and growth opportunities are positive determinants of investment in SMEs with high levels of investment, but determinants restricting investment when investment levels are low. For one thing, age appears to serve as a proxy for reputation and credibility in SMES with high levels of investment, and for another, creditors seem to recognize good opportunities for future business in SMEs with high levels of investment. This empirical evidence suggests that age and growth opportunities contribute to reducing the information asymmetry in relationships formed between SME owners/ managers and creditors when these fi rms have high levels of investment.
Fifthly, macroeconomic variables are relevant in explaining SME investment. Interest rates are a restrictive determinant of SME investment, particularly when they have low and moderate levels of investment. Higher interest rates may affect particularly SMEs with investment diffi culties, since it is these SMEs that are more restricted fi nancially. As for GNP, it is a determinant stimulating investment in SMEs when they have moderate and high levels of investment. The marginal effect of the favourable economic climate seems to be particularly relevant in explaining SME investment in situations where investment is moderate and high.
Sixth, persistence of investment over time is seen in situations where SMEs have moderate and high levels of investment, but not when investment levels are low. This result shows that SMEs with low levels of investment may have particular diffi culty in making investments of a continuous nature, this contributing to a greater likelihood of bankruptcy.
To summarize, the multiple empirical evidence obtained in this study shows that the applicability of various theories for explaining fi rm investment depends particularly on the level of SME investment. Neoclassical Theory is particularly applied I high levels of investment, and Free Cash-Flow Theory and Agency Theory are particularly applied in low levels of investment.
The fi ndings allow us to suggest important measures for economic policy in general, and industrial policy in particular. Given the particular importance of problems of information asymmetry associated with relationships between SME owners/managers and creditors, we suggest the creation of special lines of credit for SMEs with low levels of investment, to allow them to survive in their markets of operation. Increased investment seems to be an important condition for creditors to recognize good possibilities for future business, and so facilitate terms of credit. This may be particularly important in situations where internal fi nance is insuffi cient to fund the multiple investment opportunities that may arise for SMEs. For SMEs with high levels of investment, given the importance of sales and GNP as determinants promoting investment, we suggest policies to incentivize increased sales at times of economic recession, with the objective of allowing these fi rms to direct their investment towards diversifi cation of activities.