1. Introduction

Empirical evidence shows that R&D is responsible for growth in productivity. For example, ^{Bravo-Ortega et al. (2014}) use cross-sectional data to examine the relation between productivity, expenditure in R&D and exports in Chile, being found that the firms that invest in R&D are more likely to export, R&D improves productivity, and public funding complements private resources for R&D. ^{Álvarez et al. (2010}) suggest that in Chile there is no contemporary effect of innovation in products on productivity, though lagged effects are observed after two years. ^{Crespi et al. (2015}) use panel data from Colombian firms to demonstrate that the financial incentive programs for R&D have increased labor productivity. ^{Álvarez et al. (2015}) point out that in the case of Chile there is an effect of the technological and nontechnological innovation on labor productivity in the manufacturing and services sectors. More recently, ^{Crespi et al. (2016)} demonstrate that the public funding for innovation is a key factor to facilitate investment in innovation in manufacturing firms of Latin America.

R&D expenditure as a percentage of GDP is low in Chile (0.4%) compared to OECD countries (2.4%). Moreover, ^{Cabaleiro & Salce (2018}) conclude that the markets for technology in Chile are not developed. These facts could be explained by uncertain returns from investing in innovation and R&D which affect the conditions for financing this type of activities. For this reason, in recent years the Chilean State has played a more active role in innovation^{1} through the creation of diverse programs to mitigate the different obstacles and constraints faced by innovative activities in small and medium-sized firms.

The decision to allocate resources to R&D activities is influenced by the characteristics of the firm, the market and the public incentives. According to ^{Shefer & Frenkel (2005}) a 50% of the variation in R&D expenditure is explained by innovation, economic sector, total sales, export orientation and age of the firm. ^{Barge-Gil & López (2014}) point out that the evidence is mixed for the effects of financial constraints and public funding instruments on R&D expenditure. ^{González & Pazó (2008}) conclude that public funding fosters the private technological effort of small firms. ^{Clausen (2009}) shows that research subsidies stimulate R&D expenditure, while development subsidies replace that expenditure. ^{Cerulli & Potí (2012}) find a relationship between R&D expenditure and variables such as the number of employees, percentage of employees with university degree, percentage of sales from exports, capital per employee, cash flow per employee, percentage of liabilities, IPR value when the firm belongs to a foreign group, age and geographical location.

According to the international literature, the factors that affect the probability of obtaining public financing for innovation are varied. ^{Huergo et al. (2016}) indicate that the probability of participating in an R&D loan system increases when a firm has technological profile and sectoral financial constraints. ^{Afcha (2012}) demonstrates that the probability of obtaining an R&D subsidy is increased by cooperation networks, recruitment of newly graduated professionals, R&D expenditures from previous years, number of employees and exports. ^{Duch-Brown et al. (2011}) indicate that having prior experience in R&D projects increases the intensity of subsidies. ^{Cantner & Kösters (2012}) demonstrate that the work team and the initial capital of the firm affect the obtaining of public funds.

Previous studies in Chile have focused mainly on the relationship between firms’ productivity and innovative variables (^{Benavente, 2005}; ^{Álvarez et al., 2010}) and recently on the impact of knowledge obstacles to introduce innovations (^{Canales & Álvarez, 2017}) but have not analyzed what factors influence the probability of obtaining public financing. Therefore, this study seeks to determine the factors that affect the receipt of public support for innovation in small and medium-sized firms, considering cross-sectional data from the different versions of the Innovation Surveys. Then, these results are contrasted with those obtained from a pseudo-panel methodology that uses the cross-sectional databases together.

1. Methodology

1.1 Data

The Innovation Survey of Chilean firms have been collected in nine first to the fourth survey, the number of firms fluctuates between 520 different versions, the first in 1995 and the last in 2014. Figure 1 shows and 900, while this number grows by over 5600 in the most recent the number of firms surveyed in each version of the survey. From the survey. However, in the last five surveys only 55% of firms are SMEs.

The nine versions of this survey have different structures and variables Therefore, firm-level observations from the fifth to the ninth version of due to changes in its design but there is greater uniformity starting with the survey were consolidated into a single database to enable statistical the fifth version. Table 1 exemplifies this situation with an extract of analysis based on cross-sectional estimates and to facilitate a comparisome variables that are present in the different versions of the survey. son of the results with the pseudo-panel methodology.

1.2 Pseudo-panel data

A typical panel data regression can be represented as:

Where subscript *i* indicates the cross-sectional dimension that can denote, for example, individuals, families, firms, and countries, and *t* indicates the time. In this model, _{
yit
} it is the dependent variable and _{
xit
} it is a vector of *K* explanatory variables. In addition, most panel data applications use a model with two error components, _{
µi
} denoting the individual non-observable effect and _{
vit
} denoting the remaining disturbance.

Although in many developing countries there is little availability of panel data, it is possible to have repeated cross-sectional data in which the same individuals are not tracked over time. Under this focus, individuals share some common characteristics (in this study, firms belonging to the same economic sector), whereby they can be grouped into cohorts and the averages within the cohorts are treated as observations in a pseudo-panel.

^{Deaton (1985}) suggests the use of cohorts to obtain consistent estimators for *β* in (1), even if the individual effects _{
αi
} are correlated with explanatory variables. By defining *C* cohorts in which each individual is a member of a single cohort for all periods, all the observations are grouped at the cohort level, so the resulting model can be written as:

Where is the average value of all _{
γit
} in cohort *c* at time *t*. This is analogously the case for the other variables in the model. The resulting dataset is a pseudo-panel with repeated observations over *T* periods and *C* cohorts.

Subsequently, ^{Moffitt (1993}) proposes estimating pseudo-panel data through instrumental variables. The interpretation of instrumental variables is useful because it illustrates that alternative estimators can be constructed using other sets of instruments.

1.3 Binary models

Binary choice models such as *probit* or *logit* are widely known and used in empirical applications with cross-sectional data, whereas with data panel the models typically used are *probit* random effects and *logit* fixed effects. However, binary choice models can also be estimated with pseudo-panels data (^{Verbeek & Vella, 2005}; Verbeek, 2008). Specifically, the binary choice model using pseudo-panel data with instrumental variables proposed by ^{Moffitt (1993}) can be written as:

In this case, the dependent variable is not observed, but the binary variable γit is observed and defined by or 0 otherwise. This approach uses dummy variables from the cohorts as instruments for the explanatory variables. Specifically, each individual effect _{
αi
} is decomposed into a cohort effect_{
αc
} and the deviation of individual *i* from this effect. It could be defined as (*c* = 1,..., *C*) if individual *i* is a member of cohort *C*, and as 0 otherwise. Thus, _{
αi
} can be rewritten as:

Defining α=(α_{1},..., α_{c} )’ and z_{
i
} =(z_{1}
_{
i
} ,..., z_{c}
_{
i
} )’, and then substituting (6) into (4) produces the following:

The next step is to choose the dummy cohort variables in z_{
i
} , interacted in time as instruments, in which case linear predictors are:

Where _{
δkt
} is a vector of unknown parameters. The linear predictor for _{
xit
} is given by , the vector of means in cohort *c* in period *t*. In addition, if it is assumed that _{
εi
} + _{
uit
} has a normal distribution and that the instruments for are not correlated with Under these assumptions, the instrumental variable estimator produces a consistent estimator for *β* and _{
αc
} .

3. Results

The study seeks to evaluate whether a firm’s innovative actions carried out in the previous year, as well as other characteristics, affect the probability of receiving public support in the current period. This information is relevant for small and medium-sized firms because they may wish to alter their decisions before applying for these types of funds to increase their chances of obtaining them.

To determine the robustness of the results, several specifications of the empirical model are included. Model 1 only includes, as explanatory variables, expenditures on innovative actions carried out in the previous period. Model 2 controls by total sales, number of workers and whether the firm had exports in the previous period; Model 3 also controls by economic sector; Model 4 also adds a control by region of the firm’s location; Model 5 controls by size of the firm and model 6 by type of ownership.

Table 2, Table 3, Table 4, Table 5 and Table 6 present the results obtained from *probit* models that estimate the probability of obtaining public financing using cross-sectional data from the fifth to the ninth version of the Survey of Innovation, respectively.

Table 2 shows that the expenditure on external knowledge in previous year and exports in previous year have a positive, significant and robust effect on the probability of obtaining public financing. On the other hand, there is a positive, significant and robust effect between specifications for firms located in the Antofagasta Region, Coquimbo Region, Valparaíso Region, O’Higgins Region, Bío Bío Region, Los Lagos Region and Metropolitan Region. However, there is also a significant, robust and negative effect for the firms have private and foreign property.

Table 3 shows that the expenditure on external knowledge, expen- the probability of obtaining public financing. At sectoral level, it diture on introduction of innovations to the market, and exports is observed that the real state sector has a positive, significant and in previous year have a positive, significant and robust effect on robust effect.

Table 4 shows that there are no statistically significant and robust effects of expenditures on innovative activities carried out in the previous year on the probability of obtaining public support. However, there is also a significant, robust and negative effect for small sized and private property firms.

Table 5 shows that the expenditure on other innovation activities in previous year and exports in previous year have a positive, significant and robust effect on the probability of obtaining public financing. On the other hand, there is a negative, significant and robust effect between specifications for firms located in the Valparaíso Region and O’Higgins Region. However, there is also a significant, robust and negative effect for small sized firms and foreign property firms.

Table 6 shows that the expenditure on training for innovation and number of intellectual property rights in previous year have a positive, significant and robust effect on the probability of obtaining public financing. Moreover, there is also a significant, robust and negative effect of total sales in previous year. At sectoral level, it is observed that the manufacturing, commerce and transport sector have a negative, significant and robust effect.

To contrast the previous results, a binary choice model using pseudo-panel data is estimated. Table 7 shows that the expenditure on introduction of innovations to the market in previous year and exports in previous year have a positive, significant and robust effect on the probability of obtaining public financing. At sectoral level, it is observed that the real state sector also has a positive, significant and robust effect. However, the expenditures on introduction of innovations to the market and external knowledge in previous year have no robust effects in magnitude, sign and / or statistical significance.

4. Conclusions

It is possible to conclude, using pseudo-panels and cross-sectional data, that policymakers and members of evaluating committees follow a strategy of “picking the winner” because small and medium sized firms that have some type of expenditures on innovation activities in previous year are more likely to obtain public support for innovation.

By using pseudo-panels, it is observed that firms with expenditure on introduction of innovations to the market in previous year and exports in previous year have more probability to obtain public support for innovation. On the other hand, with cross-sectional data, there are different expenditures on innovation activities in previous year that affect the probability of obtaining public support, depending of the version of Innovation Survey.

When comparing the above results with the international literature, it is observed that the factors that explain the allocation of public funds for innovation in other countries are more diverse than those observed in the case of Chile, which leads to the conclusion that perhaps the award criteria of these funds should be changed to guide the earlier innovative actions of the applicant firms.