2.1. Inbound open innovation and ACAP

The concept of open innovation has attracted the attention of researchers. In this sense, it is convenient to investigate why low-tech firms are interested in putting open innovation into practice, taking into account that low-tech firms are recognized as conservative firms that invest little in research and development but that take advantage of diverse sources of external knowledge (^{Arcese, Flammini, Lucchetti, and Martucci, 2015}).

Thus, concern arises because firms strive to improve their absorptive capacity. In this sense, ^{Spithoven, Clarysse, and Knockaert (2010)} pointed out that low-tech intensity firms seek to improve their absorptive capacity to implement inbound open innovation practices. For this reason, when analyzing the Korean manufacturing industry, ^{Kim and Choi (2020)} found that a firm´s capability for innovation and development, that is, the implementation of R&D strategies, as well as the resources of firms oriented to this process, helped the firm improve its absorptive capacity.

It is necessary to point out how inbound open innovation and absorptive capacity are linked. Thus, analyzing the inbound open innovation processes, it is appreciated that firms that want to take advantage of external knowledge flows must develop their absorptive capacity. In this way, they will identify the external knowledge that is useful to them and use it to improve their innovation capability, a condition that was empirically verified by ^{Ferreras-Méndez, Newell, Fernández-Mesa, and Alegre (2015)} and ^{Aliasghar, Rose, and Chetty (2019)}.

Therefore, the following hypothesis can be formulated:

Hypothesis 1: Inbound open innovation is related to absorptive capacity in Peruvian food firms.

2.2. ACAP and technological innovation

Much has been investigated about the relationship between absorptive capacity and the development of technological innovation. For example, ^{Piening and Salge (2015)} analyzed the information provided by the Communitarian Innovation Survey (CIS-4) from Germany and found that manufacturing firms, including those of food and tobacco, are more likely to develop process innovations when they use their absorptive capacity, develop activities related to internal research and development, and acquire external knowledge.

Later, ^{Gkypali, Arvanitis, and Tsekouras (2018)}, analyzing 300 Greek manufacturing firms, found that absorptive capacity has a strong impact on innovation and plays an important role in the processing of external knowledge. Similarly, ^{Hullova, Simms, Trott, and Laczko (2019)}, analyzing food and beverage firms in the United Kingdom, concluded that to develop product or process innovations, firms in this area must not only take advantage of internal knowledge but also, through absorptive capacity, make use of external knowledge, acquiring, assimilating and taking advantage of it to improve their innovation capability. On the other hand, it must be considered that both ^{Engelman, Fracasso, Schmidt, and Zen (2017)} and ^{Albort-Morant, Henseler, Cepeda-Carrión, and Leal-Rodríguez (2018)} proved the positive relationship between absorptive capacity and the development of technological innovation.

Consequently, this study raises the following hypothesis:

Hypothesis 2: Absorptive capacity is related to technological innovation in Peruvian food firms.

2.3. Inbound open innovation and technological innovation

The relationship between open innovation and its influence on technological innovation has been frequently analyzed. Thus, ^{Bianchi, Croce, Dell ‘Era, Di Benedetto, and Frattini (2016)} analyzed how Spanish firms apply inbound open innovation to improve their innovative performance. In addition, ^{Santoro, Vrontis, and Pastore (2017)}, studying Italian food and beverage firms, found that market knowledge sources promote incremental innovations, and knowledge sources that come from universities and research centers promote radical innovations.

Empirical studies have been developed to verify the relationship between open inbound innovation and technological innovations. It is important to point out that some time ago, ^{Sofka and Grimpe (2010)}, through an empirical study, demonstrated that the specialized search for external knowledge has a positive impact on firm innovative performance. Thus, customers provide knowledge to implement new products, or suppliers provide knowledge to improve processes.

^{Gómez, Salazar, and Vargas (2016)} argued that external knowledge favors the development of technological innovations; more specifically, ^{Lefebvre, De Steur, and Gellynck (2015)} studied food firms from 6 European countries and confirmed the same relationship.

Based on the arguments above, the following hypothesis is developed:

Hypothesis 3: Inbound open innovation is related to technological innovation in Peruvian food firms.

2.4. Absorptive capacity as a mediator

Absorptive capacity has played a role as a mediator in various studies. Thus, ^{Sáenz, Revilla, and Knoppen (2014)} indicate that absorptive capacity favors interaction with customers and suppliers, facilitating the exchange of knowledge, which helps to improve a firm´s innovation capability. Moreover, ^{Rahomee and Kumar (2014)} assert that many firms acquire and assimilate external knowledge but that they are not able to take advantage of it to develop innovations and that on certain occasions, the size and age of the firm play an important role in development absorptive capacity.

Additionally, ^{Naqshbandi (2016)} deter­mines that firms that implement an open innovation strategy from the start, seeking external knowledge from various sources, promote the development of absorptive capacity. This allows firms to assimilate this knowledge and apply it to the development of new innovations. Later, other studies provided more insights into the mediating role of absorptive capacity and its role in the development of innovations.

Additionally, it is necessary to consider the analysis of ^{Moilanen, Østbye, and Woll (2014)} and ^{Jeong, Chung, and Roh (2019)}, who verified the mediating role of absorptive capacity in the relationship between sources of external knowledge and technological innovation.

Based on the arguments presented, the following can be formulated:

Hypothesis 4: Absorptive capacity mediates the relationship between inbound open innovation and technological innovation in Peruvian food firms.

3.1. Data

The study population belongs to the Peruvian food industry, which participated in the 2018 National Survey of Innovation in the Manufacturing Industry and Knowledge-Intensive Services Firms. For the analysis, the information provided for 2018 was taken into consideration. A sample of 111 firms has been considered.

Figure 1 shows the conceptual model of the relationship between open inbound innovation, absorptive capacity and technological innovation.

Source: Authors’ own elaboration

Figure 1 Conceptual Model 

3.2. Variables

The dependent variable is technological innovation, which consists of innovation in products and processes. Product innovation is a continuous variable, taking place when the firm declared that it had introduced completely new goods or services or with important modifications. Product innovation was formed by a factor analysis of two dichotomous items: (1) New good and (2) Significantly improved good, indicating 1 = if it was entered and 0 = if it was not entered. Innovation in process is also a continuous variable. It happens when the firm indicates that it had introduced some significant modifications in the production, marketing, logistics or distribution process. Innovation was formed through a factor analysis of three dichotomous items: (1) Means: techniques of promotion and/or product positioning, and/or establishment of prices of goods or services, (2) Business Administration and Management: methods of organizing the work, organization of external relations with other firms or public institutions, and (3) R&D processes: creativity or design for the development of products and business processes, indicating 1 = if it was introduced and 0 = if it did not introduce it.

On the other hand, the independent variables are inbound open innovation and absorptive capacity. For inbound open innovation, the measurement used by ^{Gentile-Lüdecke, de Oliveira, and Paul (2020)} was taken as a reference, who considered the degree of importance (1 = none, 2 = low, 3 = medium, 4 = high) from the following sources of external knowledge: (1) consultants, commercial laboratories and private R&D institutes, (2) universities and other higher education centers, (3) governmental and public research institutes, (4) conferences, fairs, exhibitions and similar, (5) scientific journals and trade/technical publications and (6) professional and industry associations, (7) clients, (8) competitors, and (9) suppliers. In absorptive capacity (ACAP), there are the following items: (1) internal research and development (R&D) development (ACAP 1), (2) training for innovation activities (ACAP 2) and (3) presentation of a research and/or development and/or innovation department (ACAP 3), according to ^{Escribano, Fosfuri, and Tribó (2009)} and ^{Rammer, Czarnitzki, and Spielkamp (2009)}. These items are dichotomous, indicating 1 = if it was implemented and 0 = if it was not implemented.

In the control variables, we have the size and age of the firm. Firm size and firm age can influence the realization of technological innovation. The firm size (expressed in logarithm) is measured by the number of employees, and the firm age is the number of years (expressed in logarithm) from its foundation to 2021. In both cases, the above is followed by ^{Park and Kim (2015)}.

3.3. Analysis method

SmartPLS 3 was applied to estimate and analyze our model using the two-step PLS technique, described by ^{Vinzi, Chin, Henseler, and Wang (2010)}. First, the measurement model is estimated when the relationship between the indicators and the latent construct is determined. Second, the estimation of the structural model is carried out, in which the relationships between the constructs are obtained by means of the path coefficients and the level of significance. The application of the partial structural equations is justified, as indicated by ^{Hair, Risher, Sarstedt, and Ringle (2019)}, for two reasons: 1) Because the information comes from a secondary database, and 2) it does not have an effect if the normality test is not met.

4.1. Descriptive statistics

Table 1 shows descriptive statistics of the firms included in the sample. The firms were classified according to seniority or age and by size.

4.2. Factor analysis

For the analysis of the two independent variables (absorptive capacity and open inbound innovation), SPSS software was used. We applied exploratory factor analysis (EFA) to determine which items measure each factor, as described by ^{Boateng, Neilands, Frongillo, Melgar-Quiñonez, and Young (2018)}, with an adequate factor load greater than 0.4, and with certain statistical criteria, such as the Kaiser-Meyer-Olkin (KMO) sampling adequacy and the Bartlett sphericity value. Obtaining the factorial structure makes for an easier and more meaningful interpretation (^{Rossoni, Engelbert, and Bellegard, 2016}). The results are shown in Table 2. According to ^{Beavers, Lounsbury, Richards, Huck, Skolits, and Esquivel (2013)}, to verify reliability and validity, the percentage of the total variance explained is 77.83%, 69.91% and 50.23% for technological innovation, absorptive capacity and open inbound innovation, respectively.

4.3. Measurement model

The research data are analyzed and presented using internal consistency reliability indicators such as Cronbach’s alpha (CA) and the composite reliability index (CR), whose values must be greater than 0.7; convergent validity, through the average variance extracted (AVE), whose value must be greater than 0.5; the analysis of multicollinearity measured by the variance inflation factor (VIF), whose values must be less than 5; and the determination coefficient (R ² ).

Table 3 shows the values of the indicators of reliability, convergent vali­dity, multicollinearity analysis, and the determination coefficient for the research model. According to ^{Vinzi et al, (2010)} when the approach of partial least square equations is applied, the composite reliability index is more reliable than Cronbach’s alpha. Regarding convergent validity, the indicators comply with the established values. In relation to the multicollinearity analysis, it is true for all the variables that the inflation factor of the variance does not exceed the value of 5. Meanwhile, the determination coefficient is 0.476, which shows a moderate relationship between the dependent and independent variables.

In relation to discriminant validity the ^{Fornell and Larcker (1981)} criterion is used, which establishes that the square root of the extracted variance (AVE) (shown in the diagonals and in bold in Table 4) must be greater than the correlations between the latent variables. In the present study, it can be seen that the model meets the discriminant validity.

4.4. Structural model

After evaluating the measurement model, we proceeded to estimate the structural model for this study. Table 5 shows the coefficient values and the p values of the model. To generate statistical significance in the hypotheses, according to ^{Benitez, Henseler, Castillo & Schuberth (2020)}, the bootstrapping technique is used, with 2000 resamples.

Table 5 shows the results of the structural model. As seen in the relationships, the coefficients are positive and statistically significant.

The model also complies with the goodness of fit (GoF) index (^{Tenenhaus, Esposito Vinzi, Chatelin, and Lauro, 2005}). This index varies between values of 0 and 1. Although there is no minimum threshold, a value greater than 0.36 is recommended (^{Wetzels, Odekerken-Schröder, and Van Oppen 2009}). The GoF index reaches a value of 0.49 for the model, which is higher than the minimum recommended to guarantee the quality of the fit of the model under study.

4.5. Control variables

Table 6 shows the coefficients of the control variables. The model shows that firm age is statistically significant. This means that a mature firm accumulates more knowledge and is in a position to develop technological innovations. At the same time, firm size is not statistically significant.

4.6. Mediation model

When analyzing absorptive capacity, certain steps are evaluated to confirm whether it is a mediating variable and the type of effect. According to ^{Hair Jr, Sarstedt, Hopkins, and Kuppelwieser (2014)} and ^{Carrión, Nitzl, and Roldán (2017)}, mediation represents a situation in which a mediating variable to some extent absorbs the effect of an exogenous construct (with independent variables) on an endogenous construct (with the dependent variable) in the PLS path model. The evaluation of explained variance (VAF) determines to what extent the mediation process explains the variance of the dependent variable. The rule is that if the VAF is less than 20 percent, one must conclude that there is no mediation; a situation in which the VAF is greater than 20 percent and less than 80 percent could be characterized as a typical partial mediation (^{Hair Jr, Hult, Ringle, and Sarstedt, 2016}); and a VAF above 80 percent indicates complete mediation. The VAF is the ratio between the indirect effect and the total effect, obtaining 41.52% for the relationship of absorptive capacity between inbound open innovation and technological innovation (Table 7). Therefore, absorptive capacity is a partial mediator in the relationship between inbound open innovation and technological innovation.