The effects of product and process innovation on employment: a meta-regression analysis

The theoretical framework of the economics of innovation has identified several arguments that explain the simultaneous positive and negative employment effects caused by the introduction of new technologies in terms of product and process innovation. The first empirical studies tried to estimate the global employment effects of innovation without disentangling the different mechanisms behind product and process innovation because of a lack of good innovative indicators. Most of the studies from the twentieth century used regional, national, or sector-level data to measure labor effects. These aggregate-level studies had problems isolating the impact of innovation on the labor market from other possible determinants such as economic growth cycles or international economic shocks.

The rise of innovation surveys in the 1990s (and other firm-level data sets) permitted more reliable firm-level analysis. Recently, some general agreement has been reached on measuring specific innovation concepts (including product and process innovation) based on standardized indicators defined in international manuals.¹ However, combining these practical aspects of measurement with more abstract theoretical concepts like “compensation mechanisms” to determine the final impact of innovation on employment is much more complicated. Moreover, once the innovation-related effect on employment is identified, the problem is to relate the practical aspects to each compensation mechanism. In fact, the empirical data available still impede decomposing the observed employment effects of innovation with all the mechanisms mentioned in the literature, although some models explain some of them.

In this sense, two main empirical approaches have tried to explain the relationship between innovation and employment at the firm level. The first one is basically an input-oriented model also known as the “derived labor demand model” based on the model proposed by Van Reenen (1997) and adapted by Bogliacino et al. (2014), and uses innovation inputs, such as research and development (R&D) expenditure as a proxy for innovation, although some studies apply this approach using patents (as a non-commercial output variable). The second one is an alternative approach that uses commercial results in terms of sales related to new products as an indicator of product innovation and a dummy for the introduction of process innovation. This output-oriented model was proposed by Harrison et al. (2014). Other branches of empirical approaches have also measured the effects of technological change on the labor market. On the one hand, some studies combine the labor effects of output innovation (product and process innovation, patents) and input innovation (R&D) (e.g., Lachenmaier & Rottmann, 2011; Goel et al., 2022). On the other hand, some studies explore the effect of specific technologies –for instance, robots– on employment (e.g., Acemoglu et al., 2020; Koch et al., 2021; Deng et al., 2021).² However, in this analysis, they are not considered because they do not adopt the most standard empirical firm-level approaches.

Most studies of the two main approaches agree on the positive labor effects generated by innovations that are captured by the introduction of new products or by R&D expenditures. However, in the case of process innovation, the studies observed contradictory effects (Calvino & Virgillito, 2018; Heijs et al., 2019; Hötte, 2023; Vivarelli, 2014). The meta-regression analysis of this paper, only for the Harrison et al. model, explains the contradictions and heterogeneity that appeared in the results of empirical studies that analyzed the relationship between innovation and employment (especially for process innovation).

We focus on the papers that used the approach proposed by Harrison et al. (2014) for four reasons. First, the Harrison et al. model detaches the direct effects of product and process innovation, which allows for verifying some of the theoretical mechanisms behind the relationship between innovation and employment. Second, it allows us to assess why contradictory results with no clear empirical pattern for the process innovation were observed. Third, we exclude or isolate the possible heterogeneity caused by the use of different empirical methodologies and can therefore focus on external determinants. Finally, a previous literature review of innovation and employment was elaborated by Ugur et al. (2018), who applied a meta-regression for the 35 articles that used the labor demand model. Their main results suggest that the effect of innovation (in terms of R&D expenditures) on employment is positive but small and highly heterogeneous. Only a small part of residual heterogeneity is explained by moderating factors (Ugur et al., 2018). The shortcoming of this first type of model is that it does not control for the kind of innovation (process or product innovation), while the Harrison et al. model does take that aspect into account.

Furthermore, several literature reviews analyze the numerous publications on the employment effects of innovation, synthesizing theoretical implications and empirical findings (e.g., Barbieri et al., 2020; Calvino & Virgillito, 2018; Heijs et al., 2019; Hötte et al., 2023; Mondolo, 2022; Vivarelli, 2014). They highlight the heterogeneity in the effects between the different types of countries. Moreover, they observe some contradictory effects found in studies of the same types of countries. One main contribution of this paper is to tackle the explanations for these countries’ heterogeneity with the meta-regression analysis.

For the analysis, we detected and considered 27 articles with 313 estimations proposed in those papers. We consider two different meta-regression models that referee the two main parameters of the model of Harrison et al. (2014). One model analyzes the heterogeneity of the employment effects of sales growth due to new products as a proxy of product innovation, and another analyzes these effects in firms that introduced “only process innovations” (referring to firms that did not introduce any new product).

We extend this analysis by splitting the sample into different types of countries (developing and developed) because several authors demonstrate that the employment effects of products and process innovations differ by the type of country (developed versus developing countries) (Vivarelli, 2014; Crespi & Tacsir, 2018; De Vries, 2020; Fu et al., 2021). Expenditures in R&D and innovation are highly concentrated in multinational companies, and firms from the most developed countries introduce an overwhelming number of innovations. By contrast, less developed countries import and adapt technologies as part of their catching-up strategy (lower-middle income countries) or their industrialization process (very low-income countries). This is because product and process innovations have different impacts, and the nature of such innovation (on the edge of the technological frontier versus imitation and adaptation of already-existing technologies) implies different labor effects (Crespi & Tacsir, 2018). Therefore, we included the type of country as an explanatory variable in our overall model of the meta-regression. However, we also estimated separate models for both kinds of countries.

In the case of firms that introduced product innovations, the empirical studies show a more homogeneous employment effect. However, the meta-regression suggests that two aspects positively impact the magnitude of the effect, “only process innovation” and instrumental variables as a methodology for correcting the endogeneity problem. Studies for periods of crisis have a negative effect on sales growth due to new products. Contrarily, the observed heterogeneity of the employment effect of “only process innovation” can be partially explained by the moderating role of the economic level of the country of the firms. Another interesting finding are the different effects-based on the historical moment of observation. The meta-regression suggests the following results. The effects of “only process innovation” on the labor market are negative when the period analyzed includes years of economic crisis and developing countries. Similar results are found for the case of manufacturing sectors. Other characteristics positively affect the sign of the impact of “only process innovation” on employment: the use of instrumental variables, high-tech sectors, and samples with large firms.

Furthermore, after splitting the samples, the results suggest more heterogeneity in developed than in developing countries in the case of sales growth due to new products, even though the real size effect estimation is almost the same in both types of countries. A contrary effect is found in the case of “only process innovation,” where the heterogeneity is higher in developing countries than in developed countries. This heterogeneity is explained mainly by the use of Methodology (IV), high-tech sectors, large and small samples (positive effects), and the manufacturing sector (negative effects).

These results shed light on the limitations of the Harrison et al. model. First, capturing the real effect of process innovation in a dummy variable is difficult. Process innovation can be related to the introduction of new or substantially improved processes in a company or the use or adoption of new equipment and machinery (often on-the-shelf-technologies) produced in other companies and sectors (e.g., adopting robots in the automobile sector). The second main concern is that the Harrison et al. model uses a simplified dummy variable associated with “only process innovation” and does not include a variable of process innovation related to product innovation. However, many new products require new processes. The results of the meta-regression analysis suggest that these limitations are more problematic in developing than in developed countries. Finally, the positive labor effect of product innovation might be mitigated because the Harrison et al. model does not consider the “business stealing effect.” This effect arises when demand for old products produced by non-innovating firms decreases because their market share is “stolen” by innovating firms that introduce new products that meet the demand for the old ones (see Acemoglu et al., 2020).

In the following section, we offer some basic notions of the theoretical framework for the effect of innovation on employment in quantitative terms. Section 3 discusses the methodologies of input-oriented and output-oriented models (the studies on which our meta-regression is based) and the impact in developing and developed countries. The methodological design of such regression is explained in Sect. 4, and the information collected from the 27 studies used is described by the statistical data presented in Sect. 5. Finally, Sects. 6 and 7 present the results and the main conclusions of the meta-analysis.

In order to explain the heterogeneity observed in the studies that apply the Harrison et al. model, we use a meta-regression analysis (MRA), estimating two models and including the principal regression coefficients of the Harrison et al. model as the dependent variables: (g2) sales growth due to new products and (d) “only process innovation.”

To achieve the goal of this section, we adapted the methodology initially proposed by Stanley and Doucouliagos (2012) called “meta-regression analysis.” This method involves the analysis of the distribution of estimated coefficients and identifying elements that drive heterogeneity, including the so-called publication bias. Such bias in the results exists because papers with statistically significant results have a higher chance of being published, not only in journals but also in working papers, PhD theses, etcetera (Stanley, 2005; Stanley & Doucouliagos, 2012). Following the authors mentioned, the MRA models the relationship between the analyzed effect and its standard error to quantify the publication bias using Eq. 12:where effect_i captures the estimated coefficients of each study i. The coefficient \({\beta }_{0}\) reflects the real employment effect (the average effect without the bias) of either sales growth due to new products (g2) or “only process innovation” (d) adjusted for the standard errors of the estimated effect_i reflected in the papers, while coefficient \({\beta }_{1}\) captures the presence of publication bias. The null hypothesis is the absence of publication bias (\({{H}_{0}: \beta }_{1}=0\)). When the null hypothesis is rejected, it implies evidence of bias.

Because the estimated coefficients (effect_i) come from different studies based on different datasets, sample sizes, and different controls or methods, they normally generate both heterogeneity and heteroskedastic error terms. Therefore, it is prudent to use a weighted least squares (WLS) regression (Costa-Font et al., 2011). Equation 12 can be transformed into Eq. 13, dividing by the standard error \({\sigma }_{i}\), which is equivalent to using WLS precision-square \((\frac{1}{{\sigma }^{2}})\) as the analytical weight.

In Eq. 13, the dependent variable becomes the t-value associated with the ith reported estimate in the MRA dataset. However, the interpretation is the same as Eq. 12. Equation 13 represents what it is known as a precision effect test (PET) and allows us to test for the presence of publication bias (H₀:\({\beta }_{0}=0\)). When H₀ is rejected, we have evidence of the presence of publication selection, while testing \({\beta }_{1}=0\) is the funnel asymmetry test (FAT). An asymmetric funnel indicates whether there is a systematic difference in the size or sign of a regression coefficient related to each study’s size or precision.

However, the specification on Eq. 13 still has some problems. According to Andrews and Kasy (2019), the conditional expectation of the effect size across studies is not lineal in the standard errors; it might cause a \({\beta }_{0}\) to be misguided in the interpretation as selection-corrected. To address this issue, some studies suggest introducing a quadratic specification (see Eqs. 14 and 15).

Equation 14 is known as the “precision-effect test corrected for standard errors” (PEESE). This specification is also used to test heterogeneity, transforming Eq. 14 into Eq. 15 by including additional regressors.

The observed heterogeneity is modeled through a set of binary (Z) variables that moderate the magnitude of the effect size estimates (Ugur et al., 2020). Equation 15 is also estimated by WLS, using the inverse of the variance of the estimated coefficients as weights \(\left(\frac{1}{{\sigma }^{2}}\right)\).

The first steps in meta-analysis are the search for or identification and selection of the studies included. Since this study aims to verify the effect of innovation on employment in developed and developing countries, international databases were reviewed. In particular, major academic websites on which the original texts were searched, like Google Scholar, Proquest, and Web of Science, were consulted. The search on these sites was based on combinations of the following keywords: “innovation,” “employment,” “product innovation,” and “process innovation.” The search was limited to scholarly journals and studies, and only studies that were written in Spanish or English were extracted. We included literature in Spanish because we found several studies for Spain and Latin America in both languages.

A total of 52 studies on the employment effects of innovation were identified, but we excluded studies that used other empirical methodologies unrelated to Harrison et al. (2014). In other words, we eliminated overlapping studies and checked the practical approach manually. We selected a total of 27 studies suitable for the purpose and scope of this study.¹⁵ In the following pages, we offer the descriptive statistics for the key variables used for the meta-regression analysis (Table 1) and additional statistics for our dependent variables (coefficients of product and process innovation) according to the subsamples analyzed (Table 2).

Table 1 reflects that the average results among the studies that estimate employment effects derived from sales growth due to new products (\({g}_{2}\)) is 0.95, and the minimum and maximum values of this variable are (−0.25) and 4.77, respectively. These results suggest that most of the studies that have applied the Harrison et al. model obtained a positive and significant effect of this variable on employment, which is in line with what is expected by the theory mentioned above. Moreover, the standard deviation associated with the estimated coefficients is low, with a mean of 0.11.

In the case of “only process innovation,” the average employment effect is negative (− 0.86). However, there is a big dispersion in the values of this regression coefficient (with a minimum value of − 12.50 and a maximum of + 26.26) reflected by a standard deviation of 4.15. These results suggest that the relationship between only process innovation and employment is very heterogeneous and includes contradictory effects. Moreover, the standard deviation associated with the regression coefficient of only process innovation suggests that many of these coefficients are not significant. The average of this variable is 2.20, with a maximum value of 12.66 and a minimum value of (− 1.30). Such results justify the meta-regression analysis to explain the underlying causes.

Table 1 also shows some other methodological specifications and the sample characteristics. For instance, around half of the studies estimate by using control variables, crisis years, and developing country samples. On the other hand, some studies (approximately 10%) estimate the differentiated effects by sector (high- or low-tech sectors). Finally, many studies (81%) carry out the analysis only for manufacturing companies.

Furthermore, Table 2 displays the mean values for sales growth due to new products and “only process innovation” estimated coefficients for all the envisaged cases of the analysis. As can be seen in the table, sales growth due to new products shows a homogeneous pattern, possessing positive coefficients. Even in the case of using subsamples, the average of the coefficients is very similar between firms of different types of sectors or sizes.

However, in the case of “only process innovations,” the coefficients differ significantly among each other. In particular, there is a change of sign in the case of developing and developed countries (0.06 and − 1.94, respectively). The second most notable difference for “only process innovation” is found for means by type of methodology followed since the average value for the estimations based on instrumental variables of is (− 1.87), while for the estimations using OLS, the value is only (− 0.29). These differences are also present when we compare by types of sectors, where the value found for the services sector is (− 0.03) and for high-tech firms (− 0.45). The negative effect is much more noticeable for manufacturing and low-tech firms (− 1.09 and − 1.06, respectively). Although the means for the majority types of (sub)samples present negative values, looking at the maximum value, it can be stated that for all the (sub)samples, at least one study reflects a positive impact. For instance, for all subgroups of Table 2, the maximum value for the coefficient of “only process innovation” is positive.

Finally, the descriptive data of the studies included reflect that the labor-creating effect of sales growth due to new products apparently seems to be slightly lower in the period during and after the crisis. The negative employment effect of “only process innovation” is clearly more intense since the beginning of the crisis. In any case, the meta-regression analysis should reveal whether the differences (in terms of descriptive statistics) explain the heterogeneity of the results obtained in a causal way.

This paper attempts to explain the apparent heterogeneous results observed in the empirical studies that measure labor effects of product and process innovations. The main conclusion is that Harrison’s model correctly estimates the effect of product innovation, but it has limitations when the effect of process innovation is considered.

In the case of product innovation, the few small differences observed between the 313 models analyzed are not related to the type of country, the sector or the size of the firms in the sample. The heterogeneity in the results can be explained basically by the methodological approach (using instrumental variables), control variables, and by “only process innovation.” On the other hand, the results suggest many possible causes of the observed heterogeneity for “only process innovation.” The negative labor effect of “only process innovation” is more notable for firms in developing countries and manufacturing sectors. Similar results are found in studies that analyze the sample during a period of crisis. However, some other factors impact positively in the real size of “only process innovation,” such as the methodological approach (using instrumental variables), control variables, and high-tech sectors.

The theoretical background, the descriptive statistics, and the results of the meta-analysis also suggest an intermediating role of the type of country on the employment effects of “only process innovation.” For this reason, we decided to extend the analysis, splitting the sample between developing and developed countries and estimating the meta-regression analysis for each type of country. The results suggest that the size effect of sales growth due to new products on employment is almost the same for both types of countries, even though we found more heterogeneity for the case of developed countries. On the other hand, heterogeneous effects were found for the case of “only process innovation,” which is more persistent in developing than in developed countries.

Specifically, for “only process innovation,” the different results found in developing countries might be explained by sales growth due to new products, methodology (IV), manufacturing sectors, high-tech sectors, and large firms. On the other hand, in the case of developed countries, the size effect of “only process innovation” is explained by methodology (IV) and small firms. It suggests that the proxy variable used for process innovation (a dichotomous variable for “only process innovation”) fails to capture firms’ specific process innovation strategies, especially in developing countries. The results show that the employment effects of the variable “only process innovation” vary greatly, and it is difficult to identify their specific size. In any case, more heterogeneity exists from its effect in developing than in developed countries.

Our meta-analysis has some limitations, the most outstanding ones are the following. First, most papers focus on Europe and Latin America. Having more articles from other parts of the world (for instance, the emerging countries in Southeast Asia) would provide more information about the differentiated effects of product and process innovation on the labor market by type of country. Second, it would be interesting to have information that could account for the “business stealing effect” to capture the possible overestimation of positive employment growth related to sales growth due to new products. Finally, it would be helpful to have other ways to measure process innovation and introduce the Harrison et al. model, for instance, embodied technological change, proposed by Pellegrino et al. (2019). However, this variable is not part of the surveys based on Community Innovation Surveys (CIS), and most of the time it is not allowed or it is impossible to merge its data with other sources of microdata, limiting the analysis. In any case, these last two aspects are more a problem of the model than of the meta-regression.