Effects of product and process innovations on the employment growth rate: Evidence for the Colombian manufacturing industry.

This paper estimates the effect of product and process innovation on the employment growth rate in Colombian manufacturing industry between 2007 and 2012. Based on the model forward put by Harrison et al. (2008), employment growth rate is explained by both the introduction of process innovations that have an effect on old products and the product innovations that have a positive effect on the growth of sales. This research uses the rm-level data panel from the Technological Development and Innovation Survey (EDIT) and the Annual Manufacturing Survey (EAM) in Colombia between 2007 and 2012. Given the rm´s production, results show a positive effect of product innovations on the employment growth rate and a negative effect of process innovations on the employment growth rate in manufacturing rms in Colombia.


Introduction
Innovation can improve competitiveness of rms and increases their total factor productivity. However, innovation also affects the intensity in which these factors are used in the production process. Speci cally, product innovations[1] tend to have a positive effect on product demand and therefore on labour demand. In contrast, process innovations can have a negative effect on employment through greater e ciency in the production process, which would lead to a saving inputs. There is no consensus in the literature about the impact of innovations on the employment, therefore this research provides empirical evidence of the effect of product or process innovations on employment growth rate in Colombian manufacturing rms between 2007 and 2012.
The effects of innovation on employment at the rm-level are evaluated in a sample of 17.980 Colombian manufacturing rms using the structural model developed by Harrison et al. (2008). The econometric methodology used for the estimation is pooled ordinary least squares. In this model, products innovations affect employment through their effect on sales of new products while process innovations affect employment through their effect on production e ciency of old products for the rm. Given the rm's production, the results of this research show a positive impact of product innovations and a negative and statistically signi cant impact of process innovations on the employment growth rate in Colombian manufacturing rms between 2007 and 2012.
According to the neoclassical theory, the effects of product innovation on employment are mostly positive since it increases the demand for new or improved products [2]. The impact of process innovation on employment depends of the displacement and compensation effects that it may have in the demand for labor. Displacement effect is a reduction of production factors per product unit often associated with an increase in productivity. However, the increase in productivity reduces production costs and through different compensation mechanisms the process innovation can generate more employment. These Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js mechanisms work when rms do not have su cient market power and the fall in prices is su cient to stimulate demand for products (Edquist, et al., 2001 andVivarelli, 1995).
In developed countries, most empirical research found a positive effect of product innovation on employment growth rate in manufacturing while the effect of process innovation is unclear. The process innovation had a negative effect on employment in UK manufacturing rms, although this effect was statistically signi cant on rms that developed only process innovations (Harrison et al., 2008;Peters, 2008;Van Reenen,1997). On the other hand, Hall et.al (2006) and Smolny (2002) found that process innovation had a positive effect on job creation in Germany and other countries.
In Latin America, most research based on the structural model developed by Harrison et al. (2008) found a positive effect of products innovations and an ambiguous effects of process innovation on employment growth rate in manufacturing [3]. These results generally do not differ between rms of different size or technological intensity. Regard to the impact of innovation on employment compositions, authors found scant evidence of a skill bias, although product innovation was more complementary to skilled than to unskilled workers.
In Colombia, Lopéz and Zárate (2014) following the model developed by Harrison et al. (2008) found that products and process innovations had a positive effect on employment in manufacturing rms between 2011 and 2012. On the other hand, Barrios (2019) found a positive effect of innovative efforts on total factor productivity (PTF) in Colombian manufacturing rms between 2008 and 2012. Given the rm´s production, this latter result can have a negative effect on the employment growth rate in Colombian manufacturing rms. This research has an analytical contribution about the effects of product and process innovations on the employment growth rate in Colombia between 2007-2012. It uses a rm-level data panel on total innovations in rms in the manufacturing sector and activities associated with technological development, which enables to control the unobservable heterogeneity between rms and obtain more e cient estimated effects. The results of this analysis are present in consideration of different sources of endogeneity in the model by the correlation between innovation outputs and the productivity.
This document is divided into three sections. First section has the theoretical framework of the structural model through which the impact of innovation on employment is evaluated. Second section shows the econometric strategy and descriptive statistics of the most relevant variables of the model. Finally, the three section presents results of the econometric estimation and conclusions.
[1] Schumpeter de nes product innovation as the introduction of a new good or better quality of goods in the market and process innovation as the introduction of a new production method.

Methodology
The effect of product and process innovations on the employment growth rate is analyzed with the conceptual framework developed by Harrison et.al (2008). This is a multi-product model that considers the displacement and compensation effects of innovation on labor demand. The main assumption in this model is the production of two types of goods in the rm: old and new products for the rm.
In order to produce these goods, rms have a production function with constant returns to scale in labor. We also assume that labor is the only factor of production and this is homogeneous. Additionally, there is a technology parameter, θ ijt , which increases the e ciency of the production process. Thus, the rm´s production function is: y ijt = θ ijt F L ijt e η j + ω 1jt (1) For i = 1 and 2; j = 1..., n and t = 1 and 2 Where η are unobservable xed factors, ω are idiosyncratic shocks, products are denoted by i and rms by j. In the following of the development of the theoretical model the subscript of the rm is omitted.
The rm´s labor cost function is de ned as[4] : c w 1t , w 2t y 1t , y 2t , θ 1t , θ 2t = c w 1t y 1t θ 1t e η + ω 1t + c w 2t y 2t θ 2t e η + ω 2t 2 Where y 1 is the production of old products for the rm and y 2 is the production of new products for the rm. In this model if t = 1all production corresponds to old products, i.e., y 21 = 0, and if t = 2 the rm has no production of new products. Similarly, w 1t and w 2t represent wages at time t in the production of old and new products for the rm, respectively. Finally, we assume that the rm's productivity levels are affected by xed unobserved factors η, idiosyncratic shocks ω and production e ciency θ .
According to Shepard´s Lemma and given the rm´s production, labor demand in the production process of each type is well expressed as follows: The employment growth rate at the rm level is given by the employment growth rate in the production of old products plus the employment growth rate in the production of new products. Since in this model the In this equation, the employment growth rate for the production of old products is approximated by the logarithm of this variable in order to obtain a linear equation in terms of the relevant variables. To simplify the model, we assumed that the salary of workers for the production of new and old products remains constant and equal during two periods. In other words, c w 11 = c w 12 = c w 22 .
After replacing the values of Eq.
(3) and assuming that ω 22 = ω 11 , the employment growth rate is given by the following equation: According to this equation, the employment growth rate is the result of: (i) the variation in e ciency in the production of old products; (ii) the growth rate in the production of old products and (iii) the share of new products in total production, i.e., the expansion in production attributable to new products. This latter effect depends on the e ciency ratio between the production of old and new products (θ 11 /θ 22 ), which is less than one if new products are produced more e ciently than old products. In this case, there could be labor savings per unit of new products and employment would not grow as much as sales for new products.
Due to the background of the model, greater e ciency in the production of new or old products reduces labor demand. Thus, an increase in the employment growth rate is only through lower production e ciency because in this model the change in labor demand is not derived from an increase in production. However, productivity gains can increase the scale of production and, therefore, the end result of this is an increase in labor demand. On the other hand, improvements in pro tability from the production of new or improved products can increase a rm's market share and scale of production and thus employment.
The expected results of the share of production by new products in the rate of employment growth are two. First, a lower relative e ciency estimate (θ 11 /θ 22 ). In this case, the rm indicates that gets more productivity from the production of new products and this lead to a displacement effect on labor. However, this is not the net effect because the model takes production as given and does not take into account that improvements in productivity increase production. The second result is a higher relative /jax/output/CommonHTML/fonts/TeX/fontdata.js e ciency estimate (θ 11 /θ 22 ). In this case the rm has more production share for older products, perhaps because obtains greater productivity in the production of old goods than in the production of new ones.
The growth rate of e ciency in the production of old products in Eq. (5) can be interpreted as an average productivity growth between rms. This e ciency may be different between innovative rms and noninnovative in productive process. So, the model has a dummy variable equal to one if the rm developed process innovation and zero otherwise. As in the theoretical model, process innovations in the empirical model only affects the production technology of old products. Thus, the equation to estimate the effects of innovation on the rate of employment growth is: In this equation, l is the growth employment rate in the Colombian manufacturing industry between 2007 and 2012; d is a dummy equal to one if the rm implemented process innovation not associated with a product innovation (only innovation process) y 1 and y 2 are the rate of production growth by old and new products, respectively. However, these latter variables are not observed in the database used, so they are replaced by the sales growth rate for old and new products. On the other hand, X i are control variables, α 0 represents the growth in e ciency in the production of old products that do not come from of innovations in process and u i is the error term that contains xed unobservable xed effects at the rm level and productivity shocks, u i = − ω 12 − ω 11 + ϵ. Additionally, the model includes a set of industry dummies to control the unobserved heterogeneity at the industry level and the common shocks to all rms.
The β 1 coe cient measures the relative e ciency between the production of old and new products. If β 1 is less than one, new products are produced more e ciently and thus the growth of production due to these increase the productivity per worker. In this case, the rm demands less amount of labor for the production of a good. However, the production of new product may increase the rm's market share, would probably lead to an increase in production and labor demand.
Through the e ciency parameter α1, the dummy variable of process innovation captures the effect of process innovations related to old products. These innovations are new or signi cantly improved methods of production, distribution, delivery, or logistics systems, implemented in the rm. This variable does not contain variations in productivity due to production of new or signi cantly improved products. Thus, the process innovation only has e ciency gains due to changes in the production of old products.
Finally, sales growth from old products may be affected by several factors. One of these is the demand substitution of old products by new ones. Another factor may be the fall in prices as a result of production e ciencies that could lead to an increase in the demand for old products. And one more, the autonomous increase in demand for old products. Since it is di cult to disentangle these factors in the ( ) model, the sales growth from old products is subtracted from both sides of Eq. (6). In this way, the estimated impact of sales growth from old products is equal to one and the model is: l i − y 1i = α 0 + α 1 d + β 1 y 2i + β 2 X i + u i 7 According to Crepon et. At (1998), the share of total sales from new products can be a proxy for the intensity of innovation. Then, this model also allows to evaluate the impact of innovation on employment taking into account the innovative effort in each rm.

Identi cation Issues
To obtain an unbiased estimator of α 0 , α 1 yβ 1 , it is necessary that the error term, u i of Eq. (7) is not correlated with the variables of process and product innovation, dand y 2 ,respectively. Since investments in innovation depend on the productivity of the rm, the results of innovation are correlated with productivity. The error term in Eq. (7) has a component of productivity and thereby the regression has an endogeneity bias on estimates of process innovation and sales from new products in the employment growth rate.
The literature has been the lags of the innovation as instruments to reduce potential bias by the correlation between results of innovation and productivity. However, sales from new products and process innovations are result of the productivity from technological investment thereby the lagged values of innovation are correlated with the productivity. It is di cult to nd a variable affecting the sales growth and uncorrelated with the productivity of the rm, since the production includes all the improvements from the innovation. Nevertheless, identifying components in the error term leading to endogeneity helps analyze potential biases in the model.
The error term in Eq. (7) has shocks productivity, ω ijt , which are external changes to rms that affect the rm productivity such as an increase in foreign investment. If these shocks are random, i.e. on average they are identical for all rms in an economy, the shocks productivity would not lead to bias on estimators. Nevertheless, if rms affect their decision to innovate in the period affected by productivity shocks, even if they are random, the results of the innovation in that period could be correlated with ω ijt and the innovation estimates would be biased. Rouvinen (2002) states that there at least a lag between technological investment and its effects on productivity. Therefore, it is possible that the technology investment has lags on the results of the innovation. This implies that although productivity shocks affect a rm's decision to participate in innovation activities its impact lagged on the results in innovation would have not a correlation with the productivity, sales and employment in the rm. Thus, the rm does not simultaneously determine investment in innovation and employment, which depends on productivity. In this case, the innovation variables in Eq. (7) are not correlated with the productivity shocks of the error term.
Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js Another cause of endogeneity is measurement errors in sales. In the database there are no prices at the rm level, so the growth of nominal sales is observed instead of the growth of real sales. Then, the producer price index is used as a de ator to obtain real sales growth. Additionally, it is di cult has sales from old and new products. For that reason, sales from new products are constructed from theirs share of total sales, s, at the end of the period and the growth rate of total sales, y t . Thus,y 22 = s * Y t Y t − 1 − 1 it is the share of new products in total sales. Meanwhile, y 11 = Y 12 Y 11 − 1 it is the growth rate for old products.
The absence of prices at the rm level in this database and the di cult to has directly sales from old products and new products leads to endogeneity in Eq. (7) due to measurement errors. This is because there is no way to identify whether price differences between rms are related to individual differences in e ciency growth or other productivity improvements from innovation, as the ability to sell more at better prices. Then, it is di culty to separate the effects on productivity generated by new and old products.
Additionally, in this model wages are assumed to be equal in the two periods in the production of old and new products. If this assumption failure and the wages in the production of new products is greater than the wages in the production of old products c w 12 cript > , there is an upward bias in the estimate of relative e ciency (θ 11 /θ 22 ). This is because in the absence of information regarding wages would be estimated an effect of productivity on the production of new products greater than the real value and therefore the impact of the production of these goods on the employment growth rate may overestimated.
In the absence of a variable that helps mitigate the correlation between innovation and productivity in the equation that determines the rate of employment growth, in this research the model is estimated using the method of ordinary least squares under the consideration that the estimates may be biased.

Data
This research uses the rm-level data panel from the Technological Development and Innovation Survey (EDIT) and the Annual Manufacturing Survey (EAM) in Colombia between 2007 and 2012. The former is a survey that DANE applies to rms registered in the EAM to know the development of innovation in manufacturing rms as well as the activities associated with technological development. The EAM includes information about performance in productive process of companies with 10 or more employees or their production value is greater than a xed amount for each year. Additionally, information about employment, output and xed assets of rms is obtained from the EAM.

( ) ( ) ( )
Information about the development of innovations in rms is obtained from EDIT V and VI. In these surveys there are categorical variables which allows identify whether a rm developed product or process innovation. A rm has innovation in product when answered a rmatively to the question as to whether have developed new or signi cantly improved products whose are signi cantly different from the products old produced by the rm. Likewise, a rm develops an innovation in process when answered a rmatively to the question as to whether have developed new or signi cantly improved methods of production, distribution or delivery during the survey's reference period.
In the Eq. (7), the dummy variable that indicates whether or not the rm developed process innovations is equal to one if this innovation is not associated with any developed of new products. To ensure that process innovation is associated only to the production of old products, rms are divided into two groups: rms with only process innovation and rms with product or process innovations. Thus, the process innovation would be associated only has productivity associated from production of old products. On the other hand, sales from new or old products are not observed but are constructed following EDIT question: how much was the percentage of sales from new or signi cantly improved goods or services introduced to the market during the survey's reference period. This allows to have nominal growth sales from new products.
Descriptive Statistics Table 1 presents the descriptive statistics of the most relevant variables used in the analysis of the effects of product and process innovation on growth employment. Moreover, this table shows the distribution of rms by type of innovation based on information from the EDIT and EAM between 2007 and 2012.   Source: DANE -EDIT IV, V andVI andEAM 2007-2012 According to the descriptive statistics obtained from table 1, approximately the 41 % of the Colombian manufacturing rms developed product or process innovations between 2007 and 2012. Meanwhile, the 21 % of the rms developed product innovation and the 11 % developed only process innovation.
Additionally, innovative rms had higher employment and sales growth. Speci cally, companies with product or process innovation in the 2007-2012 period increase the sales in 8% while the non-innovative companies increase the sales in 5,3%. Also, companies with product innovation increased their employment in 3.9 % and this result is 3 % for companies with process innovation compared to the 1,5% for non-innovative companies.
The relationship between innovation and employment is complex and according to statistics it is affected by the characteristics of the production process. The results of the econometric model given a greater knowledge to improve understanding of the impact of innovations on employment. However, this model Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js does not take into account the characteristics of the labor market, which contributes to explain the creation of new jobs.
[4] See Harrison et al (2008) where the employment growth rate is explained by the introduction of process innovations that affect old products and sales growth derived from the introduction of product innovations.

Results
The Table 2 presents the results of the estimation of the effects of innovation on employment by Ordinary Minimum Squares where the dependent variable is net employment, employment growth rate minus the real growth rate of sales for old products for the rm. Control variables include a dummy for organizational innovation, the growth rate of xed assets per capita and a dummy of rm size. This last variable is introduced to control the heterogeneity of the impact of innovation on employment in large and small rms. According to DANE, large rms are those that have more than 50 employees and small rms that have 50 or fewer employees.  Standard errors in parentheses *** p < 0.01, ** p < 0.05, * p < 0.1 Estimation by ordinary least square (OLS) from Table 2 shows that estimated effect of growth in sales of new products is positive and less than one. Given the rm's production, this estimated shows the relative pro tability of production between old and new products. Then, a coe cient less than one implies that the rm obtained more pro ts from new products than that of the production of old products.
Additionally, the product innovation, measured by sales growth from new products, had a positive impact on the employment growth rate in Colombian manufacturing rms between 2007 and 2012. Finally, as employment equation is estimated in growth rates the effects observable and unobservable speci c to rm that not vary over time are eliminated.
On the other hand, given the rm's production, only innovation process had a negative and signi cant impact on employment growth Colombian manufacturing rms, although this impact is small. The previous result shows that process innovation can lead to improvements on the productive process in a Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js rm, along with a labor savings per product unit. This result is obtained based on background of theorical model as improvements in production e ciency reduce the demand for labor. Nevertheless, is possible that rms with greater productivity increase their sales and thereby the production and employment.
The innovation activities may differ depending on the size of the rm, since in some cases smaller rms can be more innovative than large rms or vice versa. So, in the model, the rm's size dummy is expected to capture this heterogeneity. This estimated effect shows that larger rms have higher employment growth rates than small rms. Additionally, the constant coe cient in the econometric model is negative. This indicates that the contribution of productivity in the production of old products resulting by factors different from the innovation is positive. Then, rms on average have an increase in productivity that is expected to lead to lower employment growth rates. Similarly, the assets growth rate per capita generates a signi cant displacement effect at 5% in employment.

Discussion
According to results, product innovations have a positive impact on employment growth in Colombian manufacturing rms while process innovations had a negative impact. The effect of process innovation differs from López and Zárate (2014) who found that process innovation had a positive effect on the employment growth in Colombian manufacturing rms between 2011 and 2012, although the researchers used the same theoretical framework. Nevertheless, the positive effect of product innovation on employment growth is similar to those obtained by some research for Latin America (Alvarez et.al, 2011;Benavente & Lauterbach, 2007;Crespi & Tacsir, 2012).
The estimated effects could be biased by endogeneity on the econometric model mainly two issues. First, there could be measurement errors mainly because innovation can be a subjective and ambiguous concept for each people that answered the surveys. We acknowledged that this the principal restriction to analyzed issues relating to innovation. Second, since investments in innovation depend on the productivity of the rm, the results of innovation are correlated with productivity. Moreover, it is di cult to nd a variable affecting the sales growth and uncorrelated with the productivity of the rm, since the production includes all the improvements from the innovation.

Conclusions
This research nds that product innovations had a positive impact on employment growth in the manufacturing industry while process innovations had a negative impact on this. The results must be analyzed taking into account two issues. First, these estimates could be biased by the endogeneity that results of the correlation between innovation and productivity. Second, in the model greater e ciency in the production of new or old products reduces labor demand because in this model the change in labor demand is not derived from an increase in production. On the other hand, the results show that innovative and large-sized enterprises had far more employment growth than their small counterparts. The ndings in this research are preliminary article but helps to public policy-makers to design strategies that could improve the development of innovation activities in rms, given the positive results of these in job creation. Likewise, it is necessary to know the mechanisms by which the innovations developed by students bene t the employment growth. Finally, in this document was evaluated only the impact of innovation on the demand at work in rms in quantity terms, but it would be interesting that subsequent research evaluate the impact of innovation on the composition of employment.

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• Authors' contributions Fernando Barrios organized the database and analyzed and interpreted the data regarding the development of innovations in Colombian manufacturing rms. Moreover, he reviewed existing literature about this issue and actively to the drafting of the outcome document. Sandra Mora, review the theoretical framework of the structural model through which the impact of innovation on employment was evaluated and was a major contributor in writing the manuscript. All authors read and approved the nal manuscript.

Declaration of interests
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to in uence the work reported in this paper.