The contribution of innovation to farm-level productivity

Parikoglou, Iordanis; Emvalomatis, Grigorios; Läpple, Doris; Thorne, Fiona; Wallace, Michael Article — Published Version The contribution of innovation to farm-level productivity Journal of Productivity Analysis Provided in Cooperation with: Springer Nature Suggested Citation: Parikoglou, Iordanis; Emvalomatis, Grigorios; Läpple, Doris; Thorne, Fiona; Wallace, Michael (2024) : The contribution of innovation to farm-level productivity, Journal of Productivity Analysis, ISSN 1573-0441, Springer US, New York, NY, Vol. 62, Iss. 2, pp. 239-255, https://doi.org/10.1007/s11123-024-00728-0 This Version is available at: https://hdl.handle.net/10419/315408 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Journal of Productivity Analysis (2024) 62:239–255 https://doi.org/10.1007/s11123-024-00728-0 The contribution of innovation to farm-level productivity Iordanis Parikoglou1●Grigorios Emvalomatis2●Doris Läpple3●Fiona Thorne4●Michael Wallace5 Accepted: 13 June 2024 / Published online: 25 June 2024 © The Author(s) 2024, corrected publication 2024 Abstract Innovation is a key driver of productivity growth. This paper proposes a novel methodology in order to explore the impact of farm-level innovations on farm productivity and its components (i.e. technology, efficiency and scale) using representative data from Irish dairy farms. We measure innovation by an index based on employed production practices, continuous innovation activity and knowledge weighted by expert opinions. The results suggest that more innovative Irish dairy farmers are more productive. Specifically, all farmers improve their production technology and efficiency through their use of innovations, but farmers at specific levels of innovativeness may experience a decrease in productivity due to the small scale at which they operate. This indicates that innovation has a non-linear effect on productivity. We discuss the policy implications for reducing the unequal gains of innovation across farmers. JEL classification D24 ●Q12 ●O33 Keywords Agricultural Innovation System (AIS) ●Total factor productivity ●Efficiency ●Agriculture ●Dairy production ● Stochastic frontier analysis 1 Introduction Productivity and efficiency analysis is a particularly popular research topic in agricultural economics (e.g. Alvarez et al. 2012; Brümmer et al. 2002; Emvalomatis 2012; Fuglie et al. 2016; Hadley 2006; Karagiannis et al. 2004; Kellermann 2015; Latruffe 2010;O’Donnell 2012; Sauer and Latacz- Lohmann 2015; Skevas et al. 2018; Zhu and Oude Lansink 2010), due to its important policy implications. Productivity is recognized as an indicator of long-term competitiveness in agriculture (e.g. Latruffe 2010; Newman and Matthews 2006), while the efficient use of production factors can be viewed as an indicator of sustainability (e.g. Chambers and Serra 2018; Färe et al. 2005; Malikov et al. 2015; Murty et al. 2012; Sidhoum et al. 2019). For example, the Common Agricultural Policy (CAP) of the EU recognizes the necessity of productivity gains through technology and efficiency improvements at the farm level while reducing environmental pressures (Latruffe et al. 2017): increasing agricultural output with the same or smaller amounts of resources, while minimizing the impact on the environment is referred as sustainable intensification (SI) in the literature and policy documents (e.g. Benton and Bailey 2019; Campbell et al. 2014; Garnett et al. 2013; Godfray and Garnett 2014; Tilman et al. 2011). Innovation is a key driver of productivity growth and sustainability (e.g. Moreddu and Gruere 2019), and a voluminous literature on the link between innovation and productivity has developed over the years (Sauer 2017; Sauer and Latacz-Lohmann 2015). Innovation is a broad concept, which can be generally defined as the successful utilization of an idea (Knickel et al. 2009). In the case of firms/farms, innovation encompasses both creation and adoption of ideas that can be new to the firm, the market or *Iordanis Parikoglou [email protected] 1Agricultural Economics and Policy Group, ETH, ETH Zürich, CH, Switzerland 2Department of Economics, University of Crete, Rethymno, GR, Greece 3Department of Agricultural Economics and Rural Development, Georg-August University of Goettingen, Göttingen, DE, Germany 4Teagasc, Ashtown, Dublin, IE, Ireland 5Agriculture and Food Science, University College Dublin, Dublin, IE, Ireland 1234567890();,: 1234567890();,: the world (OECD and Eurostat 2005). A firm is characterized as innovative if, during the review period, it has implemented any type of innovation, including (i) new or improved product, (ii) process, (iii) marketing or (iv) organizational method (OECD and Eurostat 2005). Due to the wide nature of the concept of innovation, operationalizing it in applied research is not straightforward and, indeed various approaches to proxy innovation activity at the farm level have been employed. An established approach to measuring innovation is through investment expenditures at the farm level (e.g. Emvalomatis et al. 2011; Minviel and Sipiläinen 2018; Sauer 2017; Sauer and Latacz-Lohmann 2015; Serra et al. 2011; Silva and Stefanou 2007). However, innovation can also be nonphysical (OECD and Eurostat 2005), for example, taking the form of information acquisition, the development and use of tacit knowledge. As such, innovation can be created within the farm through learning-by-doing (Shee and Stefanou 2016; Stefanou 2009), as well as through the interaction with other actors, in particular, farmers interacting with their peers, advisors, academic institutions, input suppliers or other actors, thus forming an Agricultural Innovation System (Klerkx et al. 2012; Lamprinopoulou et al. 2014). The contribution of AIS actors to supporting SI can be considered more important than physical investments at the farm level, with the CAP and Farm to Fork strategy officially promoting the role of AIS actors to foster a more competitive, resource efficient and sustainable agricultural sector. The reason is that physical investments (e.g in machinery) are not always consistent with the SI vision, since although they result in productivity gains, these may come at the cost of sustainability, e.g. through exerting increasing pressure on the environment (e.g. FAO 2013). To achieve SI, farmers need to combine their own tacit knowledge with information coming from external AIS actors in order to adapt their farming practices, while considering the various environmental, ecological, cultural and socioeconomic characteristics (Laurent et al. 2006;Polanyi2000; Rossel and Bouma 2016). This paper builds a framework for examining whether the impact of innovation on farm-level productivity is in line within the wider definition of SI. A stochastic frontier analysis (SFA) model is employed, which examines total factor productivity (TFP) differences across farmers that arise from differences in the innovations they employ. The Irish dairy sector is considered as an interesting case study, given the ambitious growth targets set out for the industry in the post-quota environment, which is predicated on the idea of knowledge adoption augmenting productivity by farmers and other economic agents within the agricultural sector (DAFM 2015). On the basis of an innovation index, which captures the differences in the employed innovations across farmers, we construct a cross-sectional TFP index similar to Orea (2002), by extending the approach taken by Karafillis and Papanagiotou (2011), where the time dimension in a panel study of productivity growth is replaced by the innovation index. In this setup we are able to examine the contribution of innovation to cross-sectional differences in TFP and its components, i.e. on the production technology, efficiency and scale effects. Hence, the main advantages of the proposed framework is that it can examine whether the contribution of innovation to productivity is in line with the vision of SI and, in particular, the objective of producing more agricultural output with the same or less inputs. Our results suggest a non-linear effect of innovation to productivity. Specifically, more innovative farmers are more productive, which is driven mostly by a positive effect of innovation on technology and efficiency. The scale effect is negative at lower levels of innovation but positive at higher levels of innovation, i.e. innovation has a higher effect on the productivity of larger farmers. The remainder of the paper is organized as follows: Section 2 summarizes previous empirical research regarding innovation and productivity, and explains how this paper extends this stream of literature. Section 3 outlines the conceptual framework, building a TFP index in which the contribution of AIS is incorporated explicitly. Section 4 presents the data and summary statistics. Section 5 reports the results and Section 6 concludes. 2 Background and conceptual framework 2.1 Literature review Many empirical studies have examined the contribution of innovations promoted by specific AIS actors to farm-level productivity and its components, while accounting for the possibility of suboptimal utilization of resources (e.g. Bravo-Ureta and Evenson 1994; Bravo-Ureta et al. 2012; Dinar et al. 2007; Henningsen et al. 2015; Martinez-Cillero et al. 2018;O’Neill et al. 1999; Rao et al. 2012). This vein of research was undertaken using mostly cross-sectional data, possibly due to lack of panel data. The contact of a farmer with an AIS actor is measured usually with a binary variable, indicating whether a farmer contacted an AIS actor during a specific period. From a methodological perspective, cross-sectional studies either split the samples into farmers who contacted the AIS actor of interest and those who did not, and compare the differences in marginal productivities and efficiency scores between the two groups (e.g. Bravo-Ureta et al. 2012; Henningsen et al. 2015; Rao et al. 2012), or with the use of a metafrontier for more than two groups (DeLay et al. 2022). An alternative methodological approach is to include the innovation variable as part of the technology and/or inefficiency (Dinar et al. 2007; McFadden et al. 2022). 240 Journal of Productivity Analysis (2024) 62:239–255 The adopted methodologies of the aforementioned crosssectional studies have a common limitation when one investigates the impact of innovation in SFA framework: the impact of innovation on productivity through the scale effect is not taken into account. The adoption of an innovation changes the production technology and, thus, it may alter the optimal levels of factors of production and, consequently, their optimal usage ratios. In this respect, technical progress, especially embedded technical progress, tends to favor larger farms (e.g. Alvarez and del Corral 2010; Alvarez et al. 2012; Balaine et al. 2020; Läpple and Thorne 2019). During the Green Revolution, physical innovations, such as introduction of specialized machinery, enabled farmers to increase their scale of operation (Weersink et al. 2018) with a commensurate reduction in the total number of farms. However, knowledge and information, as provided by AIS actors, can assist farmers to sustainably intensify their production processes by reducing the need for large-scale farming. This is because farmers can use knowledge instead of scarce (e.g. labor, land) or harmful (e.g. chemicals) inputs (Bongiovanni and Lowenberg-DeBoer 2004; Finger et al. 2019; Gallardo and Sauer 2018; Lajoie-O’Malley et al. 2020; Mcbratney et al. 2005; Rossel and Bouma 2016) and produce more with the same or less inputs. Thus, when examining the impact of innovation on SI in a productivity and efficiency analysis framework, it is necessary to account for the impact of innovation on the technology, efficiency scores and optimal scale, simultaneously. Taking a different approach from the aforementioned studies, Karafillis and Papanagiotou (2011) estimated a profit function using cross-sectional farm-level data and constructed a TFP index on the basis of an innovation index. The index consisted of aggregate (mostly physical) technologies that were used at the farm level. The limitation in Karafillis and Papanagiotou (2011), again in relation to SI, is that their TFP index consisted only of the technology and scale effects, neglecting efficiency. Nevertheless, their approach is amenable to modifications which can include the efficiency component of TFP in the analysis. We extend this approach to examine the impact of innovation on the technology, efficiency and scale and their aggregate net effect on TFP using cross-sectional data from Irish dairy farms. 2.2 Conceptual framework Individual farmers typically have different needs and face different constraints, which leads them to utilize various technologies/sources of information at any point in time (Chavas 2001,2012). Taking this into consideration, we do not focus on the contribution of a specific actor or technology on productivity, but we consider innovation at the farm level to stem from the contribution of multiple AIS actors. Previous studies examined the simultaneous impact of multiple innovations on farm level productivity and efficiency (DeLay et al. 2022; Dinar et al. 2007; McFadden et al. 2022). Neglecting to take into account the contribution of various innovations may result in biased estimates, e.g. part of productivity gains may be attributed to a technology that is not included in the analysis. Furthermore, if one is interested in examining the impact of multiple AIS actors, then it is necessary to consider the relationship between these actors, as these usually form the wider institutional context and regional/national policy objectives (Klerkx and Jansen 2010; World Bank 2006). For instance, Dinar et al. (2007) considered the use of public and private advisors as two separate determinants of production technology and efficiency, utilizing the whole sample in the empirical application. This is because, in the context of their application, private advisors assist farmers with practical problems associated with the use of certain inputs, while public advisors focus on more general problems (Dinar et al. 2007). In the case of Ireland, the national AIS is one of the most integrated systems in the EU, with an organized and coordinated structure. Specifically, Irish dairy farmers may simultaneously use information or technologies from various Irish AIS actors, who offer complementary technologies/ advice (e.g. Prager and Thomson 2014). These technologies are related to grassland, breeding and financial management, that will, overall, allow dairy farmers to better utilize the lowcost grass-based feed system (Läpple et al. 2019;Thorne et al. 2017) and, as a result, improve competitiveness in a sustainable manner. For instance, a farmer may use milk recording, which provides more information about cows’productive capacity (Balaine et al. 2020) and then contact an advisor for assistance in order to use the information obtained for breeding management (Balaine et al. 2020; Regan 2019). Capturing the impact of complementary Irish AIS technologies by using separate variables for each technology may create issues such as multicollinearity in the empirical specification. Thus, we use the composite innovation index developed by Läpple et al. (2015) specifically for the Irish dairy sector in 2012, which captures the employed innovations at the farm level that arise from the interaction of various innovations promoted by the Irish AIS: farmers with higher index scores use more innovations promoted by AIS. Thus, the overall index reflects the degree of innovativeness of individual farmers, where innovativeness is defined as “the degree to which an individual, or any other unit of adoption is relatively earlier in adopting new ideas than other members of a system”(Rogers 2003, p. 22). Previous farm-level studies focused on examining the impact of specific components of the AIS, such as FAS or the use of specific technologies, using binary indicators on Journal of Productivity Analysis (2024) 62:239–255 241 efficiency and TFP growth (Parikoglou et al. 2022a,b). However, the TFP growth index and its components are not informative regarding the starting point in productivity, but only measure rates of change. On the contrary, in this study we focus on TFP differences in the dimension of innovativeness. In this regard, we are able to determine, at a specific point in time, whether farms with a higher innovation index are indeed more productive: instead of simply measuring the productivity level for each innovation group and comparing the results (which is particularly difficult to do or requires stronger assumptions compared to measuring productivity changes), we amend the methodology designed to measure productivity changes over time to allow us to measure productivity differentials across different levels of innovativeness. At higher levels of innovativeness, farmers experience better information flow, which can inform input use, choices and access to technology embodied in inputs (Batte and Schnitkey 1989). Better information flow may shift the production technology outwards (DeLay et al. 2022; Dinar et al. 2007;McFaddenetal.2022). Furthermore, better information flow may have a twofold impact on efficiency. First, acquisition of knowledge may improve the way inputs are used and lead to higher efficiency. For example, a farmer who starts using a grassland management system could make better use of the available area. Conversely, the introduction of a new product or production method may adversely affect efficiency if the farmer incurs learning costs when implementing the innovation, as predicted by the adjustment-cost theory (Stefanou 2009). For instance, Henningsen et al. (2015) examined cross-sectional productivity differences between contract and non-contract farmers in Tanzania in 2012. The results showed that contract farmers had much lower average technical efficiencies compared to non-contract farmers, although the former were more productive. The authors argue that this finding can be attributed to the lack of advisor services that assist farmers in making better use of the information gained from contract farming. Lastly, different types of employed technologies may lead to different optimal scales of operation (Varian 2010). For example, some technologies are input saving, e.g. grassland management techniques were developed as a response to the lack of available land. Others may be output-enhancing, such as milk recording. In the latter case, farmers may endure external adjustment costs in relation to these factors of production (Stefanou 2009) and divert resources from production to innovation investments (e.g. Serra et al. 2011). This alters the optimal scale of production, which could cause either a decrease or an increase in productivity. Ultimately, discrepancies in productivity among farmers due to varying levels of innovativeness can be attributed to the aggregate impact on the technology, efficiency and scale. 3 Modeling approach and empirical specification Irish specialist dairy farms produce more than a single output, thus we use an output distance function to represent their production technology (Newman and Matthews 2006). In general, the choice between an input-reducing and output-expanding view does not make a difference when the technology exhibits constant returns to scale (Newman and Matthews 2006; Orea et al. 2004). We choose the distance function to be output-expanding since, despite the quota scheme operating in the period covered by our data, quotas were tradeable within regions. It is conventional in applications that involve time-series or panel data to capture improvements in the production technology over time by the exogenous passage of time. These improvements result in an outward shift of the technology of the production possibilities set. Following Dinar et al. (2007); Karafillis and Papanagiotou (2011); McFadden et al. (2022), in a cross-sectional setting, differences in the technology employed by farmers are attributed to the level of their innovativeness, captured by I, where, a priori, we expect higher levels of Ito result in a similar outward shift of the technology. The output expanding distance function is defined as: Doðx;y;IÞ¼min θ:y θ2output possibility set, given I no ð1Þ where y2RMand x2RNrepresent, respectively, the vectors of outputs and inputs. Both vectors are assumed to be functions of I, as innovativeness affects the employed technology and, thus, the levels of and proportions at which inputs are combined to produce outputs. We also assume that Iis exogenously determined. 1 The output distance function in equation (1)reflects the distance of a producer from the boundary of the production possibilities set for each level of the innovation index, with the inverse of the value of the distance function indicating the maximum amount by which the output vector can be expanded to reach this boundary. Technical efficiency can be defined as: Doy;x;IðÞ¼TE ð2Þ Taking logs of both sides, totally differentiating with respect to I, and re-arranging gives: X M m¼1 ∂log Do ∂log ym ^ ymþX N n¼1 ∂log Do ∂log xn ^ xnþ∂log Do ∂I¼d log TE dIð3Þ 1We relax this assumption later, treating the variable as endogenous in our empirical framework. 242 Journal of Productivity Analysis (2024) 62:239–255 where ^ ym;^ xnrepresent growth rates in outputs and inputs in the Idimension (^ ym¼∂ym ∂I=ym¼∂log ym ∂Ifor example). Following the definition of TFP growth in the time dimension, we define TFP change in the Idimension as the weighted growth in outputs minus the weighted growth rate in inputs: d log TFP dI¼X M m¼1 ∂log Do ∂log ym ^ ymX N n¼1 εn ε ^ xnð4Þ with εn¼∂log Do ∂log xn;ε¼Pnεn. Finally, by inserting (4)in(3) and rearranging we get: d log TFP dI¼d log TE dI∂log Doðx;y;IÞ ∂Iðεþ1ÞX N n¼1 εn ε ^ xn ð5Þ This relationship decomposes TFP differences into three components: (i) efficiency effect, (ii) effect on the technology, and (iii) scale effect. This decomposition is similar to Orea (2002), but here the time variable is replaced by the innovation index. In this way, the contribution of Ito each component can be assessed and examined as to whether it is in accordance with the SI vision. An empirical counterpart to the distance function is needed to evaluate the distance elasticities that enter the formulas of the components of TFP. We depart from the typical translog specification of the distance function and, instead, specify it as Cobb-Douglas in inputs, but translog in outputs and including all interaction terms with I. This assumption was dictated by the relatively small sample size and to avoid overparameterization of the distance function. 2 The complete specification is: log yI M;i¼α0þP n αnlog xI n;iþP m βmlog yI m;i yI M;i  P mP ‘ ϕm‘log yI m;i yI M;i  log yI ‘;i yI M;i  þηIiþP n λnIilog xI n;i þP m ξmIilog yI m;i yI M;i  þνI ilogðTE I iÞ ð6Þ where iis used to index farms, yMis the normalizing output, νI iis an error term with a normal distribution and logðTEI iÞuI iis the technical inefficiency term, assumed here to be a draw from an exponential distribution (e.g. van den Broeck et al. 1994), with rate parameter eθþδIi, where θ and δare parameters to be estimated. Thus, we assume that technological innovations can result in a shift to the production technology, but also as innovativeness, as a general attitude, can also lead to improvements in the managerial ability of farmers, through the gathering and processing of relevant information, which is translated to improved efficiency. 3 The dependent variable in eq (6) is negative and logðTE I iÞis subtracted from the right-hand side. In this setup, distance elasticities should be negative with respect to inputs and positive with respect to outputs. The innovation index, I, plays a similar role as the time-trend variable in panel-data models: as Iincreases from low values to higher ones, the technology of the production possibilities set is expected to move outwards, reflecting an improvement in the employed technology. For a given combination of inputs and outputs, the value of the distance function reduces with an outward shift, as the output vector needs to be divided by a smaller number to reach this new boundary. Thus, the distance elasticity with respect to Iis expected, a priori, to be negative. So far, we assumed that innovation is exogenous. However, innovations are “are choice variables that could be correlated with the operator’s unobserved managerial ability or human capital, unobserved pest pressure, or other unobservable factors directly correlated with output” (McFadden et al. 2022, page 592). We express this algebraically as: Ii¼hðziÞþν2ið7Þ where Iimeasures the innovation at the farm level, ziis a vector of farm-specific characteristics that can explain differences in the management practices of farms, and ν2iis an error term. Thus, in our empirical framework we estimate eq. (6)–(7) simultaneously in a system, so the latter equation is used as a control function that accounts for potential endogeneity of innovation (e.g. Hausman 1978; Heckman 1978; Heckman and Robb 1985; Wooldridge 2014). The control-function approach has been discussed and used in nonlinear models, including stochastic frontier analysis (Amsler et al. 2016; Griffiths and Hajargasht 2016; Horrace and Jung 2018; Kutlu 2010; McFadden et al. 2022; Shee and Stefanou 2015; Wechsler and Smith 2018; Wechsler et al. 2018). With estimates of the distance elasticities at hand, the effect on the technology caused by an increase in I 2A simple comparison between the full translog specification and the semi-translog was performed using the Deviance Information Criterion (DIC) (Griffin and Steel 2007). The DIC value for the translog and semi-translog were 460.8 and 405.6 respectively, which suggests that the semi-translog specification is favoured by the data against the translog specification. 3We would like to thank an anonymous reviewer for pointing this out. Journal of Productivity Analysis (2024) 62:239–255 243 becomes: ∂log Doðx;y;IÞ ∂I¼ηþX n λnlog xI n;iþX m ξmlog yI m;i yI M;i ! ð8Þ Analogously to neutral and biased technical progress, η captures the common effect of innovations on the distance function, while the λns and ξms the impact of innovation on the use of inputs or the production of outputs (Alvarez and del Corral 2010; Alvarez et al. 2012; Finger et al. 2019; Gallardo and Sauer 2018). The impact of innovations on efficiency (efficiency effect) is calculated as dE log TEI i  dI¼dE uI i ðÞ dI¼δeθþδIðÞ . Since the second term in this product is always positive, the sign of δdetermines the effect of innovation on the expected value of technical efficiency: a positive (negative) δwould indicate a positive (negative) effect of Ion technical efficiency. The effect of Ion efficiency can be, as discussed, either positive or negative. Finally, the scale effect is calculated as: ðεiþ1ÞX N n¼1 εn;i εi ^ xn;ið9Þ with εn;i¼αnþλnIi;εi¼PN n¼1εn;iand ^ xn;i¼dlog xI n;i dI  is the rate of change in the quantity of input nused in the production process caused by a small change in the value of the innovation index. As discussed in the previous section, the scale effect can be positive or negative and as a result, its sign cannot be determined a priori. In applications involving time-series or panel data, the components of TFP are calculated over time. No adjustments are required when calculating the effect on the technology when the time index is replaced by I, as in both cases the effect is obtained by differentiating the distance function in the relevant dimension. Calculation of the efficiency change and scale effects, however, a typical TFP growth decomposition involves taking differences of the efficiency scores (for the efficiency change effect) or of the logarithms of inputs (to approximate ^ xn;iin the scale effect) in adjacent time periods. In the cross-sectional setting things are complicated because Iis a continuous variable with varying intervals between adjacent observations, but also because one may observe more than a single farm with a specific value of I. We proceed by transforming the composite innovation index into a discrete innovation variable, which denotes innovation groups. Farmers with similar values are then assigned to each group. More details on the construction of the innovation index and the transformation procedure are presented in the following section. The discrete innovation variable presents clusters of values and, in this setting, the required differences are approximated between each farm in a cluster of values for the innovation index and the average of the relevant variable over farms in the immediately preceding cluster. Therefore, the analysis takes place in two steps. First, we estimate the parameters of the frontier as presented in equation (6)asifIwas a continuous variable. Second, using the estimated parameters from the first step, we calculate the three components of TFP change over Ias follows: ●The efficiency difference is calculated as the average of the sum of each farmer’s logarithm of efficiency in group Igwith the average logarithm efficiency of farms in group Ig−1. ●The technology difference is calculated as the average value of ∂log Do ∂I(where log Dois predicted using the estimates of all parameters, including those whose values are restricted when imposing linear homogeneity in the distance function) at each innovation group, Ig, and the average value ∂log Do ∂Ifor the preceding group, Ig−1. ●The scale effect is calculated as the average of the sum of each farmer’s scale in group Igwith the average scale effect of farms in group Ig−1. Similarly, the growth of inputs is calculated as the difference between input nof each farmer in Igand the average input nused in Ig−1. Ultimately, the net impact of Igon TFP is conditional on the aggregated impact on the individual components of TFP. Specifically, for a farm iin group Ig, the difference in TFP relative to the innovation group Ig−1is: d TFP I i¼1 2 1 JgP j2Ig1 dEðlog TEjÞ dIþdEðlog TEiÞ dI ! 1 2 1 JgP j2Jg1 ∂log Do;j ∂Iþ∂log Do;i ∂I ! 1 2P N n¼1 1 JgP j2Ig1 εjþ1 εjεj;nþεiþ1 εiεi;n ! ^ xi;n ð10Þ where ^ xi;n¼dlog xI i;n dIlog xi;nlog 1 JgPj2Igxj;n  . Thus, the differences in TFP and its components among farmer groups are decomposed by using sample averages, similarly to Orea (2002). We note two differences in our approach compared to the TFP growth decomposition of Orea (2002). First, we do not go into the details of examining the properties of the decomposition. Second, the 244 Journal of Productivity Analysis (2024) 62:239–255 productivity growth decomposition is derived with respect to the continuous dimension of time. Nevertheless, the upper bound of the innovation index is unity, implying that farmers with the highest innovation score cannot achieve a higher level of innovation. Taking the derivative with respect to the innovation index has no meaningful interpretation for farmers at this boundary. The latter holds even when discretizing the innovation index; but it allows to calculate TFP differences as discrete differences with respect to innovation groups IG(instead of the discrete time dimension as in Orea). The practical implication of the transformation is that we do not focus in examining the absolute but rather the relative effect of innovation across farmers. Classification of farmers to innovation groups is additionally linked conceptually to the agricultural innovation theory. This will be discussed further in the data section when the classification strategy is explained. We use Bayesian inference to estimate eq. (6)–(7)ina system. 4 The posterior moments are estimated using Markov Chain Monte Carlo (MCMC) techniques (Koop et al. 1995) and the priors on the parameters are based on GriffinandSteel (2007); van den Broeck et al. (1994). We write the error terms of eq. (6)–(7) in vector form as νi¼νI i;ν2i  0and assume νiNð0;ΣÞ.ForΣwe choose a prior in the inverted Wishart family, with q=1 degree of freedom and scale matrix V=I⋅1000, where Iis the identity matrix. (e.g. see Koop 2003; Kumbhakar and Tsionas 2016,2005). A multivariate normal prior is used for the vector of slope parameters that appear in the distance function and an independent bivariate normal prior for a vector that contains the two parameters that enter the specification of the distribution of inefficiency, θ;δ½ 0. In both cases the prior mean is a vector of zeros and the covariance matrix with diagonal entries equal to 1000. 4 Data Our data are from the Teagasc National Farm Survey (NFS) database, which is part of the Irish FADN data. The NFS data are collected annually through face to face interviews by professional farm recorders, providing a statistically representative sample of Irish farming. Then, farms are classified into “specialised”farming systems conditional on their major enterprise which is calculated on a standard gross margin basis (Läpple et al. 2015). We use a representative sample of specialist Irish dairy farmers in 2012, where a supplementary survey was carried out on the topic of new technologies and knowledge transfer. We define two outputs and four categories of inputs, similar to Newman and Matthews (2006). The main output (y1) is value of milk sold 5 and other output (y2), such as sales of meat and other products. In relation to inputs, we account for capital (K)as the sum of the value of machinery and buildings, plus the value of livestock, land (A) as the utilized agricultural area, measured in hectares, labor (L) as both unpaid and paid labor units, and materials (M), including expenditures in seeds and plants, fertilizers, crop protection, energy, contract work, purchased feed, upkeep of buildings, machinery hire and upkeep of land. As a measure of the state of innovativeness at the farm level, the innovation index developed by Läpple et al. (2015) is used. Knowledge transfer and innovation experts collaborated in selecting and weighting three indicators from different components of the Irish AIS (e.g. research, education, agribusiness and advisory services etc.) that capture process innovations at the dairy-farm level. The three selected innovation indicators and their respective weights (weights reflect the perceived importance of each component of the Irish AIS) are: (i) innovation adoption with weight 0.45, which is comprised of five selected innovative technologies relating to improving farm performance (E-profit monitor usage, ICT usage, soil testing, reseeding application and milk recording), weighted by how innovative the technologies were considered and their implementation effort by farmers; (ii) continuous innovation with weight 0.15, which measures whether a farmer renewed some of his machinery, underlining the need for ongoing innovation (OECD 2013); 6 (iii) acquisition of knowledge with weight 0.40, taking into account the importance of knowledge development for innovation (Spielman and Birner 2008). The acquisition of knowledge is measured by whether a farmer had a contract with Teagasc Farm Advisory Services (FAS), without the contact being for environmental scheme assistance only (Cawley et al. 2018; Läpple et al. 2015; Parikoglou et al. 2022a). This is an important distinction because in the latter case, farmers participate for the purpose of fulfilling bureaucratic requirements to receive subsidy payments instead of receiving technical advice regarding breeding, financial and grassland management. On the contrary, farmers who are not contacting FAS for scheme assistance only, are contacting FAS for technical advice that will allow them to be more productive in line with the sustainable intensification vision. 4Estimating system of equations in Bayesian inference for accounting for endogeneity has been previously suggested in the literature (see Chan and Tobias 2020,2015). 5The quantity of milk produced in kilograms could be used alternatively. However, monetary measures are preferred, as these also capture partly differences in quality, which are reflected in prices. 6As pointed out by an anonymous reviewer, renewal of machine in a given year may have an impact on the production possibilities set not only in the year the expenditures occur, but in subsequent years as well. However, this would require re-constructing the innovation index and imposing additional ad hoc weights for lagging effects. We leave this for future work. Journal of Productivity Analysis (2024) 62:239–255 245 By aggregating them, the innovation index is constructed with values bounded between zero and one. Hence, a farmer with a score of one uses all available innovations from all three presented indicators in relation to the AIS to the greatest extent (meaning he applies more of the examined technologies, replaced higher amounts of machinery etc.), while the opposite applies for a farmer with a score of zero. Switching from zero to a higher value implies that a farmer is using more innovations, resulting in a higher level of innovativeness. We categorise farmers into groups in order to accommodate the calculation of TFP differences with respect to the innovation index. Beyond this, the categorization of farmers also offers a conceptualization explaining differences in productivity: similar to the treadmill hypothesis, differences in productivity are explained by differences in innovativeness (Cochrane 1958). Classification of farmers have been previously used in empirical studies, considering three innovation groups (Diederen et al. 2003; Läpple et al. 2015; Läpple and Thorne 2019). Rogers (2003) suggests considering five innovation groups that could be expanded potentially to six groups, allowing in this way for cases of non-adoption. The choice of six groups could also be relevant for the Irish dairy context: accounting for a smaller number of groups would require farmers to be aggregated into larger groups, which implies loss of important information regarding less innovative, smaller farms. 7 In this paper, we use the K-means clustering approach to identify the innovation groups that will be used for the TFP differences, avoiding in this way to select the number of the innovation groups and their cut-off points arbitrarily. 8 The results of the K-means clustering indicate that there are three innovation groups (IG). In Appendix A, we briefly explain how the approach resulted in the three innovation groups. Furthermore, following Läpple et al. (2015) we choose marital status (binary=1 if farmer is married), off-farm income (binary=1, if farmer has off-farm income), education (binary=1, if farmer has formal agricultural education) and farm size (measured in ha) to be the vector of Zvariables included in the control function estimation. In general, the use of a control function, either in linear or non-linear settings, requires the use of suitable instruments, such as prices (Bound et al. 1995; Smith and Landry 2021). As McFadden et al. (2022) note, the control function tends to be more robust when the choice of the selection variables is not clear (Heckman and Navarro-Lozano 2004). Alternative methods to account for potential endogeneity such as propensity score matching tend to be quite sensitive to the choice of conditioning variables (Heckman and Navarro- Lozano 2004). Table 1reports summary statistics for the entire sample and for each of the three innovation groups. It can be observed that, on average, farmers with higher values of I utilize input quantities at different proportions and produce more of both outputs. This corroborates the assumption in our conceptual framework that farmers at different states of innovativeness utilize inputs at different proportions. Notably, the average amount of employed capital is almost two times larger in group three than in group one. Farms in group three utilize, on average, much more labor and land compared to farmers in group one and two; the differences in terms of the utilized labor and area between group one and two are very small. Regarding the use of materials, farms in group three have 50% higher expenditures than farms in group two; similarly, farms in group two have 50% higher expenditures than farms in group one. Table 1 Summary statistics: Irish dairy farms, 2012 Means for each Innovation Group IG Variables 1 2 3 (N=45) (N=69) (N=140) Milk output (1000 €) 71.05 100.95 141.57 Other output (1000 €) 30.46 39.81 62.29 Capital (1000 €) 158.88 239.98 343.17 Labor (Units) 1.46 1.48 1.80 Area (Ha) 46.8 50.3 70.3 Materials (1000 €) 45.80 63.91 82.56 Innovation score I0.16 0.51 0.85 Married (binary) 0.8 0.8 0.7 Higher education (binary) 0.5 0.8 0.7 Off-farm income (binary) 0.1 0.0 0.0 Full Sample statistics (N=254) Variables Mean St. Dev. Min. Max. Milk output (1000 €) 118.04 76.65 12.29 471.14 Other output (1000 €) 50.54 35.17 3.29 276.29 Capital (1000 €) 282.17 196.02 13.49 1006.13 Labor (Units) 1.65 0.68 0.5 5.31 Area (Ha) 60.88 30.43 8.06 198.1 Materials (1000 €) 70.98 48.79 6.79 306.14 Innovation index 0.6 0.2 0 1 Married (binary) 0.8 0.3 0 1 Higher education (binary) 0.7 0.4 0 1 Off-farm income (binary) 0.1 0.1 0 1 7Smaller farms are important for the SI of the Irish dairy sector, because they play a number of socio-economic roles, such as increasing welfare by keeping rural areas populated, contributing to the rural non-farm economy and providing environmental public goods, for example, attractive landscapes (Dillon et al. 2017). 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