How to improve SME performance using iterative random forest in the empirical analysis of institutional complementarity

Institutional complementarity, the idea that the effectiveness of one organizational practice depends on the presence of others, is crucial in management science but challenging to empirically analyze. Traditional econometric methods struggle with the complex, higher-order interactions inherent in complementarity. This study addresses this limitation by employing iterative random forest (iRF), a machine learning technique that identifies stable and significant interactions among multiple variables. While iRF has been used successfully in biostatistics (e.g., analyzing gene regulation), its application to social science, particularly the empirical analysis of organizational complementarity, is novel. The study uses data from the World Management Survey (WMS) to examine how 18 management quality indicators affect SME profitability (ROCE), growth (5-year sales growth), and viability (business failure). The research aims to provide a simplified visualization of the complex relationships between institutional practices and high performance in organizations, a task that surpasses the capabilities of conventional regression analysis.

Brynjolfsson and Milgrom (2013) and Boon et al. (2019) provide comprehensive overviews of the theoretical development and empirical challenges in studying institutional complementarity. The difficulty in conducting empirical research stems from the complex, higher-order interactions between multiple factors (Athey and Stern, 1998; Roberts, 2007). Traditional econometric regression analyses struggle to capture these intricate relationships due to challenges in identifying and handling higher-order interaction terms and multicollinearity. Machine learning offers a potential solution, but interpreting the complex interaction structures identified by standard machine learning models can be problematic. Basu et al. (2018) introduced iRF, a method that addresses this challenge by iteratively weighting features based on their importance to reveal stable and predictive interactions, particularly higher-order ones. The successful application of iRF in biostatistics, specifically identifying interactions in gene regulation (Basu et al., 2018), highlights its potential in the social sciences.

This study utilizes data from the World Management Survey (Bloom et al., 2012), focusing on 6339 SMEs after excluding observations with missing values. Three dependent variables were created: a binary variable indicating whether return on capital employed (ROCE) was above one standard deviation of the mean (ROCE_1); a binary variable for 5-year sales growth exceeding one standard deviation of the mean (D5SALES_1); and a binary variable indicating business failure (DEAD). Eighteen management quality indicators, detailed in Table 1, served as independent variables. The analysis involved two stages. First, standard random forest (RF) analysis was conducted using the R package `randomForest` (Liaw and Wiener, 2002) for each dependent variable (ROCE_1, D5SALES_1, DEAD). The optimal number of features (mtry) for each tree was determined using `tuneRF`. The number of trees was set to a value greater than 100 to ensure stability. Second, iRF analysis (Basu and Kumbier, 2017), implemented using the R package `iRF`, was performed on the same data. The parameter `cutoff.unimp.feature` was set to 0.3, and `n.bootstrap` was set to 20. Feature importance scores from the RF analysis informed the weighting in the iRF process, allowing the identification of stable higher-order interactions or complementarities among the management quality indicators.

The RF analysis (Table 3) revealed that indicators related to talent management (rewarding high performers, removing poor performers, retaining human capital) and performance management (performance clarity, target time horizon) were most important across all three dependent variables. The iRF analysis (Table 4a-c) revealed stable, high-order interactions. The importance of `perf8` (target time horizon) consistently stood out across the models. A strong complementarity was observed between `perf8` and `talent2` (rewarding high performance) for ROCE_1 and DEAD, highlighting the importance of aligning short-term goals with long-term objectives while effectively rewarding high performers. For D5SALES_1, `talent2` remained important, indicating a strong relationship between rewarding high performance and sales growth. The results suggest a strong complementarity between effectively managing high and low performers (talent management) and establishing clear, interconnected performance targets (performance management) with a consideration of short and long-term perspectives.

The findings highlight the critical interplay between talent management and performance management practices in achieving superior SME performance. The importance of `perf8` (setting short-term goals aligned with long-term objectives) underscores the need for strategic planning and goal setting. The strong complementarity between rewarding high performers and establishing clear performance measures supports the notion that performance-based incentives are more effective when coupled with robust performance measurement systems. These results align with Burdin and Kato (2021), who found that high-performing organizations tend to adopt high-involvement work systems characterized by opportunities, incentives, and skills. The study confirms the importance of aligning incentives with long-term goals, contrary to the typical short-term focus often associated with outcome-based reward schemes. The study's findings emphasize the importance of simultaneously improving multiple aspects of management practices rather than focusing on individual improvements in isolation.

This study demonstrates the effectiveness of iRF as a powerful tool for uncovering complex interactions and complementarities in organizational settings. The key findings highlight the importance of robust talent management practices, clear performance measurement systems, and strategic goal setting in driving SME performance. Future research could explore the generalizability of these findings across different sectors, organizational sizes, and geographical contexts. Investigating potential endogeneity issues and exploring a broader set of management practices are also valuable avenues for future work.

The study acknowledges potential endogeneity issues, as the causal relationships between management practices and performance outcomes are not definitively established. The use of 18 specific management quality indicators may limit the generalizability of the findings to other contexts. Further research should address these limitations by employing more advanced causal inference techniques and exploring broader sets of management indicators to enhance the robustness and generalizability of the findings.