An empirical investigation of dividend determinants using parametric and nonparametric models

Introduction

Dividend policy has long been a focal point in corporate finance, with considerable debate surrounding the determinants that influence a firm's decision to distribute profits to shareholders. Traditionally, Earnings Per Share (EPS), firm size, leverage (DE), liquidity (QR), and the Creditor Turnover Ratio (CTR) have been widely recognized as key financial variables affecting dividend payouts. However, empirical evidence suggests that the relationship between these determinants and Dividend Per Share (DPS) is not always linear and may be better captured through flexible, data-driven modelling approaches. This study seeks to comprehensively examine the determinants of dividend policy using both parametric models (Linear, Log-Transformed, and Polynomial) and nonparametric models (Generalized Additive Models [GAM] and Nonlinear Least Squares [NLS]). A robust comparison of these models, based on RMSE, R-squared, and diagnostic tests (normality, heteroskedasticity, and autocorrelation), provides deeper insights into model performance and real-world applicability.

The methodological novelty of this study lies in integrating machine learning techniques with traditional econometric frameworks to better capture complex, nonlinear financial dynamics. The findings hold significant practical relevance for investors, corporate managers, and policymakers seeking to design optimal dividend strategies based on firm-specific fundamentals.

Literature Review

Dividend policy remains one of the most debated topics in financial management. Researchers have applied a variety of statistical, econometric, and machine learning techniques to investigate the factors influencing dividend payouts. The relevant literature is categorized into domestic (India-based) and international studies.

A. Domestic Literature (India-Based Studies) 1. Highlighted that Indian firms prioritize stable dividend payments, with profitability and cash flow as key determinants. 2. Employed panel regression to show that firm size, earnings, and leverage influence dividend policy among NSE-listed firms. 3. Used a fixed-effects model and reported that ownership structure and profitability significantly affect DPS. 4. Demonstrated the role of retained earnings and past dividend behaviour using pooled OLS and dynamic panel models. 5. Found that larger Indian firms with higher profitability maintain consistent dividend policies. 6. Applied nonlinear models and suggested that financial leverage has a non-monotonic relationship with dividends. 7. Used logistic regression and confirmed EPS and firm size as robust predictors of dividend decisions. 8. Investigated Indian manufacturing firms and highlighted the relevance of liquidity and market valuation in dividend distribution. 9. Compared multiple regression and artificial neural networks (ANN), indicating the superior accuracy of neural networks in DPS prediction. 10. Applied machine learning models to Indian IT firms and concluded that EPS and the debt-equity ratio are the strongest predictors.

B. Foreign Literature 11. Lintner (1956) [16]: Pioneered the empirical model of dividend policy, emphasizing earnings stability and target payout ratios. 12. Fama & Babiak (1968) [13]: Reinforced that current and past earnings determine dividend changes, using timeseries models. 13. Developed an agency-theoretic model and established that growth opportunities and risk reduce dividend payouts. 14. Showed that free cash flow and managerial discretion impact dividend behaviour. 15. Found that dividend-paying firms often have stronger earnings and governance mechanisms. 16. Surveyed U.S. corporate managers and identified earnings consistency and investor expectations as major factors. 17. Chen & Dhiensiri (2009) [15]: Used neural networks to predict dividend policy in New Zealand, achieving higher classification accuracy than logistic models.

Objectives of the Study

The primary objective of this research is to examine and compare the effectiveness of various parametric and nonparametric models in identifying the key determinants of Dividend Per Share (DPS) among selected listed Indian companies. Specifically, the study aims to: 1. Identify and assess the impact of financial performance indicators on DPS using traditional regression models (Linear, Log-Transformed, Polynomial). The dataset was standardized to ensure comparability and minimize scaling bias. Selection of independent variables for regression modelling was based on goodness-of-fit measures.

Methodological Framework

This research adopts a comparative modelling approach using five techniques:

Model Implementation

Linear and log-transformed regression models, including diagnostics such as R², RMSE, and residual plots, were estimated using the lm() function in R. Polynomial regression incorporated second-degree terms via poly() to capture curvature in EPS. GAM was implemented using mgcv::gam() with smoothing splines (s()) to identify non-linear relationships. NLS estimation was performed using nls() to test exponential and power-law relationships (e.g., DPS ~ a*(EPS^b) + c*(Size^d)).

Model Evaluation Metrics

To assess model performance, the following metrics were employed:

Hypotheses of the Study

Based on the study's objectives and literature review, the following hypotheses are proposed:  H1: Earnings Per Share (EPS) has a significant positive effect on DPS.  H2: Quick Ratio (QR) and Debt-to-Equity Ratio (DE) negatively affect DPS.  H3: Firm Size has a significant positive relationship with DPS.  H4: The performance of DPS prediction models differs significantly between parametric and nonparametric methods. The variance inflation factor (VIF) analysis indicates no severe multicollinearity (all VIFs < 5). However, moderate multicollinearity is observed for Size (VIF = 4.99). While all predictors are acceptable for inclusion, variables with higher VIFs may require attention during sensitivity analysis or stepwise regression. Debt-to-Equity Ratio (DE) also shows a negative effect on DPS in Linear and Polynomial models, suggesting that higher leverage is associated with reduced dividend payments.

Results and Discussion

Creditor Turnover Ratio (CTR) is consistently negative:

This may indicate that liquidity constraints reduce a firm's capacity to pay dividends.

Firm Size is positively associated with DPS in all models:

 Linear and Polynomial models show a small but significant positive coefficient (Size in scientific notation).  Log-transformed model reveals a strong positive influence of log(Size) (8.39851), suggesting exponential scaling.  GAM and NLS models confirm this with smoothed and exponential terms, respectively.  In NLS, Size^0.13715 contributes positively, though not independently significant.

Overall, firm size consistently enhances dividend capacity, likely due to economies of scale and cash flow stability in larger firms.

Role of Nonlinear Models

 GAM effectively captures smoothed, nonparametric relationships, making it ideal for modeling complex dividend dynamics.  NLS is useful for testing power-law behavior. However, it exhibits estimation instability in this dataset, possibly due to sensitivity to outliers or local minima.

Model-Specific Insights

 Log-Transformed Model: Best suited when variables (like EPS and Size) span wide numerical ranges.

Transformation improves interpretability and fit.  Polynomial Model: Captures curvilinear patterns in EPS, illustrating diminishing returns or threshold effects.  GAM: Offers flexibility in modeling nonlinear effects without specifying a functional form. Best performer in capturing subtleties.  NLS: Useful for theoretical models (e.g., power-law distributions) but less robust under real-world data noise or variance. A comparative assessment of model fit was conducted using Adjusted R², RMSE, and F-statistics. Among all models, the Generalized Additive Model (GAM) outperformed the others, achieving the highest Adjusted R² (0.979) and the lowest RMSE (1.579), indicating superior explanatory power and predictive accuracy. The Log-Transformed and Linear models also demonstrated satisfactory performance, whereas the Polynomial and Nonlinear Least Squares (NLS) models exhibited slightly higher error metrics.

Model Fit Comparison

Residual Diagnostics

To validate the assumptions of linear regression, diagnostic tests were conducted for normality, homoscedasticity, and autocorrelation. The key results are summarized below: The evidence supports the formulation of hybrid dividend policy frameworks that combine traditional linear predictors with advanced nonlinear techniques. Such an approach enables adaptive regulation in increasingly volatile financial markets. Given that dividend policies often evolve with firm performance, the use of static or cross-sectional models may limit the ability to capture temporal trends and causality.

Conclusion

Transformation Sensitivity:

The performance and interpretability of the log-transformed and nonlinear models were sensitive to the choice and range of transformations applied. This sensitivity may affect model comparability and the consistency of coefficient interpretation across models.

Future Research Directions 1. Incorporation of Dynamic Time-Series Models: Future studies may incorporate panel data or dynamic timeseries frameworks (e.g., VAR, LSTM networks) to capture the evolving nature of dividend decisions across years.

Inclusion of Macroeconomic and Behavioural

Variables: Broadening the scope by integrating market volatility, investor sentiment, inflation, and policy shifts could improve explanatory power and deepen insight into dividend dynamics.

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