Abstract
This chapter revisits some of the major considerations in undertaking the cross-sectional regression. The author uses the abnormal returns as the dependent variable, with the other hypotheses tested to understand the determinants of the abnormal returns. Examining the principles of setting up the models, he uses several examples and provides commentary to add additional insights. In addition, he looks at some of the common issues and problems and how they might be addressed. Next, he outlined some important diagnostic steps. Again, examples from the literature are used to illustrate important principles. Finally, the reporting of results is examined, with some conclusions drawn about the presentation of results and reporting on the use of multiple models. Together, these steps and cautions should enable researchers to draw on their experience with regression modeling in other areas and produce valuable and useful contributions using a cross-sectional regression model.
TopTheory Driven Hypotheses And Models
Publishing in leading journals and management in supply chain management requires an increasingly strong contribution to theory. The need for a theory-basis challenges the use of the event method in this area as it is necessary to connect the event and the underlying model being studied to a theory. By itself, a single event study showing the change in the market value of the companies in reaction to this event is not a substantial contribution to theory in most cases, and inclusion of an appropriate theoretical model will usually come through the cross-sectional regression analysis based on the abnormal returns calculated by the event study.
See, for example, the empirical study of re-shoring of manufacturing, with an analysis of the short-run stock market reaction in Brandon-Jones et al. (2017), where they note that future studies may include analysis of the determinants. The study itself provided evidence of shareholder value implications.
For example, Duan et al. (2014) studied the business process outsourcing and relied on transaction cost economics (TCE) as a theoretical foundation for studying outsourcing. TCE informed the development of the key hypotheses which had tested in the cross-sectional regression. While using theory makes sense and is encouraged, practice of including theory to inform the development of the model in the cross-sectional regression remains challenging as we often do not have access to data appropriate to test hypotheses derived from the theory. For example, during a survey or when conducting qualitative research, we often have the flexibility to ask a different type of question or to adapt our questions to provide a better measurement that allows us to capture and measure the variable of interest. When collecting and compiling the data for an event study, in contrast, we remain limited by the type of data and often the data availability. For example, while it might be of great interest to study the power difference in an outsourcing study, this may be easily accomplished with a survey and established scales of questions. However, it remains difficult to effectively measure power when using archival data for the cross-sectional regression in an event study.
Key Terms in this Chapter
Moderator: When one of the independent variables influences the relationship of another independent and dependent variable, depending on the value of the moderator in a particular case.
Heteroscedasticity: A situation when the variance of the error terms is not constant over the range of the independent variables.
Multicollinearity: When an independent variable is correlated with a range of other independent variables. This causes problems when, in an extreme case, it causes singularity, where two independent variables are perfectly correlated.
Influential Observation: An observation that has a significant influence on the final regression estimates. Extreme independent or dependent variables may cause it. It may be an outlier, but not necessarily.
Outlier: An observation that differs significantly and is, therefore, a poor representation of the wider population and may be discounted or removed from the sample for subsequent analysis because of the unrepresentative nature.