“Accounting Explicitly for Interaction Variables in Inequality Regressions”

Purpose: To invite researchers of inequality, especially Black American researchers, to refine and improve measures of relationships between inequality measures and related covariates using “interaction variables” (IVs). This brief essay builds on basic knowledge of econometrics, reflects no “technical burden,” is mainly conceptual, and offers salient examples. We suggest that there may be more near-term and future opportunities than now envisioned for policymakers to leverage inequality research. Hence, it is critical that Black economists produce the most accurate econometric results through our inequality research that can enable the most effective and economically efficient policies.

Introduction

Economists have defined, explained, and analyzed income and wealth inequality using a variety of covariates (independent variables) and a wide variety of econometric regression models. Our concern is whether such covariates include “interaction variables” (IVs). When important and appropriate interaction variables are excluded from regressions, then, at worst the model could be “misspecified” at worst and the model’s results deemed spurious, or estimated parameters from the model could be deemed inaccurate and/or biased at best.i If public or private sector policymakers develop policies using the results of such mismeasured or faulty regression models, then outcomes will not be optimal. The losses borne by those who extend resources for the implementation of those policies can be quite heavy depending on the magnitude of policy prescriptions for resolving particular inequality conditions.

Interaction Variables

To explore the significance and importance of IVs, we undertook the following brief analysis. First, we examined the top five—by citation count—academic articles on “inequality” that were authored by Black economists (see Endnote ii).ii We determined whether these articles reflected inequality research based on regression analysis; whether the regressions included IVs; and whether the IVs were likely to improve regression models’ estimated parameters so that policymakers who employ the research can formulate the most effective and efficient policies.iii

Second, we considered the top three—by citation count—inequality articles without regard to the race/ethnicity of the authors and explored identically the concerns mentioned in the previous paragraphs about the inclusion of IVs in inequality regressions (see Endnote ii).

Considering the table in Endnote ii and the five inequality articles authored by Black American economists, only three of the articles reported on econometric regression estimation, and only two of the three articles included IVs. For the two articles that included IVs, it is possible to argue that different or additional IVs could have produced more accurate/improved results.

Also, there may be important positive spillovers from purposely reconsidering regression models that do not include IVs; i.e., such consideration may lead to a decision to add variables to models that carry similar explanatory power as that might be inherent in IVs. Our experience is that certain inequality regressions should or could benefit by including IVs or variables that embody effects typically identified with a group’s “cultural capital.”iv

As we go deeper on this topic, please keep in mind that improved regression results, when used by policymakers, can yield saving. Such saving can help fuel other efforts to improve overall wellbeing.

Selected Examples of How IVs May Improve Regression Results

The following are a few examples of conditions under which regression IVs or variables that would underpin IVs are likely to improve estimated results significantly:

• The inclusion of IVs and/or the related underpinning variables in regression models based on panel data may yield results that are superior to those that would arise without these variables. To the extent that panels are uniquely identifiable and embody specific and measurable cultural capital-like characteristics that can influence income earnings and wealth accumulation, then inclusion of IVs or related variables that represent this cultural capital characteristics are likely to improve regression results. For example, the following cultural capital characteristics appear to be relevant and saliant: The level of inherent racism and/or discrimination; a measure of the media’s presentation of stereotypical images that affect both White (positively) and Black (negatively) Americans (i.e., the amount of media consumption and/or the share of media content that feature stereotypical images); and cultural activities that attract more Black than White American adherence/participation and that cause the former to overinvest in these activities to their economic detriment (e.g., excessive and unwarranted active or observer roles in recreation, religion, and culture activities).
• The inclusion of IVs and/or the related underpinning variables that account for unique spatial—sometimes historical—conditions that typically contribute to accelerated versus weak economic growth: e.g., the level of extant technology, the share or amount of high-quality and/or new physical infrastructure; and if metrics and data for the two foregoing conditions do not exist, then a proxy for uniquely identifiable and measurable governance or economic systems may suffice.
• As an example of a potential natural experiment consider a prospective U.S. Postal Service (USPS) closure and the liquidation of its nonfinancial assets. How could such an event aid in improving the measurement of inequality? While income inequality was the primary inequality measure cited early in the inequality literature (mainly because of readily available data), wealth inequality is of primary concern today. The sale of nonfinancial assets at a deep discount is a wonderful opportunity to acquire wealth and then to use it to earn income and to accumulate more wealth. Awareness of the sale of such nonfinancial assets opens the door to their acquisition. However, Black Americans’ awareness of such sales may be less than that of White Americans’ because of media market segmentation. More importantly, Black Americans may not be aware of the sale of these nonfinancial assets because they are not likely extant in or near Black American areas of influence (neighborhoods). Also, Black Americans may not be aware of the timing of the sale of these nonfinancial assets because the sale may occur after (possibly long after) closure of the USPS. Specifically, IVs or related variables that reflect easy access and close geographical proximity to public sector nonmarket and market institutional units (bureaus or enterprises) may serve as a good indicator of prospects for higher levels of income and wealth.

Conclusions

The recent United Nations (UN) Resolution that slavery be classified as “Crime Against Humanity” may be the match that ignites the fire that burns away the old world and old mentalities concerning unequal treatment and outcomes across racial and ethnic groups worldwide.vi Accordingly, a swinging of the pendulum or the bending of the long arc of justice may point to new and near-term opportunity to use inequality research as the basis for policy prescriptions.

Hence, it is particularly important that economists—certainly, Black American economists— ensure that our regression models provide the most accurate parameter estimates. This essay urges economists to consider including IVs and/or their underpinning variables when developing econometric regression models that define, explain, or analyze income or wealth inequality. Consideration of IVs and their related underpinning variables may also open a window to a more comprehensive command of knowledge about economic inequality and the transmission mechanisms that produce lower or higher levels of Black American income and wealth.