What are the most common issues when using linear regression in economic analysis?

1 Assumptions and violations

Linear regression is based on a set of assumptions that must be met for the method to produce unbiased, consistent, and efficient estimates. These assumptions include linearity, independence, homoscedasticity, normality, and no multicollinearity. However, in practice, these assumptions are often violated by economic data, which may exhibit nonlinearities, autocorrelation, heteroscedasticity, skewedness, and collinearity. Violating these assumptions can lead to biased, inconsistent, or inefficient estimates, as well as invalid inference and prediction. Therefore, you should always check the validity of these assumptions using diagnostic tests and graphs, and apply appropriate corrections or transformations if needed.

2 Endogeneity and causality

Another common issue when using linear regression in economic analysis is endogeneity, which occurs when an explanatory variable is correlated with the error term. This can happen due to omitted variables, measurement errors, reverse causality, or simultaneous causality. Endogeneity can cause the estimates to be biased and inconsistent, and prevent you from making causal claims about the relationship between the variables. To deal with endogeneity, you need to use instrumental variables, which are variables that are correlated with the endogenous variable but not with the error term, and use them to estimate the causal effect of the endogenous variable on the dependent variable.

3 Model selection and specification

A third common issue when using linear regression in economic analysis is model selection and specification, which involves choosing the appropriate functional form, explanatory variables, and interaction terms for your regression model. Model selection and specification can affect the fit, parsimony, and interpretability of your model, as well as the significance and magnitude of your estimates. To select and specify your model, you need to use theoretical and empirical evidence, as well as statistical criteria such as the adjusted R-squared, the Akaike information criterion (AIC), or the Bayesian information criterion (BIC). You should also avoid overfitting or underfitting your model, which can result in poor generalization or misspecification.

4 Heterogeneity and aggregation

A fourth common issue when using linear regression in economic analysis is heterogeneity and aggregation, which refers to the variation and grouping of the units of observation in your data. Heterogeneity and aggregation can affect the representativeness and comparability of your data, as well as the reliability and validity of your estimates. For example, if you use aggregate data to estimate a relationship that varies across individuals or groups, you may encounter the ecological fallacy, which is the error of inferring individual behavior from aggregate data. To address heterogeneity and aggregation, you need to use disaggregate data whenever possible, and account for the effects of grouping or clustering using fixed effects, random effects, or mixed effects models.

5 Robustness and sensitivity

A fifth common issue when using linear regression in economic analysis is robustness and sensitivity, which refers to the stability and responsiveness of your estimates to changes in the data, the model, or the methods. Robustness and sensitivity can affect the confidence and credibility of your results, as well as the generalizability and applicability of your findings. For example, if your estimates change significantly when you use a different sample, a different functional form, or a different estimation technique, you may have a problem of sensitivity, which indicates that your results are not robust or reliable. To assess robustness and sensitivity, you need to perform sensitivity analysis, which is the process of testing how your results vary under different scenarios or assumptions.

6 Communication and visualization

A sixth common issue when using linear regression in economic analysis is communication and visualization, which involves presenting and explaining your results to your audience in a clear, concise, and compelling way. Communication and visualization can affect the impact and relevance of your results, as well as the understanding and appreciation of your analysis. For example, if you use complex jargon, obscure notation, or dense tables to report your results, you may confuse or bore your audience, and lose their attention or interest. To improve communication and visualization, you need to use simple language, clear symbols, and effective graphs to convey your main messages, and highlight the key insights, implications, and limitations of your results.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?