What are the steps to avoid omitted variable bias in regression analysis?

Pruebas exploratorias adicionales como análisis de correlación podrían ayudar a considerar o descartar variables. La mejor forma de visualizar este análisis es mediante un mapa de calor de doble entrada para poder verificar a primera vista cuáles variables podrían ser consideradas.

Omitted variable bias occurs in regression analysis when a relevant variable is left out of the model, leading to distorted results. To mitigate this bias, the first step is to identify potential omitted variables by considering theoretical frameworks, existing research, domain knowledge, and exploring data relationships. By actively searching for variables that may influence the outcome but are not included in the model, researchers can enhance model accuracy and avoid erroneous interpretations.

1. Identify potential omitted variables: Review literature, consult experts, and analyze data for patterns. 2. Collect data on the omitted variables: Gather information on important variables within constraints. 3. Include the omitted variables in the regression model: Add collected variables to reduce bias. 4. Check the model for omitted variable bias: Review residuals and conduct sensitivity analysis. 5. Repeat steps 1-4 if necessary: Iterate until bias is eliminated.

Creio que é preciso ter um conhecimento prévio (base) sobre o tema objeto da análise. Realizar uma pesquisa sobre o tema, buscando identificar as variáveis relevantes que podem influencia a variável dependente é uma boa prática. Adicionalmente, consulte a literatura para embasar a seleção das variáveis a serem incluídas no modelo. Com base nessa exploração, escolha as variáveis que, segundo a teoria e o conhecimento base, possuem maior potencial explicativo para a variável dependente. Naturalmente, é preciso validar. Faça uma análise exploratória e utilize métodos estatísticos, como correlação e análise de variância, para avaliar a força da relação entre as variáveis.

Examine os resíduos do modelo de regressão para identificar padrões que podem indicar a presença de variáveis omitidas. Resíduos heterocedásticos ou com correlação serial, por exemplo, podem ser sinais de variáveis relevantes não inclusas no modelo. De forma complementar, pode-se lançar mão de regressões auxiliares para testar o viés da variável omitida. A regressão auxiliar é uma técnica que nos permite estimar o efeito de uma variável omitida na variável dependente, mesmo que essa variável não seja diretamente observada.

Testing directly for omitted variable bias (OVB) in regression analysis is not feasible due to the unobserved nature of the omitted variable. Despite this, auxiliary regressions can serve as a diagnostic tool to offer insights into potential OVB. By identifying omitted variables, running auxiliary regressions for each variable, analyzing residuals, and including them in the original model, researchers can assess the influence of potential omitted variables. Although statistically significant coefficients of the added residuals suggest potential OVB, auxiliary regressions do not definitively confirm its presence.

Data Availability: Ideally, include all relevant variables. However, data availability can be a significant hurdle. If crucial data is missing, consider alternative approaches like IV regression or using proxy variables. Multicollinearity: Be cautious of introducing variables that are highly correlated with existing regressors, as this can lead to multicollinearity and unreliable estimates. Carefully assess the correlations between variables before including them.

When including variables, researchers should prioritize relevant and theoretically justified variables that are measurable, available, and contribute to the understanding of the relationship between variables. Care should be taken to avoid multicollinearity, which can undermine the reliability of coefficient estimates. On the other hand, excluding variables should be approached cautiously, only doing so if they are truly irrelevant, highly correlated with existing variables, or measured with significant error. It is essential to base decisions on theoretical and empirical justifications rather than solely relying on statistical significance tests.

After running running different regression models one must select the final model using goodness of fit measures. - R square/ Adj. R square: the value of Rsquare lies between 0 and 1. The closer the Rsquare is to 1, the better is the model fit. - AIC/BIC: Akaike information criteria and Bayesian information criteria are used in model selection especially when lag variables are involved. A high AIC or BIC is not a good sign as it indicates a higher penalty for including too many lags. Thus a model with LOWER AIC/BIC is an optimal choice -RMSE: Root mean squared error is the standard error of regression. The model withbthe lower RMSE is a better fit

They serve as exploratory tools to help select the model that best reflects the relationship between variables. Common measures include R-squared, adjusted R-squared, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Squared Error (RMSE), and residual analysis. By running models, calculating these measures, comparing values, and analyzing residuals, researchers can evaluate model performance in the context of OVB. It's important to remember that no single measure can decisively diagnose or address OVB, so combining various measures with theoretical and domain knowledge is crucial for informed decision-making.

Diagnostic tests are valuable tools in assessing a model for potential omitted variable bias (OVB) and other issues by examining the model's assumptions and performance. Common diagnostic tests include normality tests for assessing residuals' distribution, homoscedasticity tests for constant residual variance, and serial correlation tests for autocorrelation. Influence diagnostics like Cook's distance and leverage can identify influential observations that impact coefficients.

📌Acknowledge Limitations: Explicitly discuss the limitations of the analysis, including the potential for omitted variable bias despite the mitigation efforts. This transparency is crucial for robust economic analysis. 📌Sensitivity Analysis: Conduct sensitivity analysis to assess how the results change with different assumptions or inclusion/exclusion of specific variables. This helps assess the robustness of the findings and identify potential biases.

The choice of the best" model is often subjective and depends on the specific research question, data limitations, and theoretical considerations. Economists should carefully justify their model selection process and be transparent about the trade-offs involved.

Using instrumental variables (IVs) to address issues of endogeneity in an econometric regression is useful. Isolating exogenous variation in the independent variable and obtaining unbiased estimates of its effect on the dependent variable is another great way to avoid omitted variable bias in regression analyses.