Introduction

Fixed effect and random effect are two popular statistical techniques used in panel data analysis to identify relationships between variables. Both techniques have their strengths and weaknesses, and the choice between them depends on the underlying assumptions and research questions. In this article, I will provide a comprehensive overview of fixed effect, random effect, and the key differences between them. We will also discuss how to choose between fixed effect and random effect models and the model selection criteria that can help researchers make an informed decision.

What is Fixed Effect

Fixed effect is a statistical technique used in panel data analysis to account for individual-specific effects that remain constant over time.

Definition

Fixed effect is a statistical method used to control for individual-specific effects in panel data analysis. Fixed effect models assume that individual-specific effects are constant over time and are included in the model as fixed parameters. This technique enables the researcher to identify the impact of explanatory variables on the dependent variable while controlling for individual-specific effects.

Examples

Fixed effect models are commonly used in social science research, such as economics, political science, and sociology. For instance, in economics, researchers may use fixed effect models to examine the impact of education on income while controlling for individual-specific effects such as innate abilities, family background, and personality traits. In political science, researchers may use fixed effect models to examine the impact of policies on voting behavior while controlling for individual-specific effects such as partisanship and ideology.

Advantages and Disadvantages

One of the main advantages of using fixed effect models is that it can control for individual-specific effects that may confound the relationship between the dependent and independent variables. This technique can also improve the accuracy and reliability of the results. Furthermore, fixed effect models are preferred when the research question focuses on within-unit variation rather than between-unit variation.

However, there are also some disadvantages of using fixed effect models. First, this technique assumes that individual-specific effects are constant over time, which may not always be the case. Second, fixed effect models can be computationally intensive, especially when dealing with large datasets. Third, fixed effect models may not be suitable when the research question focuses on between-unit variation rather than within-unit variation.

What is Random Effect

Random effect is a statistical technique used in panel data analysis to account for unobserved heterogeneity across individuals. In this article, I will define random effect, provide examples, and discuss the advantages and disadvantages of using this technique.

Definition

Random effect is a statistical method used to control for unobserved heterogeneity across individuals in panel data analysis. Unlike fixed effect models, random effect models assume that individual-specific effects are random variables that are uncorrelated with the explanatory variables. Random effect models estimate the individual-specific effects as random variables, which can vary across individuals but have a common distribution.

Examples

Random effect models are commonly used in social science research, such as economics, political science, and sociology. For instance, in economics, researchers may use random effect models to examine the impact of trade policies on economic growth while controlling for unobserved heterogeneity across countries. In political science, researchers may use random effect models to examine the impact of institutions on democratic governance while controlling for unobserved heterogeneity across countries.

Advantages and Disadvantages

One of the main advantages of using random effect models is that it can control for unobserved heterogeneity across individuals that may confound the relationship between the dependent and independent variables. This technique can also improve the efficiency of the estimation, especially when the number of individuals is large. Furthermore, random effect models are preferred when the research question focuses on between-unit variation rather than within-unit variation.

However, there are also some disadvantages of using random effect models. First, this technique assumes that the individual-specific effects are uncorrelated with the explanatory variables, which may not always be the case. Second, random effect models may not be suitable when the research question focuses on within-unit variation rather than between-unit variation. Third, random effect models assume that the individual-specific effects have a common variance, which may not always be the case.

Key Differences between Fixed Effect and Random Effect

Fixed effect and random effect are two popular statistical techniques used in panel data analysis to identify relationships between variables. Although they share some similarities, they differ significantly in terms of their assumptions, interpretation of coefficients, variance component estimation, and model selection criteria.

Assumptions

One of the key differences between fixed effect and random effect models lies in their assumptions. Fixed effect models assume that all individual-specific effects are constant over time and are included in the model as fixed parameters. Random effect models, on the other hand, assume that individual-specific effects are random variables that are uncorrelated with the explanatory variables.

Interpretation of Coefficients

The interpretation of coefficients is also different between fixed effect and random effect models. In fixed effect models, the coefficients represent the change in the dependent variable for a unit change in the independent variable, holding constant all other variables, including the individual-specific effects. In contrast, in random effect models, the coefficients represent the average effect of the independent variable across all individuals, including the individual-specific effects.

Variance Component Estimation

Another key difference between fixed effect and random effect models is how they estimate variance components. Fixed effect models estimate the individual-specific effects as fixed parameters, whereas random effect models estimate them as random variables. The variance components in fixed effect models are estimated using within-group variation, while random effect models use both within-group and between-group variation.

Model Selection Criteria

When it comes to selecting the best model, fixed effect and random effect models have different criteria. Fixed effect models are preferred when the individual-specific effects are correlated with the explanatory variables, whereas random effect models are preferred when the individual-specific effects are uncorrelated with the explanatory variables.

Several model selection criteria can help researchers choose between fixed effect and random effect models. Some of the popular criteria include:

Hausman Test

This test is used to compare the efficiency of the fixed effect and random effect models. The null hypothesis is that the random effect model is efficient, and the alternative hypothesis is that the fixed effect model is efficient. If the p-value of the Hausman test is less than 0.05, then we reject the null hypothesis and conclude that the fixed effect model is efficient.

Likelihood Ratio Test

This test compares the likelihood of the fixed effect and random effect models. The null hypothesis is that the restricted model (random effect model) is a better fit than the unrestricted model (fixed effect model). If the p-value of the likelihood ratio test is less than 0.05, then we reject the null hypothesis and conclude that the fixed effect model is a better fit.

Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)

These criteria compare the goodness of fit of the fixed effect and random effect models. Lower AIC and BIC values indicate a better fit. If the AIC and BIC values for the fixed effect model are lower than those for the random effect model, then the fixed effect model is preferred.