Ordinary Least Squares vs. Two Staged Least Squares

Attribute	Ordinary Least Squares	Two Staged Least Squares
Estimation Method	Single stage estimation	Two stage estimation
Endogeneity	Does not account for endogeneity	Addresses endogeneity by using instrumental variables
Efficiency	Efficient if assumptions are met	More efficient in the presence of endogeneity
Consistency	Consistent under certain assumptions	Consistent under certain assumptions
Assumptions	Assumes exogeneity of independent variables	Assumes exogeneity of instrumental variables

Introduction

When it comes to regression analysis, two commonly used methods are Ordinary Least Squares (OLS) and Two Staged Least Squares (2SLS). Both methods are used to estimate the parameters of a linear regression model, but they have some key differences in terms of their assumptions, applications, and advantages. In this article, we will compare the attributes of OLS and 2SLS to help you understand when and why you might choose one method over the other.

Assumptions

One of the main differences between OLS and 2SLS lies in their assumptions. OLS assumes that there is no correlation between the independent variables and the error term in the regression model. This is known as the assumption of exogeneity. On the other hand, 2SLS is specifically designed to handle situations where there is endogeneity, meaning that the independent variables are correlated with the error term. In this case, 2SLS is preferred over OLS because it provides consistent and unbiased estimates of the regression coefficients.

Applications

OLS is commonly used when the independent variables are exogenous and there is no correlation with the error term. This makes OLS a suitable choice for many regression analysis scenarios, such as predicting sales based on advertising spending or analyzing the relationship between education level and income. On the other hand, 2SLS is more appropriate when there is endogeneity present in the model, such as when there are omitted variables or measurement errors that are correlated with the independent variables. In these cases, using 2SLS can help to correct for bias in the estimates.

Advantages of OLS

One of the main advantages of OLS is its simplicity and ease of interpretation. OLS provides closed-form solutions for estimating the regression coefficients, making it straightforward to implement and understand. Additionally, OLS is efficient when the assumptions of the model are met, as it provides unbiased and efficient estimates of the parameters. OLS is also widely used in practice and is the default method for many regression analyses due to its simplicity and ease of use.

• Simple and easy to interpret
• Efficient when assumptions are met
• Widely used in practice

Advantages of 2SLS

While OLS is a powerful tool for regression analysis, there are situations where 2SLS has distinct advantages. One of the main advantages of 2SLS is its ability to correct for endogeneity in the model. By using instrumental variables to create two stages of estimation, 2SLS can provide consistent and unbiased estimates even when the assumptions of OLS are violated. This makes 2SLS a valuable tool for researchers who need to account for endogeneity in their regression models.

• Corrects for endogeneity
• Provides consistent and unbiased estimates
• Valuable for researchers dealing with endogeneity

Conclusion

In conclusion, both Ordinary Least Squares and Two Staged Least Squares are valuable tools for regression analysis, each with its own set of advantages and applications. OLS is a simple and efficient method that is widely used in practice when the assumptions of the model are met. On the other hand, 2SLS is specifically designed to handle endogeneity in the model and can provide consistent and unbiased estimates in these situations. Understanding the differences between OLS and 2SLS can help researchers choose the most appropriate method for their regression analysis needs.