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# The Difference Between Simultaneous Equation System Model and Linear Regression Equation

We might all be familiar with linear regression equations, but how many of us have delved deeper into the simultaneous equation system model? It’s worth noting that the simultaneous equation system model is far more complex than linear regression equations.

In the simultaneous equation system model, we can reflect the real world into a more complex model. Consequently, there are interrelated relationships among variables in this model.

While linear equations involve estimating a single equation, the simultaneous equation system model estimates several equations simultaneously. This allows for capturing the interrelationships between variables that form the model.

Considering the importance of understanding the difference between the simultaneous equation system model and linear regression equations, this article aims to delve deeper into the topic.

## Variables in Simultaneous Equation System Model: Understanding Endogenous and Exogenous Variables

When discussing linear regression equations, the concept of independent and dependent variables becomes widely recognized. However, in the context of simultaneous equation system models, we are introduced to different terms, namely endogenous and exogenous variables.

What exactly do endogenous and exogenous variables mean, and how do they differ from independent and dependent variables? Let’s explore each one step by step.

In linear regression, the dependent variable is the one influenced by other variables, while the independent variable is the one influencing (predictor).

In the simultaneous equation system model, endogenous variables are those determined within the equation. These variables are interrelated with other variables in the model.

Meanwhile, exogenous variables are those not influenced by other variables in the model. These variables affect endogenous variables in the model.

Although initially, the concept of endogenous and exogenous variables in estimation may seem similar to independent and dependent variables in linear regression.

In the context of simultaneous equation system models, a strong understanding of the interrelationship between endogenous and exogenous variables is crucial, as well as how changes in one variable can affect other variables in the model.

## The Difference Between Simultaneous Equation System and Single Equation

Before delving deeper into the simultaneous equation system model, it’s important to understand the fundamental difference between such a system and a single equation.

The commonly used linear regression equation serves as an example of a single equation. Although multiple linear regression equations can be created, if there’s no connection between the variables, it’s still considered a single equation.

However, a different scenario unfolds with simultaneous equations. In the simultaneous equation system model, each equation is interconnected with one another. Variables acting as endogenous variables in one equation can become exogenous variables in another equation.

Due to the interconnections among equations in the simultaneous equation system model, any changes made to one variable can have implications for other variables within the system.

## Delving Deeper into Structural Equations and Identities

After grasping the concepts of endogenous and exogenous variables in the context of simultaneous equation systems, the next step is to delve into structural equations and identities.

Structural equations in simultaneous equation systems provide insights into the behavior of variables being estimated. In structural equations, we can observe the estimated effects of exogenous variables on endogenous variables. These equations mark the cause-and-effect relationship between exogenous and endogenous variables.

On the other hand, identities are equations that express the mathematical relationship between variables without considering cause-and-effect relationships. For example, an identity equation might state that the supply of commodity X equals total domestic production plus imports and stock minus exports.

## Applying Estimation to Simultaneous Equation System Models

While in linear regression equations, the ordinary least squares (OLS) method is commonly used, what about estimation methods for simultaneous equation system models?

In the context of simultaneous equation system models, the two-stage least squares (2SLS) method is a common choice. The basic principle of 2SLS estimation consists of two stages conducted sequentially.

## Model Validation Testing

In an effort to build an accurate and fitting model, model validation testing is an important step to undertake. The purpose of model validation is to ensure that the developed model is capable of depicting real-world phenomena effectively.

In the context of simultaneous equation system models, validation testing can be conducted using metrics such as Root Mean Square Percentage Error (RMSPE) and U-Theil.

The smaller the value of RMSPE and the closer to zero the value of U-Theil, the better the model represents the actual data. Tested models can be used for policy simulations or forecasting events beneficial to policymakers or researchers.

That concludes this article, hoping it provides additional insights for readers. Stay tuned for more educational articles from Kanda Data. Thank you, and see you next week.

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