Exam 16: Simultaneous Equations Models

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The following equations represent a two-equation model:​ y1 = β10 + α1y2 + z1β1 + u1 Y2 = β20 + α2y1 + z2β2 + u2 Where, y1 and y2 are the:

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If a structured model contains a time trend-which may capture exogenous, trending factors that are not directly modeled-then the trend acts as its own instrumental variable.

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​The first step in estimating simultaneous equations models (SEMs) with panel data is to find instrumental variables for the endogenous variables in the transformed equation.

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In a simultaneous equations model, if any variable is determined outside of the model, then it is considered a(n):​

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The order condition is a necessary and sufficient condition for identification of an equation in a simultaneous equations model.

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Which of the following statements is true?

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The following equations represent a simultaneous equations model: K1 = The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub> +   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: 1K2 + The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub> +   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: 1z1 + u1 K2 = The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub> +   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: 2K1+ The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub> +   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> OLS will suffer from simultaneity bias if: 2z2 + u2 OLS will suffer from simultaneity bias if:

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A simultaneous equations model is suitable whenever two variables are determined simultaneously.

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In econometrics, simultaneity arises when:

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Refer to the simultaneous equations model above. The reduced form error from the reduced form equation for K2 will be a:

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The rank condition for identification of a structural equation states that the first equation in a two-equation simultaneous equations model is identified if, and only if:

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Which of the following equations is an overidentified equation?​

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OLS is biased and inconsistent when applied to a structural equation in a simultaneous equations system.

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The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Qi = The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> =   <sub>1</sub>P<sub>i</sub> +   <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> =   <sub>2</sub>P<sub>i</sub> +   <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? 1Pi + The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> =   <sub>1</sub>P<sub>i</sub> +   <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> =   <sub>2</sub>P<sub>i</sub> +   <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? 1zi1 + ui1 Qi = The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> =   <sub>1</sub>P<sub>i</sub> +   <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> =   <sub>2</sub>P<sub>i</sub> +   <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? 2Pi + The following simultaneous equations describe the demand and supply for a particular good in a competitive market. Q<sub>i</sub> =   <sub>1</sub>P<sub>i</sub> +   <sub>1</sub>z<sub>i</sub><sub>1</sub> + u<sub>i</sub><sub>1</sub> Q<sub>i</sub> =   <sub>2</sub>P<sub>i</sub> +   <sub>2</sub>z<sub>i</sub><sub>2</sub> + u<sub>i</sub><sub>2</sub> Which of the following are the endogenous variables in this model? 2zi2 + ui2 Which of the following are the endogenous variables in this model?

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The following equations represent a simultaneous equations model: K1 = The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub><sup> </sup>+   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: 1K2 + The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub><sup> </sup>+   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: 1z1 + u1 K2 = The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub><sup> </sup>+   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: 2K1+ The following equations represent a simultaneous equations model: K<sub>1</sub> =   <sub>1</sub>K<sub>2</sub><sup> </sup>+   <sub>1</sub>z<sub>1</sub> + u<sub>1</sub> K<sub>2</sub> =   <sub>2</sub>K<sub>1</sub>+   <sub>2</sub>z<sub>2</sub> + u<sub>2</sub> The reduced form equation for K<sub>2</sub> will express: 2z2 + u2 The reduced form equation for K2 will express:

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Exclusion restrictions are said to be imposed in a two-equation simultaneous equations model if it is assumed that:

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​The number of overidentifying restrictions equals the total number of exogenous variables in the system plus the total number of explanatory variables in the equation.

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Which of the following statements is true?

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Which of the following correctly identifies a characteristic of structural equations?

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An alternative to using simultaneous equation models with panel data is:

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