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Estimation of Production Functions: Random Effects in Panel DataPowerPoint Presentation

Estimation of Production Functions: Random Effects in Panel Data

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Estimation of Production Functions: Random Effects in Panel Data. Lecture IX. Basic Setup.

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### Estimation of Production Functions: Random Effects in Panel Data

Lecture IX over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

Basic Setup Data

- Regression analysis typically assumes that a large number of factors affect the value of the dependent variable, while some of the variables are measured directly in the model the remaining variables can be summarized by a random distribution

Lecture IX

- When “numerous observations” on individuals are observed over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.
- Going back to the panel specification

Lecture IX

Lecture IX over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

- The variance of over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.yit on xit based on the assumption above is
- Thus, this kind of model is typically referred to as a variance-component (or error-components) model.

Lecture IX

- Letting over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.
the panel estimation model can be written in vector form as

Lecture IX

- The expected value of the residual becomes over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

- Using the basic covariance estimator over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.
- Whether αi is fixed or random the covariance estimator is unbiased.
- However, if the αi is random the covariance estimator is not the best linear unbiased estimator (BLUE).
- Instead, a BLUE estimator can be derived using generalized least squares (GLS).

Lecture IX

The Generalized-Least-Squares Estimator over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

- Because both uit and uis contain αi , they are correlated.

Lecture IX

Lecture IX over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

- A procedure for estimation over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

- This looks bad, but think about over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

- Solving this system yields over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

- Using the inverse of a partitioned matrix over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

- Where over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.
- Where βb is the between estimator.

Lecture IX

- The variance of the estimator can be written as over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.

Lecture IX

- 3. Given that we don’t know over time, it is assumed that some of the omitted variables represent factors peculiar to individual and time periods.ψa priori, we estimate

Lecture IX

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