Economics 140 Problem Set 7

You are a new econometrician for the United States Department of Agriculture studying the egg market.  You estimate the following supply and demand curves in the structural equations model.

 

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Demand:

 

Supply:

 

 

  1. What are the endogenous variables in this system of equations?
  2. What are the exogenous variables in this system of equations?
  3. Estimate the supply and demand curves with ordinary least squares and put the coefficient estimates in a table. Demonstrate statistical significance at .01, .05, and .10 with ***, **, and *.

 

Conduct a Hausman test to determine if ordinary least squares is appropriate.

 

  1. What is the null hypothesis?
  2. Using Stata, what is the calculated Hausman test statistic for the supply curve and demand curve?
  3. For the Hausman test, what is the critical value and from which distribution?
  4. For both the supply curve and demand curve, do you need to use two stage least squares or ordinary least squares?
  5. Calculate the reduced form fitted values for both the demand and supply curves. Use these fitted values (reduced form) as proxies for price in your revised two stage least squares structural equations estimates.  Put your results in the table with the original OLS estimates.
  6. Estimate two stage least squares estimates with Stata and insert the estimated coefficients in the table with the original OLS estimates.
  7. Is your instrument relevant in the supply and demand equations?
    1. What is the name of the test?
    2. Using Stata code, what is the syntax for the test?
    3. What is the calculated test statistic?
    4. What is the critical value and from which distribution?
  8. Is your instrument exogenous?
    1. What is the name of the test?
    2. Using Stata code, what is the syntax for the test?

 

  1. What is the calculated test statistic?
  2. What is the critical value and from which distribution?
  1. Are your supply and demand curves estimated consistently?
  2. Estimate the generalized method of moments estimates with Stata and insert the estimated coefficients in the table.
  3. Estimate the limited information maximum likelihood (LIML) estimates with Stata and insert the coefficients in the table.

 

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