Problem Set 7

1. Using the data for your research paper
   1. Specify using path diagram a recursive causal model involving at least one intervening variable
      1. Explicate your model in words
      2. Write out the equations for the model.
   2. Estimate the parameters for that model.
   3. Assess the causal model you have specified and now estimated.
   4. What, if any, changes in your model are suggested by your results?
   5. How might you modify your model to be nonrecursive (show the path diagram) without worrying about identification?
      1. Write out the equations for the model.
      2. Which equations pose identification problems
      3. Discuss what, if any, variables you could add to the model to achieve identification
         
         
         
2. Suppose that the true consumption function is (C is consumption, I is income, and S is savings)

   C = 10 + .6I

where

I = C + S

You observe the following values for the three variables:

	C	I	S
	46	60	14
	31	45	14
	61	75	14
	58	80	22
	43	65	22
	73	95	22
	70	100	30
	55	85	30
	85	115	30    

1. Graph the true consumption function and the scatter of C and I.
2. Regress C on I using OLS.
   1. Graph the estimated consumption function.
   2. Is it consistent with the true function?
3. Estimate the consumption function using S as an instrumental variable (IV).
   1. Graph this estimated consumption function.
   2. Is it consistent with the true function

Bert Kritzer, 608-263-2277, Kritzer@PoliSci.Wisc.Edu
Last modified, April 8, 2004