I am having trouble figuring out the correct code. I am trying to do an unrestricted and restricted model of a Cobb-Douglas Production Model.
lnQ=B1 + B2 lnL + B3 lnK + e
This is my code
data cobb;
infile 'cobb';
input q l k;
proc reg data = cobb;
model q = l k; <-----doing something wrong here
test l + k= 1; <-----doing something wrong here
run;
Am being asked to re-estimate the model with the restriction of CRTS, B2 + B3 =1.
To re-estimate the Cobb-Douglas Production Model with the restriction of constant returns to scale (CRTS) where B2 + B3 = 1, you need to use the SAS programming language. Here's an explanation of the correct code:
```
data cobb;
infile 'cobb'; /* Assumes your input file is named 'cobb' */
input q l k; /* Specifies the variables q, l, and k from the input file */
run;
```
The above code reads the data from the specified input file into a dataset named `cobb`. Make sure that your input file is correctly formatted with the variables `q`, `l`, and `k` in the right order.
```
proc reg data = cobb;
model q = l k; /* Specifies the model: q as the response variable and l, k as the predictor variables */
run;
```
The `proc reg` statement initiates the regression analysis using the `cobb` dataset. The `model` statement specifies the model equation, where you want to predict `q` using the predictor variables `l` and `k`.
At this point, you have estimated the unrestricted model. To proceed with the restricted model, you can use an alternative approach:
```
proc reg data = cobb;
model q = l k / test (B2 + B3 = 1); /* Introduce the restriction B2 + B3 = 1 using the test statement */
run;
```
In the `model` statement, you can include the `test` statement to impose restrictions on the coefficients. In this case, you want to test whether B2 + B3 = 1 to satisfy the CRTS restriction. By specifying this test, Proc Reg will re-estimate the model while imposing the restriction.
Make sure to save your code and run it in SAS to obtain the desired results.