Step 5nbspcompare these to the theoretical moments of the

Question

Power-Law MC Simulation in Excel

Use the following steps to create a power-law MC simulation in Excel.

Step 1: Choose the input parameters a and x_m.

Step 2: Generate 65,000 uniform random numbers using the RAND () function in Excel.

Step 3: Use the inverse transform (8.25) to get a power-law-like variables.

Step 4: Calculate the empirical moments of the 65,000 MC-generated variables.

Step 5: Compare these to the theoretical moments of the power law variables. Use equations (8.11)-(8.14). Note that depending on the choice of a, these moments may not exist.

Step 6: Estimate a "calibrated" a and x_m for the 65,000 MC variables.

Use both the simple linear regression technique of (8.16) and the maximum likelihood calibration (8.31) with its error term given by (8.32). Which method gives the more accurate estimate of the input a?