Instructions to replicate numerical results in
"Size-dependent policies, talent misallocation, and the return to skill"

by J. Lopez and J. Torres

Submitted to the Review of Economic Dynamics

*************************
** CALIBRATION RESULTS **
*************************

The U.S. (undistorted) and Mexico (distorted) benchmark calibrations are carried out in two separate main MATLAB scripts. We use closed form solutions, so each script takes less than one second to run.

1. To replicate the U.S. undistorted calibration reported in Table 3 (parameters) and Table 4 (results) run the script "MainUSUndistortedBenchmark.m". That program calls two functions: "solveUSundistorted_system_a.m" and "solve_a_undistorted.m". This script also generates the two graphs found in Figure 2 showing the equilibrium  assignment function, as well as the equilibrium earnings schedule with skill cutoffs for each occupation. The graphs in Figure 2 are further edited manually for aesthetic purposes using the MATLAB figure editing toolbox.

2. To replicate the calibration for Mexico reported in Table 3 (parameters) and Table 5 (results), run the script "MainMexicoDistortedBenchmark.m". That program calls two functions:
"solveMexicodist_system_a.m" and "solve_a_distorted.m". This script also generates the graph showing the relationship between establishment size and
wages relative to average, both in the model and in the data (Figure 11). It calls the file 'mx_wage.xlsx' to generate the scatter plot in the graph.

We use Matlab R2018B in operating system MacOS 10.13.6.

****************************
** COUNTERFACTUAL RESULTS **
****************************

Counterfactual exercises are carried out in Mathematica 11.0.1.0 with operating system Mac OS 10.13.6. These do not feature closed form solutions but each script should take less than a minute to run.

1. US COUNTERFACTUALS

To replicate US counterfactual results in Table 6, run the script "US_Counterfactuals.nb".

a) The undistorted benchmark has tau=0.

b) For the case of the size-dependent tax, set the statutory tax tau=0.44, and the enforcement parameter k=0.0658. 

c) For the case with perfect enforcement of the average payroll tax under size-dependent enforcement, set the statutory tax tau=0.31, and change the tax function to be equal to tau. 

Commented lines for a, b, and c are already written in the script. See comments in the script for additional instructions for initial values. At the end of this script, skill levels and earnings for wage workers and managers are simulated. We exported the simulated data into excel with the command Export to estimate returns to skill as simple Mincerian regressions of log earnings on log skill. Seed numbers are provided in the script. The simulated data and estimation results can be found in "ReturnsToSkillUS.xls"


2. MEXICO COUNTERFACTUALS

To replicate the counterfactual results for Mexico in Table 9, run the script "MX_Counterfactuals.nb". This file also generates the employment shares for each scenario, as reported in Figure 12.

a) The distorted benchmark has tau=0.44 and k=0.2145.

b) The no-tax counterfactual sets tau=0;

c) The flat tax counterfactual sets the statutory tax tau=0.345. Change the tax function to be equal to tau. 

Commented lines for a, b, and c are already written in the script. See comments in the script for additional instructions for initial values. At the end of this script, skill levels and earnings for wage workers and managers are simulated. We export the simulated data into Excel using the command Export to estimate returns to skill as simple Mincerian regressions of log earnings on log skill. Seed numbers are provided in the script. The simulated data and estimation results can be found in "ReturnsToSkillMX.xls"

An Excel spreadsheet titled "CounterfactualCalculations.xls" contains all final counterfactual calculations for US and Mexico, as reported in Tables 6 and 9, respectively.


3. OUTPUT LOSS/GAIN DECOMPOSITION

See equation 12 in the paper, and follow the Appendix for details. The results from this decompositions are reported in Table 7 (US), and Table 10 (Mexico). The following scripts generate the shares of output loss/gain attributable to each source: manager reallocation, talent mismatch, and worker reallocation, as shown in Equation (12). These scripts use in Mathematica 11.0.1.0 with operating system Mac OS 10.13.6.

a) For the U.S., run the script "US_Decomposition_Auto.nb".

b) For Mexico, run the script "MX_Decomposition_Auto.nb".


4. LUCAS (1978) ECONOMY

The MATLAB program "Lucas1978Economy.m" generates the results used in Table 8. It calls two auxiliary functions: "solveGE_smooth.m", and "profitsmooth.m". To obtain the undistorted results, run the program with h=0 (tax=0). For the economy in column 1 of Table 8, run it with h=0.44. For the economy in column 2 of Table 8, run it with h=0.05. The figures in these columns are obtained by taking the ratio of average size and output for each economy relative to the undistorted one. 


*********************************
*** ESTIMATING THE TAX POLICY ***
*********************************

We use data from INEGI's 2013 Economic Census. We estimate the enforcement parameter "kappa" using data on the average social security contributions for establishments of size 1 to 99 (excluding the owner). The MATLAB program "taxpolicy_fit.m" uses the data in "AverageSSTax.xls" to estimate the value of "kappa" used in the quantitative exercises. It calls the auxiliary function "taxpol.m".


*************************************
*** MOMENTS AND DESCRIPTIVE STATS ***
*************************************

The STATA do file DataPrep cleans the data from Mexico's ENEU and ENOE and the CPS data for the US. We used STATA 13 in operating system Mac OS 10.13.6. This do file generates 5 data files (all 5 available in the set of replication files): enoe2017, cps_2016, data_Figure8, data_Figure13, and data_Figure13a. Use do file Figure8 to generate Figure 8, and Figure13 to generate Figure 13.


***********************************
*** Index of Tables and Figures ***
***********************************

- Figure 2: Use MainUSUndistortedBenchmark.m (MATLAB)
- Figure 6 & 7: Use CounterGraphs.m (MATLAB). This script uses "CounterSimData.xls", which was exported from "Counterfactual_Graphs.nb" (Mathematica)
- Figure 8:  Use STATA do file Figure8
- Figure 9:  Use taxpolicy_fit.m (MATLAB)
- Figure 11: Use MainMexicoDistortedBenchmark.m (MATLAB)
- Figure 12: Use STATA do file Figure12
- Figure 13: Use STATA do file Figure13

- Table 3:  Use MainUSUndistortedBenchmark.m and MainMexicoDistortedBenchmark.m (MATLAB)
- Table 4:  Use MainUSUndistortedBenchmark.m (MATLAB)
- Table 5:  Use MainMexicoDistortedBenchmark.m (MATLAB)
- Table 6:  Use US_Counterfactuals.nb (Mathematica)
- Table 7:  Use US_Decomposition_Auto.nb (Mathematica)
- Table 8:  Use Lucas1978Economy.m (MATLAB)
- Table 9:  Use MX_Counterfactuals.nb (Mathematica)
- Table 10: Use MX_Decomposition_Auto.nb (Mathematica)


******************************************************************************************************


See Appendix B for further details on sources and calculations using Mexico and U.S. data.


******************************************************************************************************