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calibration

README.md

README for code associated with calibration, plotting of output, and robustness results of Equilibrium Technology Diffusion, Trade, and Growth by Perla, Tonetti, and Waugh (AER 2020)

All in matlab or python with the associated jupyter notebooks.

Create Calibration Moments

The notebook ../../section_7-1.ipynb pulls data and computes the empirical moments used in calibration. Most data in that notebook is pulled directly from public online sources like FRED or the BLS. Some data is from the Synthetic Longitudinal Business Database.

  • See /src/calibration/SynLBD for the Stata code used to construct the SynLBD-derived moments, output log files, and instructions for how to access the SynLBD.

Data used in the paper was current from these sources as of April 5, 2020. The notebook ../../section_7-1.ipynb outputs the following .csv files to the src/calibration/data/ folder, which are then used as inputs into the calibration code:

Master File

The master file master_calibration.m produces all calibration and robustness results. In MATLAB, just run

>> master_calibration

This file runs all other files, prints the results, and generates the appropriate output files used as input when creating figures and numbers that appear in the paper.

Structure of Main Calibration File calibrate_wrap.m

The file calibrate_wrap.m calibrates the model using code that computes the BGP (balanced growth path) equilibrium. Transition dynamics are computed in Julia and described here.

The file calibrate_wrap.m does the following:

1. Reads in the moments that are generated from the python notebook described above in create calibration moments

2. Minimizes the distance between the data moments and model moments. The code that computes the model moments via simulation is organized in the following way:

  • calibrate_growth.m organizes parameters, passes them to the function to retrieve model moments, then constructs the objective function the calibration is minimizing. The moments are stacked in the following order:

    • g, lambda_{ii}, fraction of exporters, size of exporters vs non exporters, and then the quantile moments (note how these are passed through) into vector form

    • Then line 47 describes the objective function used. This is just the standard GMM quadratic objective with an identity weighting matrix

  • compute_growth_fun_cal.m takes in parameters, computes the BGP equilibrium, constructs the moments from simulated data, and calculates welfare. The following functions perform these operations:

  • eq_functions/calculate_equilibrium.m computes the BGP equilibrium

  • eq_functions/selection_gbm_constant_Theta_functions.m are the equilibrium relationships that map to equations in the paper

  • static_firm_moments.m Computes the BEJK moments, fraction of exporters, and the relative size of domestic shipments for exporters vs non-exporters

  • markov_chain/generate_transition_matrix.m constructs the transition matrix across productivity states. Note that the code markov_chain/generate_stencils.m is required to generate the grid. This is called before the calibration routine since it is kept constant

  • markov_chain/coarsen_to_quintiles_four.m maps the transition matrix into a four by four matrix over a 5 year horizon to match up with data moments

3. Given the calibration results, the following output is created:

  • A file /parameters/calibration_params.csv is created with the calibrated parameters

  • An associated .mat file cal_params.mat is generated for use within matlab. The variable new_cal has the values in the in the following order: d, theta, kappa, 1/chi, mu, upsilon, sigma

  • Comparisons of BGP equilibria associated with different parameter values are presented. To compute BGP results for different parameter values the code compute_growth_fun_cal is called with the appropriately changed parameter values

Robustness Exercises

In the paper Figures 6 and 7 display how changes to the GBM parameters $\mu$ and $\upsilon$ and to the BGP entry rate $\delta$ affect key outcomes.

  • Changes in $\delta$ The code that creates the underlying data for Figure 7 is:

    • robust_no_recalibrate_delta.m. This reads in cal_params.mat generated from the calibration routine and then works through a several loops. First it changes $\chi$ by a scale value, then for the given $\chi$ it changes delta. The main file it calls is compute_growth_fun_cal.m. The output are the following .mat files:

    • output/robust/delta/param_values_delta_xx where xx is the scale value used for the given run of different $\delta$s. Each row shows the growth rate, baseline parameter values, then $\mu$, $\upsilon$, $\sigma$, and $\delta$ for that given run

    • output/robust/delta/norecalibrate_values_delta_xx where xx is the scale value for the given run. Each row shows the growth rate, counterfactual growth rate, difference, welfare gain, and the associated $\delta$

  • Changes in $\mu$ and $\upsilon$ The code that creates the underlying data for Figure 6 is:

    • robust_no_recalibrate_gbm.m. This reads in cal_params.mat generated from the calibration routine and then works through a several loops. First it changes $\chi$ by a scale value, then for the given $\chi$ it changes $\mu$ and $\upsilon$ by a common scale value. The main file it calls is compute_growth_fun_cal.m. The output are the following .mat files:

    • output/robust/gbm/param_values_gbm_xx.mat where xx is the scale value used for the given run of different $\delta$s. Each row shows the growth rate, baseline parameter values, then $\mu$, $\upsilon$, $\sigma$, and $\delta$ for that given run

    • output/robust/gbm/norecalibrate_values_gbm_xx.mat where xx is the scale value for the given run. Each row shows the growth rate, counterfactual growth rate, difference, welfare gain, and the associated $\delta$

    • /parameters/calibration_chi_xx.csv, where xx is the value for $\chi$ at which the code is run. This file computes the parameter values which, for the given $\chi$, result in a growth rate which is closest to the targeted baseline growth rate of 0.79.

  • Robustness to changes in scaling parameter $\zeta$ This code is exactly the same as calibrate_wrap.m with the only difference being that alternative $\zeta$s are fixed and a loop over different calibrations is performed for the different $\zeta$s. The output is:

  • Comparison to Sampson (2016) This code recalibrates the model to target moments related to Sampson (2016 QJE), in part by setting GBM parameters to zero. The code calibrate_wrap_sampson.m performs the calibration. The underlying code and structure is exactly the same as in the main calibration code calibrate_wrap.m.

  • No Firm Dynamics This code recalibrates the model with GBM parameters set to zero. The code calibrate_wrap_no_firm_dynamics.m performs the calibration. The underlying code and structure is exactly the same as in the main calibration code calibrate_wrap.m.

  • Comparison to Atkeson and Burstein (2010) The base of this code was downloaded from Ariel Burstein's website at: http://www.econ.ucla.edu/arielb/innovcodes.zip. Starting from that code we set the discount rate, elasticity of substitution, the exit rate of firms, and the aggregate import share to be the same as in our baseline calibration. The code, located in /src/calibration/ABmodel/Master_ptw.m, runs the routine and returns the welfare gains from the same reduction in trade costs as studied in the baseline exercise of PTW, inclusive of the transition path.