GNRProdEst

This package implements the production function estimaton method from Gandhi, Navarro, Rievers (2020).

Installation

Use Julia's integrated package manager Pkg.jl

using Pkg
Pkg.add("GNRProdEst")

Usage

You can use estimation routine in two ways. Either run both stages using gnrprodest or run each estimation stage separately with gnrfirststage and gnrsecondstage. Versions of these functions that end with an ! modify their inputs (most importantly the dataframe).

Using `gnrprodest` and `gnrprodest!`

Both versions have exactly the same arguments. The difference is, that gnrprodest modifies its arguments (especially data). fes_returns is a NamedTuple of first stage return objects, ses_returns is the equivalent for the second stage, results_table is a DataFrame printed at the end containing key statistics, and estimation_sample is the DataFrame used in the estimation routine.

using GNRProdEst

fes_returns, ses_returns, results_table, estimation_sample = gnrprodest(data = DataFrame, output = :revenue, flexible_input = :flexible_input, fixed_inputs = [:fixed_input1 :fixed_input2 ...], id = :id, time = :time)

fes_returns, ses_returns, results_table = gnrprodest!(data = DataFrame, output = :gross_output, flexible_input = :flexible_input, fixed_inputs = [:fixed_input1 :fixed_input2 ...], id = :id, time = :time)

Arguments

All arguments in any of the functions are keyword arguments. The necessary arguments are:

data is a DataFrame that includes all columns defined by other arguments.
output is the Symbol and represents the firms natural logarithm of gross output.
flexible_input is a Symbol representing the natural logarithm of the flexible input of the production function.
fixed_inputs is a Symbol or a vector of Symbols representing any natural logarithm of fixed production inputs.
id is a Symbol of each firm's unique identifier.
time is a Symbol identifying the observation`s time period.

Optional Arguments

ln_share_flex_y is a Symbol for the natural logarithm of the flexible input share of revenue. If it is not defined by the user, the package calculates it internally.
share_degree is the degree of the polynomial series in the share regression. Its default value is 3 if it is not defined by the user.
lm_tfp_degree is the degree of the law of motion for $\omega$ (tfp) over time. The default value if not defined by user is 3.
int_const_series_degree is the degree of the polynomial series of the constant of integration in the second stage. Its default value is 3 if not defined by the user.
fes_starting_values is a vector of starting values for the first stage non-linear least squares regression. If the user does not define them, the package chooses them using a linear regression.
ses_starting_values is a vector of starting values for the second stage GMM estimation routine. If the user does not define them, the package chooses them using a linear regression.
boot_reps is an integer indicating the number of repetitions the Bootstrap algorithm uses in the standard error estimation. The default is 200.
opts is a dictionary of futher options.
- fes_print_starting_values prints first stage starting values if set to true.
- fes_print_results prints first stage results if set to true.
- fes_optimizer can be used to change the numerical optimization algorithm in the first stage. The default is NelderMead. You can find a list of available optimizers with an in-dept description here: Optim.jl
- fes_optimizer_options allows the user to configure the options of the first stage numerical optimization routine. Use an Optim.Options() object to define them. The configurable options depend on the optimizer chosen. You can find a list of options here: Optim.Options
- ses_print_starting_values prints first stage starting values if set to true.
- ses_print_results prints first stage results if set to true.
- ses_optimizer can be used to change the numerical optimization algorithm in the second stage. The default is NelderMead. You can find a list of available optimizers with an in-dept description here: Optim.jl
- ses_optimizer_options allows the user to change the options of the second stage numerical optimization routine. Use an Optim.Options() object to define them. The configurable options depend on the optimizer chosen. You can find a list of options here: Optim.Options
- print_results prints a summary table of key statistics including (among others) standard errors and confidence intervals. Deflaut is true.

Using `gnrfirststage` and `gnrfirststage!`

Instead of using one command for both stages, you can estimate both stages independently. The command for the estimation of the first stage is gnrfirststage or gnrfirststage!. The difference is that the latter changes its inputs (especially the data). See the list of argument descriptions above.fes_returns is a NamedTuple of first stage return objects and estimation_sample is the DataFrame used in the estimation routine.

using GNRProdEst

fes_returns, estimation_sample = gnrfirststage(data = DataFrame, output = gross_output, flexible_input = :flexible_input, fixed_inputs = [:fixed_input1 :fixed_input2 ...],ln_share_flex_y = :ln_share_flex_y, share_degree = :share_degree, starting_values = :starting_values [, opts = Dict])

fes_returns = gnrfirststage!(data = DataFrame, output = gross_output, flexible_input = :flexible_input, fixed_inputs = [:fixed_input1 :fixed_input2 ...],ln_share_flex_y = :ln_share_flex_y, share_degree = :share_degree, starting_values = :starting_values [, opts = Dict])

Using `gnrsecondstage` and `gnrsecondstage!`

The command for the estimation of the second stage is gnrsecondstage or gnrsecondstage!. The difference is that the latter changes its inputs (especially the data). See the list of argument descriptions above. The only additional argument is fes_returns representing the object returned from the first stage estimation. Use opts as described above to modify additional options, such as the numerical optimization algorithm. ses_returns is a NamedTuple of return objects from the second stage estimation.

using GNRProdEst

ses_returns, estimation_sample = gnrsecondstage(data = DataFrame,flexible_input = :flexible_input, fixed_inputs = [:fixed_input1 :fixed_input2 ...], id = :id, time = :time, fes_returns = fes_returns, int_const_series_degree = int_const_series_degree, lm_tfp_degree = lm_tfp_degree, starting_values = ses_starting_values [, opts = Dict])

ses_returns = gnrsecondstage!(data = DataFrame,flexible_input = :flexible_input, fixed_inputs = [:fixed_input1 :fixed_input2 ...], id = :id, time = :time, fes_returns = fes_returns, int_const_series_degree = int_const_series_degree, lm_tfp_degree = lm_tfp_degree, starting_values = ses_starting_values [, opts = Dict])

Example

This example uses 500 firms from Gandhi, Navarro, Rivers (2020)'s replication package data. It estimates a gross output production function with one flexible input $i$ and one fixed input $k$.

# Load required dependencies (use 'using Pkg' and Pkg.add("DataFrames"), Pkg.add("GNRProdEst") or Pkg.add("CSV") if you do not have any of these packages in your environment.)
using GNRProdEst, DataFrames, CSV

# Read in replication data
rep_data = CSV.read("test/GNR_data_500.csv", DataFrame)

# Run both estimation stages at the same time
gnr_res = GNRProdEst.gnrprodest!(data = rep_data, 
                                output = :yg, 
                                flexible_input = :i, 
                                fixed_inputs = :k, 
                                ln_share_flex_y = :si, 
                                id = :id, 
                                time = :time);

Output should be

.......................................................................................
.......................................................................................
..........................
Number of observations: 14500
┌────────────────────┬──────────┬─────────┬──────────┬─────────┬──────────┬───────────┐
│           Variable │     Stat │      SE │   t_stat │ P_Value │ Conf_low │ Conf_high │
├────────────────────┼──────────┼─────────┼──────────┼─────────┼──────────┼───────────┤
│ mean elasticity: i │  0.28664 │ 0.07321 │  3.91529 │ 0.00009 │  0.14315 │   0.43013 │
│ mean elasticity: k │  0.62627 │ 0.06637 │  9.43551 │ 0.00000 │  0.49618 │   0.75637 │
│               cons │  0.16831 │ 0.03189 │  5.27709 │ 0.00000 │  0.10580 │   0.23082 │
│                  ω │  0.76883 │ 0.04673 │ 16.45362 │ 0.00000 │  0.67725 │   0.86042 │
│                 ω² │  0.06571 │ 0.06038 │  1.08843 │ 0.27641 │ -0.05262 │   0.18405 │
│                 ω³ │ -0.03986 │ 0.02377 │ -1.67664 │ 0.09361 │ -0.08645 │   0.00674 │
└────────────────────┴──────────┴─────────┴──────────┴─────────┴──────────┴───────────┘

Alternatively, you can estimate both stages sparately with

# Load required dependencies (use 'using Pkg' and Pkg.add("DataFrames"), Pkg.add("GNRProdEst") or Pkg.add("CSV") if you do not have any of these packages in your environment.)
using GNRProdEst, DataFrames, CSV

# Read in replication data
rep_data = CSV.read("test/GNR_data_500.csv", DataFrame)

# Define some options to print results
opts = Dict("fes_print_results" => true, "ses_print_results" => true)

# Run the first estimation stage
fes_return_obj, est_sample = GNRProdEst.gnrfirststage(data = rep_data,
                                                      output = :yg,
                                                      flexible_input = :i,
                                                      fixed_inputs = :k,
                                                      ln_share_flex_y = :si,
                                                      opts = opts);

Output should be

First stage results:
┌──────────┬──────────┬──────────┐
│ Variable │        γ │       γ' │
├──────────┼──────────┼──────────┤
│ constant │  0.65239 │  0.67590 │
│        k │ -0.00146 │ -0.00152 │
│      k⋅k │ -0.00050 │ -0.00052 │
│    k⋅k⋅k │ -0.00033 │ -0.00035 │
│    k⋅k⋅i │  0.00111 │  0.00115 │
│      k⋅i │  0.00123 │  0.00128 │
│    k⋅i⋅i │ -0.00112 │ -0.00116 │
│        i │ -0.02119 │ -0.02195 │
│      i⋅i │  0.00476 │  0.00494 │
│    i⋅i⋅i │ -0.00005 │ -0.00005 │
└──────────┴──────────┴──────────┘

Afterwards, you can run the second estimation step with

ses_res = GNRProdEst.gnrsecondstage(data = est_sample,
                                    flexible_input = :i,
                                    fixed_inputs = :k,
                                    id = :id,
                                    time = :time,
                                    fes_returns = fes_return_obj,
                                    opts = opts);

The output should be

Integration constant series parameters
┌──────────┬──────────┐
│ Variable │ Estimate │
├──────────┼──────────┤
│        k │  0.38825 │
│      k⋅k │ -0.02485 │
│    k⋅k⋅k │  0.00247 │
└──────────┴──────────┘
All output elasticities:
┌──────────┬─────────┬─────────┬─────────┬─────────┐
│ Variable │    Mean │      SD │     Min │     Max │
├──────────┼─────────┼─────────┼─────────┼─────────┤
│        k │ 0.28670 │ 0.01767 │ 0.27269 │ 0.38782 │
│        i │ 0.62627 │ 0.00454 │ 0.60449 │ 0.65235 │
└──────────┴─────────┴─────────┴─────────┴─────────┘
Productivity:
┌──────────┬──────────┬─────────┬──────────┬─────────┐
│ Variable │     Mean │      SD │      Min │     Max │
├──────────┼──────────┼─────────┼──────────┼─────────┤
│        ω │  0.80982 │ 0.34225 │ -0.47409 │ 1.67487 │
│        Ω │  2.38170 │ 0.82280 │  0.62245 │ 5.33810 │
│        v │ -0.00007 │ 0.23424 │ -1.27870 │ 1.25506 │
└──────────┴──────────┴─────────┴──────────┴─────────┘
Productivity Law of Motion:
┌──────────┬──────────┐
│ Variable │ Estimate │
├──────────┼──────────┤
│ constant │  0.16803 │
│        ω │  0.76907 │
│       ω² │  0.06544 │
│       ω³ │ -0.03980 │
└──────────┴──────────┘

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

License

Please cite this package if you use it for published research.

MIT

GNRProdEst.jl

GNRProdEst

Installation

Usage

Using `gnrprodest` and `gnrprodest!`

Arguments

Optional Arguments

Using `gnrfirststage` and `gnrfirststage!`

Using `gnrsecondstage` and `gnrsecondstage!`

Example

Contributing

License

Required Packages

Used By Packages

Suggest Category

GNRProdEst

Installation

Usage

Using gnrprodest and gnrprodest!

Arguments

Optional Arguments

Using gnrfirststage and gnrfirststage!

Using gnrsecondstage and gnrsecondstage!

Example

Contributing

License

Required Packages

Used By Packages

Julia Packages

Using `gnrprodest` and `gnrprodest!`

Using `gnrfirststage` and `gnrfirststage!`

Using `gnrsecondstage` and `gnrsecondstage!`