Alexis Akira Toda and Kieran James Walsh, "Fat Tails and Spurious
Estimation of Consumption-Based Asset Pricing Models", Journal of
Applied Econometrics, Vol. 32, No. 6, 2017, pp. 1156-1177.
All files are ASCII files in DOS format. They are zipped in the file
tw-files.zip. Unix/Linux users should use "unzip -a".
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DIRECTORY STRUCTURE:
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-- "shiller-data.csv": CSV file containing the Shiller data used to
calibrate the model.
-- "GMM" folder: Contains Matlab files for replicating GMM estimation
results.
-- "ME_discretization" folder: Contains Matlab files to discretize
VARs as in Farmer and Toda "Discretizing Nonlinear, Non-Gaussian
Markov Processes with Exact Conditional Moments", Quantitative
Economics, forthcoming. These files are only used to compute
financial moments in the asset pricing model in the paper.
-- "Simulate_Economy" folder: Contains Matlab files for simulating a
heterogeneous-agent general equilibrium model in the paper.
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DETAILED DESCRIPTIONS:
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1. "shiller-data.csv"
This file contains Shiller's data on US real consumption, dividend,
and asset prices, as described in Chapter 26 of Robert Shiller's book
"Market Volatility", MIT Press, 1989. The source data are available as
an Excel spreadsheet at
http://www.econ.yale.edu/~shiller/data/chapt26.xlsx Each row
corresponds to the year 1889-2009 (121 rows in total). There are five
columns, as follows.
-- Column 1: real per capita consumption (Column I in Shiller's spreadsheet)
-- Column 2: real dividend on S&P 500 (Column O in Shiller's spreadsheet)
-- Column 3: real S&P 500 index (Column K in Shiller's spreadsheet)
-- Column 4: gross real risk-free rate (Column H in Shiller's spreadsheet)
-- Column 5: gross real returns on S&P 500 (1 plus Column P in Shiller's
spreadsheet)
2. "GMM" folder
"RunGMM4.m" is the main file to do GMM estimation. You need to set T
(sample size; 100, 300, or 500 in paper) on line 12, M (number of
monte carlo replications; 10000 in paper) on line 14, and unc (type of
model: 0, 1, 2 for unconditional, conditional, and exactly identified
model; see paper for details) on line 15.
After running RunGMM4.m, you can run the following three files to
create figures and compute test statistics.
-- "GMM_figs.m" creates figures (scatter plots and histograms of pricing
errors).
-- "GMM_figs_Appendix.m" does the same for the Online Appendix.
-- "GMM4_stats.m" computes the test statistics and conduct hypothesis tests.
"get2troughs.m" simulates economies until you get an example of GMM
criterion with two troughs.
The rest are subroutines:
-- "GELObjective.m" defines the objective function of GEL.
-- "GMM4_stage1.m" does a single GMM estimation.
-- "GMM4GEL.m" does a single GEL estimation.
-- "GMMcrit4.m" defines the GMM criterion.
-- "GMMcrit4GEL.m" defines the GEL criterion.
-- "NeweyWestHAC.m" computes the Newey-West HAC estimator.
-- "parfor_progress.m" is used for parallel computing.
-- "perror4.m" computes the pricing errors of GMM.
-- "residual4.m" computes the GMM residuals.
3. "ME_discretization" folder
The file "discreteVAR.m" is the main file to discretize VAR processes.
See "example.m" for examples.
The rest are subroutines:
-- "allcomb2.m" create a matrix of all combinations of elements.
-- "discreteApproximation.m" does the maximum entropy discretization of
probability distributions as in Tanaka and Toda "Discrete Approximation
of Continuous Distributions by Maximum Entropy" (2013, Economics Letters).
-- "entropyObjective.m" defines the objective function of ME discretization.
-- "GaussHermite.m" computes nodes and weights of Gauss-Hermite quadrature.
-- "minVarTrace.m" finds a unitary matrix U that makes U'*AU as close to a
multiple of identity matrix as possible.
-- "polynomialMoment.m" computes the moment defining function used in
discreteApproximation.
-- "unitaryConstraint.m" defines the constraint function used in minVarTrace.
4. "Simulate_Economy" folder
-- "cCAPM_Sim3.m" simulates an economy.
-- "test_cCAPM_Sim3.m" replicates the histograms, QQ plots, and asset
returns series in Section 3 of paper.
The rest are subroutines:
-- "AL_pdf.m" computes the probability density function of asymmetric
Laplace distribution.
-- "ALrnd.m" generates random numbers from asymmetric Laplace.
-- "NL_pdf.m" computes the PDF of normal-Laplace distribution.
-- "NLrnd.m" generates random numbers from normal-Laplace.
-- "paramSet.m" sets the parameter values used in the paper.
-- "shillerVAR.m" estimates the VAR(1) for consumption/dividend growth.