Instrumental variable identification of dynamic variance decompositions

Matlab code for inference on variance decompositions and the degree of invertibility/recoverability in a general Structural Vector Moving Average (SVMA) model identified by external instruments (IVs, also known as proxies)

Reference: Plagborg-Møller, Mikkel and Christian K. Wolf (2020), "Instrumental Variable Identification of Dynamic Variance Decompositions", https://scholar.princeton.edu/mikkelpm/decomp_iv (paper + online appendix)

Tested in: Matlab R2020a on Windows 10 PC (64-bit)

Contents

functions: Matlab routines

• SVMAIV_estim.m: main function for SVMA-IV inference
• SVARIV_estim.m: SVAR-IV inference (assumes invertibility)

application: empirical example

• run_gk.m: example based on Gertler & Karadi (2015)

illustration: numerical illustration

• run_sw.m: SVMA-IV and SVAR-IV analysis of Smets & Wouters (2007) model

simulations: simulation study

• run_sim.m: run Monte Carlo experiments for various DGPs
• print_results.m: display results for all DGPs

Example

addpath('functions');
% Given (T x n_y) data matrix Y with endogenous variables
% and (T x 1) data vector Z with external instrument
[bounds, id_recov, inv_test] = ...
  SVMAIV_estim(Y, Z, ...
               'ic', 'aic', ...   % Select lag length using AIC
               'signif', 0.1, ... % 10% significance level
               'n_boot', 500, ... % 500 bootstrap iterations
               'horiz', 1:24);    % Compute horizons 1-24 of FVR/FVD

Output:

• bounds structure: partial identification bounds
  • bounds.estim: point estimates of bounds
  • bounds.ci: confidence intervals for identified set
• id_recov structure: results under additional assumption of recoverability
  • id_recov.estim: point estimates of parameters
  • id_recov.ci: confidence intervals for parameters
• inv_test structure: pre-test for invertibility, implemented as a Granger casuality test, either in all equations jointly (subfield all) or in each y equation separately (subfield eqns)
  • inv_test.wald_stat: Wald statistics
  • inv_test.df: degrees of freedom
  • inv_test.pval: p-values

Parameter names:

• alpha: scale parameter
• R2_inv: degree of invertibility
• R2_recov: degree of recoverability
• FVR: forecast variance ratio
• FVD: forecast variance decomposition

See the empirical application for a concrete example. Additional optional arguments to SMVAIV_estim.m are listed at the top of the function.