*! version 1.0.1 27may2026

Title

dnqr_impulse -- Tail-event impulse response (post-estimation)

Syntax

dnqr_impulse , network(name) horizon(#)
[options]

Required
network(name) adjacency / weights matrix used in estimation

horizon(#) IRF horizon (>= 1)

Quantile and shock
quantile(#) quantile at which to evaluate; default = the middle column of e(quantile)

shocknode(#) node receiving the unit shock; default 1

shocksize(#) size of the shock; default 1

Network handling
mata declare that network() is a Mata matrix

rowstd row-standardise W

Plot
plot draw a line plot of the top nodes by peak |IRF|

top(#) number of nodes plotted (default 6)

scheme(string) graphics scheme

name(string) graph name (default dnqrimpulse)

saving(filename) save the graph to disk

title(string) custom title

Description

dnqr_impulse computes the tail-event-driven impulse response of the
reduced-form network process at a chosen quantile. Letting
gamma1(tau), gamma2(tau), gamma3(tau) denote the
contemporaneous, lagged-network and own-lag coefficients from the most
recent dnqr or nqar estimation, the one-step propagation
matrix is

G(tau) = (I - gamma1(tau) W)-1 * (gamma2(tau) W
+ gamma3(tau) I)

A unit shock v0 = e_j is applied to the chosen node and propagated
forward for H periods as G(tau)h v0. For NQAR the
contemporaneous term drops out so G simplifies to gamma2 W
+ gamma3 I. See Zhu et al. (2019) Section 3 and Xu et al. (2024).

Options

network(name) adjacency / weights matrix; must be the same
W that was used in estimation.

horizon(#) number of propagation steps (>= 1).

quantile(#) the quantile at which to evaluate the IRF. Must
be one of the values stored in e(quantile). Default = middle
column.

shocknode(#) index of the node that receives the initial
shock (1..N).

shocksize(#) magnitude of the initial shock (default 1).

mata indicates the network matrix is in Mata.

rowstd row-standardises W before propagation.

plot draws the IRF for the top responding nodes.

top(#) controls how many nodes are plotted (sorted by the
peak |IRF| over the horizon).

scheme/name/saving/title cosmetic graph options.

Examples

. dnqr y, network(W) rowstd q(0.1 0.5 0.9) z(Z1 Z2) factors(F1 F2)

. * IRF at the upper tail; plot top-5 reactive nodes

. dnqr_impulse, network(W) rowstd horizon(12) quantile(0.9) shocknode(1) plot top(5)

. * harvest the IRF matrix for custom analysis

. matrix IRF = r(irf)

. matrix list IRF

Returned results (r-class)

r(tau) quantile used

r(gamma1) contemporaneous coefficient

r(gamma2) lagged-network coefficient

r(gamma3) own-lag coefficient

r(irf) N x (H+1) matrix of impulse trajectories

r(norms) 2 x (H+1) matrix: row 1 = L2 norm of IRF at each horizon, row 2 = max |IRF|

References

Xu, X., W. Wang, Y. Shin, and C. Zheng. 2024. Dynamic Network
Quantile Regression Model. SSRN Working Paper 3690631.

Zhu, X., W. Wang, H. Wang, and W. K. Härdle. 2019. Network quantile
autoregression. Journal of Econometrics 212(1): 345-358.

Also see

Package TOC: dnqrlib

Estimators: nqar, dnqr

Plotting: dnqr_plot, dnqr_postestimation

Author: Dr Merwan Roudane -
merwanroudane920@gmail.com