Algorithm 2.

Estimation for the infinite-horizon setting

Input: Observed data $\left\{\left(A_{it},{\mathit{M}}_{it},R_{it}\right):i=1,\dots ,n,t=1,\dots ,T\right\}$, the number of bootstrap samples $B$, and the significance level $\alpha$.
Output: Estimated individual mediation effect ${\widehat{\eta }}_j^{(\infty )}$, for $j=1,\dots ,d$.
1:	Pool data across all $t$ stages, $t=1,\dots ,T$.
2:	Estimate parameters $\widehat{\mathit{W}},{\widehat{𝚯}}_1,{\widehat{𝚯}}_2$ using the pooled data.
3:	Estimate ${\mathit{\theta }}_{M_{1j}\to {\mathit{M}}_1}$ and ${\theta }_{M_{1j}\to R_1}$ using the pooled data.
4:	Compute ${\mathit{B}}_1$ to ${\mathit{B}}_7$ using (25).
5:	Compute ${\widehat{\eta }}_j^{(\infty )}$ using (24).
6:	for $b=1,\dots ,B$ do
7:	Sample $n$ trajectories from the observed data with replacement.
8:	Repeat Lines 1 to 5 to compute ${\hat{\eta }}_j^{(\infty ,b)}$ using the bootstrap samples.
9:	end for
10:	Construct the CI $\left[{\widehat{\eta }}_j^{(\infty ,L)},{\widehat{\eta }}_j^{(\infty ,U)}\right]$ for ${\eta }_j^{(\infty )}$, where ${\widehat{\eta }}_j^{(\infty ,L)}$ and ${\widehat{\eta }}_j^{(\infty ,U)}$ are the empirical lower and upper $\alpha /2$ quantiles of ${\left\{{\widehat{\eta }}_j^{(\infty ,b)}\right\}}_{b=1}^B$, respectively.