diff --git a/docs/book/content/calibration/demographics.md b/docs/book/content/calibration/demographics.md index ce09f62..9f09f24 100644 --- a/docs/book/content/calibration/demographics.md +++ b/docs/book/content/calibration/demographics.md @@ -293,7 +293,7 @@ We discuss the approach to estimating fertility rates $f_{s,t}$, mortality rates Theoretical steady-state population distribution vs. population distribution at period $t=120$ ``` - Further, we find that the maximum absolute difference between the population levels $\hat{\omega}_{s,t}$ and $\hat{\omega}_{s,t+1}$ was $1.3852\times 10^{-5}$ after 160 periods. That is to say, that after 160 periods, given the estimated mortality, fertility, and immigration rates, the population has not achieved its steady state. For convergence in our solution method over a reasonable time horizon, we want the population to reach a stationary distribution after $T$ periods. To do this, we artificially impose that the population distribution in period $t=120$ is the steady-state. As can be seen from {numref}`Figure %s `, this assumption is not very restrictive. {numref}`Figure %s ` shows the change in immigration rates that would make the period $t=120$ population distribution equal be the steady-state. The maximum absolute difference between any two corresponding immigration rates in {numref}`Figure %s ` is 0.0028. + Further, we find that the maximum absolute difference between the population levels $\hat{\omega}_{s,t}$ and $\hat{\omega}_{s,t+1}$ was less than $1\times 10^{-4}$ after 160 periods. That is to say, that after 160 periods, given the estimated mortality, fertility, and immigration rates, the population has not achieved its steady state. For convergence in our solution method over a reasonable time horizon, we want the population to reach a stationary distribution after $T$ periods. To do this, we artificially impose that the population distribution in period $t=120$ is the steady-state. As can be seen from {numref}`Figure %s `, this assumption is not very restrictive. {numref}`Figure %s ` shows the change in immigration rates that would make the period $t=120$ population distribution equal be the steady-state. The maximum absolute difference between any two corresponding immigration rates in {numref}`Figure %s ` is very small. ```{figure} ./images/OrigVsAdjImm.png --- @@ -303,7 +303,7 @@ We discuss the approach to estimating fertility rates $f_{s,t}$, mortality rates Original immigration rates vs. adjusted immigration rates to make fixed steady-state population distribution ``` - The most recent year of population data come from {cite}`Census:2015` population estimates for both sexes for 2013. We those data and use the population transition matrix {eq}`EqPopLOMstatmat2` to age it to the current model year of 2015. We then use {eq}`EqPopLOMstatmat2` to generate the transition path of the population distribution over the time period of the model. {numref}`Figure %s ` shows the progression from the 2013 population data to the fixed steady-state at period $t=120$. The time path of the growth rate of the economically active population $\tilde{g}_{n,t}$ is shown in {numref}`Figure %s `. + We begin with 2023 population data and use the population transition matrix {eq}`EqPopLOMstatmat2` to age it to the start year of the model (e.g., 2024 or 2025). We then use {eq}`EqPopLOMstatmat2` to generate the transition path of the population distribution over the time period of the model. {numref}`Figure %s ` shows the progression from the 2023 population data to the fixed steady-state at period $t=120$. The time path of the growth rate of the economically active population $\tilde{g}_{n,t}$ is shown in {numref}`Figure %s `. ```{figure} ./images/pop_distribution.png ---