The goal of DTtiming is to estimate the timing of the demographic transition using the model by Delventhal, Fernandez-Villaverde, and Guner (2023)
You can install the development version of DTtiming like so:
remotes::install_github("https://github.com/m-g-h/DTtiming")Setup example data:
library(DTtiming)
library(ggplot2)
## Create example data:
T_max = 100
t = 1950+(1:T_max)
tau_2 = 2000
tau_3 = 2025
y = matrix(make_z1_scalar(t, tau_2, tau_3)*10 + rnorm(T_max, sd = 0.2),
ncol = 1)
# Plot the data:
ggplot(data.frame(x = t,
y = y),
aes(x = x, y = y)) +
geom_point()
Now we can fit the model:
DT_fit = grid_Search_best_DT_fit(y)
plot_DT_fit(DT_fit)
All relevant parameters are returned:
DT_fit
#> $alpha
#> alpha_1 alpha_3
#> 9.995653271 -0.004006004
#>
#> $sigma_sq
#> sigma_sq_1 sigma_sq_3
#> 0.03993147 0.04411771
#>
#> $tau
#> tau_2 tau_3
#> 50 75
#>
#> $y
#> [1] 9.778335878 9.746206272 10.502007190 10.009691704 9.806878834
#> [6] 10.052783039 9.962129142 10.048436901 9.451010166 9.939745051
#> [11] 10.261685758 9.804002748 9.875303533 10.381729420 10.034761826
#> [16] 10.187610486 9.757610336 9.953055668 9.957150813 9.977056609
#> [21] 9.955638086 9.611269617 10.040870006 10.073008441 9.887960918
#> [26] 9.836340783 10.152124320 9.682753062 10.090093782 9.645082948
#> [31] 9.877686401 9.950349820 10.057980428 10.028116758 9.923932361
#> [36] 10.184358161 9.593299362 10.248139680 10.038237185 10.272491366
#> [41] 10.095585310 10.003994938 10.020377432 10.134691405 9.926175822
#> [46] 10.099570996 10.471493981 10.242249915 10.106899664 9.927156112
#> [51] 9.488703297 8.894230697 8.784071962 8.562633310 8.021322943
#> [56] 7.547481786 7.467006463 6.881295521 6.636532362 6.171618920
#> [61] 5.566847473 5.098184384 4.514286251 4.544126875 3.871268596
#> [66] 3.369698407 3.492537413 2.680955318 2.451824957 2.018175277
#> [71] 1.911467418 1.267722881 0.606147351 0.754163306 -0.275136096
#> [76] 0.063529423 0.224959948 -0.070460794 -0.360395942 0.376174598
#> [81] -0.118426738 -0.003743479 -0.360079259 -0.135952699 -0.057007220
#> [86] 0.294625021 -0.033572858 -0.121094362 -0.254093893 0.241040102
#> [91] 0.231601627 0.151532580 -0.185003515 -0.212212303 -0.012761739
#> [96] 0.071908999 -0.065604139 0.251360559 0.188830995 -0.519167724
#>
#> $y_hat
#> [1] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [6] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [11] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [16] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [21] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [26] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [31] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [36] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [41] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [46] 9.995653271 9.995653271 9.995653271 9.995653271 9.995653271
#> [51] 9.595666900 9.195680529 8.795694158 8.395707787 7.995721416
#> [56] 7.595735045 7.195748674 6.795762303 6.395775932 5.995789561
#> [61] 5.595803190 5.195816819 4.795830448 4.395844077 3.995857706
#> [66] 3.595871335 3.195884964 2.795898593 2.395912222 1.995925851
#> [71] 1.595939480 1.195953109 0.795966738 0.395980367 -0.004006004
#> [76] -0.004006004 -0.004006004 -0.004006004 -0.004006004 -0.004006004
#> [81] -0.004006004 -0.004006004 -0.004006004 -0.004006004 -0.004006004
#> [86] -0.004006004 -0.004006004 -0.004006004 -0.004006004 -0.004006004
#> [91] -0.004006004 -0.004006004 -0.004006004 -0.004006004 -0.004006004
#> [96] -0.004006004 -0.004006004 -0.004006004 -0.004006004 -0.004006004
#>
#> $RSS
#> [1] 4.423988Delventhal, Matthew J, Jesus Fernandez-Villaverde, and Nezih Guner. 2023. “Demographic Transitions Across Time and Space.” Working {{Paper}} 2022-031. Chicago: HCEO Human Capital and Economic Opportunity Global Working Group.
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