MIT Press

We investigated the sensitivity of the model to several key assumptions, three of which we discuss here. The first is the prior distribution for $σ_{m}$ ⁠, the long-run standard deviation of the growth rate trend for $f_{t}$ in equation (5). The results are summarized in table 4.

Table 4.

Sensitivity of Selected Results to the Prior for $σ_{m}$ ⁠, the Number of Low-Frequency Periodic Functions Used $(q)$ ⁠, and Sample Period

a. Posterior for $f$ process (in percentage points)
			$σ_{Δ a}$			$σ_{m}$
			Percentiles of posterior			Percentiles of posterior
Prior for $σ_{m}$	$q$	Start Date	0.17	0.50	0.84	0.17	0.50	0.84
Baseline	16	1900	2.70	3.33	4.14	0.73	1.13	1.52
0.5 $\times$ Baseline	16	1900	2.95	3.55	4.3	0.33	0.56	0.76
1.5 $\times$ Baseline	16	1900	2.52	3.10	3.84	1.1	1.69	2.29
Baseline	9	1900	1.91	2.91	4.19	0.81	1.29	1.68
Baseline	23	1900	3.40	3.95	4.66	0.65	1.05	1.52
Baseline	9	1950	1.25	1.76	2.57	1.05	1.37	1.68
		Using $Y / L$ instead of $Y / P o p$
Baseline, 1950–2017	9	1950	1.22	1.78	2.71	1.13	1.45	1.76

a. Posterior for $f$ process (in percentage points)
			$σ_{Δ a}$			$σ_{m}$
			Percentiles of posterior			Percentiles of posterior
Prior for $σ_{m}$	$q$	Start Date	0.17	0.50	0.84	0.17	0.50	0.84
Baseline	16	1900	2.70	3.33	4.14	0.73	1.13	1.52
0.5 $\times$ Baseline	16	1900	2.95	3.55	4.3	0.33	0.56	0.76
1.5 $\times$ Baseline	16	1900	2.52	3.10	3.84	1.1	1.69	2.29
Baseline	9	1900	1.91	2.91	4.19	0.81	1.29	1.68
Baseline	23	1900	3.40	3.95	4.66	0.65	1.05	1.52
Baseline	9	1950	1.25	1.76	2.57	1.05	1.37	1.68
		Using $Y / L$ instead of $Y / P o p$
Baseline, 1950–2017	9	1950	1.22	1.78	2.71	1.13	1.45	1.76

View Large

b. Posterior for $c$ process (pooled across all countries)
			Half-life (years)			$σ_{(c_{t + 50} - c_{t})}$
			Percentiles of posterior			Percentiles of posterior
Prior for $σ_{m}$	$q$	Start Date	0.17	0.50	0.84	0.17	0.50	0.84
Baseline	16	1900	130	233	389	0.44	0.63	0.86
0.5 $\times$ Baseline	16	1900	129	232	387	0.45	0.63	0.86
1.5 $\times$ Baseline	16	1900	130	233	391	0.45	0.63	0.86
Baseline	9	1900	107	209	398	0.43	0.66	0.94
Baseline	23	1900	137	245	395	0.44	0.60	0.82
Baseline	9	1950	120	229	438	0.39	0.66	0.92
		Using $Y / L$ instead of $Y / P o p$
Baseline, 1950–2017	9	1950	119	252	479	0.35	0.61	0.91

b. Posterior for $c$ process (pooled across all countries)
			Half-life (years)			$σ_{(c_{t + 50} - c_{t})}$
			Percentiles of posterior			Percentiles of posterior
Prior for $σ_{m}$	$q$	Start Date	0.17	0.50	0.84	0.17	0.50	0.84
Baseline	16	1900	130	233	389	0.44	0.63	0.86
0.5 $\times$ Baseline	16	1900	129	232	387	0.45	0.63	0.86
1.5 $\times$ Baseline	16	1900	130	233	391	0.45	0.63	0.86
Baseline	9	1900	107	209	398	0.43	0.66	0.94
Baseline	23	1900	137	245	395	0.44	0.60	0.82
Baseline	9	1950	120	229	438	0.39	0.66	0.92
		Using $Y / L$ instead of $Y / P o p$
Baseline, 1950–2017	9	1950	119	252	479	0.35	0.61	0.91

View Large

c. 100-year-ahead predictive distributions for average growth rates (PAAR)
			Global factor $(f_{t})$			2017-population weighted average of country growth rates
			Percentiles of posterior			Percentiles of posterior
Prior for $σ_{m}$	$q$	Start date	0.17	0.50	0.84	0.17	0.50	0.84
Baseline	16	1900	0.92	1.87	2.72	1.06	2.04	2.96
0.5 $\times$ Baseline	16	1900	1.34	1.97	2.64	1.45	2.17	2.87
1.5 $\times$ Baseline	16	1900	0.53	1.75	2.88	0.69	1.95	3.11
Baseline	9	1900	0.65	1.67	2.63	0.85	1.92	2.91
Baseline	23	1900	0.97	1.89	2.81	1.09	2.04	3.01
Baseline	9	1950	0.86	1.84	2.75	1.03	2.05	3.02
		Using $Y / L$ instead of $Y / P o p$
Baseline	9	1950	0.65	1.72	2.70	0.78	1.88	2.96

c. 100-year-ahead predictive distributions for average growth rates (PAAR)
			Global factor $(f_{t})$			2017-population weighted average of country growth rates
			Percentiles of posterior			Percentiles of posterior
Prior for $σ_{m}$	$q$	Start date	0.17	0.50	0.84	0.17	0.50	0.84
Baseline	16	1900	0.92	1.87	2.72	1.06	2.04	2.96
0.5 $\times$ Baseline	16	1900	1.34	1.97	2.64	1.45	2.17	2.87
1.5 $\times$ Baseline	16	1900	0.53	1.75	2.88	0.69	1.95	3.11
Baseline	9	1900	0.65	1.67	2.63	0.85	1.92	2.91
Baseline	23	1900	0.97	1.89	2.81	1.09	2.04	3.01
Baseline	9	1950	0.86	1.84	2.75	1.03	2.05	3.02
		Using $Y / L$ instead of $Y / P o p$
Baseline	9	1950	0.65	1.72	2.70	0.78	1.88	2.96

View Large

This Feature Is Available To Subscribers Only