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

Table 4.

Sensitivity of Selected Results to the Prior for σm, the Number of Low-Frequency Periodic Functions Used (q), and Sample Period

a. Posterior for f process (in percentage points)
σΔaσm
Percentiles of posteriorPercentiles of posterior
Prior for σmqStart Date0.170.500.840.170.500.84
Baseline 16 1900 2.70 3.33 4.14 0.73 1.13 1.52 
0.5 × Baseline 16 1900 2.95 3.55 4.3 0.33 0.56 0.76 
1.5 × Baseline 16 1900 2.52 3.10 3.84 1.1 1.69 2.29 
Baseline 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 1950 1.25 1.76 2.57 1.05 1.37 1.68 
  Using Y/L instead of Y/Pop 
Baseline, 1950–2017 1950 1.22 1.78 2.71 1.13 1.45 1.76 
a. Posterior for f process (in percentage points)
σΔaσm
Percentiles of posteriorPercentiles of posterior
Prior for σmqStart Date0.170.500.840.170.500.84
Baseline 16 1900 2.70 3.33 4.14 0.73 1.13 1.52 
0.5 × Baseline 16 1900 2.95 3.55 4.3 0.33 0.56 0.76 
1.5 × Baseline 16 1900 2.52 3.10 3.84 1.1 1.69 2.29 
Baseline 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 1950 1.25 1.76 2.57 1.05 1.37 1.68 
  Using Y/L instead of Y/Pop 
Baseline, 1950–2017 1950 1.22 1.78 2.71 1.13 1.45 1.76 

b. Posterior for c process (pooled across all countries)
Half-life (years)σ(ct+50-ct)
Percentiles of posteriorPercentiles of posterior
Prior for σmqStart Date0.170.500.840.170.500.84
Baseline 16 1900 130 233 389 0.44 0.63 0.86 
0.5 × Baseline 16 1900 129 232 387 0.45 0.63 0.86 
1.5 × Baseline 16 1900 130 233 391 0.45 0.63 0.86 
Baseline 1900 107 209 398 0.43 0.66 0.94 
Baseline 23 1900 137 245 395 0.44 0.60 0.82 
Baseline 1950 120 229 438 0.39 0.66 0.92 
  Using Y/L instead of Y/Pop 
Baseline, 1950–2017 1950 119 252 479 0.35 0.61 0.91 
b. Posterior for c process (pooled across all countries)
Half-life (years)σ(ct+50-ct)
Percentiles of posteriorPercentiles of posterior
Prior for σmqStart Date0.170.500.840.170.500.84
Baseline 16 1900 130 233 389 0.44 0.63 0.86 
0.5 × Baseline 16 1900 129 232 387 0.45 0.63 0.86 
1.5 × Baseline 16 1900 130 233 391 0.45 0.63 0.86 
Baseline 1900 107 209 398 0.43 0.66 0.94 
Baseline 23 1900 137 245 395 0.44 0.60 0.82 
Baseline 1950 120 229 438 0.39 0.66 0.92 
  Using Y/L instead of Y/Pop 
Baseline, 1950–2017 1950 119 252 479 0.35 0.61 0.91 

c. 100-year-ahead predictive distributions for average growth rates (PAAR)
Global factor (ft)2017-population weighted average of country growth rates
Percentiles of posteriorPercentiles of posterior
Prior for σmqStart date0.170.500.840.170.500.84
Baseline 16 1900 0.92 1.87 2.72 1.06 2.04 2.96 
0.5 × Baseline 16 1900 1.34 1.97 2.64 1.45 2.17 2.87 
1.5 × Baseline 16 1900 0.53 1.75 2.88 0.69 1.95 3.11 
Baseline 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 1950 0.86 1.84 2.75 1.03 2.05 3.02 
  Using Y/L instead of Y/Pop 
Baseline 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 (ft)2017-population weighted average of country growth rates
Percentiles of posteriorPercentiles of posterior
Prior for σmqStart date0.170.500.840.170.500.84
Baseline 16 1900 0.92 1.87 2.72 1.06 2.04 2.96 
0.5 × Baseline 16 1900 1.34 1.97 2.64 1.45 2.17 2.87 
1.5 × Baseline 16 1900 0.53 1.75 2.88 0.69 1.95 3.11 
Baseline 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 1950 0.86 1.84 2.75 1.03 2.05 3.02 
  Using Y/L instead of Y/Pop 
Baseline 1950 0.65 1.72 2.70 0.78 1.88 2.96 

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