Effect of climate and geography on worldwide fine resolution economic activity

mode, but the nMAE remains relatively high and equal to about 0.45 and 0.40, respectively. As an additional check, the performance of the RF model is also tested using the out-of-bag (OOB) prediction statistics (this is computed using withheld data within the sample used by the RF trees, and a useful benchmark). The ranked top 10 variables are shown in Table 4 and in Fig 3. The latter shows how the nMAE, and the correlation, levels off after six-seven predictors, even if some small error reduc- tions are seen with the subsequent predictors. Thus, while we retain the top 10 variables (as a round number) to display the asymptotic behaviour of the error, the focus should mainly be on the top five-six variables. Our analysis confirms that latitude is the dominant predictor for GCP-PC. However, it is also important to note that the nMAE with latitude only is around 0.65, hence relatively large, compared to the asymptotic value of ca. 0.15, obtained when at least six predictors are used. The limitations of using latitude-only are also apparent from the geographical reconstruction map (see Fig 4, top left). It is also worth noting that the mean air temperature, which is some- times used as the main geographical variable instead of latitude in economic studies (e.g. [9]), in our data has a large, but not excessively so, linear correlation with latitude, namely 0.65. Somewhat unexpectedly, however, the second most important variable is a meteorological var- iable, and specifically MSLP SD S, namely the month-to-month variations of mean sea level

pressure (or just air pressure). This variable reduces the nMAE to 0.44, when added to latitude. Table 4. Top 10 predictors and (�) their one-to-one linear correlation coefficient with GCP-PC for the cases of all-grid-point, top tercile, middle tercile, and bottom tercile. Green cells indicate predictors in common with the four cases, light blue in common with three cases and purple in common with two cases. Highlighted in salmon are the largest one-to-one correlation values for each of the four cases. All grid points Top tercile Middle tercile Bottom tercile Rank Predictor Corr.� Predictor Corr.� Predictor Corr.� Predictor Corr.� 1 Latitude 0.35 MSLP top Q 0.05 Latitude 0.24 Latitude 0.30 2 MSLP SD S -0.05 Dist. M. River 0.06 MSLP SD S 0.08 Dist. M. River -0.13 3 Dist. M. River -0.07 Latitude 0.06 Dist. M. River -0.09 Dist. Ocean -0.03 4 MSLP +ve ch (1) 0.42 Dew Point SD S 0.00 Dew Point bot. Q -0.36 MSLP SD 0.33 5 Solar Rad median 0.45 MSLP SD 0.07 MSLP SD 0.35 Dew Point bot. Q -0.23 6 Dist. Lake 0.00 Dist. River -0.03 Dist. River -0.16 Dist. Lake 0.20 7 Dist. River 0.06 MSLP SD S -0.22 Dew Point SD S 0.29 Solar Rad median -0.18 8 Dew Point SD S 0.23 MSLP +ve ch (1) -0.23 Dist. Lake -0.28 MSLP mean 0.18 9 Dist. Ocean -0.08 Dist. Lake -0.05 MSLP +ve ch (1) 0.33 MSLP +ve ch (3) 0.32 10 MSLP mean 0.26 Dist. Ocean 0.06 Solar Rad bot. Q -0.36 Dist. River 0.17 https://doi.org/10.1371/journal.pone.0229243.t004

Table 3. Comparison statistics for different number of variables and different models (RF, GB and ML) and for all grid points (first two columns), the top tercile of GCP-PC (third and fourth columns, the middle tercile of GCP-PC (fifth and sixth columns), the bottom tercile of GCP-PC (last two columns). OOB stands for Out- of-bag prediction (a feature of the RF model). The top 10 predictors have been selected using the procedure described in the Methodology section. The row with the top 10 predictors for RF, which is used in the rest of the study, has been highlighted in grey. All grid points Top tercile Middle tercile Bottom tercile nMAE CORR nMAE CORR nMAE CORR nMAE CORR RF 121 (all) variables (OOB) 0.152 0.970 0.276 0.893 0.386 0.840 0.251 0.909 RF 121 (all) variables (5-fold) 0.162 0.966 0.291 0.885 0.403 0.830 0.262 0.906 GB 121 (all) variables (5-fold) 0.346 0.874 0.449 0.755 0.526 0.699 0.386 0.822 RF top 10 predictors (5-fold) 0.153 0.970 0.262 0.898 0.385 0.839 0.250 0.910 GB top 10 predictors (5-fold) 0.368 0.862 0.500 0.695 0.534 0.690 0.417 0.800 ML top 10 predictors (5-fold) 0.600 0.679 0.764 0.314 0.730 0.453 0.661 0.533 https://doi.org/10.1371/journal.pone.0229243.t003 PLOS ONE Effect of geography on fine resolution economy PLOS ONE | https://doi.org/10.1371/journal.pone.0229243 March 2, 2020 8 / 20