Effect of climate and geography on worldwide fine resolution economic activity

meteorology and GCP are stationary over the period considered, namely 1979–2016 for the meteorological variables, and the four years of G-Econ, 1990, 1995, 2000 and 2005 for the GCP. A temporal correlation between GCP and climate, while possible, would not yield robust statistical results as GCP is only available for four years. Clearly within any given period the cli- mate will vary, but the wide-ranging statistical characteristics we use here are designed to take into accounts such variations. More importantly, GCP changes in parts of the globe, particu- larly for China, over the G-Econ period. Accordingly, the stationarity assumption for GCP has been tested by perturbing it with GCP plus and minus one standard deviation (computed using the four years available), respectively: in both cases, the main predictors are the same as for the (mean) GCP, thus confirming the validity of this assumption (not shown). Because a single target (or predictand), namely the GCP for each geographical location, is required, this is taken as the average of the four years in G-Econ. To reduce the noise in the analysis, grid cells where the GCP is smaller than 1 USD are not considered. Also, as normally done [e.g. 4], GCP is converted into a logarithm (base 10). The (log of the) GCP thus com- puted is shown in S1 Fig while the corresponding GCP-PC can be seen in Fig 1. Its Probability Density Function (PDF) is shown in Fig 2. As already remarked, the focus of this work is the assessment of the dependency of GCP-PC on climate and geography variables. Formally this can be expressed as:

GCP PC ¼ f ðGeography; ClimateÞ þ hðInstitutions; National Resources; . . .Þ þ ε |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} GCP PC ¼ f ðGeography; ClimateÞ þ d ð1Þ where ε is the error term, which captures factors controlling GCP-PC not accounted for by the other terms, therefore including errors in GCP, climate and geography variables; δ is a term not explicitly modelled in this work. By assessing the spatial geographical patterns of δ it may be possible to identify the source of potential mismatches, or residual, between GCP-PC and the geography and climate predictors used here through the modelled function, f. However, a direct assessment of the role of institutions is discussed in the next section. The main tool used in our analysis is a non-linear statistical model called Random Forests (RF). This is a well-known and popular method consisting of a set of decision trees built to minimise their correlation [24, 25]. The model has been chosen after a comparison with other models, Gradient Boosting (GB, a non-linear statistical model) [25] and the multi-linear (ML) regression model, following extensive tests of tuning hyper-parameters, using the caret (Classi- fication And REgression Training) package in R. With the RF model the issue of overfitting Table 2. Geography parameters. Aside from latitude and elevation (the latter has been taken from the ERA-Interim

reanalysis), the other variables are from the G-Econ dataset. Geography parameter Unit Latitude Degrees Elevation m Distance to coast 1 km Distance to coast 2 km Distance to Lake km Distance to Major River km Distance to River km Distance to Ocean km Vegetation category category [0–31] Soil category category [0–250] https://doi.org/10.1371/journal.pone.0229243.t002 PLOS ONE Effect of geography on fine resolution economy PLOS ONE | https://doi.org/10.1371/journal.pone.0229243 March 2, 2020 5 / 20