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Statistical learning for climate-GDP panels: Data cleaning, flexible trend controls, and predictive validation [1]

['Christof Schötz', 'Department Of Aerospace', 'Geodesy', 'Munich Climate Center', 'Earth System Modelling Group', 'Tum School Of Engineering', 'Design', 'Technical University Of Munich', 'Munich', 'Research Department']

Date: 2026-08 

Abstract We assess the panel-regression approach to climate econometrics—the dominant framework for estimating the effect of climate on GDP in global country–year data—using modern statistical learning techniques. Common implementations are sensitive to outliers, do not fully account for the dependence structure across countries and years, and rarely combine formal model selection with genuine out-of-sample evaluation. To address these issues, we implement knowledge-based data cleaning, nonparametric time-trend controls, and out-of-sample validation across 700 + climate variables. Our analysis reveals that widely used models and predictors—such as mean temperature—have little out-of-sample predictive power. A previously overlooked humidity-related variable emerges as the most consistent predictor, though even its performance remains limited. These findings question the robustness of common empirical practices in this literature and point toward a more data-driven approach built on data cleaning, flexible trend controls, and predictive validation.

Citation: Schötz C, Hassel J, Otto C (2026) Statistical learning for climate-GDP panels: Data cleaning, flexible trend controls, and predictive validation. PLOS Clim 5(7): e0000962. https://doi.org/10.1371/journal.pclm.0000962 Editor: María Dolores Gadea Rivas, University of Zaragoza, SPAIN Received: January 29, 2026; Accepted: June 20, 2026; Published: July 20, 2026 Copyright: © 2026 Schötz et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All data and code necessary to reproduce the results are publicly available at https://doi.org/10.5281/zenodo.20415574. Funding: J.H. and C.O. acknowledge support from the European Union’s Horizon Europe research and innovation programme under grant agreement No. 101081358 (ACCREU) and No. 101135481 (COMPASS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction Climate econometrics is the study of how weather, climate, and climate change affect economic outcomes using statistical methods. Understanding these relationships is essential for informing policy, managing climate-related risks, and guiding adaptation strategies. As interest in the economic implications of climate variability and change has grown, the field has developed at the intersection of economics, climate science, and statistics [1,2]. A widely used empirical approach in climate econometrics is fixed effects panel data regression, where macroeconomic indicators—such as a country’s GDP—are regressed on climate variables like average annual temperature. This method aims to quantify the extent to which economic variation can be statistically attributed to fluctuations in climatic conditions. Fixed effects account for time-invariant country characteristics and global shocks shared across countries, while additional controls, such as country-specific time trends, are often included to capture heterogeneous growth trajectories. Numerous influential studies have adopted this methodology using global country-year panel datasets. For example, Dell et al. [3] estimate linear effects of temperature and precipitation on economic output, finding that higher temperatures negatively affect economic growth in poorer countries. Burke et al. [4] extend this framework by including quadratic terms for temperature and precipitation as well as quadratic time trends, uncovering a significant nonlinear (inverted U-shaped) relationship between temperature and GDP growth. Pretis et al. [5] incorporate measures of monthly variance and extreme temperatures, along with dummy variables for outlier events, to assess differences in projected economic damages under 1.5° C and 2° C warming scenarios. Other contributions have expanded the analysis by increasing the spatial resolution of the panel. Kalkuhl and Wenz [6] use economic data of subnational regions to explore temperature effects. Continuing the analysis of subnational data, Kotz et al. [7] investigate the role of intra-annual temperature variability, while Kotz et al. [8] examine the effects of diverse precipitation-related indicators. Newell et al. [9] assess model performance through out-of-sample testing, finding no significant predictive power of temperature on GDP growth, though more robust effects are observed for GDP levels. Kahn et al. [10] study deviations from long-term temperature norms, and Krichene et al. [11] incorporate extreme weather events to examine longer-term macroeconomic consequences. Several meta-analyses and review articles provide a broader synthesis of this literature and the methodologies it employs [1,2,12–17]. A related strain of literature emphasizes spatial heterogeneity in climate impacts and the role of adaptation through migration, trade, and innovation, as reviewed by Desmet and Rossi-Hansberg [18]. A separate tradition within climate econometrics, surveyed by Castle and Hendry [19], works in a time-series rather than panel-regression framework and emphasizes explicit modeling of non-stationarity, structural breaks, and the underlying data generating process. The present paper contributes to the panel-regression strand with control variables, while engaging formally with time series stationarity in Section A.2 in S1 Appendix and with the temporal stability of estimated relationships in Stationarity. While fixed effects panel regression is a standard tool in applied econometrics [20,21], its limitations have received increasing attention. Hill et al. [22] and Imai and Kim [23] emphasize that the validity of such models hinges on strong assumptions about functional form, treatment homogeneity, and independence, which are often untested in practice. Violations of these assumptions can create unreliable and misleading findings. Although techniques such as out-of-sample testing and formal variable selection are standard in other empirical disciplines, they are rarely applied in the current climate econometrics literature. This limits the robustness and generalizability of existing findings. In this article, we address several of these methodological gaps and present results based on more rigorous, data-driven approaches. While outliers and structural breaks have been treated within climate econometrics using model-based detection methods such as indicator saturation [5,19,24], we take a complementary and more granular approach. We distinguish between data errors, genuine non-climate shocks, and imputation artifacts, screening each using external, source-based knowledge together with correlation- and segment-based diagnostics. This lets us remove spurious observations while retaining the extreme-climate events we wish to study, and we provide a correspondingly cleaned dataset that enhances the robustness of our results. To address temporal confounding, we introduce nonparametric time trend controls that flexibly account for slowly evolving, country-specific characteristics. These controls avoid the arbitrary specification of polynomial time trends and their induced long-range serial correlation biases. In addition to examining temporal dependencies, we assess spatial correlation and its implications for standard error estimation. In our main analysis, we apply various statistical learning methods for variable selection and evaluate models in an out-of-sample framework to identify the most predictive climate indicators of GDP growth and levels. Our approach considers orders of magnitude more variables and models than any prior study in climate econometrics: we select from a pool of over 700 variables, resulting in roughly 10213 possibilities of predictor combinations. Among the methods, penalized regression techniques—LASSO, Ridge regression, and Elastic Net [25]—consistently yield the best predictive accuracy. The most robust predictor we identify is the squared maximum specific humidity of the previous year, which may influence economic activity through channels such as wet-bulb temperatures or extreme precipitation events. In contrast, commonly used variables such as mean annual temperature and its square show no predictive power, calling into question some earlier findings in the literature. Overall, even the best-performing models exhibit limited predictive power. We identify a lack of temporal stationarity as a possible reason for the limited out-of-sample predictive performance.

Setup We first provide a description of the basic statistical framework, the panel data regression, and the data and variables used in this framework. Panel data regression with fixed effects Our goal is to obtain empirical evidence of the influence of climate variables on a target economic variable . All variables are indexed by two dimensions: One is spatial (here: countries), denoted by . The other one is temporal (here: years), denoted by , where is a set of consecutive time points. Thus, the data forms a panel and panel data analysis methods can be applied. We do not assume that the panel is full, i.e., we may only observe certain region–time combinations for some index set . Denote the total number of observations as . To achieve our goal, we apply a linear regression model of the form (1) Here are features derived from the climate variables. These can, e.g., be transformations like or ; or time lags like , , ...; or interaction terms like . The terms are fixed effect variables, e.g., dummy variables for a given time point or time trends for a given region . The parameters , are unknown. They differ in that we are interested in statistical inference on , whereas are nuisance parameters that model unobserved effects that we want to control for but have no further interest in. The errors are modeled as centered random variables, which are normally distributed or fulfill moment conditions that allow to use asymptotic normality in later analysis. In matrix notation, we have (2) where (3) (4) (5) Aside from statistical inference on , we are also interested in variable selection to identify models with high predictive power for unseen observations. While our primary metric is predictive accuracy, this framework supports causal interpretation due to the strict exogeneity of weather shocks: short-term economic fluctuations do not influence concurrent climatic conditions. Consequently, a model that robustly predicts out-of-sample is plausibly capturing stable structural relationships rather than spurious correlations, thereby validating the causal links necessary for future projections. In order to find such a model, we need the set of selected features to be as small as possible while explaining as much as possible of the variation of the target . Model selection is explored in Step 3: Model Selection via Out-of-Sample Test. Year fixed effects cannot be estimated for unseen years, and time trends extrapolated forward are not guaranteed to remain predictive. With such time controls, the model is not intended to predict the absolute value of ; the goal is to identify the time-persistent influence of the climate features on . Data Our primary data source is the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP). Specifically, we utilize climate variables from the GSWP3-W5E5 dataset [26], the tropical cyclone data [27], as well as GDP (PPP) [28] and country-level population data [29]. In addition, we incorporate gridded population data from the History Database of the Global Environment (HYDE), version 3.3 [30]. To assess the robustness of our findings with respect to economic data sources, we also employ World Development Indicator GDP data [31]. All datasets are restricted to the period 1960–2018, and our analysis covers a total of 203 countries. Climate econometric model Our target variable in the regression is the economic growth rate , where is the gross domestic product per capita in country s and year t either using the ISIMIP or the World Bank data. Most of the predictor variables we use, are based on the 11 climate variables given in Table 1. All variables are first given as daily gridded ( ) values. For each grid cell, they are aggregated to yearly values using the mean, standard deviation, minimum, and maximum. This results in 44 variables indexed by grid cell and year. We have additional 12 variables derived from and (Table 1) by calculating the deviation from a rolling window of 11, 31, and 91 days ( , , , , , ) and the rate of extreme events larger than , , of the whole observation time distribution ( , , , , , ). All yearly gridded values are aggregated to country means using population as grid weights. Furthermore, we add the number of people affected by tropical cyclones of at least 34 knots, 48 knots and 64 knots ( , , ) to our mix of variables. We arrive at 44 + 12 + 3 = 59 variables. PNG larger image

TIFF original image Download: Table 1. Climate-related base variables from GSWP3-W5E5 and their descriptions. https://doi.org/10.1371/journal.pclm.0000962.t001 For each of the 59 base variables, we create linear and squared terms and up to 5 lags. This leaves us at predictors to choose from. We do not include lagged growth-rate terms on the right-hand side, following the standard specification in the climate-econometrics literature [4,3]. Instead, we rely on weather variables and time-dependent controls to capture dynamic effects. The country and year fixed effects together with the time-trend controls absorb a large part of the systematic economic variation in growth—persistent cross-country differences in development and growth regimes, globally common shocks, and slowly evolving country-specific trajectories—so that climate is evaluated against the residual, higher-frequency variation. Supporting a causal interpretation of the influence of climate on GDP would rest on the assumption that year-to-year climate anomalies are exogenous to contemporaneous economic activity. This assumption is plausible in our setting: the long-run channel through which economic activity affects climate via emissions operates at low frequency and is absorbed by our nonparametric time-trend controls. We have all variables in a base form ( ) and a difference form ( ), leading to two different kinds of regression models. We follow the terminology of Newell et al. [9] and distinguish a growth and a level regression, where the labels refer to whether the climate level is related to GDP growth or to the GDP level. In the growth regression, the climate predictors enter in original (level) form and relate directly to the growth-rate target . In the level regression, the predictors enter in differenced form ; since the target is also a difference, this is the differenced form of a relationship between the climate level and the GDP level , which is the source of the “level” label, even though the climate level itself does not appear explicitly in the estimated equation. We do not mix original and differenced predictors within the same model and do not delve into the interpretation of the two modeling strategies here. Instead, we refer readers to Newell et al. [9] for a detailed discussion and present results for both approaches. Summary statistics of all variables are given in Section A.1 in S1 Appendix. We verify in Section A.2 in S1 Appendix that the GDP growth-rate target and the differenced climate variables are stationary, and that the original climate variables show no detectable non-stationarity once our sufficient time-trend controls are included. Both modeling strategies therefore yield balanced regressions, so the choice between them is not pinned down by stationarity considerations and is best interpreted in economic terms, as discussed in Newell et al. [9].

Step 2: Controlling for global shocks and regional time trends To find evidence for a causal connection between economic and climate variables, we have to control for time-point specific and region specific effects. To illustrate, let us consider the following version of (1), (7) Here is a function that models the influence of the predictors on the response; is the global time-specific fixed effect (growth of the global economy in year t); is the region specific time trend control (the smooth time trend of economic growth of a given region), e.g., for a linear time trend; and models the remaining error of the model. The fixed effect accounts for time-specific shocks affecting all regions, such as global economic crises, while captures region-specific long-term trends in economic growth, such as persistent differences between developing and developed countries. The power of Frisch–Waugh–Lovell The number of control parameters for may be large while the total number of observations may be too small to accurately estimate their values. Fortunately, the Frisch–Waugh–Lovell (FWL) theorem demonstrates that this limitation has minimal impact on the accuracy of the estimator of the parameters of interest, . Recall the general regression setup introduced in Panel Data Regression with Fixed Effects. By the FWL theorem, the least squares estimate of the parameters of interest in the model is equivalent to the least squares estimate of in the transformed model (8) where the transformed variables and are obtained by removing the components explainable by . Specifically, and , with M being the linear projection onto the complement of the column space of : (9) where is the identity matrix. This result not only allows an accurate estimation of without precise estimation of , but also offers substantial computational advantages when analyzing panel data with many control variables. Given the raw data , we can streamline the computation by first creating the features to analyze. Next, we apply a control variable design and transform the target and features to obtain the controlled dataset . This preprocessing step decouples the estimation of from the high-dimensional controls, substantially reducing computational complexity. This approach is especially advantageous when the dimension q of is large relative to the dimension p of . For instance, in the example described in (6), we have 225 countries and 61 years, requiring q = 733 control parameters if quadratic time trends are included. In contrast, the parameter of interest, , has dimension p = 8. While q may still be manageable for a single regression, scenarios involving bootstrap or cross-validation (as discussed in Step 3: Model Selection via Out-of-Sample Test) often require thousands of regressions with the same controls. In such cases, the two-step procedure enabled by the FWL theorem provides immense computational benefits. Furthermore, covariance matrices needed for confidence intervals and hypothesis tests can be computed in the dimensions of the transformed model instead of dimensions of the original model equation (if small sample corrections are adjusted correctly). Local time trends To account for the long-term time trend of each country, the function in (7) must be specified. A common approach is to model as a polynomial in t, with the degree typically ranging from 0 (constant, capturing only the country-specific mean growth) to 3 (cubic, allowing for up to two changes in direction). While low-degree polynomials capture only simple trends, higher degrees may inadvertently remove meaningful information that should be attributed to the parameters of interest. However, polynomial time trends have notable drawbacks. First, practitioners must choose the polynomial degree, and there is no universally accepted rule for making this decision. This may (involuntarily) lead to p-hacking when the choice of polynomial degree is influenced by the desired claim of the research article. Second, even the best-fitting polynomial may fail to adequately approximate the time trend for all regions. Third, polynomials can also introduce artificial long-distance correlations, which may distort the results (see Fig 1). PNG larger image

TIFF original image Download: Fig 1. Effect of different control variable designs on temporal correlation of residual economic growth after controlling. Each black dot is an empirical correlation value between two different years calculated from the ISIMIP economic data. The gray curve shows a Loess smoother of these correlations. For each fixed temporal difference, we test whether the correlations values for pairs of years with this given difference are significantly different from zero via a conservative permutation test, see Section D in S1 Appendix. Furthermore, we apply the Benjamini-Hochberg correction (with false discovery rate level of 0.05) to account for the multiple testing issue. Blue and red triangles show correlations significantly different from zero, whereas green squares indicate that non-zero correlation cannot be detected. MAC is the mean absolute correlation. Without controls (None), we observe a high positive correlation for more than 20 years. If only year fixed effects are applied, the result is exactly the same as this only changes the means of the correlated variables. All polynomial time trends are able to reduce the positive correlation of small temporal difference, but introduce negative correlations of temporal differences between 3 and 14 (and more) years. Both local control designs remove correlations in later years. Only (mostly negative) correlations remain for temporal differences of six to seven years. Overall the Kernel-based method seems to show the best results. https://doi.org/10.1371/journal.pclm.0000962.g001 Rather than relying on polynomials, we propose a more flexible nonparametric approach that directly embodies the idea of a typical value for a given time period—longer than a single time point but shorter than the entire time interval. Specifically, we use a local linear estimator for the time trend. We refer to this method as Window and Kernel, respectively, depending on whether all observations are weighted equally or according to a quadratic kernel. These local linear methods resemble a rolling window approach (local constant) but offer statistical advantages, particularly near the edges of the time interval [34]. An alternative nonparametric time trend approach using basis functions instead of local regression can be found in Kneip et al. [35]. As with the rolling window method, the local linear estimator requires a parameter to define how much of the surrounding data influences the estimate at each time point. This parameter, known as the bandwidth, determines the threshold for considering neighboring time points when calculating the trend. To make the method fully automatic, we propose using leave-one-out cross-validation with the economic response variable as target to select the optimal bandwidth. The automatically selected values are such that 10–12 years before and after a given year are used to calculate the local time trend. Figs 1 and 2 contrast the temporal and spatial correlations, respectively, resulting from different control variable designs. The local linear kernel approach yields the least systematic temporal and spatial correlations and does not introduce spurious correlation artifacts over extended time periods. Furthermore, using the automatic bandwidth choice, we remove further control design decisions ensuring objectivity of results. PNG larger image

TIFF original image Download: Fig 2. Effect of different control variable designs on spatial correlation of residual economic growth. Plotting details and significance testing are the same as in Fig 1, except that the horizontal axis shows the distance between country centroids. Significance tests are performed on 40 bins of spatial distances with roughly equal numbers of pairs. Results: Without controls (None), we observe a high positive correlation for any spatial distance. As soon as year fixed effects are applied, only low distance positive correlations remain, but some negative correlations for larger distances get newly introduced. Adding polynomial or local time trends to the controls reduces the negative correlations. From this perspective, local time trends or polynomial time trends of degree at least 1 should be preferred. https://doi.org/10.1371/journal.pclm.0000962.g002 Correlations and standard errors Our investigation of correlations focuses primarily on the economic growth variable and its residual values after controlling for global shocks and regional time trends. This approach is a justified heuristic approximation: after controlling, the estimated residuals are nearly identical to the residual of a full regression model with climate variables. This holds because, in our application, no climate variable explains a large portion of the variation in economic growth. Consequently, a preliminary correlation analysis for the climate variables is not crucial. Nonetheless, should we identify a highly predictive variable, it would be appropriate to redo the analysis of correlations based on the residuals from the final regression model. Different standard error designs. After controlling, some correlation in the error term typically remains. In order to ensure valid inference, we must choose a standard error estimator that properly accounts for the remaining correlations. In our work, we have considered several approaches, each of which deals with spatial and/or temporal dependence in distinct ways. In what follows we briefly summarize these methods and their key properties. HAC (Newey–West) Standard Errors. The Newey–West estimator [36] is specifically designed to address auto-correlation in time series data. It applies a kernel (typically the Bartlett kernel) that weights observations based on their temporal distance, thereby correcting for serial correlation and heteroskedasticity. However, Newey–West standard errors do not address cross-sectional (spatial) dependence. Clustered Standard Errors by Year. Clustering standard errors [37] by year allows for arbitrary correlation among cross-sectional units (e.g., countries) within the same time period. This approach assumes that, within each year, the error terms may be correlated in an unrestricted manner across units, but that there is no serial (temporal) correlation across different years. Clustered Standard Errors by Country. In contrast, clustering by country accommodates arbitrary temporal correlation within each country. Here, it is assumed that errors within a given country over time may be arbitrarily correlated, while errors across different countries are treated as independent. In contrast to estimators that deal with temporal auto-correlation where the correlation is determined by the lag (difference between two years), here any two years can be arbitrarily correlated. Two-Way Clustered Standard Errors by Country and by Year. Multi-way clustered standard errors [38,39] require uncorrelated error terms only for observations that do not share a common cluster in any clustering dimension. In our case, we require an observation from country s and year t to be uncorrelated with an observation from country and year for and . But we account for correlations between observations at (s, t) and as well as for correlations between (s, t) and . To have a reliable estimate of two-way clustered standard errors, we need to have enough clusters for each clustering dimension (enough different years, and enough different countries). Conley Standard Errors. While Newey–West account for temporal correlation based on temporal distance, Conley standard errors [40] account for spatial correlation based on spatial distance. A kernel is applied that downweights correlations as the distance increases. The distance is typically taken as the physical distance, but if other notions of distance exist, they can also be used. Some implementations can additionally deal with temporal auto-correlation (in R, the package conleyreg). Driscoll–Kraay Standard Errors. Driscoll–Kraay standard errors [41] extend the HAC idea by first averaging the estimating equations over the cross-sectional units and then applying a Newey–West type correction. This method is robust to both arbitrary cross-sectional (spatial) correlation (not necessarily based on distance) and temporal auto-correlation (based on temporal distance). A potential drawback is that this estimator is more data hungry (i.e., it requires a sufficiently long time dimension) and tends to be less precise when the number of time periods is small. Correlations in the economic growth rate. We emphasize that spatial correlation in economic data is often not driven solely by the physical distance between countries. While neighboring countries frequently exhibit strong trade links (which is an argument in favor of distance based spatial correlation), being members of the same economic union or sharing similar economic policies can induce strong correlations even if the countries are not immediate neighbors or geographically close. To demonstrate this point, we compare correlations between countries of the European Union (EU) with correlations of countries that are geographically close. We use the countries of the EU that were members in the year 1996 (EU membership does not change thereafter until 2004) so that the effect of being part of the EU shows in the observation time series (1967–2018). The mean correlation between non-neighboring EU countries is 0.36 whereas neighboring countries globally have an average correlation of 0.15. This difference is highly significant (p < 10-5 according to a bootstrap test). Similarly, the mean correlation between EU countries with a centroid distance larger than the median EU centroid distance (1534km) is 0.33, which is significantly (p < 10-5 according to a bootstrap test) larger than 0.07, the global mean correlation of countries with less centroid distance than the aforementioned threshold. Thus, being part of a common economic zone such as the EU is more relevant than geographical proximity. Furthermore, our residual analysis reveals that there are some instances of long-distance (negative) spatial correlations (Fig 2), while long temporal correlations are absent (Fig 1) when using Kernel controls. In view of these features, we advocate for the use of Driscoll–Kraay standard errors. Despite their higher data requirements, they offer a robust solution that simultaneously addresses both arbitrary spatial correlation and temporal auto-correlation, without suffering from the systematic bias observed in alternative estimators. This also speaks to the concern that omitted economic determinants of growth—such as shared policies or common economic shocks—may induce residual correlation: such correlation is exactly what the Driscoll–Kraay estimator is designed to absorb, leaving the consistency of our climate estimates unaffected under the exogeneity of short-run anomalies. Small sample correction. To account for the degrees of freedom already removed in the controlled data set, the small sample correction in the calculation of standard errors has to be adjusted appropriately. In the case of local linear time trends, we use the effective number of parameters, i.e., the trace of the smoother matrix S, which fulfills , where is the temporally smoothed economic data, so that the controlled data is .

Step 3: Model selection via out-of-sample test Traditionally, studies have relied on annual averages of temperature ( ) and precipitation ( ) to predict GDP growth. However, such models may be overly simplistic. More recent research has introduced complex variables—often derived from and —such as measures of extreme rainfall or temperature fluctuations. In addition, studies examining specific channels through which weather impacts the economy often incorporate variables like the number of people affected by tropical cyclones. When accounting for all plausible combinations and transformations of these variables, the number of potential predictors grows dramatically. Selecting a model based solely on its fit, without acknowledging the many alternatives considered and discarded, risks p-hacking and fosters unwarranted confidence in the results. This underscores the necessity of a formal, transparent variable selection procedure. In the analysis that follows, we implement a suite of formal model selection procedures. Crucially, model performance is assessed using out-of-sample metrics, rather than in-sample fit, which can be misleading due to reliance on assumptions that may not hold in practice. This approach provides a more robust evaluation of predictive accuracy. Variable selection and testing are carried out on the controlled dataset, allowing us to isolate the effect of the predictors from that of the control variables. To assess the robustness of the results, we repeat the analysis across multiple datasets, each defined by a different control specification. However, it is important to emphasize that test-set performance cannot be directly compared across different control variants, as each defines a distinct prediction objective. Methods The controlled data is split into training (pre-2007) and testing (2007 onward) subsets, yielding 41 years of training and 11 years of testing data. To assess robustness, we also evaluate alternative splits using 1997 and 2002 as threshold years. We avoid shorter test periods, as they reduce the reliability of evaluation statistics. The split at a threshold year maintains spatial dependencies and reduces the influence of temporal auto-correlation. Furthermore, it exactly mimics the main use case of the model results in which economic damages are projected into the future. This design reduces the influence of temporal auto-correlation but does not eliminate it: after residualizing against the controls, the data may retain some short-range dynamic dependence, and the earliest test years in particular share information with the adjacent training years. Such residual dependence would tend to make the test error slightly optimistic. We do not introduce a temporal gap (“padding”) between the training and test sets to suppress this further, for two reasons. First, with only about 50 annual observations per country, the test set must remain large enough to detect an effect in this highly noisy setting; padding would consume scarce observations. Second, padding introduces an additional hyperparameter with its own trade-offs. We retain the simpler split because our central results are negative: most models show little to no predictive power even in this potentially favorable setting, so any optimistic bias from residual dependence works against our conclusions rather than inflating them. Most selection methods involve tuning hyperparameters, which we optimize via five-fold cross-validation on the training set. Folds are composed of consecutive years (for the 2007 train-test split: 1966–1974, 1975–1982, 1983–1990, 1991–1998, 1999–2006), ensuring that all data from a given year remains in the same fold. This design again respects both spatial correlation and reduces the influence of temporal auto-correlation. We emphasize that cross-validation here serves only to tune hyperparameters; our reported conclusions rest on the held-out test set, evaluated in temporal order. The fold structure thus affects only model tuning and not the validity of the final out-of-sample assessment. Once optimal hyperparameters are identified, each model is retrained on the full training set and used to predict the (controlled) economic response in the test set. We assess the predictive pseudo-significance of each model by benchmarking its performance against a random prediction independent of any predictor variables and modeled by an isotropic Gaussian random vector with optimally chosen variance. See Section F in S1 Appendix for details. To assess the stability of predictor selection, we employ a block bootstrap approach with yearly blocks, resampling the training data 1000 times. Each resample includes a number of years equal to the original training period, drawn with replacement. When a year is drawn multiple times, all data from this year appears multiple times in the resampled dataset. For each bootstrapped sample, we reapply the selection procedure (but not the hyperparameter tuning) and track how often the originally selected predictors are re-selected. This re-selection rate serves as an indicator of the robustness of the variable selection process. Note that all of these calculations happen on the controlled data. This is necessary, as we cannot estimate the controls of the test data using the training data, and all analysis has to be carried out orthogonally to the controls. We expand on this issue and compare our framework with that of Newell et al. [9] in Section G in S1 Appendix. Information criteria. A common way of model selection is using information criteria such as the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Unfortunately, these are not applicable in our setting as they require independent and identically distributed variables [42]. We instead have a complex dependence structure with temporal and spatial correlation and possible heteroskedasticity. Extending the information criteria to such dependence structures is highly non-trivial. Therefore, we do not use these criteria in our experiments. Subset, pair, and forward selection. In Subset Selection, we fix the number of predictors . For each subset of k predictors, we fit the model using ordinary least squares (OLS) and compute the residual sum of squares (RSS), selecting the subset that yields the lowest RSS. The value of k is a hyperparameter to be chosen via cross-validation. However, because there are possible subsets of size k from p predictors, this approach is computationally demanding for large k: For our case with p = 708, the number of subsets for k = 2, 3, 4 is approximately , , and , respectively. While specialized algorithms can perform subset selection more efficiently than brute-force enumeration [43], the computational cost remains prohibitive in our high-dimensional setting. To address this, we instead employ a more computationally efficient selection method variant known as Forward Selection [25]. This method builds the model sequentially by adding, at each step, the single predictor that most reduces the RSS. While this approach drastically reduces computation time, it has a key limitation: It may fail to select predictor combinations that are jointly informative but not individually strong. For instance, a variable like and its squared term might only be useful when included together, and Forward Selection might overlook them individually. In contrast, Subset Selection could capture such combinations. To assess the impact of this limitation, we also implement Pair Selection, i.e., Subset Selection restricted to k = 2, to evaluate whether jointly informative pairs are being missed by Forward Selection. LASSO, ridge, and elastic net. The LASSO and Ridge Regression penalize the absolute values of the regression coefficients so that small absolute values are preferred. For a hyperparameter , the respective coefficient estimates can be written as (10) (11) The penalties allow these methods to be applied in settings with a large number of coefficients compared to the sample size. Meaningful estimates are possible even in settings with more coefficients than observations. The different penalties between LASSO (L1) and Ridge (L2) yield different coefficient estimates: LASSO prefers to set many coefficients to exactly 0 (thus implying a selection of variables), whereas Ridge typically does not estimate any coefficient to be exactly 0 but all coefficients will be shrunken sufficiently close to 0. Note that both methods tend to estimate coefficients with lower absolute values than OLS, i.e., they imply a form of shrinkage. The Elastic Net combines both LASSO and Ridge Regression: (12) The penalty parameter and the trade-off parameter for ElasticNet are chosen using 5-fold cross validation on the training set with the folds consisting of all data from mutually exclusive consecutive years. Ensuring promotes ElasticNet to set some coefficients to exactly 0 as happens in LASSO implying variable selection. Fordge. As pair and forward selection yield much worse results than the shrinkage methods LASSO, Ridge, and Elastic Net, we hypothesize that the missing shrinkage is the problem. Thus, we additionally test the usage of Ridge regression on the variables chosen by forward selection. We call this procedure Fordge (a portmanteau of forward and ridge).

Discussion This paper advances global panel data regression in climate econometrics by addressing key methodological shortcomings in existing research and proposing data-driven solutions. Our enhanced empirical strategies challenge earlier findings and underscore the need for more robust modeling practices. To improve future research, we provide methodological recommendations for future climate econometric research. Outlier treatment and data integrity. We document the substantial influence of outliers on empirical results, present procedures for their identification and treatment, and provide a cleaned dataset to facilitate more reliable analyses. Only few previous works [5] treat outliers at all. Flexible time-trend controls and correlations. We replace arbitrary, parametric time-trend specifications with a nonparametric, fully automatic procedure. This reduces practitioner bias and more effectively captures complex temporal dynamics in panel data. Furthermore, we show the influence of different control designs revealing undesirable long term temporal correlations introduced by previously common polynomial time trends. High-dimensional variable selection with out-of-sample validation. To navigate over 700 candidate predictors, we employ formal variable-selection methods—most notably LASSO, Ridge, and Elastic Net—which guard against overfitting, p-hacking, and cherry picking. Crucially, we benchmark all models via out-of-sample testing, providing a realistic assessment of predictive power under unknown dependency structures and avoiding untested assumptions inherent in classical inference methods. Empirical findings. Strikingly, almost none of the tested variables—including those emphasized in prior studies—retain meaningful predictive power out-of-sample. A key reason appears to be the violation of temporal stationarity, an assumption often made but rarely tested. Among the penalized methods, a humidity-related variable consistently emerges as the strongest predictor of economic damage. Investigating this variable—and its interactions with temperature—from both statistical and mechanistic perspectives is a promising avenue for future work. Implications. By integrating outlier robustness, adaptive trend controls, rigorous variable selection, and out-of-sample validation, our approach reveals the fragility of many conventional findings and calls for a paradigm shift toward methodologies that prioritize predictive accuracy and generalizability in climate econometrics. Recommendations. From our finding, we derive the following recommendations for future work in climate econometrics to improve robustness and avoid wrong conclusions. Check the data for outliers and analyze their influence. Check temporal and spatial correlations in controlled data to be able to choose a suitable standard error and cross-validation design, and to be able to compare different control designs. Use a formal model selection procedure to avoid a subjective model choice or cherry picking (e.g., use LASSO, Ridge Regression, or Elastic Net). Use out-of-sample testing that is robust against potential dependence structures in the data to verify that the chosen model generalizes. Check temporal stationarity if results are used for future projections. Check spatial stationarity if results are interpreted as country specific or interpret results as global averages only. Try shrinking estimated coefficients, e.g., using penalized regression methods (such as LASSO, Ridge Regression, or Elastic Net) to improve predictive power and mitigate against problems with data dependency and a lack of stationarity.

Acknowledgments The authors gratefully acknowledge Simon Philippssohn for his valuable contributions to the classification of economic outliers.

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[1] Url: https://journals.plos.org/climate/article?id=10.1371/journal.pclm.0000962

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