2.1. Empirical model specification

Weather shocks can have potentially complex dynamic effects on GDP. We start by relating GDP per capita in country i at time t (y_i,t) to a vector of weather variables (X_i,t) with a very flexible specification:

where $\underset{k=0}{\overset{K}{\Sigma }}{a}_{k,i}{t}^k$ are country-specific polynomial trends in weather patterns or economic activity, Z_t is a vector of variables capturing global shocks, and ε_i,t is the error term. This specification encompasses various models estimated in the literature (Hsiang, 2010; Dell et al., 2012; Deryugina and Hsiang, 2014; Burke et al., 2015; Kalkuhl and Wenz, 2020; Kahn et al., 2021), potentially allowing weather variables to have persistent dynamic effects on GDP.

To address serial-correlation and the fact that country GDP levels are non-stationary, we estimate equation (1) in first difference. It becomes a standard ARDL equation for GDP per capita growth:

We test alternative restrictions on the order of the polynomial and on the vector ∆Z. Note that very persistent effects of level shocks to weather variables on GDP growth can still be captured with a long trail of significant ${\beta }_p^{\text{'}}$.

We don’t allow for a relationship between GDP growth and levels of the weather variables because GDP growth is stationary whereas many weather variables exhibit trends and are not stationary. Table A.2 in appendix presents evidence that average temperature and most variables built using temperature data are trended in most countries, as noted in the context of this literature by Kahn et al. (2021). This implies that GDP growth and these level variables cannot be related without additional manipulation (Tol, 2019; Kahn et al., 2021).

Climate variables can exhibit trends that are significant and different by country, requiring use of country fixed effects.⁴ In our specification, country-specific trends imply that the country average of first differences in weather variables take different and significant values. If we did not include country fixed effects, we would fail to control for these country-specific averages.⁵ Our specification is only valid if trends are constant over time. To handle time-varying trends, Kahn et al. (2021) subtract the 30-year moving average from each climate variable and take first differences. While effective, this would be very costly for us because our weather data starts in 1979 unlike their data that starts in 1960. Our method is not totally immune to bias from changes in trends but this does not seem to be a major problem in practice because many variables (Table A.2) and especially those used in our main specification do not show unambiguous evidence of a significant break in the past forty years (Table A.4 in appendix).

2.2. Local projection method

The complex dynamic effect of weather on GDP might not be immediately revealed by the estimation results from equation (2). There might be persistent weather effects because weather shocks themselves are persistent, because of feedback effects if current GDP per capita depends on past GDP levels, or because of a combination of both.

We use a local projection method following Jorda (2005) to estimate impulse response functions from a shock to one or more of our independent weather variables. As shown in Jorda’s seminal paper, this procedure is more robust to misspecification than auto-regressions, easily accommodates flexible specifications, and allows for a simple visualization of the dynamic responses to weather shocks. We estimate variants of equation (2) where the dependent variables are long-differences between GDP per capita between time t+h and time t:

where h indexes the estimation horizon measured in years. Equation (2) correspond to horizon 0 and coefficient estimates β^0′ captures the contemporaneous effects of weather shock. We consider dynamics up to horizon 7 as in Acevedo et al. (2020). In case of growth effects, the coefficient ${\beta }_p^h{}^{\prime }$ would be expected to become increasingly large as time goes by. Alternatively, if the shock has a permanent level effect, we would obtain constant coefficient estimates. If instead the shock is mean-reverting, ${\beta }_p^h{}^{\prime }$ would be expected to converge to zero as time goes by.

2.3. Selecting relevant weather variables and estimating their effects

Our most important contribution to the literature is to study the effect of a wide set of climate variables. In total, we construct and examine 164 weather variables in X, as described in Section 3.

If all the variables that we consider were entered simultaneously in equation (2), the model might still be estimated thanks to our large panel, but estimation would easily run into over-fitting issues. To avoid this problem, we use the Least Absolute Shrinkage and Selection Operator (LASSO) (Tibshirani, 1996; Belloni et al., 2014) in a process where machine learning (ML) and expert judgement concur in selecting a parsimonious number of relevant variables.

The LASSO selects coefficients to minimize the sum of squared errors in equation (2) plus a weighted penalty term equal to the sum of the absolute value of each coefficient. The weight attributed to the penalty term is a hyper-parameter λ that needs to be selected before the minimization. Specifically, the LASSO solves the following problem:

where

Intuitively, the LASSO chooses coefficient estimates by comparing benefits measured by a reduction in the sum of squared errors in equation (2) with costs measured by the size of non-zero coefficients. When a coefficient β_j,p is shrunk to zero, the variable is effectively omitted from the regression. The penalty term measures the costs associated with having a model with too many variables. The larger is λ, the smaller are coefficient estimates and the smaller the number of variables selected.

Before implementing the LASSO operator, we follow Belloni et al. (2014) and we impose that the model must use country fixed effects and in some specifications, year fixed effects or country quadratic trends. We do so in two stages, first by regressing all the dependent and independent variables on the selected fixed effects and trends, and second by applying the LASSO to the estimated residuals from the first stage (the “partialed-out” variables).⁶

As there is no universal “optimal” way to choose λ, the LASSO must be complemented by optimality conditions set by the analyst. In the ML literature, this is known as the “no free lunch theorem”: there is no optimization algorithm that is capable of guiding the identification of a prior for the penalty weight when starting the analysis (Adebayo and Fokoue, 2019).

For the selection of the penalty weight, we rely on a two-stage process. In the first stage, we choose the value of λ that gives the highest R-square out-of-sample using k-fold cross validation. We start by dividing all our observations in a training set and in a test set. We run the LASSO on the training set for a randomly selected value of λ, use the selected variables to calculate the R-square in the test set and repeat this calculation many times. We choose the value of λ that maximizes the R-square in the test sets. This “random search” process is considered to be the most efficient in the ML literature (Bergstra and Bengio, 2012).⁷

The random search process leads to the selection of a very small value for λ with the effect of keeping about 20 variables or more. While this procedure helps with reducing over-fitting, many variables are not statistically significant in the OLS regression and are inter-correlated. Interpretation is the other important goal of our analysis in addition to out-of-sample accuracy. To preserve a compact number of variables whose effects can be easily interpreted, we refine further the choice of λ.

In the second stage, we further select variables affecting GDP per capita by increasing the value of λ in small increments until no variable is dropped for three consecutive increments. When selecting variables affecting fiscal variables, we simply focus on the first selected variable for parsimony because we keep using the three variables selected for GDP. This second method, known as “grid search” in the ML literature, helps us both to refine the selection of a parsimonious model and to analyze the robustness of selection of climate variables. We also use the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) to assess the relative quality of the selected models.

The LASSO produces “biased” coefficient estimates because the penalty term shrinks them.⁸ To estimate the “unbiased” effect of weather shocks, we finally re-estimate the model with the climate variables selected by the LASSO using standard OLS methods.⁹

3.1. Weather data sources and aggregation over time and space

We use temperature and precipitation data from the ERA5 dataset compiled by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Hersbach et al., 2018). ERA5 provides hourly reanalysis weather data on a global grid from 1979 to 2019.¹⁰ The grid resolution varies with latitude with cells of 30 × 30 km at most (at the equator).¹¹

Weather data is available at a much higher spatial and temporal resolution than typical annual country macro-economic data. Our goal is to reduce the millions of weather measurements in every country and year to construct a manageable number of potentially meaningful climate variables. We aggregate raw ERA5 weather data over space and time to construct our variables using the cloud computing power of Google Earth Engine (GEE) (Gorelick et al., 2017).¹²

We can use the high spatial and temporal granularity to reveal weather events that would be lost when averaging weather variables over an entire country during a whole year. Country and year averages may bias estimates of weather impacts in at least three important ways.

First, averages miss local and infra-year extreme weather events if events of opposite nature cancel out each other. For example, droughts in a specific region in summer can coincide with intense precipitation in another part of the country or in a different season. Country annual averages would then be unable to reflect these extreme events. Second, the relationship between a weather shock and the economy can be non-linear and dependent on duration, spatial coverage, and intensity. For example, both prolonged high temperatures (a heatwave) and short-lived but very high temperature could impact the economy in different ways. Even if average temperature might approximately reflect the occurrence of various hot weather events, it would fail to capture the different effects associated with the different characteristics of these events. Third, deviations from local seasons could be relevant even if they are not reflected in averages or as outliers in the full annual distribution. For example, unusually high precipitation in central Europe in summer could have an impact on the economy even if the same level of precipitation would be totally normal and irrelevant in another time of the year or in other regions that are more accustomed to heavy precipitation.

We build variables that describe the distribution of temperature and precipitation as well as notable extreme events following the climate literature (Kim et al., 2020; Perkins and Alexander, 2013). When the literature uses similar alternatives, we include all of them and let the LASSO select the most relevant option. While we could have used additional ML techniques to reduce the full matrix of weather measurements into country-year variables, we choose to start from definitions of weather events that are frequently used in the climate literature to obtain results that are easier to interpret and can be linked to other work.

When deriving country-level variables by aggregating grid-level information, we construct both unweighted and population-weighted variables. Unweighted variables do not introduce bias in the characterization of climate that could lead to miss impacts in areas with low economic and population density (Bandt et al., 2021). For example, droughts in agricultural areas may be more important for economic activity than droughts in urban areas. Lack of snow or rain in remote areas that supply water to economic centers may be missed completely using population weights. However, unweighted data may give excessive importance to weather, and particularly temperature, in areas with relatively little economic contribution to total output, especially in countries with large uninhabited regions. For these reasons, we construct both unweighted and weighted variables using year 2000 population weights.¹³ We include both sets of variables in the LASSO exercise.¹⁴

3.2. Variable definitions

This Subsection provides an overview of all the weather variables we construct from the raw data and of macro-fiscal variables. Appendix A.2 provides a complete description of definitions, exact formulas, and summary statistics for the selected variables.

Defining extreme weather. A practical problem for empirical research is the lack of unambiguous definitions of extreme weather. In general, a weather event is extreme if some of its characteristics exceed some thresholds. Specifically, definitions are ambiguous about the thresholds to use with respect to major characteristics, like intensity, frequency, or duration.

The literature has used both “relative” and “absolute” thresholds. In some cases, extreme weather is defined as weather “that is rare at a particular place and/or time of year” (Cubasch et al., 2013, p 134). This suggests the use of thresholds that are specific to locations and seasons (“relative thresholds”). For example, definitions can rely on the 90^th percentile of the local distribution of temperature at a certain time of the year. Relative thresholds account for the importance of adaptation to average conditions and emphasize the effects of deviations from local averages. In other cases, extreme weather is defined using thresholds that are constant across space and time (“absolute thresholds”). For example, maximum daily temperature greater than 40°C are generally considered harmful everywhere. Absolute thresholds are better suited to capture physical limits beyond which weather causes damages, no matter when or where it occurs (e.g., IPCC, 2021a). We consider both “relative” and “absolute” weather extremes as they can both be relevant for the economy in different ways.

We typically capture extreme events at the country-year level by both counting their occurrences and measuring their intensity. To this end, we count the share of grid-cells and days with weather events that are defined for different thresholds. We also construct a wide range of variables that measure the average or maximum intensity of extreme events. We do so for temperature, precipitation and wetness/drought as detailed below.

Temperature variables. We consider average temperature, the variance of daily temperature, and the average diurnal temperature range (the difference between the minimum and maximum temperature in a day). We calculate the number of cold nights, cold days, warm nights and warm days using relative thresholds based on the 1979–2019 distributions for every 5-day window centered on each day of the year.

We build various heatwave and coldwave variables based on the climate literature.¹⁵ We follow Perkins and Alexander (2013) and consider various thresholds to define heat and cold waves in daytime and nighttime. We then count the length of the longest wave, the number waves in a year, the number of days and the average maximum or minimum temperature during such waves. We also follow Kim et al. (2020) and additionally define the duration of cold and warm spells as the number of days exceeding alternative relative temperature thresholds for prolonged periods.

We use the fine spatial resolution of our data to define minimum and maximum variables that are used in the literature to capture local extremes. We compute the annual minimum of night temperatures and the maximum of daytime temperatures for every cell of a country’s grid, and average them out over space.

We also define another set of extreme temperature variables using absolute temperature thresholds often used in the climate literature (e.g., IPCC, 2021a). With absolute thresholds, using the highest possible level of spatial resolution is essential to avoid missing the potentially meaningful events that would otherwise be averaged out. For example, Figure 1 illustrates how country averages can miss when maximum temperatures exceed would miss many instances of days with temperature 35°C in only parts of a country. To avoid this, we count how often temperature crosses various absolute thresholds (e.g., below 0°C, above 35°C and 40°C) over the 365 days of a year and over each of a country’s grid cells.

Illustrating the role of high spatial resolution when using absolute thresholds

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: This figure illustrates the importance of high spatial resolution when accounting for daily maximum temperatures exceeding 35°C (TX35). As seen in the top row, at the beginning of summer 2019, only a small share of the US (8%) experienced temperatures higher than 35°C. These temperatures would average out if we were to use country means. Similarly for Brazil in December 2019, the bottom row shows that only 12% of the country crosses the 35°C threshold. In both cases, country averages would fail to capture these extreme temperatures.

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Illustrating the role of high spatial resolution when using absolute thresholds

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: This figure illustrates the importance of high spatial resolution when accounting for daily maximum temperatures exceeding 35°C (TX35). As seen in the top row, at the beginning of summer 2019, only a small share of the US (8%) experienced temperatures higher than 35°C. These temperatures would average out if we were to use country means. Similarly for Brazil in December 2019, the bottom row shows that only 12% of the country crosses the 35°C threshold. In both cases, country averages would fail to capture these extreme temperatures.

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Illustrating the role of high spatial resolution when using absolute thresholds

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: This figure illustrates the importance of high spatial resolution when accounting for daily maximum temperatures exceeding 35°C (TX35). As seen in the top row, at the beginning of summer 2019, only a small share of the US (8%) experienced temperatures higher than 35°C. These temperatures would average out if we were to use country means. Similarly for Brazil in December 2019, the bottom row shows that only 12% of the country crosses the 35°C threshold. In both cases, country averages would fail to capture these extreme temperatures.

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Finally, to capture potential non-linear effects of temperature on macro-economic variables, we define 3°C-wide intervals from -9°C and below to 30°C and above and we count how often temperatures fall in these intervals over space and time (see for example Schlenker and Roberts, 2009). This approach allows us to capture the impact of temperature on macro-fiscal variables at different temperature levels imposing minimal restrictions on the temperature response functional form.

Precipitation variables. We use the term precipitation throughout this paper because our data measures both rain and snow precipitations (converted into rain equivalents). We sometimes focus on “wet days”, that are days with 1 mm precipitation or more, or on “dry days” with precipitation below 1 mm. Our variable set includes the country-year averages and the variance of daily precipitation, which we construct twice, on all calendar days and on wet days. We also measure precipitation on very wet and extremely wet days, where these days are defined using relative thresholds.

We build several variables to capture extended wet and dry periods. We count the largest number of consecutive dry days, wet days, very wet days, and extremely wet days. We measure precipitation in the longest period of wet, very wet and extremely wet days respectively.

Floods are among the most destructive climate disasters. To capture short but intense precipitation that may cause floods, we use the maximum amount in a year of rainfall in 1-day or 5-day intervals. To capture extreme precipitation at the local level, we also examine total monthly precipitation in each grid cell. We use these to calculate the country average of maximum and minimum monthly precipitation.

As for temperature, we make use of our data high spatial resolution to define precipitation extremes using absolute thresholds. We calculate the number of consecutive days in which a minimum percentage of the country area is experiencing a dry day using different percentage thresholds. Similarly to what we do with temperature, we define four precipitation intervals (divided by 1, 10, and 20 mm thresholds), and measure how often precipitation is in any of these intervals. We define the maximum extent of heavy and very heavy precipitation as the maximum surface of a country where precipitation exceeds 10 mm and 20 mm respectively. We also construct an indicator that measures deviations from a balanced level of precipitation. This indicator measures the absolute deviation from having precipitation between 1 and 10 mm half the time over space and time.

Wetness and drought variables. We use the Palmer Drought Severity Index (PDSI) (Palmer, 1965) to introduce a measure of dry and wet periods that combines temperature and precipitation data to estimate cumulative deviations in soil moisture from normal conditions (Dai et al., 2004; Abatzoglou et al., 2018; Lai et al., 2020).¹⁶ The PDSI ranges from -10 to +10, but values below -4 and above +4 are very rare. To capture extreme conditions during a year we build variables measuring the share of total grid-months subject to droughts and harsh droughts (with PDSI respectively below -3 and -4), and to periods with high and very high moisture (with PDSI respectively above 3 and 4). As for precipitation, we also seek to capture the maximum geographical extent of droughts and wet conditions. For each of the four categories, we compute the share of affected grid-cells in the month where the share is at its maximum. In sum, in our empirical analysis, we consider 45 different temperature variables, 29 precipitation variables, and 8 wetness-drought variables, for a total of 82 unique climate variables. For the empirical estimation, we remove perfectly collinear variables. We add the first and second lag of these variables as well as their population-weighted counterparts and we obtain a set of 480 climate variables.

Macro-fiscal variables. We use GDP per capita from the World Bank’s World Development Indicators (WDI).¹⁷ For fiscal outcomes, we collect variables from the IMF World Economic Outlook (WEO) because it has a wider coverage than the WDI. We use government revenue and expenditure expressed in percentage of GDP, also from the WEO database.¹⁸ To examine gross debt, we draw from the Global Debt Database which improves on other databases by constructing long series with a consistent coverage over time (Mbaye et al., 2018).¹⁹ For some countries (all countries in the case of debt), the fiscal variables only cover the central government, implying that our analysis will miss local governments’ response.

3.3. Summary statistics

We start our analysis by considering all countries for which we have at least 7-year long time series for GDP per capita and climate variables. We exclude Libya, Iraq, Equatorial Guinea and Bahrain because of outliers. This leads to selecting 199 countries for a total of 6,550 country-year observations. Data on fiscal aggregates have smaller coverage. We remove Kuwait and Sao Tome and Pr´ıncipe because of outlier observations, and all observations with any missing fiscal value. As a result, the sample for analyzing fiscal outcomes has 159 countries for a total of 3,859 country-year observations.

Our empirical and identification approach relies on inter-annual variation within country. Therefore, we use a standard approach to decompose the variance of variables into between and within components.²⁰ The between standard deviation measures variation of average country weather around the global mean. The within standard deviation measures the average deviation from country averages.

GDP per capita grew by 1.6 percent per year on average in our largest sample used for GDP analysis and by 2.0 percent per year on average in the smaller sample used for fiscal policy analysis (Table A.3 in appendix). The within standard deviation of GDP per capita growth is large, ranging from 4.7 (larger sample) to 3.7 (smaller sample) percentage points. The ratios of government revenue and expenditure to GDP grew at the same average rate of 0.1 percentage points per year. The inter-annual variation of these variables is substantial, with within standard deviations ranging from 3.2 to 4.0 percentage points. Government debt-to-GDP ratios were stable on average but with a large within standard deviation of 11.1 percentage points.

The within standard variation of climate variables in first differences is typically much higher than the between standard deviation. This indicates that the average change in climate variables over the sample period is relatively similar across countries. By comparison, the change in climate variables from one year to the next in every country varies considerably more.

Many weather variables exhibit a trend over the sample period. Table A.2 in appendix reports results from a systematic analysis of trends in all weather variables in all countries from 1979 to 2019. We find evidence of positive and statistically significant country-specific trends in a majority of countries for variables related to temperatures. Such trends are more rare for other variables.

In our model specification, we assume that trends are time-invariant. To check the validity of this assumption, we test for a structural break in trends with unknown break date for all variables in every country. For most variables in most countries, we cannot reject the null hypothesis that there are no significant structural breaks. We conclude that the assumption of time-invariant trends is acceptable. We also test all first differences of weather variables for the presence of a unit root and we reject it in all cases with p-values close to zero.

4.1. Climate variable selection

In our baseline specification, we use country and year fixed effects. The collinearity test of Belloni et al. (2013) does not suggest dropping any of the 480 weather variables. The random search process selects 30 out of these variables, with A = 0.0166. The selected variables include the first two lags of GDP per capita growth and a mix of variables derived from both temperature and precipitation, unweighted and weighted, contemporaneous and lagged. The full list is reported in the appendix Table A.7.

The first phase of our variable selection process reduces the total number of variables by approximately 95 percent, but many of the climate variables selected by the random search are statistically insignificant, indicating that while they contribute to explaining the variation of the dependent variable, they do not help much to understand the effect of weather on GDP growth. Therefore, we further reduce the number of variables using the grid search algorithm as described in Section 2.3.²¹

Our final selection includes three climate variables and the first two lags of the dependent variable. Figure 2 panel (a) shows how much the within R-square decreases when the number of selected variables decline as we increase A. We examine the within R-square to focus on the explanatory power of climate variables and set aside the explanatory power of fixed effects. Our preferred specification improves the within R-square by 7 percent relative to a specification with just the 2 lags of the dependent variable as independent variables. This is a sharp reduction in the within R-square from the 17 percent improvement obtained with the specification using all the 30 variables selected by the LASSO after the random search. However, this reduction corresponds to a much more parsimonious model that we can more easily interpret. If the main goal of the analysis is prediction of GDP growth, all the variables selected in the first random search step should instead be used.

Other information criteria for model selection support our preferred specification. The Bayesian information criterion (BIC) obtained for the different variable selections is minimized for selections of 4 to 6 variables (Figure 2 panel b). The Akaike information criterion (AIC) declines monotonously as the selection of variables increase to the set chosen by the random search. Therefore, our preferred selection of 5 variables appears sensible.

4.2. The effect of weather variables on GDP growth

The three selected weather variables for our baseline specification are the share of grid-days with harsh drought conditions (Harsh Drought Prevalence — PDSI_<-4), the share of grid-days with maximum daily temperature above 35°C (Max T°C above 35 — TX35), and the share of grid-days with mean temperature in the interval 9–12°C (Mean T°C in [9; 12) — TS_9,12). The LASSO selects population-weighted variables except for Mean T°C in [9; 12). Summary statistics of first differences of these variables are displayed in Table A.4 and correlation coefficients between GDP growth, the fist two lags of GDP growth, and first differences of the selected climate variables are shown in Table A.5.

The correlation between the first differences and GDP growth is generally very low, ranging from 0.04 to 0.05 in absolute value. However, as a comparison, the correlation between first differences of average annual temperature (Mean Temperature — T) and GDP growth is even smaller and equal to only -0.006. Among the climate variables, the largest correlation is found between Harsh Drought Prevalence and Max T°C above 35 (0.183). Harsh Drought Prevalence is also positively correlated with Mean Temperature (0.159) because temperature plays a role in the definition of the PDSI drought indicator. Max T°C above 35 and Mean Temperature are modestly correlated (0.356) but Mean Temperature is not retained by the LASSO.

Variable selection and OLS estimation outcomes as λ varies (country and year effects)

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Note: The figures show various outcomes from implementing the LASSO for different penalty parameters. The estimated model has GDP per capita growth as the dependent variable and includes country and year effects. The within R-square, AIC, and BIC are computed based on the OLS estimation. The within R-square is reported as a percentage change relative to the within R-square obtained with a specification that only includes the first two lags of the dependent variable (within R² “ .0937).

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Variable selection and OLS estimation outcomes as λ varies (country and year effects)

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Note: The figures show various outcomes from implementing the LASSO for different penalty parameters. The estimated model has GDP per capita growth as the dependent variable and includes country and year effects. The within R-square, AIC, and BIC are computed based on the OLS estimation. The within R-square is reported as a percentage change relative to the within R-square obtained with a specification that only includes the first two lags of the dependent variable (within R² “ .0937).

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Variable selection and OLS estimation outcomes as λ varies (country and year effects)

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Note: The figures show various outcomes from implementing the LASSO for different penalty parameters. The estimated model has GDP per capita growth as the dependent variable and includes country and year effects. The within R-square, AIC, and BIC are computed based on the OLS estimation. The within R-square is reported as a percentage change relative to the within R-square obtained with a specification that only includes the first two lags of the dependent variable (within R² “ .0937).

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The selected climate variables have an intuitive effect on GDP, as shown in Table 1 where all the variables are standardized to facilitate interpretation. We find that an increase in Harsh Drought Prevalence and in Max T°C above 35 have adverse effects on contemporaneous GDP growth. By contrast, we find that an increase in Mean T°C in [9; 12) has beneficial effects on GDP. These effects are highly significant and robust across alternative model specifications.

In our baseline specification (column A) we use the unbalanced panel and year fixed effects. A positive shock equal to one standard deviation of the first difference of Harsh Drought Prevalence in a country reduces GDP growth by 0.21 percentage points. An increase in Max T°C above 35 has an equally large and significant effect on GDP growth. A positive shock equal to one standard deviation in the first difference of Max T°C above 35 reduces GDP growth by 0.20 percentage points. A positive shock equal to one standard deviation in Mean T°C in [9; 12) leads to an increase in the growth rate equal to 0.16 percentage points. In this case, the unweighted variable was chosen over the population-weighted one.

These effects are similar to those found by other studies that have included droughts using indicators for selected natural disasters (Cantelmo et al., 2019; IMF, 2020). Average annual temperature is correlated with extreme and moderate temperatures, but the correlation among first differences is generally very low. It is thus important to provide a more complete characterization of weather events than what is typically done in the literature.

The selection of significant weather shocks includes variables constructed with both absolute (Max T°C above 35, Mean T°C in [9; 12)) and relative thresholds (Harsh Drought Prevalence). For droughts, we find that drier than average conditions are harmful, no matter what is the average precipitation level. For temperature, we find that the 35°C absolute threshold is selected over alternative definitions of high temperatures based on the deviations from local and seasonal norms.

^{Table 1:}

The effect of changes in selected climate variables on GDP per capita growth

Note: The table presents results from the OLS estimation with country fixed effects of the effect of climate variables on the first difference of log real GDP per capita expressed in constant 2015 USD. All regressions include controls such as two lags of the dependent variables. Column E includes world growth as a control. Column G is estimated on a balanced subsample of 135 countries for 1983–2019. Coefficient estimates of additional climate variables selected in column E, F and G are reported in appendix A.4 Table A.14. Climate variables are standardized and their definitions are detailed in Appendix A.2 Table A.1. (W) indicates population-weighted variables. Standard errors are clustered by country. * p < 0.10, ** p < 0.05, *** p < 0.01

^{Table 1:}

The effect of changes in selected climate variables on GDP per capita growth

	(A)	(B)	(C)	(D)	(E)	(F)	(G)
First difference in
Harsh Drought Prevalence (W)	-0.211*** (0.0544)	-0.251*** (0.0527)			-0.231*** (0.0552)	-0.191*** (0.0568)	-0.257*** (0.0749)
Max T°C above 35 (W)	-0.201*** (0.0745)		-0.244*** (0.0727)		-0.175** (0.0745)	-0.215*** (0.0752)	-0.254*** (0.0929)
Mean T°C in [9; 12)	0.155*** (0.0395)			0.174*** (0.0402)	0.153*** (0.0380)	0.142*** (0.0400)
Observations	6,550	6,550	6,550	6,550	6,550	6,550	4,860
Year fixed effects	Yes	Yes	Yes	Yes	No	Yes	Yes
World GDP growth	No	No	No	No	Yes	No	No
Country quadratic trends	No	No	No	No	No	Yes	No
Balanced	No	No	No	No	No	No	Yes
R-square	0.264	0.261	0.261	0.260	0.253	0.350	0.224
Within R-square	0.0998	0.0967	0.0965	0.0952	0.149	0.0375	0.0790

Note: The table presents results from the OLS estimation with country fixed effects of the effect of climate variables on the first difference of log real GDP per capita expressed in constant 2015 USD. All regressions include controls such as two lags of the dependent variables. Column E includes world growth as a control. Column G is estimated on a balanced subsample of 135 countries for 1983–2019. Coefficient estimates of additional climate variables selected in column E, F and G are reported in appendix A.4 Table A.14. Climate variables are standardized and their definitions are detailed in Appendix A.2 Table A.1. (W) indicates population-weighted variables. Standard errors are clustered by country. * p < 0.10, ** p < 0.05, *** p < 0.01

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^{Table 1:}

The effect of changes in selected climate variables on GDP per capita growth

	(A)	(B)	(C)	(D)	(E)	(F)	(G)
First difference in
Harsh Drought Prevalence (W)	-0.211*** (0.0544)	-0.251*** (0.0527)			-0.231*** (0.0552)	-0.191*** (0.0568)	-0.257*** (0.0749)
Max T°C above 35 (W)	-0.201*** (0.0745)		-0.244*** (0.0727)		-0.175** (0.0745)	-0.215*** (0.0752)	-0.254*** (0.0929)
Mean T°C in [9; 12)	0.155*** (0.0395)			0.174*** (0.0402)	0.153*** (0.0380)	0.142*** (0.0400)
Observations	6,550	6,550	6,550	6,550	6,550	6,550	4,860
Year fixed effects	Yes	Yes	Yes	Yes	No	Yes	Yes
World GDP growth	No	No	No	No	Yes	No	No
Country quadratic trends	No	No	No	No	No	Yes	No
Balanced	No	No	No	No	No	No	Yes
R-square	0.264	0.261	0.261	0.260	0.253	0.350	0.224
Within R-square	0.0998	0.0967	0.0965	0.0952	0.149	0.0375	0.0790

Note: The table presents results from the OLS estimation with country fixed effects of the effect of climate variables on the first difference of log real GDP per capita expressed in constant 2015 USD. All regressions include controls such as two lags of the dependent variables. Column E includes world growth as a control. Column G is estimated on a balanced subsample of 135 countries for 1983–2019. Coefficient estimates of additional climate variables selected in column E, F and G are reported in appendix A.4 Table A.14. Climate variables are standardized and their definitions are detailed in Appendix A.2 Table A.1. (W) indicates population-weighted variables. Standard errors are clustered by country. * p < 0.10, ** p < 0.05, *** p < 0.01

We examine whether our selected climate variables have an effect on their own or whether their estimated effects result from their combination. To this end, we enter each variable separately in our specification with year and country effects as reported in columns B-D of Table 1. Coefficients estimates are very similar to those in the baseline column A, suggesting that the main effect of each variable is mostly independent and additional to the effect of the other variables.

We test the robustness of our variable selection and coefficient estimates by considering alternative specifications. For each model we repeat the LASSO exercise as for our baseline specification. In column E, we retain country fixed effects but we use world GDP per capita growth instead of year effects to control for common world-wide developments. A random search over possible penalty parameters leads to a first selection of 36 variables (see Table A.8 in appendix). The overlap of the selections resulting from the random search is remarkable. The procedure selects the same 26 variables for the baseline and the specification without year effects. Only 4 out the 30 variables selected for the baseline were not selected again. We then narrow down the number of selected variables to 8, including the two lags of the dependent variable and world growth (see Figure A.2 in appendix). The 5 selected climate variables include the same 3 used in the baseline, the duration of cold spells, and the lag of the average over space of grid-cell maximum temperatures. Column E of Table 1 shows that the coefficients of the 3 climate variables used in our baseline specification are robust to this new specification.

We additionally consider a specification with country-specific quadratic trends in addition to year effects. The random search procedure leads to the selection of 24 variables (see Table A.9 in appendix). Once again, there is a good overlap between the selection under this specification and under the baseline, with 22 common variables. After we increase the penalty parameter, we get to a stable set of 7 variables, including also in this case the same 3 climate variables selected in our baseline and the 2 lags of the dependent variable. Column F of Table 1 shows that the coefficient estimates from the OLS estimation of the climate variables that are common to the baseline and to this new specification are, once again, very similar.

Finally, we also implement our selection method on a balanced subsample with the 135 countries that have non-missing observations continuously from 1984 to 2018. The random search procedure selects 18 variables, including the 3 variables selected in our baseline. In the grid search, we lose Mean T°C in [9; 12) while the algorithm adds 2 other variables: the first lag of Cold Spell Duration (CSD) and the maximum of 1-day total precipitation in the country (1-Day PPT Maximum — PXp1q) (see Tables A.10 and A.14 in appendix). Results in column G in Table 1 shows that the effects of Harsh Drought Prevalence and of Max T°C above 35 remain robust.

4.3. Comparisons with the literature

Does the set of variables we select improve substantially our understanding of GDP variations? We examine this question by comparing our results with key models from the literature. We focus on two central papers in the literature, Burke et al. (2015) and Kahn et al. (2021).

We estimate the two papers’ respective baseline models using our sample and confirm their robustness.²² We follow the specification in Burke et al. (2015) and regress GDP growth on annual average temperature, precipitation, the two squares of these variables, and include two lags of GDP growth, country quadratic trends and year effects. Despite the fact that our sample is much smaller and other minor differences, we obtain very similar coefficient estimates.²³ Results in column B in Table 2 feature an inverted U-shaped relationship between temperature and growth that is quantitatively close to that found by Burke et al. (2015), with optimal temperature estimated to be equal to 13.3°C (instead of 13.1°C).

^{Table 2:}

Estimation of the effect of climate shocks on GDP growth: comparisons with the literature

Notes: Each column corresponds to a fixed-effect regression of the first difference in log real GDP per capita on two lags of the dependent variables and on climate variables for column B, C, E, and F. Climate variables are introduced sequentially by columns. PDSI_<-4: Harsh Drought Prevalence; TX35: Max T°C above 35; TS_{9_12}: Mean°C in [9; 12). (W) indicates population-weighted variables. See appendix Table A.1 for further details. Coefficient estimates are reported in appendix Table A.15.

^{Table 2:}

Estimation of the effect of climate shocks on GDP growth: comparisons with the literature

	Burke et al. (2015			Kahn et al. (2021
	(A) base	(B) unchanged	(C) augmented	(D) base	(E) unchanged	(F) augmented
Climate variables	none	temperature, temperature2, precipitation, precipitation2	temperature, temperature2, precipitation, precipitation2, PDSI<-4 (W), TX35 (W), TS9,12,	none	temperature, precipitation, (deviations from trend for both), both their 4 lags	temperature, precipitation, (deviations from trend for both), both their 4 lags, PDSI<-4 (W), TX35 (W), TS9,12,
Country fixed effects	yes	yes	yes	yes	yes	yes
Country quadratic trends	yes	yes	yes	no	no	no
Year effects	yes	yes	yes	no	no	no
R-squared	0.403	0.407	0.413	0.216	0.220	0.228
Within R-squared	0.0165	0.0233	0.0334	0.110	0.114	0.123
AIC	-14,731	-14,752	-14,789	-16,151	-16,154	-16,200
BIC	-14,712	-14,708	-14,726	-16,132	-16,070	-16,096

Notes: Each column corresponds to a fixed-effect regression of the first difference in log real GDP per capita on two lags of the dependent variables and on climate variables for column B, C, E, and F. Climate variables are introduced sequentially by columns. PDSI_<-4: Harsh Drought Prevalence; TX35: Max T°C above 35; TS_{9_12}: Mean°C in [9; 12). (W) indicates population-weighted variables. See appendix Table A.1 for further details. Coefficient estimates are reported in appendix Table A.15.

View Table

^{Table 2:}

Estimation of the effect of climate shocks on GDP growth: comparisons with the literature

	Burke et al. (2015			Kahn et al. (2021
	(A) base	(B) unchanged	(C) augmented	(D) base	(E) unchanged	(F) augmented
Climate variables	none	temperature, temperature2, precipitation, precipitation2	temperature, temperature2, precipitation, precipitation2, PDSI<-4 (W), TX35 (W), TS9,12,	none	temperature, precipitation, (deviations from trend for both), both their 4 lags	temperature, precipitation, (deviations from trend for both), both their 4 lags, PDSI<-4 (W), TX35 (W), TS9,12,
Country fixed effects	yes	yes	yes	yes	yes	yes
Country quadratic trends	yes	yes	yes	no	no	no
Year effects	yes	yes	yes	no	no	no
R-squared	0.403	0.407	0.413	0.216	0.220	0.228
Within R-squared	0.0165	0.0233	0.0334	0.110	0.114	0.123
AIC	-14,731	-14,752	-14,789	-16,151	-16,154	-16,200
BIC	-14,712	-14,708	-14,726	-16,132	-16,070	-16,096

Notes: Each column corresponds to a fixed-effect regression of the first difference in log real GDP per capita on two lags of the dependent variables and on climate variables for column B, C, E, and F. Climate variables are introduced sequentially by columns. PDSI_<-4: Harsh Drought Prevalence; TX35: Max T°C above 35; TS_{9_12}: Mean°C in [9; 12). (W) indicates population-weighted variables. See appendix Table A.1 for further details. Coefficient estimates are reported in appendix Table A.15.

We compare the performance of our approach with the model in Burke et al. (2015) by introducing climate variables sequentially. Relative to a specification without climate variables (column A in Table 2), the introduction of annual average temperature and precipitation and their squares improve the within R-square by 10 percent. If we additionally include our four selected climate variables, the within R-square increases by 102 percent (column C in Table 2). Similarly, the information criteria (AIC and BIC) unambiguously show improvement with our selected variables, while they do not clearly support the introduction of annual averages and their squares.

Turning our attention to Kahn et al. (2021), we adopt the same baseline specification focusing on the absolute deviations of annual average temperatures and precipitations relative to their respective 30-year moving average.²⁴ Column E in Table 2 reports results that are again extremely similar to those originally reported despite the smaller size of our sample.²⁵ In this case, the introduction of their climate variables relative to a basic case abstracting from climate improves the within R-square by 4 percent (columns D-E in Table 2). By contrast, additionally including our selected variables improves the within R-square by 12 percent.²⁶ The superior performance of our selected variables is again confirmed by the information criteria. Therefore, a range of performance indicators suggests that our climate variables are much more relevant in explaining GDP growth variations than annual average temperature and precipitation.

Persistence of selected weather shocks on GDP per capita

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel depicts the impulse response of per capita output in levels to a one standard deviation shock of the corresponding climate variable. Horizon 0 is the year of the shock. The shaded areas show the 90 percent confidence intervals around estimates. (W) indicates population-weighted variables.

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Persistence of selected weather shocks on GDP per capita

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel depicts the impulse response of per capita output in levels to a one standard deviation shock of the corresponding climate variable. Horizon 0 is the year of the shock. The shaded areas show the 90 percent confidence intervals around estimates. (W) indicates population-weighted variables.

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Persistence of selected weather shocks on GDP per capita

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel depicts the impulse response of per capita output in levels to a one standard deviation shock of the corresponding climate variable. Horizon 0 is the year of the shock. The shaded areas show the 90 percent confidence intervals around estimates. (W) indicates population-weighted variables.

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4.4. The dynamic effects of climate shocks

We examine the persistence of the GDP effects of a shock on the selected climate variables by using the local projection method. For each variable, we estimate the impulse response to a one standard deviation shock as described in the Section 2.2. The flexibility of this approach allows us to investigate if a climate shock has a temporary effect, a persistent effect on GDP levels, or a persistent effect on GDP growth.

The results in Figure 3 show that our selected climate shocks have very persistent effects on GDP levels that remain broadly significant over the 7-year horizon we consider. Specifically, a one-year increase in Mean T°C in [9; 12) has a positive effect that remains stable and significant throughout the period considered (Panel (c)). The respective adverse effects of an increase in Harsh Droughts Prevalence and in Max T°C above 35 are also stable, albeit subject to slightly more uncertainty (Panels (a) and (b)). The effects still remain significant over most of the horizons considered. The results in Figure 3 also show clearly that all effects have a persistent effect on GDP levels but no effect on GDP growth.²⁷

4.5. Heterogeneity

We test if results obtained using the whole sample of countries are different from those obtained using sub-groups of homogeneous countries. This exercise provides both a robustness test and new insights on the channels thought which climate shocks affect growth of GDP per capita.

We separate countries in rich and poor, hot and cold, agricultural and non-agricultural, agricultural cold and agricultural hot, and we divide countries in six macro-regional groups. For a detailed description of each group see Notes to Figure 5. For each subgroup, we use the same variables selected by the LASSO for the baseline specification because we are primarily concerned with the robustness of estimates across groups. We leave selection of variables by group to future research.

Table A.6 in appendix features summary statistics by sub-group for GDP per capita and climate variables. Figure 4 provides a graphic representation of the standard deviation of first differences for each variable by percentile. When absolute thresholds are used to derive climate variables, their frequency changes over space as a function of local climate. It is more likely to cross the 35°C threshold in hotter countries, keeping anything else constant. In very cold countries temperatures this high are almost never observed while in other countries they may be observed almost every year. This implies that both groups of countries will have low standard deviation of Max T°C above 35.²⁸ The standard deviation of Mean T°C in [9; 12) tends to be larger at the higher latitudes, and particularly in Europe. The prevalence of harsh droughts is instead measured using the PDSI indicator, which uses relative dryness or wetness with respect to average local conditions, including the effect of both precipitation and temperature. For this reason, the spatial distribution of the standard deviation of Harsh Drought Prevalence follows a pattern that reflects regional precipitation and temperature variation.

Global distribution of standard deviations of climate shocks

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel shows the percentiles of the global distribution of the standard deviation of the first difference of a climate variable over the period 1979–2019. (W) indicates population-weighted variables.

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Global distribution of standard deviations of climate shocks

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel shows the percentiles of the global distribution of the standard deviation of the first difference of a climate variable over the period 1979–2019. (W) indicates population-weighted variables.

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Global distribution of standard deviations of climate shocks

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel shows the percentiles of the global distribution of the standard deviation of the first difference of a climate variable over the period 1979–2019. (W) indicates population-weighted variables.

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These regional differences bear important implications for our estimation strategy because the identification of impacts from extreme weather events defined using absolute thresholds rely on variation from countries that predominantly have certain climatic, geographic and also socio-economic characteristics (e.g., income per capita and average temperature are highly correlated). Instability of coefficients across groups would warrant special attention because it may be a sign of omitted variable bias.

We find that our main results are generally confirmed across groups (Figure 5). If significant, coefficients tend to remain significant. There are no significant sign switches. Coefficients are almost never significantly different between groups. However, there is suggestive evidence that aggregate results my be driven by specific vulnerabilities in sub-groups of countries.

Harsh Drought Prevalence is significantly harmful in almost all groups. Severe droughts are harmful in both agricultural and non-agricultural countries, in rich and poor countries. Being hot does not necessarily mean that droughts are significantly harmful. Across regions, droughts in Middle East and North Africa (MENA) and Sub-Saharan Africa (SSA) have large and significant negative impacts. Droughts are also significantly harmful in the Europe and Central Asia region (ECA), an area with high frequency of droughts (see Figure 4). The effect of droughts is instead not significant in Latin American and the Caribbean (LAC) and in Eastern Asia and Pacific (EAP).

Weather Coefficients Across Groups

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel depicts the estimated coefficient for each weather variable using our baseline specification (column A in Table 1) for different sub-groups. Climate variables are standardized and their definitions are detailed in appendix Table A.1. The vertical lines show the 95 percent confidence intervals using standard errors clustered by country. (W) indicates population-weighted variables. Hot (N=3,472): 1979–2019 average temperature ≤22°C. Cold (N=3,078): 1979–2019 average temperature ď 22°C. Agricultural (N=3,130): share of “Agriculture, forestry, and fishing, value added (% of GDP)” in 2002 is above median across countries. Non Agricultural (N=3,062): countries that are not Agricultural. Agricultural Cold (N=1,124): agricultural and cold. Agricultural Hot (N=2,006): agricultural and hot. Rich (N=3,823): “High Income” and “Upper Middle Income” in WDI. Poor: “Low Income” and “Lower Middle Income” in WDI (N=2,727). SSA (N=1,629): Sub-Saharan Africa. MENA (N=538): Middle-East and North Africa. LAC (N=1,372): Latin America and the Caribbean. ECA (N=1,638): Eastern and Central Asia. EAP (N=1,013): Eastern Asia and Pacific. None of the coefficients is significant for North America and South Asia, due to the low number of countries in these regions.

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Weather Coefficients Across Groups

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel depicts the estimated coefficient for each weather variable using our baseline specification (column A in Table 1) for different sub-groups. Climate variables are standardized and their definitions are detailed in appendix Table A.1. The vertical lines show the 95 percent confidence intervals using standard errors clustered by country. (W) indicates population-weighted variables. Hot (N=3,472): 1979–2019 average temperature ≤22°C. Cold (N=3,078): 1979–2019 average temperature ď 22°C. Agricultural (N=3,130): share of “Agriculture, forestry, and fishing, value added (% of GDP)” in 2002 is above median across countries. Non Agricultural (N=3,062): countries that are not Agricultural. Agricultural Cold (N=1,124): agricultural and cold. Agricultural Hot (N=2,006): agricultural and hot. Rich (N=3,823): “High Income” and “Upper Middle Income” in WDI. Poor: “Low Income” and “Lower Middle Income” in WDI (N=2,727). SSA (N=1,629): Sub-Saharan Africa. MENA (N=538): Middle-East and North Africa. LAC (N=1,372): Latin America and the Caribbean. ECA (N=1,638): Eastern and Central Asia. EAP (N=1,013): Eastern Asia and Pacific. None of the coefficients is significant for North America and South Asia, due to the low number of countries in these regions.

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Weather Coefficients Across Groups

Citation: IMF Working Papers 2022, 156; 10.5089/9798400217203.001.A001

Notes: Each panel depicts the estimated coefficient for each weather variable using our baseline specification (column A in Table 1) for different sub-groups. Climate variables are standardized and their definitions are detailed in appendix Table A.1. The vertical lines show the 95 percent confidence intervals using standard errors clustered by country. (W) indicates population-weighted variables. Hot (N=3,472): 1979–2019 average temperature ≤22°C. Cold (N=3,078): 1979–2019 average temperature ď 22°C. Agricultural (N=3,130): share of “Agriculture, forestry, and fishing, value added (% of GDP)” in 2002 is above median across countries. Non Agricultural (N=3,062): countries that are not Agricultural. Agricultural Cold (N=1,124): agricultural and cold. Agricultural Hot (N=2,006): agricultural and hot. Rich (N=3,823): “High Income” and “Upper Middle Income” in WDI. Poor: “Low Income” and “Lower Middle Income” in WDI (N=2,727). SSA (N=1,629): Sub-Saharan Africa. MENA (N=538): Middle-East and North Africa. LAC (N=1,372): Latin America and the Caribbean. ECA (N=1,638): Eastern and Central Asia. EAP (N=1,013): Eastern Asia and Pacific. None of the coefficients is significant for North America and South Asia, due to the low number of countries in these regions.

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The harmful effect of Max T°C above 35 is significant in most groups, with the exception of cold countries and agricultural cold countries, where maximum daily temperatures above 35°C are rarely observed. SSA, with mostly agricultural, poor and hot countries, and EAP are the only regions with a significant harmful effect. Extreme temperatures appear to be particularly harmful in agricultural hot countries as well as in poor countries. This suggests that high vulnerability of agriculture to these high temperatures in mostly agricultural poor economies may explain the large impact on GDP growth.

The effect of Mean T°C in [9; 12) is not significant in countries that are hot, agricultural and hot, and poor. This is due to the relatively low frequency of these temperatures in these groups. The positive impact is particularly large in agricultural cold countries. This suggests that the variable is picking the beneficial effect of a longer growing season during both spring and fall in cold agricultural countries (Massetti et al., 2016). Among regional groups, the effect is positive and significant only in the EAC region, which comprises many cold agricultural countries.

5.1. A systematic empirical approach to macro-fiscal impacts

Fiscal outcomes can be affected by weather shocks through multiple channels. In the absence of active policy, the effect of climate on GDP can affect government finances as automatic stabilizers operate. Extreme weather shocks, like floods, can also hinder daily public operations by preventing government workers to go to work or by impairing public infrastructure. Alternatively, fiscal policy may respond actively to weather shocks to provide support, foster recovery, or address fiscal sustainability issues.

We consider three main fiscal indicators: government revenue, expenditure, and debt. We start by studying the effect of climate shocks on these variable measured by their GDP ratio as is standard practice in fiscal policy analysis. We then supplement this analysis by considering implications for the fiscal balance (revenue minus expenditure), also in this case measured as a GDP ratio. Finally, we study the effect of climate shocks on the percent change of the fiscal variables expressed in constant 2011 USD.²⁹ Examining variations in levels allows us to separately identify the effects of climate shocks on the numerator (fiscal variable) and denominator (GDP) of the ratios, as these can be of different magnitude and opposite sign. The government revenue-to-GDP ratio can be affected if a weather shock disproportionately reduces activity in sectors or economic agents that are taxed above- or below-average. For example, the revenue-to-GDP ratio can increase when the impact of a drought disproportionately affects sectors that pay little or no taxes. In such a case, the reduction of taxes because of the drought would be smaller than GDP losses, thereby increasing the ratio. Governments might also actively respond to a shock with countercyclical policies, for example, by lowering taxes in vulnerable sectors when a shock hits. Depending on the relative magnitude of the fiscal response and the GDP impact, the revenue-to-GDP ratio can either increase, stay constant, or decrease.

We expect the expenditure-to-GDP ratio to increase in countries with counter-cyclical fiscal policy. Under this assumption, the numerator (expenditure) increases to provide support in response to an adverse shock while the denominator declines (GDP), leading to an unambiguous increase in the ratio. For example, social transfers could increase to support those affected by adverse weather shocks, through automatic or active policy responses such as unemployment insurance or ad-hoc compensation schemes. In the case of weather catastrophes, government could raise capital expenditure to address reconstruction needs and foster a post-disaster recovery. A positive shock would lead to opposite effects, leading to a reduction of the expenditure-to-GDP ratio. However, for very severe shocks, a low-capacity government may indeed suffer from disorganization leading to delayed expenditure and a public recovery lagging the private sector’s. In such a case, the expenditure-to-GDP ratio may fall with an adverse shock.

When a shock leads to changes in revenue and expenditure that deteriorate the fiscal balance (i.e., when the fiscal deficit increases), this creates financing needs and we expect government debt to increase. However, timing issues could remove the correlation between fiscal variables, as a government could contract loans before actually implementing expenditure plans. Further, debt can be affected by other channels. When a government chooses to provide loans to help the private sector (or bail-outs), this form of support does not affect the fiscal balance but requires financing which is also likely to increase debt. Additionally, we cannot exclude the possibility that weather events have an effect on the exchange rate and, in turn, on the valuation of existing foreign debt. For example, this could be the case if a weather shock affects the price of export-oriented crops and thereby the terms of trade.

5.2. Estimates of the impact of climate shocks on macro-fiscal outcomes

We present empirical OLS estimates of the relationships between weather shocks and fiscal outcomes in Table 3. Our goal is to study how climate shocks affect GDP and all fiscal outcomes systematically while keeping the selection of variables compact. Therefore, we restrict the selection of climate variables: we focus on the three climate variables selected in our baseline for GDP and on the first weather variable selected by the LASSO for each of the three main fiscal ratios. The full list of the variables selected by LASSO with a random search is reported in appendix in Tables A.12-A.13. The algorithm performance as a function of the penalty parameter λ is reported in appendix in Figures A.7-A.6. We additionally report the effect of these variables on the fiscal balance and on the percentage change in the level of the other fiscal variables.

Our sample becomes smaller when we introduce fiscal variables because of their narrower coverage. To allow for a meaningful comparison across fiscal outcomes, we implement our analysis on the sample with non-missing values for all fiscal variables. The smaller sample size and the addition of other weather variables explain the difference in results obtained for GDP growth compared to the previous section (column A in Table 1 versus column A in Table 3). Weather effects tend to become smaller and the effect of Max T°C above 35 becomes slightly smaller and insignificant.

The three climate variables selected by LASSO for expenditure, revenue, and debt are new. For the revenue-to-GDP ratio, the LASSO procedure selects the contemporaneous value of the population-weighted number of days in the longest dry spell , which is defined as an uninterrupted period in which at least 80% of a country’s grid cells have precipitations less than 1 mm per day (Longest Dry Spell (.80) — LLDS_.80). The first lag of Continued Heavy Precipitation (PC95WD) is selected as a key driver of the expenditure-to-GDP ratio. This variable is constructed as the largest number of consecutive days with precipitation above the 95^th percentile of a country’s daily precipitation distribution. Wetness Intensity (MPDSI_>3) is selected for the debt-to-GDP ratio. To construct this variable, we first compute the share of grid cells with moisture conditions far exceeding their typical level in every month and then retain the maximum share among the 12 months of the year. Therefore, this variable measures the extent of abnormal moisture at its peak and can proxy for flood-like conditions. Table 3 shows that these newly selected variables have negative impacts on GDP growth. This was expected because they represent adverse weather conditions, but the effects are not significant.

Turning our attention to fiscal outcomes, we find that the fraction of within variation in the fiscal variables explained by the model is at least as large as for GDP growth, as shown by the within R-square. The magnitudes of the estimated effects of the new climate variables are somewhat similar to the estimated effect of weather shocks on GDP reported in the previous section.

The climate variables that we previously selected for GDP have mixed effects on fiscal variables. In some cases, the effects are small and insignificant, indicating that fiscal policy remains cyclically neutral (first three rows of climate variables in Table 3). However, there is also evidence of non-neutral fiscal responses.

First, we find evidence that Harsh Drought Prevalence increases the expenditure-to-GDP ratio. This seems to be the result of a combined increase in expenditure levels and decline in GDP (columns A, C and G). This would support the hypothesis of increased support from governments in the form of additional spending. Droughts do not seem to have an impact on the other fiscal variables.

Second, we find that revenue collection declines in response to an increase in Max T°C above 35. This results from a sharp reduction in the level of revenue (column F), which affects the revenue-to-GDP ratio (column B), even if GDP is also declining (column A). The revenue loss translates into a weakly significant negative effect on the balance-to-GDP ratio.

Third, we find that an increase in Mean T°C in [9; 12) (column F) raises revenue significantly but in roughly the same proportion as it raises GDP. This suggests that that the positive shock estimated on GDP translates into higher tax collection. As a result, the impact on the revenue-to-GDP ratio is positive but insignificant. In the absence of a significant response of expenditure (column C), the balance-to-GDP indicates an unambiguous positive effect on the fiscal balance (column D).

The new variables selected by the LASSO for the fiscal variables also have mixed effects, although they mostly point towards the counter-cyclical response of the fiscal variables.

An increase in Wetness Intensity (a proxy flood-like conditions) leads to a significant increase in public expenditure (column G) and in the expenditure-to-GDP ratio (column C). We also find that the debt and the debt-to-GDP ratio significantly increase (column E and H). The debt increase could come from a rise in expenditure, but it could additionally be due to the extension of public loans to the private sector as support. Wetness Intensity has a negative but insignificant effect on GDP, indicating a that the policy response to the shock is counter-cyclical and that the fiscal response might be effective in mitigating the effect of the shock on GDP.

An increase in Longest Dry Spell (0.80) is associated with a sizeable but insignificant increase in the fiscal deficit (column D) and a significant increase in the debt-to-GDP ratio (column E). An increase in the lag of Continued Heavy Precipitation has a similar and also insignificant negative impact on the fiscal balance. However, in the case of this shock, the response of expenditure (column G) is large and significant. These weather variables would be expected to have a negative effect on GDP but we only find very weak and insignificant negative coefficient estimates (column A). Overall and despite noisy results, we find systematic evidence of economic support from fiscal policy in response to these likely adverse weather shocks, especially in the form of increased public spending and debt.

When we consider slight variations in the definition of the weather variables selected for fiscal outcomes, we can find significant and negative effects on GDP and retain significance for the fiscal outcomes (Table A.16). For dry spells, we experiment with spells that affect 95 percent instead of 80 percent of the country (Longest Dry Spell (0.90) – LLDS_.95). Instead of Wetness Intensity, we use a variable based on a higher threshold and average annual conditions rather than on the worse month (Very Wet Conditions — PDSI_≥4). The LASSO only selects variables that are relevant for one fiscal variable at a time. Therefore, the resulting selection can miss alternative definitions with better explanatory power for other fiscal variables. By experimenting with close alternative variable definitions, we confirm that these types of weather shocks can have adverse effects on the economy.

We investigate further whether the lack of fiscal space can prevent a counter-cyclical fiscal policy response and imply more adverse GDP impacts. To this end, we interact weather shocks with a measure of fiscal space. To reflect country fiscal space, we compute the standardized deviation of the debt-to-GDP ratio from its mean by country. Our assumption is that a large deviation of debt-to-GDP above the country mean should be correlated with lower fiscal space. We experiment with non-linear functions and retain the cube of the deviation as having explanatory power. As reported in Table A.17 in appendix, we only find a significant interaction in the case of Continued Heavy Precipitation. For this weather shock, countries having more debt than they have on average experience a muted increase in debt but experience a significant reduction in GDP per capita, thereby providing support to our hypothesis.

In summary, we find that weather shocks can have rich and large effects on fiscal aggregates, although impacts are not always significant. The cyclicality and policy mix of fiscal responses depend on the nature of the weather shock. We find evidence that the response of revenue to an adverse increase in Max T°C above 35 and to a beneficial increase in Mean T°C in [9; 12) is pro-cyclical. Conversely, we find that government expenditure and debt increase in a counter-cyclical manner in response to various weather shocks related to droughts or intense precipitation.

^{Table 3:}

Estimates of macro-fiscal effects of selected climate variables

Note: The dependent variables are indicated in the column titles and are expressed in percentages. We use the same three climate variables used for GDP growth and the first climate variables selected by the LASSO respectively for government revenue, expenditure, and debt. All climate variables are standardized with standard deviations equal to 100 to ease interpretation. (W) indicates population-weighted variables. Controls include the first two lags of the dependent variable (reported in the first two rows), and year and country fixed effects. Standard errors are clustered by country and reported in brackets. * p < 0.10; **p<0.05, ***p<0.01.

^{Table 3:}

Estimates of macro-fiscal effects of selected climate variables

		(A)	(B)	(C)	(D)	(E)	(F)	(G)	(H)
		$\Delta \ln \frac{GDP}{POP}p.c.$	$\Delta \frac{\mathrm{Re}venue}{GDP}p.p.$	$\Delta \frac{Expenditure}{GDP}p.p.$	$\Delta \frac{Balance}{GDP}p.p.$	$\Delta \frac{Debt}{GDP}p.p.$	Δ In Revenue p.c.	Δ In Expenditure p.c.	Δ In Debt p.c.
Lag(l) of Fiscal Variable		0.169*** (0.0562)	-0.256*** (0.0494)	-0.250*** (0.0502)	-0.310*** (0.0315)	0.074** (0.0292)	-0.199*** (0.0534)	-0.102*** (0.0340)	0.136*** (0.0318)
Lag(2) of Fiscal Variable		0.018 (0.0189)	-0.133*** (0.0175)	-0.062** (0.0301)	-0.122*** (0.0240)	0.137** (0.0685)	-0.074 (0.0467)	-0.054 (0.0401)	0.027 (0.0233)
	First difference in
	Harsh Drought Prevalence (W)	-0.146** (0.0661)	0.084 (0.0514)	0.131** (0.0525)	-0.047 (0.0516)	-0.053 (0.1274)	0.261 (0.2106)	0.327* (0.1891)	-0.143 (0.2384)
	Max T°C above 35 (W)	-0.109 (0.0808)	-0.150** (0.0636)	-0.013 (0.0483)	-0.133* (0.0745)	-0.067 (0.1461)	-1.094** (0.4881)	-0.301 (0.3329)	0.063 (0.2433)
	Mean T°C in [9; 12)	0.146*** (0.0455)	0.047 (0.0340)	-0.064 (0.0565)	0.107** (0.0516)	0.003 (0.1117)	0.247** (0.1207)	-0.003 (0.1347)	-0.072 (0.2286)
	Longest Dry Spell (.80) (W)	-0.008 (0.0514)	-0.107 (0.1026)	0.017 (0.0562)	-0.131 (0.0963)	0.343* (0.1974)	-0.356 (0.3077)	-0.051 (0.2450)	-0.101 (0.3096)
	Lag(1) of Cont’d Heavy PPT	-0.019 (0.0603)	0.056 (0.0673)	0.132 (0.0886)	-0.066 (0.1060)	0.218 (0.1436)	0.171 (0.3100)	0.522* (0.2655)	0.336 (0.2391)
	Wetness Intensity	-0.039 (0.0514)	0.046 (0.0563)	0.128** (0.0596)	-0.081 (0.0797)	0.358* (0.1949)	0.022 (0.2276)	0.387* (0.1995)	0.829*** (0.2748)
	Constant	1.606*** (0.1134)	0.143*** (0.0057)	0.099*** (0.0047)	0.041*** (0.0017)	0.020 (0.0131)	5.041*** (0.2936)	4.456*** (0.2411)	3.458*** (0.1628)
	Observations	3849.000	3849.000	3849.000	3849.000	3849.000	3849.000	3849.000	3849.000
	R-square	0.267	0.114	0.118	0.151	0.139	0.128	0.078	0.167
	Within R-square	0.037	0.072	0.063	0.094	0.030	0.050	0.018	0.024

Note: The dependent variables are indicated in the column titles and are expressed in percentages. We use the same three climate variables used for GDP growth and the first climate variables selected by the LASSO respectively for government revenue, expenditure, and debt. All climate variables are standardized with standard deviations equal to 100 to ease interpretation. (W) indicates population-weighted variables. Controls include the first two lags of the dependent variable (reported in the first two rows), and year and country fixed effects. Standard errors are clustered by country and reported in brackets. * p < 0.10; **p<0.05, ***p<0.01.

View Table

^{Table 3:}

Estimates of macro-fiscal effects of selected climate variables

		(A)	(B)	(C)	(D)	(E)	(F)	(G)	(H)
		$\Delta \ln \frac{GDP}{POP}p.c.$	$\Delta \frac{\mathrm{Re}venue}{GDP}p.p.$	$\Delta \frac{Expenditure}{GDP}p.p.$	$\Delta \frac{Balance}{GDP}p.p.$	$\Delta \frac{Debt}{GDP}p.p.$	Δ In Revenue p.c.	Δ In Expenditure p.c.	Δ In Debt p.c.
Lag(l) of Fiscal Variable		0.169*** (0.0562)	-0.256*** (0.0494)	-0.250*** (0.0502)	-0.310*** (0.0315)	0.074** (0.0292)	-0.199*** (0.0534)	-0.102*** (0.0340)	0.136*** (0.0318)
Lag(2) of Fiscal Variable		0.018 (0.0189)	-0.133*** (0.0175)	-0.062** (0.0301)	-0.122*** (0.0240)	0.137** (0.0685)	-0.074 (0.0467)	-0.054 (0.0401)	0.027 (0.0233)
	First difference in
	Harsh Drought Prevalence (W)	-0.146** (0.0661)	0.084 (0.0514)	0.131** (0.0525)	-0.047 (0.0516)	-0.053 (0.1274)	0.261 (0.2106)	0.327* (0.1891)	-0.143 (0.2384)
	Max T°C above 35 (W)	-0.109 (0.0808)	-0.150** (0.0636)	-0.013 (0.0483)	-0.133* (0.0745)	-0.067 (0.1461)	-1.094** (0.4881)	-0.301 (0.3329)	0.063 (0.2433)
	Mean T°C in [9; 12)	0.146*** (0.0455)	0.047 (0.0340)	-0.064 (0.0565)	0.107** (0.0516)	0.003 (0.1117)	0.247** (0.1207)	-0.003 (0.1347)	-0.072 (0.2286)
	Longest Dry Spell (.80) (W)	-0.008 (0.0514)	-0.107 (0.1026)	0.017 (0.0562)	-0.131 (0.0963)	0.343* (0.1974)	-0.356 (0.3077)	-0.051 (0.2450)	-0.101 (0.3096)
	Lag(1) of Cont’d Heavy PPT	-0.019 (0.0603)	0.056 (0.0673)	0.132 (0.0886)	-0.066 (0.1060)	0.218 (0.1436)	0.171 (0.3100)	0.522* (0.2655)	0.336 (0.2391)
	Wetness Intensity	-0.039 (0.0514)	0.046 (0.0563)	0.128** (0.0596)	-0.081 (0.0797)	0.358* (0.1949)	0.022 (0.2276)	0.387* (0.1995)	0.829*** (0.2748)
	Constant	1.606*** (0.1134)	0.143*** (0.0057)	0.099*** (0.0047)	0.041*** (0.0017)	0.020 (0.0131)	5.041*** (0.2936)	4.456*** (0.2411)	3.458*** (0.1628)
	Observations	3849.000	3849.000	3849.000	3849.000	3849.000	3849.000	3849.000	3849.000
	R-square	0.267	0.114	0.118	0.151	0.139	0.128	0.078	0.167
	Within R-square	0.037	0.072	0.063	0.094	0.030	0.050	0.018	0.024

Note: The dependent variables are indicated in the column titles and are expressed in percentages. We use the same three climate variables used for GDP growth and the first climate variables selected by the LASSO respectively for government revenue, expenditure, and debt. All climate variables are standardized with standard deviations equal to 100 to ease interpretation. (W) indicates population-weighted variables. Controls include the first two lags of the dependent variable (reported in the first two rows), and year and country fixed effects. Standard errors are clustered by country and reported in brackets. * p < 0.10; **p<0.05, ***p<0.01.