TThe economic impact of weather and climate
Richard S.J. Tol a,b,c,d,e,f,1, ∗ a Department of Economics, University of Sussex, Falmer, United Kingdom b Institute for Environmental Studies, Vrije Universiteit, Amsterdam, The Netherlands c Department of Spatial Economics, Vrije Universiteit, Amsterdam, The Netherlands d Tinbergen Institute, Amsterdam, The Netherlands e CESifo, Munich, Germany f Payne Institute for Earth Resources, Colorado School of Mines, Golden, CO, USA
I propose a new conceptual framework to disentangle the impacts of weather and climate oneconomic activity and growth: A stochastic frontier model with climate in the productionfrontier and weather shocks as a source of ineﬃciency. I test it on a sample of 160 countriesover the period 1950-2014. Temperature and rainfall determine production possibilitiesin both rich and poor countries; positively in cold countries and negatively in hot ones.Weather anomalies reduce ineﬃciency in rich countries but increase ineﬃciency in poor andhot countries; and more so in countries with low weather variability. The climate eﬀect islarger that the weather eﬀect.
Keywords : climate change; weather shocks; economic growth;stochastic frontier analysis
JEL codes : D24; O44; O47; Q54
Climate matters to the economy. Not in the way that classical thinkers such as Guan Zhong,Hippocrates or Ibn Khaldun, or modern thinkers such as Huntington (1915) or Diamond(1997) argue it does. Environmental determinism is inconsistent with the observations. ∗ Jubilee Building, BN1 9SL, UK
Email address: [email protected] (Richard S.J. Tol)
URL: (Richard S.J. Tol) Marco Letta expertly assisted with data collection and regressions. Peter Dolton, Jurgen Doornik, BillGreene, David Hendry, Andrew Martinez, Pierluigi Montalbano and Felix Pretis had excellent commentson earlier versions of this work. I also thank seminar participants at the EMCC-III conference, Universityof Sussex, UNU-MERIT University, the 2019 IAERE conference, Cambridge University, London School ofEconomics, Sapienza University of Rome, Shanghai Lixin University, Edinburgh University, University ofSouthern Denmark, Federal Reserve Bank of San Francisco, and CESifo.
Preprint submitted to Elsevier March 1, 2021 a r X i v : . [ ec on . GN ] F e b here are thriving economies in the desert, in the tropics, and in the polar circle. There isdestitution, too, in all these places. Climate is not destiny, but it does matter.The prevailing view among economists, with some exceptions (Bloom and Sachs, 1998,Sachs, 2003, Olsson and Hibbs, 2005, Barrios et al., 2010), is that climate does not matter foreconomic development, only institutions do (Easterly and Levine, 2003, Rodrik et al., 2004).Some argue that climate and geography partly shaped institutions in the past, but havebecome irrelevant since (Acemoglu et al., 2001, 2002, Alsan, 2015). Institutional determinismis just as inconsistent with the observations. The two halves of the Korean Peninsula andof the island of Hispaniola are powerful reminders of the importance of institutions, butclimate matters for agriculture (Mendelsohn et al., 1994, Schlenker et al., 2005), for energydemand (Mansur et al., 2008), for tourism (Lise and Tol, 2002), for transport (Koetse andRietveld, 2009), for labour productivity (Kjellstrom et al., 2009, Zander et al., 2015), andfor health (Sachs and Malaney, 2002)—and thus for the economy as a whole.Climate matters, but it has been an empirical challenge to demonstrate this using countrydata. Climate changes only slowly over time, its signal swamped by confounders, many ofwhich change more quickly than climate. Climate varies substantially over space, but so do agreat many other things that we know are important for development. The insigniﬁcance ofclimate variables in cross-country studies may be due to a lack of statistical power. Indeed,a climate association is signiﬁcant in subnational income data (Nordhaus, 2006, Dell et al.,2009, Henderson et al., 2018, Kalkuhl and Wenz, 2020) and, as is shown below, in long panels.Because of the confounders, this association cannot be given a causal interpretation.Unlike the impact of climate , the impact of weather can be identiﬁed—or so people haveargued. Identiﬁcation rests on the fact that weather is random (Heal and Park, 2016), atleast from the perspective of the economy. The problem with this argument is that bynow many diﬀerent economic activities have been found to be aﬀected by the weather (seeAuﬀhammer and Aroonruengsawat, 2011, Barreca et al., 2016, Deschenes and Greenstone,2007, Graﬀ Zivin et al., 2020, Leightner, 1999, Li et al., 2018, Pechan and Eisenack, 2014,Ranson, 2014, Zhang et al., 2018, among others), and these activities impact one another.Causality notwithstanding, these studies show that weather matters to the economy. How-ever, the impacts of weather shocks cannot readily be extrapolated to the impacts of climatechange (Dell et al., 2014, Kolstad and Moore, 2020). Climate is what you expect, weather iswhat you get. Weather are draws from an probability distribution. Climate is that distribu-tion. Climate change shifts the moments of the weather distribution (Auﬀhammer, 2018b).Weather is unpredictable for more than a few days ahead. Adaptation to weather shocksis therefore limited to immediate responses—put up an umbrella when it rains, close theﬂood gates when it pours. Adaptation to climate change extends to changes in the capi-tal stock—buy an umbrella, build ﬂood gates. Furthermore, adaptation to climate changedepends on updates of the expectations for weather (Severen et al., 2018, Lemoine, 2017, Andersen et al. (2016) argue that it is UV radiation, rather than climate, that aﬀects development. short-run elasticity,whereas the long-run elasticity is needed to estimate the impact of climate change.Hsiang (2016) and Deryugina and Hsiang (2017) argue that the marginal eﬀect of a weathershock equals the marginal climate eﬀect. Climate change is not marginal but its total impactis an integral of marginals. Their assumptions are quite restrictive, however. Economicagents need to be (1) rational and their adaptation investments (2) optimized. Adaptationneeds to be (3) private and adaptation options (4) continuous. The economy needs to be ina (5) spatial equilibrium and (6) markets complete. Adaptation investments are often long-lived, so both spot and future markets should be complete. Spatial zoning and transporthubs distort the spatial equilibrium. Adaptation is often lumpy, be it air conditioning orirrigation. Some adaptation options, such as coastal protection, are public goods. Otheradaptation options, such as protection against infectious disease, have externalities. Agentsare not always rational, and decisions suboptimal. The result by Deryugina and Hsiang isalmost an impossibility theorem.Weather aﬀects economic activity, and so the measurement of the impact of climate oneconomic activity. Weather can be seen as noise, but that noise may well be correlatedwith climate, the right-hand-side variable of interest. I therefore propose a new way tosimultaneously model the impact of climate and weather, to show that both matter andthat previous work is misspeciﬁed.The empirical strategy rests on the following assumptions. Climate aﬀects production pos-sibilities. This is obvious for agriculture: Holstein cows do well in Denmark but jasminerice does not; the reverse is true in Thailand. Climate also aﬀects energy and transport,and thus all other sectors of the economy. Weather aﬀects the realization of the productionpotential. Hot weather may slow down workers, frost may damage crops, ﬂoods may disrupttransport and manufacturing. Conceptualized thus, climate aﬀects the production frontier,and weather the distance from that frontier. The econometric speciﬁcation is therefore astochastic frontier analysis with weather variables in ineﬃciency and climate variables in thefrontier. Climate aﬀects potential output, weather the output gap.I apply the proposed method to a panel of output per worker, measured at the country level.Dell et al. (2012), Letta and Tol (2018) and Newell et al. (2018) ﬁnd that weather shocks hitthe economic growth of poorer countries harder. Burke et al. (2015) instead ﬁnd that hotter countries are hit harder, a speciﬁcation adopted by Pretis et al. (2018) and Kalkuhl andWenz (2020). Generoso et al. (2020) has a similar result. Within sample, it is diﬃcult todistinguish between these two speciﬁcations as hotter countries tend to be poorer. However,out of sample, a hotter, richer world would be more vulnerable to weather shocks accordingto Burke, but less vulnerable according to Dell. Kahn et al. (2019) reject heterogeneity.The results below shed new light on these questions. Kumar and Khanna (2019) estimate the impact of temperature and rainfall on ineﬃciency in output growth . I here study ineﬃciency in output. They omit climate from the frontier. In the model below, climate andweather interact at the same level.The cross-validation study of ? ﬁnds that weather aﬀects the level of GDP rather than itsgrowth rate, a speciﬁcation adopted here in line with the intuition sketched above. Fur-thermore, I assume that the economy is aﬀected by unusual weather rather than weather.Frost of -10 ℃ brought Texas to a standstill in February 2021, but is a regular occurrence inNorth Dakota without major consequences. I therefore standardize the weather, expressingtemperature and precipitation in standard deviations from the mean. This introduces aninteraction between weather and climate, and an implicit model of adaptation.The paper proceeds as follows. Section 2 describes methods and data. Section 3 presentsthe baseline results. Section 4 conducts the sensitivity analysis. Section 5 discusses theimplications for climate change. Section 6 concludes.
2. Methods and data
I assume a Cobb-Douglas production function: Y c,t = A c,t K βc,t L − βc,t (1)Total factor productivity A c,t is the Solow residual in country c at time t : It captureseverything that aﬀects output Y c,t that cannot be explained by capital K c,t or labour L c,t .I concentrate Equation (1) by dividing K and L by labour force L , and denote the resultingvariables in lower case.Taking natural logarithms, the equation to be estimated is:ln y c,t = α + β ln k c,t (2)I assume that total factor productivity is a function of moving averages of weather variables(average temperature, ¯ T c,t , and precipitation, ¯ R c,t ). This is loosely based on Nordhaus(1992). Weather shocks aﬀect the variance of the stochastic component of permanent income.Hence, Equation (2) becomes:ln y c,t = β ln k c,t + f (cid:0) ¯ T c,t , ¯ R c,t (cid:1) + µ c + t + v c,t − u c,t (3)where ¯ T c,t and ¯ R c,t are the average temperature c.q. precipitation in country c in the thirtyyears preceding year t , µ c is a full set of country ﬁxed eﬀects, t is a linear time trend, Bigano et al. (2006) use a similar model for tourist destination choice, with climate at destination atthe bottom and climate at origin at the top. c,t ∼ N (0 , σ v ) and u c,t ∼ E ( λ c,t ) = E (cid:18) γ + γ g (cid:18) T c,t − ¯ T c,t τ c,t (cid:19) + γ g (cid:18) R c,t − ¯ R c,t ρ c,t (cid:19)(cid:19) (4)where τ and ρ are the standard deviations of temperature and rainfall, respectively. Insteadof the unwieldy T − ¯ T / τ , I write z ( T ); ditto for R . This is standardized temperature andprecipitation. In the base speciﬁcation, f (cid:0) ¯ T c,t , ¯ R c,t (cid:1) ≡ β ¯ T c,t + β ¯ T c,t + β ¯ R c,t + β ¯ R c,t + β ¯ T c,t ¯ R c,t and g ( · ) ≡ | · | . I refer to Equation (3) as the frontier or potential output, and toEquation (4) as ineﬃciency or the output gap.I use the True Fixed-Eﬀect (TFE) model (Greene, 2005) to estimate a one-step stochasticfrontier model in a ﬁxed-eﬀect setting with explanatory variables in the ineﬃciency pa-rameter. I use the sfmodel package for Stata (Kumbhakar et al., 2015) to estimate themodel.Equation (3) assumes that both error terms are stationary. This is a tall assumption. Iam not aware of any statistical test for stationarity that applies to this particular estimatorand these distributional assumptions. I use three remedies. First, I include a time trend inEquation (3), and try many variants of that trend. Second, I show robustness to diﬀerentspeciﬁcations. Third, I reformulate the model as an error-correction one. The output gapfollows ∆ ln y c,t = ψ ∆ z ( T c,t ) + ψ ∆ z ( R c,t ) + ψ V c,t + µ c + w c,t (5)where potential output is V c,t = ln y c,t − µ c − µ t − ϑ ln k c,t − f ( ¯ T c,t , ¯ R c,t ) (6)and µ t are time dummies which act as a non-parametric time trend. This alternativeestimation strategy shows that the ﬁndings are robust to the inclusion of non-parametrictime trends. This alternative speciﬁcation is also better suited to explicitly model the path ofconvergence towards the long-term equilibrium in a stochastic setting and provide empiricalevidence for the speed of recovery after weather perturbations. I of course also perform theusual stationarity tests on the error-correction model.I test for heterogeneity by interacting the variables of interest with dummies for poor coun-tries and hot countries. I deﬁne a country as “poor” if the World Bank does. Alternative,a country is deemed poor if its GDP per capita was below the 25th percentile of the dis- Taking ﬁrst diﬀerences of all variables may get rid of unit roots in the frontier but would change thedistributional assumptions in ineﬃciency. Rob Engle (personal communication) suggests that standard stationary tests would roughly apply here. The use of a non-parametric time trend was not possible in the baseline SFA model because the inclusionof so many time dummies causes convergence issues in an already computationally cumbersome maximumlikelihood estimation. The WB classiﬁcation of high-income economies is available here. A “hot” country is deﬁned as a country whose average annualtemperature is above the 75th percentile of the distribution.
The dataset is an unbalanced panel consisting of 160 countries over the period 1950-2014.Data for this study come from two sources. Economic data on output, capital and labourforce are taken from the Penn World Table (PWT), PWT 9.0 (Feenstra et al., 2015). Weatherdata are from the University of Delaware’s
Terrestrial air temperature and precipitation:1900-2014 gridded time series, (V 4.01) (Matsuura and Willmott, 2015). These griddeddata have a resolution of 0 . × . ×
55 kilometers atthe equator. Following previous literature (Dell et al., 2014, Burke et al., 2015, Auﬀhammeret al., 2013), we aggregate these grid cells at the country-year level, weighting them bypopulation density in the year 2000 using population data from Version 4 of the
GriddedPopulation of the World . , with the exception of Singapore. We use these weather data toconstruct both the climate and weather variables as deﬁned in Section 2.1. Table 1 presentsdescriptive statistics for the key variables.
Table 2 shows the results of the base speciﬁcation outlined in Equations (3) and (4). Sixvariants are presented. Column 1 reports homogeneous eﬀects in both the frontier andthe ineﬃciency. In the frontier, capital per worker has a signiﬁcant impact on output perworker. The output elasticity is around 0.63, in line with previous estimates. This estimateis robust to speciﬁcation. Long-run temperature (i.e. climate) has a signiﬁcant impact onthe production frontier, but precipitation does not, as in earlier papers (Dell et al., 2012,Burke et al., 2015, Letta and Tol, 2018). Short-term weather anomalies, either temperatureor precipitation, are insigniﬁcant in determining ineﬃciency.Columns 2 and 3 show heterogeneous impacts between rich and poor countries. The hy-pothesis is that poor countries are disproportionately aﬀected by climate and weather, aseconomic activity is concentrated in agriculture and public investment in protective mea-sures is limited. Column 2 allows heterogeneity only in the production frontier. That is,I interact climate variables with the poor country dummy deﬁned in Subsection 2.1. Theinteraction terms are individually insigniﬁcant. Column 3 adds heterogeneity in ineﬃciency.Results for the production frontier are almost unchanged. Impacts on ineﬃciency sharply Available here. Singapore has a surface smaller than the size of the weather grids. Given it is one of the few countriesthat are both rich and hot and thus increase the statistical power of the analysis, we kept it in the sampleby attributing to it the weather data of the grid cell in which it is situated. See the Appendix for a complete list of countries and regions in the sample. either poor countries (e.g. Dell et al., 2012, Letta and Tol, 2018) or hot countries (Burkeet al., 2015) particularly vulnerable to weather anomalies. I ﬁnd both .Columns 1-4 specify that, in the frontier, hot and cold countries respond diﬀerently totemperature, and dry and wet countries diﬀerently to rainfall. Column 5 adds the interactionbetween rainfall and temperature to the frontier. This interaction is negative, but less so inpoor countries. The rainfall terms are now signiﬁcant too: Wetter countries are richer, andthis eﬀect is weaker for poor countries.Dropping the insigniﬁcant interaction terms between temperature and poverty (column 6)hardly aﬀects the parameter estimates. Column 6 is the preferred speciﬁcation.Weather anomalies increase ineﬃciency in poor countries, as expected. Weather anomalies decrease ineﬃciency in rich countries—that is, unexpectedly much or little water, or unusu-ally hot or cold weather stimulate the economy. This is harder to explain. It may reﬂect therestoration eﬀort after ﬂoods, and crop insurance and government support after droughts.The data are GDP rather than NDP, and thus suﬀer from Bastiat’s broken window. Thiseﬀect is not observed in poor countries because restoration after natural disasters is limitedand delayed (Cavallo and Noy, 2011).I interpret the eﬀect size below, after discussing the robustness of the results.
I implement three diﬀerent types of robustness checks: sensitivity to diﬀerent speciﬁcationsin the SFA model; an alternative distributional assumption for the ineﬃciency parameter;and an error-correction model to formally test for non-stationarity. For all these sensitiv-ity tests, with the exception of the error-correction model, I only report estimates of thepreferred speciﬁcation, column 6 of Table 2.
This ﬁrst set of robustness checks implements the same baseline model described in Equa-tions (3) and (4) but adopts a broad set of diﬀerent speciﬁcation choices for key variablesand interactions.
I test whether the core ﬁndings are driven by the somewhat arbitrary discrimination betweenrich and poor countries. I replace the World Bank classiﬁcation of countries that are rich Available here.
7y the “poorest 25% in 1990”. Results are in column 2 of Table 3. Column 1 repeats thebase speciﬁcation (column 6) of Table 2.For the production frontier, results are qualitatively the same as in Table 2. The maindiﬀerence is that precipitation loses much of its predictive power, highlighting that diﬀerenteconomies do respond diﬀerently to the availability of water resources. As for the ineﬃciency,results are again qualitatively similar to the baseline model, but coeﬃcients are closer tozero and less signiﬁcant. The log-pseudolikelihood is much lower.
Second, I replace absolute weather anomalies in the ineﬃciency term with squared anomalies.This places a heavier weight on larger anomalies. See column 3 of Table 3. The results forthe production frontier are largely unaﬀected, and the qualitative results for the ineﬃciencyare as above. The log-pseudolikelihood falls.
The weather anomalies in Equation (4) are absolute anomalies. Cold and hot weather, wetand dry spells are assumed to equally increase technical ineﬃciency. Column 4 of Table 3instead use the anomalies. Estimates for the production frontier are almost unaltered. Theparameters for ineﬃciency become insigniﬁcant. Economies are aﬀected by unusual weather,rather than by the weather per se . Adaptation matters.
I also test for asymmetric anomalies, disentangling negative and positive weather shocks onineﬃciency. This is the preferred speciﬁcation of Kahn et al. (2019). Results are in column5 of Table 3. The frontier is not aﬀected. The results are much as above, with anomalousweather being good for rich countries but bad for hot and poor countries. While there issome evidence for asymmetry between the impact of wet and dry spells, cold and hot spells,the increase in the log-pseudolikelihood is minimal (less than 6 points) for the six additionalparameters estimated.
I also look at weather eﬀects on productivity, moving weather anomalies from the ineﬃciencyparameter to the production frontier. Results are in column 6 of Table 3. The frontier doesnot change. Coeﬃcients of weather variables are individually insigniﬁcant and the log-pseudolikelihood is sharply lower. This speciﬁcation, variations of which are often used inliterature, is not the preferred one.
Equation (4) assumes an exponential half-normal distribution for ineﬃciency. Column 7 ofTable 3 show results for the half-normal distribution. The estimates for the frontier are as Truncated-normal models with ﬁxed-eﬀects are known to suﬀer severe convergence issues, and this casewas no exception. It is therefore excluded. √ . π − I ﬁnd a signiﬁcant association between climate and economic performance. In the con-centrated Cobb-Douglas production function, Equation (1), there are two determinants ofoutput per worker: climate and capital per worker. In this speciﬁcation, capital is a defacto substitute for climate, with a constant elasticity. I test that assumption, answeringthe question whether suﬃcient capital would make a country immune from the inﬂuenceof its climate. I therefore interact long-run temperature variables with capital per workerin the production frontier. See Table 4, Columns 2 and 3; column 1 reproduces the basemodel from Table 2. Rainfall is signiﬁcant and so are its interactions with capital. The in-teractions have the opposite signs. That is, climate’s inﬂuence on output shrinks as capitaldeepens. The interaction between temperature, rainfall and capital is insigniﬁcant. The log-pseudolikelihood increases by 7 points. However, interactions work both ways. The outputelasticity of capital now depends on rainfall, varying between 0.73 in the driest countriesand 0.93 in the wettest ones. A 5.5% increase in rainfall, well within the climate changeprojections for this century, would lead to increasing returns to scale and explosive economicgrowth. I therefore keep the base speciﬁcation as is.Column 2 only changes the frontier. In column 3, I replace the interaction with the povertydummy by an interaction with capital per worker. Signs change and the log-pseudolikelihoodfalls. Poverty is more than a lack of capital, and poverty drives vulnerability to weathershocks.
In the debate on the long-run determinants of growth and development, some ﬁnd thatclimate plays a fundamental role in shaping long-run development, whereas others arguethat the impact of climate disappears when accounting for institutions, although climatemay have shaped those institutions. I test this in column 4 of Table 4. As a proxy forinstitutional quality, I use the
Polity2 Score . This categorical variable is an aggregatescore which ranges from -10 (hereditary monarchy) to 10 (consolidated democracy). Whilethis is not the best indicator for institutional quality, it is correlated with other indicators.Historical depth is the key advantage of Polity2 over other indicators, which are availableonly for recent years. I interact it with long-run precipitation in the production frontier. The Polity Project Database, annual national data for the period 1800-2017, can be downloaded here.
Non-stationarity is a key concern in any long panel of economic data. The residuals of thestochastic frontier model do not pass a stationarity test. See Table A1. Panel stationaritytests require that the residuals of every country are stationary. Equation (3) has a commontrend for all countries. The panel is unbalanced, with fewer observations for hotter andpoorer countries in the early years. It should therefore not come as a surprise that themodel fails the test for panel cointegration.Table A2 shows the results if the model is estimated without a trend, a linear trend (asabove), and a polynomial trend of order two or three; and if a diﬀerent linear trend is usedfor poor and for other countries. Qualitatively, the impact of climate and weather is thesame. The diﬀerences between estimates are not signiﬁcant. Although the residuals of thealternative models are not stationary (results not shown), the stability of the results suggestthat the regression results are not spurious.Table A1 supports that suggestion. Output and capital per capita are non-stationary, butthe climate and weather variables are. That means that the residuals of the model are non-stationary because output and capital do not cointegrate (after inclusion of a trend). Theimpact of climate and weather on output per worker is not spurious—climate and weatherdo not explain the residual trend in output because there is no trend in the climate andweather data.The rightmost column of Table A1 re-estimates the model in ﬁrst diﬀerences. Note thatthe diﬀerence between two exponential distribution is not an exponential distribution; anstochastic frontier model in ﬁrst diﬀerences is a diﬀerent speciﬁcation. Reassuringly, theoutput elasticity of capital does not signiﬁcantly change when the model is estimated in ﬁrstdiﬀerences. The impact of weather and climate either becomes insigniﬁcant or much smaller.In the frontier, this is because the impact of climate is primarily estimated from cross-sectional variation, which disappears when diﬀerencing. The weather impact on ineﬃciency,rainfall in poor countries excepted, disappears in the noise.
As a further empirical test, I estimate the error-correction model (ECM) deﬁned in Equa-tions (5) and (6). I assume that weather anomalies cause short-term deviations from thelong-run equilibrium, while climate aﬀects the long-run equilibrium growth path of the econ-omy. The error-correction model is dynamic, unlike the stochastic frontier models above,tracking the time needed to absorb the perturbation caused by weather anomalies. TheECM speciﬁcation allows for country and year ﬁxed-eﬀects, replacing the linear time trendin the stochastic frontier. 10able 5 presents the results for the long-run co-integrating vector, Table 6 for the short-runerror-correction. In the short-run error-correction estimates, V is the residual of Table 6,Column 4, since this speciﬁcation ﬁts the data best.The output elasticity of capital in the co-integrating vector is much the same as above.The climate variables and their interactions with the poverty dummy are not individuallysigniﬁcant, with a few occasional exceptions, but the log-pseudolikelihood reveals that theyare jointly signiﬁcant: 162 points gain for 10 parameters. This is conﬁrmed by Table A4:Without the climate variables, the Im et al. (2003) test ﬁrmly rejects the null-hypothesisthat the residuals are stationary.The cointegrating vector and the stochastic frontier model have the same signs on theclimate variables and on their interactions with poverty. Qualitatively, the above ﬁndingsare conﬁrmed.Table A4 shows that the residuals of the short-run equation are stationary. Table 6 showsthe estimates. The cointegrating vector is highly signiﬁcant. The parameter estimate of0.06 indicates rather fast convergence to the equilibrium relationship. Precipitation is notsigniﬁcant but temperature is, in poor countries. This result is qualitatively diﬀerent fromthe stochastic frontier model—but similar to Dell et al. (2012).Note that the results in Table 6 are for the standardized temperature and precipitation,rather than their absolute values. This is a further deviation from the stochastic frontiermodel. Table A3 shows the results for the absolute anomalies. The results are much thesame, except that temperature now also aﬀects rich countries. The log-pseudolikelihood islower, however.
The impact of climate change is highly nonlinear in this model. The eﬀect size is thereforehard to grasp. Furthermore, there are 160 countries in the database. There are manyscenarios and models of climate change, and many scenarios and models of future economicgrowth. Exploring all possible futures is a combinatorial explosion, and would shed little lighton how the model presented here works. So instead, I used stylized scenarios to illustratethe impact of climate change, according to column 6 in Table 2, on the 2014 population,economy and climate.The production frontier, Equation (3), depends on the thirty-year average of the level oftemperature and precipitation. This is projected to change over time. Ineﬃciency, Equation(4), depends on the absolute value of the standardized temperature and rainfall. Withoutclimate change, there are weather shocks to ineﬃciency and hence economic output. Withclimate change, weather shocks are diﬀerent.I consider warming between 1 ℃ and 6 ℃ , and 0.01 ℃ /year and 0.06 ℃ /year. This is therange shown in the Fifth Assessment Report of the Intergovernmental Panel on Climate11hange (IPCC). I let rainfall increase or decrease by up to 30%, again within the range ofexpectations for this century. The impact of these scenarios on the frontier is immediate.The impact of climate change on ineﬃciency follows from the deviation of the actual weatherfrom the expected weather. Without climate change, the expected temperature shock is zero.With a 3 ℃ per century warming, the expected temperature shock is 15 × . /τ c per year,where the factor 15 is there because I use the 30-year average and standard deviation fornormalization.Climate aﬀects production possibilities, and anomalous weather the realisation of thosepossibilities. Climate change will aﬀect both. Extrapolating statistical models is alwaystricky. Here, the frontier is estimated on a wide range of climates, while ineﬃciency dependson time-varying standardization of weather variables. Both help to make extrapolation morereliable.Figure 1 shows the global average impact, separately for changes in temperature and pre-cipitation. The impact on the frontier is not out of line with previous studies (Tol, 2018): A5% loss for 3 ℃ warming. The function is almost linear. The impact on ineﬃciency is morenon-linear, but smaller and positive because the impact on rich countries dominates.This is conﬁrmed by the second set of graphs in Figure 1. The above results computethe global average output. The two remaining graphs compute the global average utility,expressed in its income equivalent, assuming a rate of risk aversion of one (Fankhauser et al.,1997). At the frontier, these equity-weighted impact are more linear and larger if warmingexceeds 3 ℃ . This is because poorer countries are hit harder by climate change at the frontier.This is more pronounced in ineﬃciency: The sign ﬂips, and the global average impact issubstantially larger than on the frontier.The right panel of Figure 1 show the impact of changes in precipitation. At the frontier,the impacts are large. Drying would be a loss, wettening a gain. These impacts are lesspronounced if the national impacts are equity-weighted. This follows from Table 2: Poor,hot countries have smaller parameters. For ineﬃciency, change matters rather than thedirection of change; ineﬃciency is determined by deviations from experience, regardless ofwhether that deviation is more or less water than expected. The impacts are more modest.Equity-weighting again ﬂips the sign: Poor countries are negatively aﬀected, rich countriespositively.Figure 2 shows the results by country, for a 3 ℃ warming and a 20% increase in precipitationover a century. In all ﬁgures, the size of the bubble is proportional to the population size in2014.The top left ﬁgure shows the impact of warming on the frontier, plotted against the averagetemperature for 1985-2014. The spread is quite large, ranging from a 90% increase to a 70%decrease. Colder countries see more positive impacts, hotter countries more negative ones.The ﬁgure separates poor countries—which are essentially on a continuous lines—and richones—which are more dispersed because the impact of wealth is interacted with precipita-12ion. Richer countries face more negative impacts.The top right ﬁgure shows the impact of warming on ineﬃciency, plotted against the standarddeviation of the temperature for 1985-2014. Eﬀect sizes are smaller than on the frontier,ranging between a 20% decline and a 15% increase, and fall for countries with greater climatevariability. There are three separate graphs, corresponding with the interactions in Table2. Rich countries see beneﬁts, poor but cool countries moderate losses, and poor and hotcountries large losses.The bottom left ﬁgure plots the impact of wettening on the frontier against average precipi-tation in 1985-2014. Heterogeneity is again large, ranging from the 15% loss to a 90% gain.There is little structure in the graph.The bottom right ﬁgure plots the impact of wettening on ineﬃciency against the standarddeviation of precipitation in 1985-2014. Eﬀect sizes are smaller than on the frontier, rangingbetween a 10% loss and the 15% gain, and fall with greater climate variability. There areagain three separate graphs. Rich countries see gains, poor and cool countries small losses,and poor and hot countries large losses.
6. Discussion and conclusion
I use stochastic frontier analysis to jointly model the impacts of weather and climate oneconomic activity in most countries over 65 years. I distinguish production potential, aﬀectedby climate, and the realisation of economic output, aﬀected by weather. Weather shocks thushave a transient eﬀect, climate change a permanent impact. Warming aﬀects productionpotential, negatively in cold, positively in hot countries; and more so in rich, wet countries.Changes in precipitation also aﬀect the frontier. The impacts are heterogeneous without anobvious pattern. Climate change also aﬀects ineﬃciency, particularly in countries with littleclimate variability, reducing the output gap in rich countries but increasing it in poor andhot countries. The weather eﬀect is small compared to the climate eﬀect. These results arequalitatively and quantitatively robust to alternative speciﬁcations, controls, and estimators.Dell et al. (2012) ﬁnd that poor countries are particularly vulnerable to weather shocks,Burke et al. (2015) ﬁnd that hot countries are. In the Burke (Dell) speciﬁcation, countrieswould grow more (less) vulnerable to unusual weather in a hotter and richer future. I ﬁndthat both are true, and that the impact of heat is about as strong as the impact of poverty.Reduced outdoor work and manual labour, decreased relative importance agriculture inoutput and work force, and greater diﬀusion of adaptive capital such as air conditioningwould help poorer countries to dampen the negative eﬀects of weather shocks—but only toa degree, as the eﬀort needed to alleviate the heat rises with the temperature.The impact of weather shocks found here cannot directly be compared to previous studies.Letta and Tol (2018) model economic growth as a function of the change in temperature,Dell et al. (2012), Burke et al. (2015), Pretis et al. (2018) and Kalkuhl and Wenz (2020)as a function of the temperature level. Kahn et al. (2019) come closest to my speciﬁcation,13ut they use (asymmetric) weather anomalies rather than standardized weather. Anotherkey diﬀerence with those papers is that, here, the impact of a weather shock is transitory.Unusual weather increases ineﬃciency, but the economy bounces back the next year, regis-tering higher growth. If my speciﬁcation is right, then previous studies that excluded laggedtemperature eﬀects are wrong. Previous studies, Barrios et al. (2010) and Generoso et al. (2020) excepted, did not ﬁnda signiﬁcant impact of precipitation. This is a puzzling result, as droughts and ﬂoods aremore devastating than heat and cold. The same result is found here, in the frontier, unlessI interact precipitation with temperature and poverty. Net water—rainfall minus evapo-ration—matters rather than gross water—rainfall—and more so in countries that dependmore on agriculture. Precipitation also has a signiﬁcant eﬀect on ineﬃciency, one that variesstrongly with its variability. Previous studies did not standardize weather variables.The impact on the frontier is larger than in previous studies of the impact of climate change(Tol, 2018). Compared to some previous empirical studies (Easterly and Levine, 2003, Ro-drik et al., 2004), climate has a signiﬁcant eﬀect, also when controlling for institutionalquality, perhaps because I used more data (as did Nordhaus, 2006, Dell et al., 2009, Hender-son et al., 2018, Kalkuhl and Wenz, 2020), perhaps because I modelled heteroskedasticity.Previous studies did not do this and therefore their estimators would be ineﬃcient and, ifweather-related heteroskedasticity correlates with climate, may be biased.Higher income, more capital nor better institutions fully insulate countries from the inﬂuenceof their climate. This contradicts earlier studies (Acemoglu et al., 2001, 2002, Alsan, 2015).I do not include all impacts of climate change. I omit direct impacts on human welfare, suchas biodiversity and health. The model does not capture the range of events which could betriggered by climate change but lie outside the current range of historical experience, suchas thawing permafrost(Wirths et al., 2018), a thermohaline circulation shutdown (Anthoﬀet al., 2016) or unprecedented sea level rise (Nordhaus, 2019). Because of data availability,I use democracy as a proxy for high-quality government. I limit the attention to aggregateeconomic activity. Adaptation and expectations are implicit in the model, as are productionrisks and risk preferences. The projections with respect to climate change are static, notdynamic.The numerical results are therefore far from ﬁnal. 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Journal of Environmental Economics andManagement , 88:1 – 17, 2018. ISSN 0095-0696. doi: https://doi.org/10.1016/j.jeem.2017.11.001. URL . able 1: Descriptive statisticsVariable Unit Symbol Mean Std Dev Min Max ObsOutput per worker ln( $ ) ln( y ) 9.768 1.183 6.047 13.318 7753Capital per worker ln( $ ) ln( k ) 10.831 1.392 5.650 14.524 7753Temperature ℃ ¯ T R | z ( T ) | | z ( R ) | P H G able 2: Baseline results.Dependent variable: ln(output per worker). (1) (2) (3) (4) (5) (6)frontierln( k ) 0.628 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (79.19) (79.35) (77.16) (77.18) (76.24) (77.76) T ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (6.28) (3.76) (3.78) (4.02) (5.23) (8.58) T -0.00380 ∗∗∗ -0.00662 ∗∗ -0.00750 ∗∗ -0.00730 ∗∗ -0.00320 -0.00457 ∗∗∗ (-5.87) (-2.75) (-2.89) (-3.15) (-1.47) (-5.42) R ∗∗∗ ∗∗∗ (1.77) (1.34) (1.01) (1.42) (6.75) (6.89) R -0.000236 -0.00133 -0.000973 -0.00148 0.00554 ∗∗ ∗∗ (-0.69) (-0.97) (-0.70) (-1.09) (2.94) (2.85) P × T P × T P × R -0.00236 0.00565 0.000946 -0.140 ∗∗ -0.146 ∗∗ (-0.08) (0.19) (0.03) (-2.68) (-3.05) P × R ∗∗ -0.00614 ∗∗ (0.68) (0.42) (0.69) (-3.08) (-2.96) T × R -0.0198 ∗∗∗ -0.0199 ∗∗∗ (-8.55) (-8.45) P × T × R ∗∗∗ ∗∗∗ (6.20) (6.50)ineﬃciency | z ( T ) | ∗ -0.189 ∗∗ -0.200 ∗∗∗ -0.202 ∗∗∗ (1.27) (1.30) (-2.10) (-3.17) (-3.47) (-3.54) | z ( R ) | ∗ -0.229 ∗∗∗ -0.269 ∗∗∗ -0.266 ∗∗∗ (0.15) (0.19) (-2.39) (-3.86) (-4.56) (-4.53) P × | z ( T ) | ∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (3.24) (3.70) (3.95) (4.05) P × | z ( R ) | ∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (3.06) (3.48) (4.02) (4.01) H × | z ( R ) | ∗∗ ∗∗∗ ∗∗∗ (3.11) (3.50) (3.49) H × | z ( R ) | ∗∗ ∗∗ ∗∗ (2.83) (3.26) (3.25)Observations 7753 7753 7753 7753 7753 7753LpL 2441.1 2454.8 2487.0 2507.9 2557.9 2556.5 t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . able 3: Robustness checks. Dependent variable: ln(output per worker). (1) (2) (3) (4) (5) (6) (7)frontierln( k ) 0.631 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (77.76) (79.66) (78.92) (78.62) (77.05) (79.67) (79.73) T ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (8.58) (7.43) (8.32) (8.14) (8.46) (8.14) (10.89) T -0.00457 ∗∗∗ -0.00337 ∗∗∗ -0.00446 ∗∗∗ -0.00449 ∗∗∗ -0.00451 ∗∗∗ -0.00452 ∗∗∗ -0.00666 ∗∗∗ (-5.42) (-4.90) (-5.18) (-5.01) (-5.30) (-5.14) (-8.26) R ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (6.89) (5.90) (6.54) (6.22) (6.96) (6.16) (7.58) R ∗∗ ∗∗ ∗∗ ∗∗ ∗∗ ∗∗∗ (2.85) (0.59) (2.83) (2.61) (2.78) (2.68) (5.44) T × R -0.0199 ∗∗∗ -0.00553 ∗∗∗ -0.0192 ∗∗∗ -0.0189 ∗∗∗ -0.0202 ∗∗∗ -0.0187 ∗∗∗ -0.0245 ∗∗∗ (-8.45) (-7.24) (-7.92) (-7.52) (-8.67) (-7.34) (-10.70) P × R -0.146 ∗∗ -0.148 ∗ -0.135 ∗∗ -0.134 ∗∗ -0.151 ∗∗ -0.130 ∗∗ -0.205 ∗∗∗ (-3.05) (-2.16) (-2.79) (-2.69) (-3.12) (-2.63) (-4.56) P × R -0.00614 ∗∗ -0.000814 -0.00613 ∗∗ -0.00582 ∗∗ -0.00605 ∗∗ -0.00599 ∗∗ -0.00911 ∗∗∗ (-2.96) (-0.94) (-2.94) (-2.67) (-2.92) (-2.75) (-5.40) P × T × R ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (6.50) (3.31) (6.05) (5.67) (6.63) (5.67) (9.29) | z ( T ) | -0.000452(-0.13) | z ( R ) | -0.000418(-0.12) P × | z ( T ) | -0.00469(-0.88) P × | z ( R ) | H × | z ( R ) | -0.00892(-1.35) H × | z ( R ) | f ( z ( T )) -0.202 ∗∗∗ -0.0641 -0.0778 ∗∗∗ -0.0508 -0.224 ∗∗∗ (-3.54) (-1.52) (-3.52) (-1.17) (-4.08) f ( z ( R )) -0.266 ∗∗∗ -0.120 ∗∗ -0.0961 ∗∗∗ -0.0195 -0.254 ∗∗∗ (-4.53) (-2.73) (-4.64) (-0.48) (-4.15) P × f ( z ( T )) 0.259 ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ (4.05) (2.96) (4.52) (1.79) (4.31) P × f ( z ( R )) 0.282 ∗∗∗ ∗∗∗ ∗∗∗ -0.0307 0.292 ∗∗∗ (4.01) (3.65) (3.58) (-0.60) (3.72) H × f ( z ( T )) 0.229 ∗∗∗ ∗ ∗ ∗ H × f ( z ( R )) 0.231 ∗∗ ∗ ∗∗∗ ∗ (3.25) (2.21) (3.73) (1.09) (2.08) ( T ) + -0.148 ∗ (-2.25) z ( T ) − ∗∗∗ (3.94) z ( R ) + -0.306 ∗∗∗ (-4.62) z ( R ) − ∗∗ (3.28) P × z ( T ) + ∗∗ (2.86) P × z ( T ) − -0.351 ∗∗∗ (-3.41) P × z ( R ) + ∗∗∗ (3.37) P × z ( R ) − -0.326 ∗∗∗ (-3.49) H × z ( T ) + ∗∗ (3.04) H × z ( T ) − -0.349 ∗∗ (-2.83) H × z ( P ) + ∗∗∗ (3.57) H × z ( P ) − -0.114(-1.32)Observations 7753 7753 7753 7753 7753 7753 7753LpL 2556.5 2517.9 2527.5 2499.8 2561.2 2496.2 2185.8 P = Poverty dummy, World Bank deﬁnition except in Column (2): 25%ile of 1990 income distribution.Columns (1), (2), (6), (7): f ( z ( · )) ≡ | z ( · ) | ; column (3): f ( z ( · )) ≡ z ( · ) ; column (4): f ( z ( · )) ≡ z ( · )Columns (1)-(6): Exponential distribution; column (7): Half-normal distribution. t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . able 4: Robustness checks. Dependent variable: ln(output per worker). (1) (2) (3) (4)frontierln( k ) 0.631 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (77.76) (27.15) (29.57) (76.47) T ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (8.58) (7.69) (7.95) (11.66) T -0.00457 ∗∗∗ -0.00307 ∗∗∗ -0.00342 ∗∗∗ -0.00457 ∗∗∗ (-5.42) (-4.52) (-4.90) (-6.93) R ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (6.89) (6.73) (6.43) (7.25) R ∗∗ -0.0103 ∗∗∗ -0.00950 ∗∗∗ T × R -0.0199 ∗∗∗ -0.00730 ∗∗∗ -0.00630 ∗∗∗ -0.00611 ∗∗∗ (-8.45) (-4.57) (-4.02) (-9.06) P × R -0.146 ∗∗ (-3.05) P × R -0.00614 ∗∗ (-2.96) P × T × R ∗∗∗ (6.50)ln( k ) × R -0.0277 ∗∗∗ -0.0236 ∗∗∗ (-5.26) (-4.92)ln( k ) × R ∗∗∗ ∗∗∗ (6.75) (6.50)ln( k ) × T × R × R -0.000467(-0.99)Polity2 × R × T × R ∗ (2.38)ineﬃciency | z ( T ) | -0.202 ∗∗∗ -0.233 ∗∗∗ ∗∗∗ -0.201 ∗∗∗ (-3.54) (-3.88) (3.64) (-3.61) P × | z ( T ) | ∗∗∗ ∗∗∗ ∗∗∗ (4.05) (4.38) (4.06)ln( k ) × | z ( T ) | -0.0792 ∗∗∗ (-3.72) | z ( R ) | -0.266 ∗∗∗ -0.237 ∗∗∗ ∗ -0.180 ∗∗∗ (-4.53) (-3.91) (1.96) (-3.40) P × | z ( R ) | ∗∗∗ ∗∗∗ ∗∗ (4.01) (3.57) (2.87) n( k ) × | z ( R ) | -0.0531 ∗ (-2.21) H × | z ( T ) | ∗∗∗ ∗∗ ∗∗ ∗∗∗ (3.49) (2.69) (2.60) (4.27) H × | z ( R ) | ∗∗ ∗ ∗ ∗∗ (3.25) (2.25) (2.11) (3.07)Observations 7753 7753 7753 7099LpL 2556.5 2563.6 2547.1 2621.2 t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . able 5: Cointegrating vector.Dependent variable: ln(output per worker) (1) (2) (3) (4) (5)ln( k ) 0.609 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (14.65) (14.42) (15.36) (17.30) (17.28) T ∗ ∗∗ (1.66) (1.18) (2.11) (2.68) T -0.00697 ∗∗ -0.0112 ∗ -0.00783 -0.00810 ∗∗∗ (-3.26) (-2.41) (-1.63) (-3.37) R -0.0234 0.0196 0.261 0.287 ∗ (-0.47) (0.22) (1.84) (2.12) R P × T P × T P × R -0.0392 -0.222 -0.270(-0.37) (-1.35) (-1.78) P × R T × R -0.0235 ∗ -0.0262 ∗ (-1.98) (-2.51) P × T × R ∗ (1.65) (2.34)Observations 7753 7753 7753 7753 7753LpL 2186.2 2250.7 2295.4 2342.6 2339.1 t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . able 6: Short-run error-correction.Dependent variable: ∆ln(output per worker) (1) (2) (3) (4) (5)Output gap 0.0634 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (7.54) (7.52) (7.50) (7.50) (7.51)∆ z ( T ) -0.00134 ∗ z ( R ) 0.0000500 -0.000546 -0.000463(0.09) (-0.85) (-0.78)∆ P × z ( T ) -0.00253 ∗∗ -0.00246 ∗ -0.00266 ∗∗ (-2.71) (-2.29) (-2.95)∆ P × z ( R ) 0.000845 0.000949(0.81) (0.81)∆ H × z ( T ) -0.000258(-0.20)∆ H × z ( R ) -0.000629(-0.43)Observations 7591 7591 7591 7591 7591LpL 10223.0 10225.8 10228.7 10228.8 10228.3 t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . igure 1: The change in global average output per worker due to changing temperature (left panel) andprecipitation (right panel). igure 2: The change in national average output per worker due to changing temperature (top panels) andprecipitation (bottom panels), in the frontier (left panels) and ineﬃciency (right panels). The bubble sizeis proportional to population size. able A1: Stationarity tests series statistic value p-valuedependent variableln( y ) Z ¯˜ t k ) Z ¯˜ t T Z ¯˜ t -5.9142383 1.667e-09 T Z ¯˜ t -4.8816254 5.261e-07 R Z ¯˜ t -4.0643271 .00002409 R Z ¯˜ t -4.827023 6.929e-07 T × R Z ¯˜ t -6.5881907 2.226e-11 | z ( T ) | Z ¯˜ t -47.886946 0 | z ( R ) | Z ¯˜ t -49.250722 0residualsFrontier Z ¯˜ t -.19176587 .4239628Ineﬃciency Z ¯˜ t -.42786821 .33437354Frontier + ineﬃciency Z ¯˜ t -.205783 .41848021The null hypothesis is stationarity for each country (Im et al., 2003).29 able A2: Robustness. Dependent variable: ln(output per worker). no trend linear quadratic cubic split ﬁrst diﬀ.frontierln( k ) 0.692 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (117.70) (77.76) (77.91) (74.82) (75.62) (21.21) T ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗ (9.46) (8.58) (7.71) (6.11) (8.08) (2.17) T -0.00244 ∗∗ -0.00457 ∗∗∗ -0.00463 ∗∗∗ -0.00440 ∗∗∗ -0.00392 ∗∗∗ -0.00233(-3.10) (-5.42) (-5.31) (-6.01) (-4.65) (-1.60) R ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ R ∗∗ ∗∗ ∗∗ ∗ ∗∗ T × R -0.0185 ∗∗∗ -0.0199 ∗∗∗ -0.0199 ∗∗∗ -0.0200 ∗∗∗ -0.0221 ∗∗∗ -0.00209(-6.82) (-8.45) (-8.44) (-8.75) (-9.00) (-1.79) P × R -0.138 ∗ -0.146 ∗∗ -0.146 ∗∗ -0.197 ∗∗∗ -0.212 ∗∗∗ -0.119 ∗ (-2.47) (-3.05) (-3.05) (-4.82) (-4.55) (-2.11) P × R -0.00438 ∗ -0.00614 ∗∗ -0.00617 ∗∗ -0.00461 ∗ -0.00664 ∗∗ -0.00121(-2.22) (-2.96) (-2.95) (-2.41) (-2.99) (-1.25) P × T × R ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗ (4.45) (6.50) (6.50) (7.42) (7.57) (2.68)ineﬃciency | z ( T ) | -0.216 ∗∗∗ -0.202 ∗∗∗ -0.203 ∗∗∗ -0.207 ∗∗∗ -0.187 ∗∗∗ -0.118(-3.76) (-3.54) (-3.53) (-3.48) (-3.33) (-1.28) | z ( R ) | -0.215 ∗∗∗ -0.266 ∗∗∗ -0.268 ∗∗∗ -0.299 ∗∗∗ -0.282 ∗∗∗ -0.106(-3.75) (-4.53) (-4.50) (-4.74) (-4.88) (-0.82) P × | z ( T ) | ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ P × | z ( R ) | ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗ (3.41) (4.01) (3.98) (4.13) (4.35) (2.05) H × | z ( T ) | ∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ H × | z ( R ) | ∗∗ ∗∗ ∗∗ ∗∗∗ ∗∗∗ -0.0492(2.70) (3.25) (3.25) (3.33) (3.73) (-0.28) L. | z ( T ) | L. | z ( R ) | -0.0305(-0.29) P × L. | z ( T ) | -0.201(-1.75) P × L. | z ( R ) | H × L. | z ( T ) | -0.0466(-0.39) H × L. | z ( R ) | bservations 7753 7753 7753 7753 7753 7591LpL 2439.0 2556.5 2556.7 2775.4 2585.7 11337.1 t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . able A3: Short-run error-correction.Dependent variable: ∆ln(output per worker) (1) (2) (3) (4) (5)Output gap 0.0634 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ (7.54) (7.54) (7.54) (7.54) (7.54)∆( | z ( T ) | ) -0.00107 0.00120 ∗ ∗∗ ∗ (-1.51) (2.32) (2.77) (2.40)∆( | z ( R ) | ) -0.00121 -0.000721 -0.00119(-1.76) (-0.65) (-1.18)∆( P × | z ( T ) | ) -0.00329 ∗∗ -0.00297 ∗ -0.00338 ∗∗ (-2.92) (-2.43) (-3.05)∆( P × | z ( R ) | ) -0.000632 -0.000951(-0.45) (-0.61)∆( H × | z ( T ) | ) -0.00171(-1.07)∆( H × | z ( R ) | ) 0.00251(1.35)Observations 7591 7591 7591 7591 7591LpL 10223.0 10225.3 10227.6 10229.1 10226.3 t statistics in parentheses ∗ p < . ∗∗ p < . ∗∗∗ p < . able A4: Stationarity tests—Error-Correction Model model statistic value p-valueLong-run(1) Z ¯˜ t -.62047954 .26747106(2) Z ¯˜ t Z ¯˜ t -2.7926792 .00261368(4) Z ¯˜ t -1.9118767 .027946(5) Z ¯˜ t -.32010646 .37444381Short-run(4) + (1) Z ¯˜ t -41.963767 0(4) + (2) Z ¯˜ t -42.106363 0(4) + (3) Z ¯˜ t -41.939126 0(4) + (4) Z ¯˜ t -41.941283 0(4) + (5) Z ¯˜ t -41.95429 0The null hypothesis is stationarity for each country (Im et al., 2003).“model” refers to columns in Tables 5 and 6.33 ist of countries AlbaniaAlgeriaAngolaArgentinaArmeniaAustraliaAustriaAzerbaijanBahamasBangladeshBelarusBelgiumBelizeBeninBhutanBoliviaBosnia and HerzegovinaBotswanaBrazilBruneiBulgariaBurkina FasoBurundiCabo VerdeCambodiaCameroonCanadaCentral African RepublicChadChileChinaColombiaComorosCongoCosta RicaCroatiaCyprusCzech RepublicD.R. of the CongoDenmarkDjibouti 34ominican RepublicEcuadorEgyptEl SalvadorEquatorial GuineaEstoniaEthiopiaFijiFinlandFranceGabonGambiaGeorgiaGermanyGhanaGreeceGuatemalaGuineaGuinea-BissauHaitiHondurasHungaryIcelandIndiaIndonesiaIranIraqIrelandIsraelItalyIvory CoastJamaicaJapanJordanKazakhstanKenyaKuwaitKyrgyzstanLao People’s DRLatviaLebanonLesothoLiberia 35ithuaniaLuxembourgMacedoniaMadagascarMalawiMalaysiaMaliMauritaniaMauritiusMexicoMongoliaMontenegroMoroccoMozambiqueMyanmarNamibiaNepalNetherlandsNew ZealandNicaraguaNigerNigeriaNorwayOmanPakistanPanamaParaguayPeruPhilippinesPolandPortugalQatarRepublic of KoreaRepublic of MoldovaRomaniaRussian FederationRwandaSao Tome and PrincipeSaudi ArabiaSenegalSerbiaSierra LeoneSingapore 36lovakiaSloveniaSouth AfricaSpainSri LankaSt. Vincent and the GrenadinesSudan (Former)SurinameSwazilandSwedenSwitzerlandSyriaTaiwanTajikistanTanzaniaThailandTogoTrinidad and TobagoTunisiaTurkeyTurkmenistanUgandaUkraineUnited Arab EmiratesUnited KingdomUnited StatesUruguayUzbekistanVenezuelaVietnamYemenZambiaZimbabwe