# The Health Effects of Climate Change: A Survey of Recent Quantitative Research

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## Abstract

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**JEL Classification:**C2; C3; I1; Q54

## 1. Introduction: Some Facts and Opinions on the Relationship Between Climate Change and Health

**Time series models**, among which ARMAX (Auto Regressive Moving Average with exogenous variables) models, ECM (Error Correction Models), and non-parametric forecasting models such as single and double exponential smoothing, Holt-Winters methods (additive, no seasonal, multiplicative);**Panel data and spatial models**, such as fixed and random effects models, dynamic panel data models, spatial lag and spatial error models;**Non-statistical approaches**, such as Integrated Assessment Models (IAMs), Computable General Equilibrium (CGE) models, Global Trade Analysis Project Models (GTAP), and Comparative Risk Assessments (CRA).

## 2. Quantitative Models for the Relationship Between Climate Change and Health: Methods and Examples

#### 2.1. Time Series Models

#### 2.1.1. Methods

_{t}, t = 1,…,T, is the Auto Regressive Moving Average model, where the autoregressive component is of order p and the moving average part is of order q, or ARMA(p, q) (see, among others, [12]):

_{t}and X

_{r,t}are non-stationary, given the presence of deterministic and/or stochastic trends, or exhibit seasonalities.

_{t}and X

_{t}, both integrated and cointegrated, can be represented via an Error Correction Model (ECM), with possible asymmetric terms:

_{t}= X

_{t}−X

_{t−}

_{1}; ΔX

^{+}= ΔX if ΔX ≥ 0 and ΔX

^{+}= 0 otherwise; ΔX

^{−}= ΔX if ΔX < 0 and ΔX

^{−}= 0 otherwise; ECT

_{t}are the residuals from the cointegrating regression of Y

_{t}on X

_{t}; ECT

^{+}= ECT if ECT ≥ 0 and ECT

^{+}= 0 otherwise; ECT

^{−}= ECT if ECT < 0 and ECT

^{−}= 0 otherwise. Parameters α

^{+}and α

^{−}are the short-run marginal effects, while parameters λ

^{+}and λ

^{−}are the speeds of adjustment of Y

_{t}from t−1 to t to the equilibrium, once a disequilibrium has occurred in t−1.

_{t}, observed at S equally spaced time intervals per year, is said to be seasonally integrated of order d, or SI(d), if Δ

_{S}

^{d}Y

_{t}is a stationary and invertible ARMA process of the type described by equations (3) [13]. The simplest seasonal model for non-stationary variables is the seasonal random walk (SRW): Y

_{t}= Y

_{t-S}+ ε

_{t}. The SRW model can be generalized to the seasonal integrated ARMA (SARIMA) model:

_{t}, t = 1,..., T, is the time series to be predicted and Y

_{t}

^{*}is the smoothed series, Y

_{t}

^{*}is calculated according to the following recursive model:

_{t}. Model (5) is referred to as single smoothing, and is appropriate for stationary, non-seasonal time series. By repeated substitutions in (5), Y

_{t}

^{*}can be written as a weighted average of past values of Y

_{t}, where the weights (1−α)

^{t}decline exponentially with time. The out-of-sample forecasts from single smoothing are constant for all observations and are given by: Y

_{T+h}

^{*}= Y

_{T}, for all h > 0, h = T + 1,…,T + H. The method known as double smoothing applies single smoothing twice and is appropriate for time series which are non-stationary for the presence of a linear deterministic trend.

_{t}and b

_{t}are the permanent component and trend parameters, while c

_{T+h}represent the additive seasonal factors.

_{t}is a time series characterized by the presence of a linear trend and multiplicative seasonal variability, the multiplicative Holt-Winters model is typically applied. In this case, the smoothed series is given by the following modified version of (6):

#### 2.1.2. Examples

^{2}for forecasting the data “out-of-fit”. Seasonal autoregressive models that incorporate climatic covariates are found to provide the best forecasting performance. Additionally, a simulation exercise shows that the relationship of the disease time series with the climatic covariates is strong and consistent for the seasonal autoregressive (SAR) modeling approach. While the autoregressive part of the model is not significant, the exogenous forcing due to climate is always statistically significant. Prediction accuracy can vary from 50% to over 80% for diseases burdens at time scales of one year or shorter. Other time series studies in the context of cutaneous leishmaniasis include [17,18]. A different strategy for predicting the pattern of diseases is given by [19], who investigate the dynamics of diarrhea, acute respiratory infection (ARI), and malaria in Niono, Mali. The authors observe that these disease time-series often (i) suffer from non-stationarity; (ii) exhibit large inter-annual plus seasonal fluctuations; (iii) require disease-specific tailoring of forecasting methods. To accommodate these characteristics they suggest using a non-parametric technique, the multiplicative Holt-Winters method (MHW). This is a recursive method that can be described as follows: (i) based on past information and pseudo-parameters initialization the MHW produces point forecasts (the method also decompose the time series into level, trend (rate of change), seasonal, and approximately serially uncorrelated residual TS components); (ii) point forecasts are recursively revised through residuals bootstrap to produce median forecasts and their 95% confidence interval bounds; (iii) these median forecasts and contemporaneous time-series information is used by the MHW program to update the forecasts and prediction interval bounds. Step (i) also decompose the time series (TS) into level, trend (rate of change), seasonal, and approximately serially uncorrelated residual TS components.

#### 2.2. Panel Data and Spatial Models

#### 2.2.1. Methods

_{it}, is said to have a panel data structure [29].

_{it}is a classical error term. This model is appropriate if individual heterogeneity is systematically distributed among individuals, i.e., the sample of data is non-random. Since individual heterogeneity is represented by the additional regressors α

_{i}, correlation between explanatory variables X

_{it}and individual heterogeneity is allowed for in the fixed effects model. On the contrary, the random effects model assumes that individual heterogeneity is randomly distributed among individuals, hence it has to be represented as a classical random normal variable µ

_{i}, which contributes to a composite error term, v

_{it}:

_{r}, r = 2,…,K, of model (8), while GLS is consistent for the parameters in model (9). Since individual heterogeneity is part of the model error term in equation (9), correlation between individual heterogeneity and the explanatory variables X

_{it}would lead to inconsistent estimates.

_{it}, leading to inconsistency of the LS estimators. This inconsistency is still present if the variables involved in model (9) are transformed in first differences, in order to eliminate the random effects μ

_{i}:

_{i}= f (Y

_{j}), i = 1,…,N; j ≠ i. In general, the dependence is among several observations, as the index i can take on any value from i = 1,...,N.

#### 2.2.2. Examples

#### 2.3. Non-Statistical Approaches

#### 2.3.1. General Equilibrium Models: Methods and Examples

#### 2.3.2. Comparative Risk Analyses: Methods and Examples

## 3. Integrating Results from Multiple Quantitative Studies: The Case of Malaria

#### 3.1. Time Series Studies

#### 3.2. Cross-Section and Panel Data Studies

#### 3.3. Non-Statistical Studies: General Equilibrium

_{0}) as the vector capacity multiplied by the duration of the infectious period in humans. The factors that are involved in the calculation of (R

_{0}) include: the mosquitoes/people ratio, the number of mosquito bites per person per day, the probability that an infected mosquito infects a human, the chances that a mosquito becomes infected during a blood meal, the incubation period, and the daily survival probability of the mosquito. Indirect factors include: the availability of breeding sites which is related to precipitation, human population density, human population migration, the feeding habits of the mosquitoes, the presence of other animals on which the mosquitoes feed, human exposure (which can be affected by the use of bed nets or other interventions), temperature the immunological and nutritional status of the population, the effectiveness of medical treatment, natural enemies of the mosquitoes, and control efforts. This model is further complicated by algorithms that predict changing genetic adaptations in the parasite and vector that lead to resistance. Based on this approach, evidence is found that the number of people in developing countries likely to be at risk of malaria infection will increase by 5–15% because of climate change, depending on which the Global Circulation Model (GCM) and climate change scenario is used. The areas that are expected to have the most increase in malaria transmission are ones at the fringes of transmission. Unless they are able to use effective control strategies, these regions have low levels of immunity and are likely to experience epidemics [37].

## 4. Using Quantitative Results Toward Managing Human Health

#### 4.1. The Economics of Climate Change

#### 4.2. Managing the Health Effects of Climate Change

#### 4.3. Developing Diseases and Early Warning Systems

## 5. Conclusions

- – The attribution of weather-related disasters to climate change, as no consensus estimate of the global attribution has yet been made;
- – Estimate of economic losses today, as the current models are forward looking;
- – Regional analysis, as the understanding of the human impact at regional level is often very limited but also crucial to guide effective adaptation interventions.

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**MDPI and ACS Style**

Grasso, M.; Manera, M.; Chiabai, A.; Markandya, A. The Health Effects of Climate Change: A Survey of Recent Quantitative Research. *Int. J. Environ. Res. Public Health* **2012**, *9*, 1523-1547.
https://doi.org/10.3390/ijerph9051523

**AMA Style**

Grasso M, Manera M, Chiabai A, Markandya A. The Health Effects of Climate Change: A Survey of Recent Quantitative Research. *International Journal of Environmental Research and Public Health*. 2012; 9(5):1523-1547.
https://doi.org/10.3390/ijerph9051523

**Chicago/Turabian Style**

Grasso, Margherita, Matteo Manera, Aline Chiabai, and Anil Markandya. 2012. "The Health Effects of Climate Change: A Survey of Recent Quantitative Research" *International Journal of Environmental Research and Public Health* 9, no. 5: 1523-1547.
https://doi.org/10.3390/ijerph9051523