2. The theoretical model and the estimated equations

We describe consumers’ preferences at time t in a multiperiod framework, using a two-argument utility function U(C _t , E _t ), where C _t is consumption and E _t is the level of environment quality. We assume that the level of E _t is given for the agent (see Smulders and Gradus, Reference Smulders and Gradus1996; Ayong Le Kama and Schubert, Reference Ayong Le Kama and Schubert2004). We also assume that U(C _t , E _t ) is increasing and concave with respect to each of its arguments; that is: U _C (C _t ,E _t )>0, U _E (C _t ,E _t )>0, U _CC (C _t ,E _t )<0 and U _EE (C _t ,E _t )<0, where U _C (C _t ,E _t )≡∂ U/∂ C, U _E (C _t ,E _t )≡∂ U/∂E, U _CC (C _t ,E _t )≡∂² U/∂C ² and U _EE (C _t ,E _t )≡∂² U/∂ E ². Similarly, we define the third derivatives of the utility function as: U _CCC (C _t ,E _t )≡∂³ U/∂ C ³, U _CCE (C _t ,E _t )≡∂³ U/∂ C ²∂E and U _CEE (C _t ,E _t )≡∂³ U/∂C∂E ². Conditions U _CC (C _t ,E _t )<0 and U _EE (C _t ,E _t )<0 are particularly important, since they indicate aversion toward risk on consumption and aversion toward risk on the quality of the environment, respectively.

We extend the univariate framework of Carroll (Reference Carroll1992, Reference Carroll1997) by means of the bivariate intertemporal consumption model:

(1) $$\eqalign{&\max_{C_{t}} {\open E} \sum^{T}_{t=0} \beta^{t}U(C_{t},E_{t})\cr W_{t+1} &= (1 + r)(W_{t} + Y_{t} - C_{t})} $$

where Y is income, W is net wealth, r is the constant interest rate, R=1+r is the interest factor, δ is the subjective intertemporal discount rate, and β=1/(1+δ) is the subjective intertemporal discount factor.

According to a wide strand of literature, we analyze consumption dynamics assuming that income and interest rate are exogenous.Footnote ² Consequently, we do not model either production or financial markets. It is crucial to emphasize that, from an empirical perspective, this partial equilibrium approach provides a clearer and more direct interpretation of the empirical results. Actually, we are able to derive comparable estimates for parameters measuring risk aversion and preferences for environmental quality for each MED country.

Problem (1) is solved by maximizing the Lagrangian:

$$L= {\open E} \sum^{T}_{t=0} \beta^{t}[U(C_{t},E_{t})-\lambda_{t}(W_{t+1}-R(W_{t}+Y_{t}-C_{t}))].$$

The first-order conditions are:

(2) $${\partial L \over \partial C_{t}} =\beta^t \lsqb U_C(C_t, E_t) - R\lambda_{t} \rsqb = 0, $$

(3) $${\partial L \over \partial W_{t+1}} = - \beta^t \lambda_{t} + \beta^{t + 1} R {\open E} [\lambda_{t + 1}] = 0, $$

(4) $${\partial L \over \partial \lambda_{t}} = W_{t + 1} - R(W_{t} + Y_{t} - C_{t}) = 0. $$

Combining first-order conditions (2) and (3), we obtain the Euler's equation:

(5) $$\beta R {\open E}[U_{C}(C_{t + 1}, E_{t + 1})] = U_{C} (C_{t}, E_{t}). $$

Following Dynan (Reference Dynan1993), we substitute a second-order Taylor approximation of U _c (C _t ,E _t ) into the left-hand side of condition (5), obtaining the condition:

(6) $$\eqalign{{\open E} \left[{(C_{t+1} - C_{t}) \over C_{t}} \right] & = {1 - \beta R \over \beta R} {U_C \over C_{t}U_{CC}} - {\open E} [(E_{t + 1} - E_{t})] {U_{CE} \over C_{t}U_{CC}} \cr &\quad - {1 \over 2} {\open E} [(C_{t + 1} - C_{t})^2] {U_{CCC} \over C_{t} U_{CC}} - {1 \over 2} {\open E} [(E_{t + 1} - E_{t})^2] {U_{CEE} \over C_{t}U_{CC}} \cr &\quad - {\open E} [(C_{t + 1} - C_{t})(E_{t + 1} - E_{t})] {U_{CCE} \over C_{t}U_{CC}}.} $$

Along the lines suggested by Smulders and Gradus (Reference Smulders and Gradus1996), Ayong Le Kama and Schubert (Reference Ayong Le Kama and Schubert2004) and Baiardi et al. (Reference Baiardi, Manera and Menegatti2013), we consider the two-argument constant relative risk aversion (CRRA) utility function:

(7) $$U(C_{t},E_{t}) = {C_{t}^{1 - \gamma} E_{t}^{\phi (1 - \gamma)} - 1 \over 1 - \gamma} $$

where γ>0 and ϕ>0 are the parameters of interest. Parameter γ represents the index of relative risk aversion $\left(\!- {U_{CC}C_{t} \over U_{C}}\right)$ , while the index of relative prudence $\left(\!-\!{U_{CCC}C_{t} \over U_{CC}} \right)$ is equal to 1+γ. Note that γ>0 ensures risk aversion toward uncertainty on consumption (i.e., U _CC <0). On the other hand, parameter $\phi = {U_{E}E_{t} \over U_{C}C_{t}}$ ‘[…] represents relative preference for environmental quality […]’ (see Ayong Le Kama and Schubert, Reference Ayong Le Kama and Schubert2004: 34).

Using specification (7), risk aversion toward the quality of environment requires:

(8) $$U_{EE} = \phi [\phi (1 - \gamma) - 1] C_{t}^{1 - \gamma} E_{t}^{\phi (1 - \gamma) - 2} \lt 0. $$

This condition has some implications for the sign of the coefficients to be estimated, discussed below. Moreover, it implies an additional restriction between parameters γ and ϕ, given by

(9) $$\gamma>1 - {1 \over \phi}. $$

Uncertainty is introduced into the model by assuming that both arguments of the utility function are affected by random shocks.Footnote ³ According to the empirical literature which starts from Carroll (Reference Carroll1992) and studies the effects of multiple sources of uncertainty on optimal consumption level, we do not explicitly model any of the risks involved in the analysis.Footnote ⁴

The environmental quality level E _t is difficult to measure directly. In this paper, we assume E _t =P _t ⁻¹; that is, the level of environmental quality is a decreasing function of the level of pollution P _t . This assumption, together with equation (7), implies that our utility function becomes

(10) $$U(C_{t},P_{t})= {C_{t}^{1 - \gamma} P_{t}^{-\phi (1 - \gamma)} - 1 \over 1 - \gamma }. $$

Combining equation (6) with specification (10), we obtain:

(11) $$\eqalign{{\open E} \left[{(C_{t + 1} - C_{t}) \over C_{t}} \right] &= {r - \delta \over (1 + r)\gamma} - {\phi (1 - \gamma) \over \gamma} {\open E} \left[{(P_{t + 1} - P_{t}) \over P_{t}} \right] \cr &\quad + {(1 + \gamma) \over 2} {\open E} \left[{(C_{t + 1} - C_{t}) \over C_{t}} \right]^{2} + {\phi (1 - \gamma) [\phi (1 - \gamma) + 1] \over 2\gamma} \cr &\quad \times {\open E} \left[{(P_{t + 1} - P_{t}) \over P_{t}} \right]^{2} \cr &\quad + \phi (1 - \gamma) {\open E} \left[{(C_{t + 1} - C_{t}) \over C_{t}} {(P_{t + 1} - P_{t}) \over P_{t}} \right].} $$

Consequently, given that $\Delta log(C_{t + 1})\cong {C_{t+1} - C_{t} \over C_{t}}$ and $\Delta log(P_{t + 1})\cong {P_{t+1}-P_{t} \over P_{t}}$ , equation (11) can be re-written as:

(12) $$\eqalign{\Delta log(C_{t+1})&=\alpha _{0}+\alpha _{1}\Delta log(P_{t+1})+\alpha_{2}Var_{t}[\Delta log(C_{t+1})]\cr &\quad +\alpha _{3}Var_{t}[\Delta log(P_{t+1})] \cr &\quad + \alpha_{4} Cov_{t}[\Delta log(C_{t+1}),\Delta log(P_{t+1})]+u_{t+1}} $$

where

(13) $$\alpha_0 = {r - \delta \over (1+r)\gamma}, $$

(14) $$\alpha_1 = - {\phi (1 - \gamma) \over \gamma}, $$

(15) $$\alpha_2 = {(1 + \gamma) \over 2}, $$

(16) $$\alpha_3 = {\phi (1 - \gamma)[\phi (1 - \gamma) + 1] \over 2\gamma}, $$

(17) $$\alpha_4 = \phi (1 - \gamma). $$

It is important to note that the term $Var_{t}[\Delta log(C_{t + 1})]$ in equation (12) describes consumption variability due to random shocks and measures consumption risk. Similarly, the term $Var_{t}[\Delta log(P_{t+1})]$ indicates the variability in environmental conditions and proxies environmental risk. Finally, the covariance term $Cov_{t}[\Delta log(C_{t+1}),\Delta log(P_{t+1})]$ represents the interaction between the rate of growth of consumption and the rate of growth of pollution. According to equation (12), the rate of growth of consumption is directly influenced by the rate of growth of pollution, consumption risk and environmental risk, and indirectly affected by the interaction between the two risks through the covariance between the two growth rates.Footnote ⁵

Furthermore, from conditions (14) and (15) we obtain:

(18) $$\gamma = 2 \alpha_2 - 1 $$

and

(19) $$\phi = {-\alpha_1 \gamma \over (1 - \gamma)}. $$

Moreover, combining equation (17) with equation (18), condition (14) can be rewritten as:

(20) $$\alpha_1 = {-\alpha_4 \over 2\alpha_2 - 1} $$

and, similarly, from equations (14), (16) and (17), we derive:

(21) $$\alpha_3 = - {1 \over 2} \alpha_1[\alpha_4 + 1]. $$

Coefficient α₁ introduces the direct effect of pollution on consumption growth rate, while coefficients α₂ and α₃ show the influence of consumption and environmental uncertainty on consumption dynamics. The covariance between the two growth rates, related to coefficient α₄, describes the indirect effect of the interaction between the two risks. Note that the assumptions of our theoretical model have implications for the signs of these parameters. In particular, γ>0 ensures α₂>0, while condition (8) implies that α₄<1.

On the other hand, the theoretical model does not impose any a priori assumptions about the sign of coefficients α₁ and α₃. In order to have some theoretical indications about the sign of these coefficients, it is necessary to introduce an additional condition. In this respect, our model assumes aversion toward uncertainty on environmental quality (U _EE <0), while equation (10) introduces an indirect measure of the environmental quality E _t based on pollution P _t . Since the relationship between E _t and P _t is decreasing by assumption, but not linear, U _EE <0 does not guarantee that U _PP <0. Therefore, an additional condition is required, which indicates aversion toward uncertainty on the level of pollution:

(22) $$U_{PP} = \phi [\phi (1 - \gamma) + 1] C_{t}^{1 - \gamma} P_{t}^{-\phi^{(}{1 - \gamma) - 2}} \lt 0. $$

Notice that condition (22) implies α₁>0 and α₃>0. In other words, by introducing the assumption of aversion toward uncertainty on the level of pollution, we obtain a positive sign restriction on parameters α₁ and α₃.

Moreover, condition (22) implies a complementary restriction between parameters γ and ϕ given by

(23) $$\gamma \gt 1 + {1 \over \phi}. $$

Restriction (23) is stronger than condition (9), which satisfies inequality (8). For this reason, inequality (22) is a sufficient condition for inequality (8).

3. The data

Our empirical analysis is focused on the MED countries. In particular, we consider the following 13 countries: Albania, Algeria, Croatia, Cyprus, Egypt, Greece, Israel, Lebanon, Malta, Morocco, Slovenia, Tunisia and Turkey, organized in three distinct groups according to their geographical position along the MED Sea (Gürlük, Reference Gürlük2009): Euro-MED (Albania, Croatia, Greece, Malta and Slovenia), Euro-Asian-MED (Cyprus, Israel, Lebanon and Turkey) and African-MED (Algeria, Egypt, Morocco and Tunisia).

The main variables considered in our analysis are annual aggregate per capita CO₂ emissions (metrics tons) and annual aggregate per capita consumption (i.e., aggregate household final consumption expenditure, measured in constant US$ 2,000). Data are collected from the World Bank Development Indicators, 2013 Edition.

We use the growth rate of CO₂ emissions as a proxy of environmental pollution, following a common practice within the environmental economic literature (in this respect, see, among others, Friedl and Getzner, Reference Friedl and Getzner2003; Fodha and Zaghdoud, Reference Fodha and Zaghdoud2010; Wang, Reference Wang2012). Actually, CO₂ emissions are produced by human activities, such as burning oil, coal and gas for energy use, wood and waste materials, and some industrial processes (e.g., cement production). CO₂ is also the reference gas for measuring and evaluating other greenhouse gases. Moreover, it also accounts for the largest share of greenhouse gases contributing to global warming and climate change, as confirmed by the emphasis which many industrial and developing countries, from the Kyoto Protocol onwards, have put on curbing CO₂ emissions globally. Finally, CO₂ data, differently from other pollutants, are generally available since 1960.

We define the logarithmic transformations of per capita consumption and CO₂ emissions as cons _t and poll _t , respectively, while CONS _t and POLL _t indicate the first differences of cons _t and poll _t . The variances of consumption and pollution rates of growth are represented by the variables VARCONS _t and VARPOLL _t , respectively, while the covariance between consumption and pollution rates of growth is indicated with COV _t . Following Dynan (Reference Dynan1993) and Guariglia and Kim (Reference Guariglia and Kim2003), the two variances and the covariance are computed, at each year t, using observations of the previous five years.

Table 1 shows the periods of data availability (in general, from 1960 to 2008) for each country. Table 1 also presents the World Bank classification of each country based on per capita gross national income (GNI). According to this classification, Egypt and Morocco are the only lower middle income (LMI) countries in our sample, while Albania, Algeria, Lebanon, Tunisia and Turkey are upper middle income (UMI) countries. Finally, Croatia, Cyprus, Greece, Israel, Malta and Slovenia are classified as high income (HI) countries.Footnote ⁶ It is worth noticing that the comparison between the three groups highlights that the African-MED countries generally exhibit lower income levels than countries belonging to the two other groups.

Table 1. Descriptive statistics

Notes: CONS _t and POLL _t are the first differences of the logarithmic transformation of per capita consumption and CO₂ emissions, respectively; Jarque-Bera tests the null hypothesis of normal distribution (p-values in parentheses). According to the World Bank classification of the world's economies based on estimates of per capita gross national income (GNI), lower middle income (LMI) countries have a per capita GNI between US$ 1,036 and US$ 4,085, upper middle income (UMI) countries have a per capita GNI US$ 4,086 to US$ 12,615, high income (HI) countries have a per capita GNI equal to or greater than US$ 12,616.

Descriptive statistics on the variables of interest are summarized in table 1. Albania is the only country with an average negative consumption rate of growth (−0.44 per cent). Algeria and Lebanon show the lowest consumption growth rates (0.32 per cent and 0.26 per cent, respectively). On the other hand, CONS _t is on average particularly high in HI countries, especially Cyprus (2.18 per cent), Malta (1.85 per cent) and Slovenia (1.80 per cent). With regard to POLL _t , Israel is the only country with a sizable, negative pollution growth rate (−2.14 per cent) in the period spanned by our data. The growth rate of pollution is also particularly low in Lebanon (0.25 per cent) and Albania (0.60 per cent). The highest increments in pollution are recorded in Greece and in all the African-MED countries.

The order of integration of the variables involved in model (12) is assessed using the unit root tests of Kwiatkowski et al. (Reference Kwiatkowski, Phillips, Schmidt and Shin1992) (henceforth KPSS) and Clemente et al. (Reference Clemente, Montañés and Reyes1998) (henceforth CMR).

As shown in table 2, we find the presence of a unit root for log-transformed per capita consumption and pollution in all countries, while their rates of growth are stationary.Footnote ⁷

Table 2. Unit root tests

Notes: For each country, two unit root tests are presented, namely KPSS and CRM; KPSS is reported in the first row and assumes that the series is stationary under the null hypothesis; CRM is reported in the second row and assumes that the series has a unit root under the null hypothesis; both tests are calculated by including the intercept in the test equations. CRM is computed with the inclusion of single mean shift (additive outlier model). For KPSS, asymptotic critical values at 1 and 5 % significance levels are 0.74 and 0.46, respectively; for CRM, the critical value at 5 % significant level is −3.56 and is reported in Perron and Vogelsang (Reference Perron and Vogelsang1992). Variables cons _t and poll _t are the logarithmic transformations of per capita consumption and CO₂ emissions, while CONS _t and POLL _t are their first differences. **(***) indicate rejection of the null hypothesis at 5 % (1 %) significant level, respectively.

4. Empirical results

The estimated version of equation (12) is:

(24) $$CONS_{t} = \alpha_0 + \alpha_1 {POLL}_{t} + \alpha_{2} {VARCONS}_{t} + \alpha_{3} {VARPOLL}_{t} + \alpha_{4} {COV}_{t} + u_{t}. $$

Non-linear restrictions (20) and (21) are imposed on the parameters α₁, α₂, α₃ and α₄. In order to take into account problems related to endogeneity, possible biases due to omitted variables and measurement errors which potentially affect CO₂ emissions and consumption data (as noted by Carroll, Reference Carroll1997), equation (12) is estimated with the generalized method of moments (GMM). In this last respect, moment conditions are satisfied by instrumenting potentially endogenous variables with their past values. Furthermore, based on the high correlation between the explanatory variables in equation (24) and per capita GDP in each country, lagged values of per capita GDP are also used as instruments. Similarly to CONS _t and POLL _t , we define the first differences of the logarithmic transformation of per capita GDP as GDP _t . Furthermore, COVGDP _t and VARGDP _t indicate the covariance between GDP _t and POLL _t and the variance of GDP _t , respectively. The variance of GDP _t is computed following the same procedure used for calculating VARCONS _t and VARPOLL _t .

More precisely, since VARCONS _t is a potentially endogenous variable (see Carroll, Reference Carroll1992; Hahm and Steigerwald, Reference Hahm and Steigerwald1999; Menegatti, Reference Menegatti2007, Reference Menegatti2010; Baiardi et al., Reference Baiardi, Manera and Menegatti2013), lagged values of GDP _t , VARCONS _t and VARGDP _t are used as instruments. The potential endogeneity of VARPOLL _t , POLL _t and COV _t is treated by instrumenting the first two variables with their lagged values, while COV _t is instrumented with its own lagged values and the lagged values of COVGDP _t . Estimates are obtained by using Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors.

Tables 3, 4 and 5 show the results for each group of countries. The J-statistic indicates that the null hypothesis of valid over-identifying restrictions is not rejected in all countries, while residual autocorrelation and heteroskedasticity do not in general affect the estimated equations.Footnote ⁸ The null hypothesis of residual normal distribution is not rejected by the Jarque–Bera test in most of the countries, with Malta and Cyprus as the only exceptions among the Euro-MED and Euro-Asian MED countries, and Egypt and Morocco among the African-MED countries. Contemporaneous correlations among the residuals obtained from country-by-country estimation of equation (24) are generally low and statistically insignificant at conventional levels.Footnote ⁹

Table 3. Euro–MED countries: GMM estimation of the regression model (24)

Notes: All variables are expressed in log-differences; asymptotic standard errors are reported in brackets. *(**)[***] indicate significance at 10(5)[1] % level. A Wald test supports the conclusion that the coefficient α₄ is smaller than one, as imposed by the theoretical restriction of the model; the J-statistic tests the validity of the over-identifying restrictions when the number of instruments is larger than the number of estimated parameters; the Q-statistic at lag k tests the null hypothesis of no residual serial correlation up to order k, k=1, …, 10; to save space; the Q-statistic and the corresponding p-value reported in the table are for k=1. The White statistic is a test of the null hypothesis of no heteroskedasticity against heteroskedasticity of some unknown general form. The Jarque–Bera statistic tests the null hypothesis that the standardized residuals are normally distributed. The estimated coefficient covariance matrix is weighted with Kernel Bartlett Bandwidth Fixed without prewhitening for Albania and Croatia; Kernel Quadratic Bandwidth Andrews (with prewhitening) and Kernel Bartlett Bandwidth Andrews (without prewhitening) are used for Greece and Slovenia, respectively. Instruments (I) for each country are: Albania I = [constant, CONS _t−1, COV _t−1, POLL _t−1, VARCONS _t−1, VARPOLL _t−1, GDP _t−1]; Croatia I = [constant, COV _t−1, COVGDP _t−1, VARC _t−1, VARY _t−1, GDP _t−1]; Greece I = [constant, CONS _t−1, COVCONSPOLL _t−i , COVGDP _t−i , POLL _t−i , VARCONS _t−i , VARPOLL _t−i , GDP _t−i , for i=1, …, 5]; Malta I = [constant, CONS _t−1, COV _t−i , COVGDP _t−i , POLL _t−i , VARCONS _t−j , VARPOLL _t−i , GDP _t−k , for i=1, …, 3, j=1, …, 4, k=1, …, 5]; Slovenia I = [constant, COV _t−1, COVGDP _t−1, POLL _t−1, VARCONS _t−1, VARPOLL _t−1, VARGDP _t−1, GDP _t−1].

Table 4. Euro-Asian MED countries: GMM estimation of model (24)

Notes: See table 3. The estimated coefficient covariance matrix is weighted with Kernel Quadratic Bandwidth Andrews (with prewhitening) for Lebanon and Israel and with Kernel Bartlett Bandwidth Andrews (without prewhitening) for Cyprus; Kernel Bartlett Bandwidth Variable Newey-West (1) with prewhitening is used for Turkey. Instruments (I) for each country are: Cyprus I = [constant, COV _t−1, COVGDP _t−1, P _t−1, VARCONS _t−1, VARPOLL _t−1, GDP _t−1]; Israel I = [constant, COV _t−i , COVGDP _t−i , POLL _t−i , VARCONS _t−i , VARPOLL _t−i , VARGDP _t−i , GDP _t−j , for i=1, …, 4, j=1, …, 5 ]; Lebanon I = [constant, COV _t−1, COVGDP _t−1, POLL _t−1, VARCONS _t−1, VARPOLL _t−1, VARGDP _t−1, GDP _t−1]; Turkey I = [constant, COV _t−i , COVGDP _t−i , POLL _t−i , VARCONS _t−i , VARPOLL _t−i , VARGDP _t−i , GDP _t−j , for i=1, …, 4, j=1, …,5].

Table 5. African-MED countries: GMM estimation of model (24)

Notes: See table 3. The estimated coefficient covariance matrix is weighted with Kernel Bartlett Bandwidth Fixed without prewhitening for Algeria; Kernel Quadratic Bandwidth Andrews (with prewhitening) and Kernel Bartlett Bandwidth Andrews (without prewhitening) are used for Morocco and Egypt, respectively; Kernel Bartlett Bandwidth Variable Newey-West (1) without prewhitening is used for Tunisia. Instruments (I) for each country are: Algeria I = [constant, CONS _t−i , COV _t−i , VARCONS _t−i , GDP _t−i , for i=1, …, 4]; Egypt I = [constant, VARCONS _t−i , GDP _t−i for i=1, …, 6]; Morocco I = [constant, COVGDP _t−i , VARGDP _t−i , GDP _t−i , for i=1, …, 4]; Tunisia I = [constant, COV _t−i , COVGDP _t−i , POLL _t−i , VARCONS _t−i , VARPOLL _t−i , VARGDP _t−i , GDP _t−i , for i=1, …, 4].

Coefficient α₂ analyzes the effects of consumption risk on consumption and saving dynamics. In line with economic theory, we find that α₂ is always positive and highly statistically significant in all three groups of countries, with the only exception being Morocco. This result validates the hypothesis that consumption risk raises precautionary saving in a context where environmental risk is also considered.Footnote ¹⁰

Coefficient α₃ captures the direct effect of environmental risk on consumption growth rate. This parameter is positive, as expected, and statistically significant in half the Euro-MED countries (Croatia and Slovenia) and Euro-Asian-MED countries (Cyprus and Israel). Conversely, α₃ is not significant in three out of four of the African-MED countries, and actually negative in the case of Tunisia. These results indicate a direct effect of environmental risk on consumption dynamics, although the effect clearly emerges only in a subgroup of Euro-MED and Euro-Asian-MED countries, while it is not as clear in the African-MED countries.

The expected positive sign of coefficient α₃ is related to aversion toward uncertainty on pollution.Footnote ¹¹ In our sample, the presence of this kind of risk aversion is confirmed only in a sub-group of countries, suggesting that the sensibility to pollution risk is not high in the other MED economies. Coefficient α₃ is a function of both parameters γ and ϕ. Consequently, this empirical result may depend either on the level of risk aversion or on the level of concern toward environmental quality.

Coefficient α₄ measures the indirect effect of the interaction between environmental and consumption risks. It is highly significant and less than 1 for almost all countries, as required by the theoretical constraint of our model.Footnote ¹² This means that the interaction between consumption and environmental risks is relevant in determining consumption growth. This conclusion, together with previous findings on coefficient α₃, suggests that the influence of environmental risk on consumption dynamics is indirect, i.e., through its interaction with consumption risk.

Additional constraint (22) finally suggests a positive sign for coefficient α₁, which measures the effect of environmental degradation on consumption growth. The expected sign is confirmed in our estimates for eight countries out of 13, mostly in the subgroup of Euro-MED countries.

To summarize, we find that the coefficients generally have the expected sign in most of the Euro-MED and the Euro-Asian MED countries. The African-MED countries are instead characterized by less clear-cut evidence: the variables which proxy consumption risk and the interaction between environmental and consumption risks (whose coefficients are α₂>0 and α₄<1, respectively) exhibit the expected marginal effects on consumption dynamics (with the only exception being Morocco), whereas the evidence of the influence of environmental risk on consumption (measured by parameters α₁ and α₃) is less robust.

These findings can be interpreted in the light of the strong economic, social and cultural differences which characterize the MED countries. In particular, as highlighted in table 1, the MED countries show significant differences in terms of development. Furthermore, as already noted in the previous section, pollution considerably increased in all the African countries during the time period taken into account. These stylized facts, together with the deep structural changes that have affected these emerging economies, have important consequences in terms of environmental preferences, which are discussed at the end of the following section.

5. Estimates of risk aversion and prudence

The results obtained in the previous section can be used to derive estimates for the parameters γ and ϕ in the utility function (10) which are specific to each MED country. Table 6 reports the estimated parameters γ and ϕ, together with the indices of partial relative risk aversion and partial relative prudence, for the three groups of countries. The two indices directly depend on the magnitude of the parameter γ, since they equal $-{U_{CC}C_{t} \over U_{C}} = \gamma$ and $-{U_{CCC}C_{t} \over U_{CC}} = 1 + \gamma$ , respectively. According to Gollier (Reference Gollier2003), if the utility function is a CRRA, plausible values of the relative risk aversion index (and, consequently, of γ) vary from 1 to 4.

Table 6. Estimation of relative risk aversion, relative prudence and relative preference for environmental quality

Notes: Asymptotic standard errors are reported in brackets. The relative risk aversion index is equal to $- {U_{CC}C_{t} \over U_{C}} = \gamma$ . The relative prudence index is equal to $- {U_{CCC}C_{t} \over U_{CC}} = 1 + \gamma$ . Indirect estimates from tables 3, 4 and 5.

In general, we find that the presence of two sources of uncertainty provides reasonable estimates for parameters γ and ϕ.Footnote ¹³ With regard to parameter γ, it is worth noticing that our results confirm the conclusions reached by Baiardi et al. (Reference Baiardi, Manera and Menegatti2013), who interpret the omission of relevant sources of uncertainty, such as environmental risk, as the main cause of the implausible estimates of the relative risk aversion index based on consumption risk only (Dynan, Reference Dynan1993).

More specifically, we find that the parameter γ varies from 0.94 to 2.31 among the Euro-MED countries. The most risk-averse countries in this group are Croatia (2.31) and Greece (2.28), while the least risk averse is Malta, where the parameter is fairly low (0.98), but not different from 1 at the 5 per cent significance level.

The Euro-Asian MED countries show the highest variability in this parameter, which assumes values ranging from 0.78 to 2.85. In this group, Lebanon and Turkey are the most risk-averse countries (2.85 and 2.11, respectively), while Cyprus is the least risk-averse country (0.78). The estimated value of γ for Israel is too high, at least according to the literature.

Focusing on the African-MED countries, we note that Egypt is the only country with a plausible value of the parameter γ, which is equal to 3.03. For Algeria and Tunisia, γ is positive as expected, but it shows values which are too low and inconsistent with the theoretical indications provided by Gollier (Reference Gollier2003). In case of Morocco, this parameter is actually negative. These results may be due to the specific characteristics of these countries. In particular, the literature shows the significant role played in these countries by additional sources of uncertainty, such as political risk (see, among others, Al Khattab et al., Reference Al Khattab, Anchor and Davies2008; Komendantova et al., Reference Komendantova, Patt, Barras and Battaglini2012). Furthermore, our results may be influenced by the relative size of personal remittances, which are a significant source of funds in North Africa (World Bank Development Indicators, 2013).Footnote ¹⁴ When personal remittances are high, the consumption growth rate may be affected by the variability of income in foreign countries, in addition to the variability of domestic income.

Considering all the MED countries together, our estimates imply that Egypt is the most risk-averse country (3.03), followed by Lebanon (2.85), Croatia (2.31) and Greece (2.28). The least risk-averse countries are Cyprus and Malta (0.78 and 0.98, respectively). Excluding the implausible estimates obtained for Israel among the Euro-Asian MED group and for the African-MED countries (as already noted, Egypt is the only exception), we find that the Euro-MED countries are less risk averse (relative risk aversion is on average equal to 1.60) than Euro-Asian MED countries (γ, on average, is equal to 1.91). Moreover, given that the relative prudence index is equal to γ+1, the estimates for this index range between 1.78 and 4.03. These results suggest the presence of a strong precautionary saving motivation in Egypt, Lebanon, Greece, Croatia and Turkey, which becomes less intense for Albania and Slovenia, and reaches its lowest levels in Cyprus and Malta.

Table 6 also proposes the estimates of parameter ϕ, which, according to Ayong Le Kama and Schubert (Reference Ayong Le Kama and Schubert2004), measures the relative preference of agents for environmental quality. As expected, this parameter shows positive values. Israel, Lebanon and Tunisia are the only exceptions, since this parameter is negative, although very close to zero. If we exclude countries with a negative value of ϕ, the Euro-MED and the Euro-Asian MED groups prove to be environmentally concerned (with preference levels toward the environment, on average, equal to 2.21 and 2.26, respectively). The opposite holds for African-MED countries, where ϕ is near to zero.

Our findings on the cross-country variability of the values of parameter ϕ can also be interpreted according to a complementary point of view. Starting from the World Bank classification of the world's economies reported in table 1, the countries included in our analysis can be divided into two groups: higher income economies (Croatia, Cyprus, Greece, Israel, Malta and Slovenia) and lower income economies (Albania, Algeria, Egypt, Lebanon, Morocco, Turkey and Tunisia).Footnote ¹⁵ Parameter ϕ generally exhibits higher values in the first group than in the second, where this indicator tends to be close to zero. This finding is in line with Arouri et al. (Reference Arouri, Youssef, M'henni and Rault2012), who provide evidence in favor of the environmental Kuznets curve hypothesis (EKC) in the MED region, when CO₂ emissions are considered as a proxy of environmental degradation.Footnote ¹⁶ This implies that only when higher levels of income are achieved do people recognize the importance of a clean environment and move toward more sustainable consumption. As noted above, our results support the EKC, since higher levels of preference toward the environment are recorded in the higher income nations of the sample, while lower income countries generally do not present awareness about environmental issues.

The reasoning above provides a possible justification for the specific results which characterize the African MED countries. The very low values of parameter ϕ in these economies are also coherent with the most recent findings within the empirical environmental and energy literature, which provide empirical evidence supporting poor environmental concern in North African nations (M'henni, Reference M'henni2005; Gürlük, Reference Gürlük2009; Fodha and Zaghdoud, Reference Fodha and Zaghdoud2010; Arouri et al., Reference Arouri, Youssef, M'henni and Rault2012).

Our conclusions on parameters γ and ϕ are strictly related to the low effect of pollution growth rate and environmental risk on consumption dynamics captured by coefficient α₃. As shown by inequality (22), a low level of concern toward the quality of environment and a low value of risk aversion potentially contradict the assumption of pollution risk aversion, which determines the expected sign of α₃. As a consequence, the elements that justify low values of γ and ϕ can also provide some rationale for the low values of coefficient α₃.

Lastly, as shown in section 3, our model also implies constraints (9) and (23) on parameters γ and ϕ. Restriction (9) holds in 10 out of 13 countries, with Israel, Lebanon and Tunisia as the only exceptions. On the other hand, restriction (23) is satisfied by Croatia, Slovenia, Israel, Lebanon, Turkey and Tunisia. These results may be due to the specific functional form postulated to describe the relationship between environmental quality and pollution (i.e., E _t =P _t ⁻¹), which implies that inequality (23) is a stronger condition than (9). Moreover, environmental quality is a very complex phenomenon, characterized by other dimensions that are not completely captured by the pollution variable.